Patricia Coulié

Laurent A Messonnier

Baptiste Morel

Thomas Rupp

Hervé Caroline Prince

Di Domenico

Thibaut Gregoire

Valentin Bottollier

Christelle Bonnin Arnould

Bruno Fleury

Loïc Le Quellec

Christine Quilez

Laurent Schmitt

Lucas Bernat-Salles

Bill Brenier

Jérémy Coint

Claude Romain François

Thibault Hurtault

Adrien Trameau

Jeremy Reymond

Robin Miahle

Schmidt

Pierre-Florent Busseneau

Scott R Brown

Daniel Buckingham

Eric Helms

Luke Mcqueen

Seth Lenetsky

Riki Lindsay

Simon Rogers

Stefan Lindinger

Josef Kröll

Michael Mcguigan

Nicola Maffiuletti

Matthew Rex Cross

Dr Pierre Samozino

Prof Jean-Benoit Morin

Professor Jean Monnet

J R Rivière

N Peyrot

FORCE PRODUCTION IN ALPINE SKIERS: ON-AND OFF-SNOW ASSESSMENT AND RELATIONSHIP WITH PERFORMANCE

The literature characterizing force production during skiing, and the associated capacities of skiers, is complicated to synthesize due to aging results or relatively unspecific assessments. The overarching aim of this doctoral thesis was to clarify the importance of force output for skiing and of specific force-production capacities for different ski disciplines. The thesis comprised two themes: 1) characterizing the force output of skiers (N=15) on a giant-slalom course using kinematic and kinetic data from a global positioning system and boot-mounted force-platforms, respectively; and 2) measurement of dynamic and isometric force, the effect of countermovement on force production at different velocities, and specific strength-endurance across disciplines, and performance levels, in national skiers (N=31). The conclusions from Theme 1 were that radial force output applied to turn the skis was linked with performance (r=0.55-0.72, p<.032) and depended on both total magnitude and the ability to apply the force effectively (β=0.64-1.00, p<.001). Higher total force was associated with a greater output of the outside limb and a smaller difference between the limbs (β=0.92-1.00 and -0.65--0.92, respectively, p<.001). For Theme 2, athletes from speed and technical disciplines displayed different dynamic and isometric force qualities, with the former showing superior dynamic force at low velocities (ω 2 =0.17, p<.001) and in isometric conditions (ω 2 =0.16-0.22, p<.003). Overall, performance was linked with a more force-dominant profile (ω 2 =0.34; r=0.60-0.67, p<.001) and increased rate of force development characteristics (r=-0.50--0.82, p<.048). Robust associations existed between maximum isometric force and speed discipline performance (r=-0.88, p<.001), and a trend for higher values in better technical athletes (r=-0.49, p=.052). Force production at moderate velocities did not separate disciplines, nor was it associated with performance.

Variability in the shift of mechanical characteristics and inverse correlations between force augmentation at different velocities (rs=-0.74, p<.001) indicated countermovement effect depended on extension velocity. Skiers exhibited a smaller countermovement effect at low velocities (rrb=-0.68, p<.001), with the opposite observation for sprinters (rrb=0.43, p=.008). 'Moderate' velocities failed to differentiate groups. Better skiers viii take on numerous topics, both within and outside of your main domain of expertise.

Thank you for teaching me the ways of the 'force' (-endurance) and playing 'translator' in testing sessions where the validity of the data depended on the accuracy of imparted information. Your unwavering personal support-particularly during difficult private moments in the middle of the PhD-was unquestionably part of getting across the finishing line. I owe you many beers for simplifying the puzzling process of French administrative tasks.

Maximilien Bowenthank you for the time spent working together to develop a variety of interesting, exciting, and completely-outside-of-my-area technologies

produced greater force at low speeds with a smaller countermovement effect, which supports velocity-specific strength qualities. The ski-specific strength-endurance assessment yielded some discriminative results, but, due to difficulties selecting and assessing the relevant capacities, the principal value of this section lies in direct future protocol design. This thesis generally supports the assertion that force-production capacities partly limit force output during skiing. On snow, both high force-output capacity and effectiveness of application were associated with performance. Off snow, better-ranked athletes possessed the highest capacity for specific force-production capabilities. High-level skiers appear to display a dominance of force production at low speeds and in isometric conditions compared to other sports, which should be considered in their testing and training.

PRODUCTION DE FORCE DES SKIEURS ALPINS : EVALUATION SUR ET HORS NEIGE ET RELATION AVEC LA PERFORMANCE

La littérature caractérisant la production de force en ski alpin, et les capacités associées des skieurs, est compliquée à synthétiser en raison de résultats anciens ou d'évaluations relativement peu spécifiques. L'objectif global de cette thèse de doctorat était de clarifier l'importance de la production de force en ski et des capacités de production de force spécifiques pour différentes disciplines. La thèse comprenait deux thèmes expérimentaux: 1) la caractérisation de la production de force des skieurs (N=15) sur un parcours de slalom géant à l'aide de données cinématiques et cinétiques issues d'un système de positionnement global et de plates-formes de force montées sur les chaussures; et 2) la mesure des capacités de force dynamique et isométrique, l'effet du contre-mouvement sur la production de force à différentes vitesses et l'évaluation spécifique de l'endurance de force dans les deux disciplines de ski alpin à différents niveaux de performance, chez les skieurs nationaux (N=31). Les conclusions du Thème 1 étaient que la force radiale appliquée sur les skis lors des virages était liée à la performance (r=0,55-0,72, p<,032), et dépendait à la fois de l'intensité de la force résultante et de la capacité à appliquer cette force efficacement (β=0,64-1,00, p<,001). Un niveau élevé de force résultante produite était associé à des niveaux élevés de force sur la jambe extérieure et intérieure au virage (β=0,92-1,00 et -0,65--0.92, respectivement, v p<.001). Pour le Thème 2, les athlètes des disciplines de vitesse et technique ont présenté différentes qualités de force dynamique et isométrique, les premiers montrant une force dynamique supérieure à basse vitesse (ω 2 =0,17, p<,001) et dans des conditions isométriques (ω 2 =0, 16-0,22, p<,003). Dans l'ensemble, la performance était liée à la fois à un profil à dominance force (ω 2 =0, 34; r=0,60-0,67, p<,001) et à un taux de développement de la force élevé (r=-0,50--0,82, p<.048). Des associations très fortes existaient entre la force isométrique maximale et la performance pour les disciplines de vitesse (r=-0,88, p<,001) et pour les athlètes de technique (r=-0,49, p=,052). La production de force à des vitesses modérées ne distinguait pas les disciplines, ni n'était associée à la performance.

La variabilité du décalage des relations force-vitesse avec le contre-mouvement et les corrélations inverses entre l'augmentation de la force à différentes vitesses (rs=-0,74, p<,001) indiquait que l'effet de contre-mouvement dépendait de la vitesse d'extension.

Les skieurs ont montré un effet de contre-mouvement plus faible à basse vitesse (rrb=-0,68, p<,001), avec l'observation contraire pour les sprinteurs (rrb=0, 43, p=,008). Les vitesses « modérées » n'ont pas réussi à différencier les groupes. Les meilleurs skieurs ont produit une plus grande force à basse vitesse avec un effet de contre-mouvement plus petit, ce qui soutient l'existence de qualités de force spécifiques à la vitesse.

L'évaluation de l'endurance de force spécifique au ski a fourni des informations discriminantes entre les disciplines mais, en raison des interactions entre les paramètres de test et les capacités réelles de l'athlète, la valeur principale de ce projet n'a été que d'orienter la conception future du protocole. Cette thèse soutient généralement l'affirmation selon laquelle la production de force en ski est en partie limitée par les capacités de production de force. Lors du ski, la capacité de production de force élevée et l'efficacité de l'application étaient associées à la performance. Les athlètes les mieux classés possédaient la plus grande capacité de production de force des membres inférieurs sur des qualités spécifiques. Les skieurs de haut niveau semblent afficher une meilleure capacité de production de force à basse vitesse et dans des conditions isométriques par rapport aux autres sports.

Firstly, thank you, Pierre Samozino, for your clear and unwavering direction of the thesis. You are someone whom I enjoy working with immensely, as one of the few individuals who seem to balance incredible attention to detail and scientific scrutiny, with a perspective firmly rooted in practicality. Thank you for taking a leap of faith in supervising me, and calmly managing the numerous difficulties we met in this project.

Whenever I was in doubt, or struggling with various scientific concepts, you were always able to provide a clear and leveled perspective of the way forward-always one foot in front of the other, and stepping out from among the trees to see the forest. Your patience and good humor were continually grounding, and precisely what I needed in a supervisor.

Thank you, Nicolas Coulmy, for making this unique position possible, and supporting me in balancing the challenging new factors associated with my PhD-working role with the Federation. My situation was (to say the least) unique, and it was a 'steep' learning curve to be thrust into a new sport with a limited scientific (and sporting!) background.

Thank you for persisting, and for the enjoyable moments shared on-and off-snow.

Jean-Benoît Morin -thank you for your ongoing support, and the clear and balanced voice you brought to the thesis. As always, it's a pleasure to work and tweet with you -I look forward to future exciting collaborations that progress our field a little further forward each project.

To my PhD office mates, Clément Delhaye and Jean Romain Rivièreyou both have been an invaluable part of my journey. Clément, thank you for the many hours we spent together setting gates in frigid temperatures at 6 am, followed by even greater hours spent working together with the (often painstaking) data analysis. Some of my favorite memories in France were from our work together, and it is difficult to state how much I learned from you. Jean, thank you for being willing to discuss and give your valuable

GENERAL INTRODUCTION

Alpine skiing is an exciting and complicated elite sport. A unique interaction of physical, technological, environmental, tactical, and social factors present challenges to both athletes and conditioning staff and drives research and development intending to increase the sport's professionality.

Alpine skiing continues to progress each year, with athletic performance advancements on the back of enhancements in technology, environmental control, enhanced conditioning of the athletes themselves (physical, mental, or otherwise; see Figure 1), and more optimized integration of these factors. Improving in any dimension requires a deep understanding of the sport, which is impossible for either practitioners or scientists in isolation. Unfortunately, ski science is notoriously challenging due to complex interactions between the athlete and a volatile environment, which complicates data collection efforts. Consequently, while there have been substantial signs of progress in recent years (Supej & Holmberg, 2019), the literature concerning ski performance is generally sparse and spans almost a half-century. While the sport has benefited from notable advancements that have changed the field (e.g., technology that changes how athletes turn), our understanding of the biomechanical and physiological constraints is based on often outdated evidence. These factors might be partially responsible for the lack of consensus on various aspects of the performative research surrounding the sport.

In any case, it seems clear that competitive alpine skiers require a variety of physical and technical competencies. Broadly, athletes must possess advanced force production and endurance, balance, and aerobic and anaerobic capacity (Hydren, Volek, Maresh, Comstock, & Kraemer, 2013). The need for acuity across this broad set of physiological dimensions has led many authors to conclude that training and talent identification should focus on the extensive and 'multi-faceted' demands of the sport (R. E. Andersen & Montgomery, 1988;Ferland & Comtois, 2018;Hebert-Losier, Supej, & Holmberg, 2014;Hydren et al., 2013;Turnbull, Kilding, & Keogh, 2009;White & Johnson, 1993).

Nevertheless, in the aim of targeted and efficient training implementation, a more nuanced approach based on updated science regarding the underlying determinants of the sport is likely valuable. While debatable, this figure suggests the potential dimensions affecting the performance of ski racers. In this figure, the relative effect of each parameter is unknown, but all are interrelated (indicated by the arrows). The 'Physical' dimension is in bold, as it is the focus of this thesis work. Image adapted as an amalgam of that presented by [START_REF] Nilsson | Competitive performance prediction of elite alpine skiers[END_REF] and Supej and Holmberg (2019).

Athletes continue to stress their limits in competitive skiing, and their physical profile is part of the bedrock of their performance. On the one hand, unlike other sports where movement is directly limited by the capacity to produce energy, the primary energy mechanisms in skiing are external. Thus (theoretically), the central role of physical competency is in setting a barrier above which it is impossible to ski effectively. On the other hand, an athlete possessing specific advanced physical capacities that elevate their 1.2. GENERAL INTRODUCTION xvii ability to perform on the skis relative to their peers (i.e., raise said barrier) is at an advantage. For elite athletes, the difference between winning and losing a race is often slim, and the physical profile of the athlete is a directly controllable and contributing factor that can be developed in periods when the athlete is not skiing (unlike various uncontrollable factors or technical competencies). Consequently, understanding the specific constraints the sport places on athletes is vital to optimizing physical training and progress performance. At the same time, while some elements are unlikely to differentiate the best athletes in the world (given the variability in characteristics exhibited in world-class performers (Giroux, Rabita, Chollet, & Guilhem, 2016)), this does not detract from the efficacy of advanced knowledge for athletes performing across ski disciplines or at developing levels.

Athletes control skiing motion (i.e., turn) by applying force to the snow. While the importance of force output and capacity in skiing performance is regularly discussed, and several authors provide clear biomechanical/physics principals that all but confirm its relevance (Supej & Holmberg, 2019;Turnbull et al., 2009), the relationship is not necessarily a priori clear. Assumedly, the roots of force application during skiing are both physical (i.e., the magnitude of force) and technical (i.e., how the force is applied); however, the degree to which each factor is determinant is unclear, as is the relative effect of improving either on performance. As such, we would benefit from clarifying the relationships between performance, force output during skiing, and specific force capacity of skiers. The second step would be associating distinct force-production capabilities with contextual performance to understand whether athletes who possess specific and advanced abilities are those who similarly produce higher forces on the skis and perform better.

THESIS OVERVIEW

The overarching questions associated with this thesis were:

• Does force output limit skiing performance?

• Is force output during skiing limited by specific force-production capacities?

Videlicet, if the best skiers produce higher forces while skiing, is it because they possess higher specific force capacities than their peers or that they can more effectively utilize their force capacity during skiing? These questions are addressed throughout the thesis via various specific aims (expounded in Sections 2.4) via various experimental works, interpreted in respect to the surrounding literature.

This thesis was completed as part of an 'Industrial Agreement of Training through Research' (CIFRE), which represents an agreement between the doctoral candidate, an industrial partner (the French Ski Federation), and an academic body (the University Savoie Mont Blanc). Consequently, this project was developed and realized in a practical environment.

THESIS FORMAT

This thesis is presented in a quasi-thesis-by-publication format. Consequently, the main experimental sections (Sections 3 and 4) have been formatted for submission in scholarly publications. Each section was written to be understood in isolation from the thesis body and, as such, features an introduction, methods, results, and discussion section. While the content has been adapted to be coherent and avoid undue repetition, essential themes and specific statements may reoccur.

THESIS STRUCTURE

The main structure of the thesis body is depicted in Figure 2. At the core of this thesis are two experimental 'Themes' bookended by a general and three-part scientific introduction and a summary and general discussion chapter. The author's published work associated with the chapter, and any other co-authored works (outside the direct purview of the thesis) referenced within it, are presented in the opening pages. The

THESIS OVERVIEW xix

rationale is summarized in a brief prelude within each experimental chapter. However, briefly:

Chapter 2, 'Scientific background,' features three overlapping sections that provide a scientific basis for the experimental works. Broadly, the three sections aim to characterize the current understanding regarding the importance of force output, and subsequently force capacities, in skiing. To fully realize the background on this topic, the sections generally transition from a macroscopic view of the sport of skiing (Section 2.1), through the characterization of skiing performance and the biomechanical constraints experienced by competitors (Section 2.2), to the specific force capacities (including underlying mechanisms) measured in skiers and their association with performative level (Section 2.3).

Chapter 3, 'Experimental Theme 1: Force output', is the first experimental Theme of the thesis, which addresses the measurement and characterization of force output in the field, based on the current gaps in the literature.

Chapter 4, 'Experimental Theme 2: Force capacity' is the second experimental Theme of the thesis, which addresses the measurement and characterization of force-capacities using various skiing specific field-tests, directed by the findings from the Scientific overview and that directly assessed in Theme 1.

Chapter 5 is a synthesis of the findings of the experimental themes of the thesis, with concluding remarks. In the subchapters, the results are placed within the broader scope of the field, with reflections and perspectives for future work on the subject.

Chapters 6 and 7 are the Bibliography and Appendices, respectively. The in-review or published versions of various scholarly works associated with the experimental works of the thesis can be found in the latter section.

CHAPTER 1. OVERVIEW This section provides an overview of the sport of alpine skiing. The following content was shaped by the thorough work of previous PhD candidates [START_REF] Gilgien | Characterisation of skiers' mechanics, course setting and terrain geomorphology in world cup alpine skiing using global navigation satellite systems[END_REF][START_REF] Kröll | Muscle activity during recreational alpine skiing determined by a new methodological approach in alpine skiing surface EMG analysis[END_REF]Meyer, 2012;[START_REF] Nilsson | Competitive performance prediction of elite alpine skiers[END_REF]Reid, 2010;[START_REF] Spörri | Biomechanical aspects of performance enhancement and injury prevention in alpine ski racing[END_REF], the summary work in Lind and Sanders (2004), and information in the archives of the relevant governing and competitive bodies -the Fédération Internationale de Ski (i.e., the International Ski Federation; FIS) (2018) and the International Olympic Committee (IOC) (2020a).

LIST OF TABLES

HISTORY

Skiing has a long and varied history. The earliest variations of skis appear ~6000 years ago, where they were used primarily to traverse areas of snow more easily than on foot or by wearing snowshoes. Initially used by hunters and subsequently military personnel, it was not until recently that skis were used in their primary modern manner of descending the mountain (i.e., alpine skiing). The first notable skiing manual publication-'Die Alpine Lilienfelder Skilauftechnik' by Matthias Zdarsky in 1897-is widely regarded as the catalyst for the popularization of the steep downhill skiing style we see today (Lind & Sanders, 2004).

Alpine skiing was not competitive until the early 20 th century, with the founding of the International Skiing Commission in 1910. The commission was formalized as the FIS during the International week of skiing in 1924 in Chamonix, France (Fédération Internationale de Ski, 2018;International Olympic Committee, 2020b). The FIS is the governing body for many alpine sports, for which it sets competitive regulations. 1936 saw the introduction of alpine skiing into the Olympic program (International Olympic Committee, 2020a), after which the sport has become increasingly professionalized.

Figure 3. Depiction of a downhill ski racer

The image shows the 'tucked' aerodynamic position characteristic of the speed disciplines.

Technical discipline

The technical events take place on shorter but steeper courses with gates set to provide sharper turns. The consequences are lower overall course speeds and shorter course times than their speed counterparts (45 to 90 sec across the two events). SL is the shorter of the two, with regularly set gates forcing the athlete to perform rhythmic turns and characteristically 'punch' gates out of the way as they pass (see depiction in Figure 4).

PERFORMANCE

Attaining the shortest time from start to finish (without disqualifying factors), as measured by a FIS approved timing system, describes performance in skiing competitions. In the speed events, each skier performs a single run of a course, with the best time crowning the victor (in DH, several practice runs are allowed, which cover multiple days before the event). In the technical events, two runs are performed on the same course but with slightly differing gate settings, and the athlete with the lowest combined time is the competition winner. Unlike speed events, where there are limited The image displays the relatively upright position, turning close to and 'punching' a gate out of the way.

slopes available worldwide, and the courses do not change much between races (i.e., approximately the same gate setting for the same venue), technical events can be held in numerous locations and with considerable variation in the gate and course setting.

Despite the challenging and variable nature of courses at the highest competitive level, mere milliseconds regularly separate top finishing athletes, which increases the spectacle of the sport. Winning on the world stage represents a significant success for athletes and federations, with large sums of prize money on offer and more extensive viewership (both on-location spectatorship and televised coverage) providing lucrative opportunities for sponsorships. Notably, the most prestigious events offer ~100K Swiss francs for the top qualifying athlete, and according to the 2020 season standings (Fédération Internationale de Ski, 2020c), the top three male and female athletes each earned over 290K Swiss francs in prize money.

FIS points (FISpt) represent the overall competitive performance level of athletes, provide a means of comparing athletes to each other, and a marker of functional performance in research. Briefly, points regulate starting position in competitions and are regularly scaled based on the best athletes per event (zero and six points, for the first ranked and 30 th athlete, respectively). For each race, FISpt are calculated as:

Eq. 1

𝐹𝐼𝑆 𝑝𝑡 = ( 𝐹 𝑑𝑖𝑠𝑐 • 𝑡 𝑎𝑡ℎ 𝑡 𝑏𝑒𝑠𝑡 ) -𝐹 𝑑𝑖𝑠𝑐
where Fdisc is a scaling factor dictated seasonally by the FIS, tath is the athlete's course time, and tbest is the time of the best athlete on the course. The athlete's overall score is a representation of their best two scores for the current period.

COMPETITION AND TRAINING SCHEDULES

As of writing, the world is currently in the throes of the COVID-19 pandemic.

Quarantine procedures disrupted the 2019-2020 season, and its effect on the upcoming competitive season is yet unclear. Usually, the competition calendar for ski athletes depends on their specialist event, level, and geography. The full FIS calendar begins in

July, but most high-level athletes plan their first core races around October (the beginning of the World Cup Circuit) and finish around late-March. In the following period, athletes typically transition into national events and preference on-snow training (developing and individualizing new technology with sponsors and working on specific facets of skiing technique) while the snow is reasonable. Athletes will often engage in non-specialist ski events during this period; for example, the Super Slalom event in Europe popularized by French World Cup slalom skier Julien Lizeroux, which consists of 320 gates set approximately to SL regulations, is over 4 km in length and lasts over 4 min in duration.

During the 'off-season,' training for high-level skiers consists of periods of physical conditioning, punctuated by ski camps on glacial mountains, that become more frequent or lengthy as the competitive season approaches (see Figure 5). The frequency of these camps is dictated by training group, with higher-level groups benefiting from increased access to costly ski-camps. Generally, coaches follow a non-specific-to-specific transition of conditioning during the pre-season, with an early focus on aerobic base and muscular hypertrophy, followed by strength, power, anaerobic metabolism, and work in hypoxic environments (Hydren et al., 2013). Focus towards the end of the period transitions to skiing and maintaining underlying qualities while fostering on-snow performance (Gilgien, Reid, Raschner, Supej, & Holmberg, 2018).

High-level athletes can spend almost a half year skiing or up to 150 days of on-snow training and competition during the competitive season, depending on the discipline [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF]. Each on-snow training day typically lasts around 2 to 4 hours, with most of that time spent in recovery (purposeful or returning to the top of the slope).

Athletes will perform warm-up runs of the course and up to 14 training runs, depending on the discipline (less for speed, more for technical). The total physical load experienced by the athletes varies per discipline, the training objectives, and the course constraints, among other factors; however, reports from various national federations are that technical disciplines can perform up to 700 turns per session, and speed disciplines between 100 and 300 [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF]. During ski camps, coaches and athletes will continue to perform conditioning sessions but are careful to minimize the accumulation of fatigue and ultimately maintain the quality of on-snow training. For more information regarding the specific training practices of skiers, see the works of Hydren et al. (2013) and [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF].

TECHNOLOGY

Technology is central to skiing (e.g., see Figure 1) and includes skis, bindings and binding plates, ski-suits, and safety equipment (e.g., helmet, poles, guards, and back protectors), each of which conform to FIS regulations (Fédération Internationale de Ski, 2020d). Since the beginning of the professionalization of skiing with its introduction into the competitive sphere, the association of competitive teams and technology companies has driven the advancement of skiing technology. Notably, the introduction of parabolic carving skis in the 1990s (superseding the traditional straight skis of the time) drastically changed the predominant skiing techniques by allowing athletes to perform more rounded turns with the skis on edge (i.e., carving) rather than frequently skidded turns (Supej, Kugovnik, & Nemec, 2002). Moreover, carving skis in tandem with molded ski boots and elevated binding plates allow athletes to direct and transfer force with greater precision and increase their inclination angle to the snow. The result of these developments is the more dynamic skiing style typified in modern ski racing [START_REF] Müller | Skiing with carving skis: What is new?[END_REF]. Note that while this plan typifies a technical specialist, the main difference for speed athletes is that the primary competitive season does not begin until late November (regardless, the preceding period focuses on skiing). Note that the frequency of ski camps is not fixed and depends on financial availability, evolving meteorological conditions, and the agreed direction between coaches and conditioning staff (e.g., denoted by the '*'). However, for high-level French athletes, it is uncommon to undergo conditioning blocks longer than six weeks in duration without attending a ski camp.

While bindings and boots vary mostly regarding athletes' preferences, the ski lengths are drastically different. For example, SL skis are >1.65 m for the men, with no strict regulation of the radius (although other shaping regulations apply). However, DH skis are >2.18 m for the men, with a radius >50 m. These rulings effectively manipulate the range of turning approaches of the athletes, and this area continues to attract research in balancing the elevation of performance and its restriction (or even regression) to improve athlete safety and fair play [START_REF] Spörri | How to prevent injuries in alpine ski racing: What do we know and where do we go from here?[END_REF].

INJURY

The danger of alpine skiing was painfully illustrated in 2018 (during this project's tenure)

when the French downhill skier David Poisson was tragically killed during a training run on the World Cup circuit. Unfortunately, while accidents like this are rare and hopefully avoidable, a degree of risk is inevitable and likely contributes to the sport's spectacle. In any case, the sport is renowned for having high rates of injury, with approximately a third of World Cup athletes injured each season, and 30% of these being severe and season-ending (notably anterior cruciate ligament, or associated injury of the knee) [START_REF] Florenes | Injuries among male and female World Cup alpine skiers[END_REF]. In addition to acute injuries resulting from falls and other mistakes on the slope, overuse injuries expected of athletes at the elite level are common (notably, lower back)-potentially a consequence of the interaction between specific genetic factors and the relatively unnatural skiing motion [START_REF] Spörri | Course setting as a prevention measure for overuse injuries of the back in alpine ski racing: A kinematic and kinetic study of giant slalom and slalom[END_REF], 2018). While not the focus of this thesis, injury and performance are invariably coupled, and a better understanding of the physiological and biomechanical environments of elite skiing should enhance both fields. For example, better knowledge of skiing specific neuromuscular factors might aid in performance enhancement and injury risk reduction on the slope by improving an athlete's ability to adapt to environmental constraints and perhaps improve return to sports practices (Jordan, Aagaard, & Herzog, 2018). In any case, the long-term health impacts of high-level skiing-and methods through which injury risk can be better assessed and managed for current skiers [START_REF] Spörri | How to prevent injuries in alpine ski racing: What do we know and where do we go from here?[END_REF]-is an area that warrants more attention in tandem to performance enhancement.

SKIING PERFORMANCE & FORCE OUTPUT

PRELUDE

The following is a narrative account of the current stance of skiing biomechanics research and the interplay with various athletic capacities (focusing on the 'physical' sphere). For further reading, we recommend several notable reviews that cover each topic in this overview in greater detail (R. E. Andersen & Montgomery, 1988;Hebert-Losier et al., 2014;[START_REF] Ropret | Limiting factors for the success in alpine skiing[END_REF]Supej & Holmberg, 2019;Turnbull et al., 2009), and the summary works by Lind and Sanders (2004), and LeMaster (2010).

OVERVIEW

In competition, alpine skiers perform turns (typically alternating) around gates set on a course conforming to event-specific regulations. Traditionally, there are four main events (slalom [SL], giant slalom [GS], super giant slalom [SG], and downhill [DH]), which are part of technical (SL and GS) and speed (SG and DH) 'disciplines.' Events are characteristically dissimilar based on the length, vertical drop, and specific setup of the course and gates (e.g., vertical and horizontal offset). Skiing performance, as in many sports, relies on a variety of factors. While inevitably interrelated and interacting in nature, these capabilities typically fall under either internal or external control. Athletes cannot directly control external factors (e.g., environmental conditions, such as course setup and slope preparation), but knowledge, preparation, and planning can mediate their impact. For example, training runs and subsequent imagery and tactical approaches discussed between athletes and coaching staff can manage the effects of challenging course setups. More relevant to this thesis, a better understanding of the biomechanical constraints of skiing allows athletes and coaches to better prime athletes for competition-be it via physical and technical training, technological approaches, or otherwise. In this overview, we will examine the current state of the literature regarding the physiological and biomechanical constraints of high-level skiing, centering on force output.

SKIING PERFORMANCE

Skiing is at the forefront of technological integration and development. Accordingly, it has benefited from advanced scientific methods of investigation, and a range of methods have been used in quantifying performance. Biomechanical analysis in alpine skiing appears in the published literature as early as the 1980s and likely prior in non-published mediums. Notably, the quadrennial International Congress on Science in Skiing is crucial in the ongoing development and dissemination of applied science within the skiing disciplines -although the competitive nature of particular subject matter leads some notable research pieces within its proceedings to not be published in scholarly journals. Unfortunately, several factors limit consensus on central skiing biomechanical topics. Namely, it is challenging to synthesize results across broad methodological approaches, and modifications to the ruling structures and ski-binding technologies have changed the performative landscape decidedly in the past few decades.

Consequently, seminal scientific investigations may lack relevance to modern skiing practice, and while several essential and illuminating studies have been released in recent years (Supej & Holmberg, 2019), the community would benefit from updated scientific information.

Definition and quantification

On a ski course, the ruling structure (Fédération Internationale de Ski, 2020a) dictates 'macroscopic performance' as the shortest time between the start and finish lines.

Typically, ski courses consist of 'sections,' separated either per the official FIS timed and reported splits or from a conceptual perspective based on the slope's geomorphology (e.g., starting, steep, flat sections) or gate numbers. Since this performance measure is macroscopic, one clear means of winning is to perform maximally and attain the best time across all sections (Hebert-Losier et al., 2014;Supej & Cernigoj, 2006). Another approach is to perform disproportionately better during sections that play to the athlete's strengths. Both tactics have been observed in high-level athletes (Supej & Cernigoj, 2006), but remain notoriously difficult to research (Spörri, Kröll, Schwameder, & Müller, 2018). While from a granular perspective 'performance' is relatively clear-cut (e.g., winning a race or possessing the best ranking), the definition and method of quantifying performance and how athletes perform is pivotal to understanding skiing.

Since competitive performance is ultimately decided based on successfully negotiating the course in the shortest time, it logically attracts interest in quantifying performance.

Inevitably, coaches regularly use optical gates to provide course and sectional splits in corroboration with visual feedback (e.g., high-speed video) to surmise how time is lost or gained (Federolf, 2012). Similarly, skiing biomechanics research typically includes some measure of timing into their subsequent analytical comparisons as a top-tier representation of performance (Supej, Kipp, & Holmberg, 2011). The limitations of this approach have been discussed at length (Federolf, 2012;Supej & Holmberg, 2010), which revolve around the interrelated concerns of bias induced by the characteristics of the turns or sections directly preceding the analysis window and an inability to provide precise information regarding the factors contributing to performance. Notably, sectional times varying by up to 10% among world-cup competitors (Supej & Cernigoj, 2006) underscores the importance of understanding the underlying contributors to differences in timing (see Figure 6).

Several analytical measures use time as a central factor: notably, time expressed relative to theoretical best or 'lag' during a section (Supej & Cernigoj, 2006;Supej & Holmberg, 2011) and time 'lost' or 'gained' relative to the change in elevation (Federolf, 2012). These methods attempt to provide higher fidelity information than raw section-time data for research and 'instantaneous' level feedback for practice. While promising, these informative approaches have not been regularly integrated into research in the proceeding years, potentially due to the difficulty in integrating and measuring the associated variables used to enhance the value of timing data (i.e., high-speed video and Global Navigation Satellite System [GPS], discussed in Section 2.2.6.2).

Trajectory and energy dissipation 2.2.3.2.1. Speed-trajectory 'trade-off'

Probably the most concise description of the objectives to ski well is selecting and maintaining more direct turn trajectories while minimizing the loss of energy at high speeds (Hebert-Losier et al., 2014). As well discussed in several papers (notably Spörri, Kröll, Schwameder, et al. (2018)), there is a 'trade-off' between trajectory and speed. In general, there are two intertwining approaches to minimizing sectional times: selecting an 'advantageous' and a more direct path between gates or a trajectory that enables higher speeds to be gained or maintained. The former approach subdivides into shortening the path length the skier travels, and the 'quickest descent' which maps a theoretical model of the most direct route between gates (i.e., follows a 'Z' shape or a straight trajectory following a tighter turn) [START_REF] Hirano | Quickest descent line during alpine ski racing[END_REF]. The benefit of such an approach is evident since the athletes travel less distance or spend longer orienting their body-mass towards the fall line and gaining speed. However, shorter trajectories necessitate turns with smaller radii performed closer to the gates. Tighter turns might induce energy dissipation and velocity loss, either due to exceeding force production capabilities of the athlete or the technological/environmental limits of the ski-snow interaction and inducing skidding. In the latter approach, greater distances are typically traveled (Spörri, Kröll, Schwameder, et al., 2018;Supej et al., 2011). Still, the typified rounder turns may allow higher speeds to be attained or maintained as a product of less energy dissipation due to reduced ski-snow friction from skidding (Spörri, Kröll, Schwameder, & Müller, 2012;Supej, 2008;Supej & Holmberg, 2011;Supej et al., 2013).

This is notable as while isolated differences in trajectory only momentarily effect performance (assuming no other deleterious outcomes), unnecessarily dissipated energy continues to affect subsequent sections until the lost speed is regained (Spörri, Kröll, Schwameder, & Müller, 2012;Spörri, Kröll, Schwameder, et al., 2018;Supej et al., 2011).

A related concept is the turn radius of the athlete, which represents the curvature of the athlete's trajectory as a section of the circumference of a circle (see Figure 7). The range of turn radii are first determined by the course setting (Supej & Holmberg, 2010), and are subsequently a product of the tactical approach of the athlete mediated by various complex technology-environment interactions. For example, the turn radius in carving is partially a product of the design of the ski (i.e., the side-cut, as r=30m in GS (Fédération Internationale de Ski, 2020d)) and two main changeable factors that the athlete controls:

1) the on-edge angle of the skis, and 2) the degree to which the ski is bent against the slope (i.e., via the force applied, against the camber and flexural stiffness (Lind & Sanders, 2004)). Skiing with a greater side-cut and at increased edging angles requires more force to flex the ski so the edges are in contact with the snow; the result is tighter turn-radii than otherwise performed, provided the athlete has the faculties to ski in such conditions without skidding (implications discussed in Section 2. 2.3.2.3). In combination with energy behaviors and distinct geographical information (e.g., position relative to gates), data regarding turn radii can enhance our understanding of the behaviors of athletes, the impact of course settings, and provide insight into other technological and environmental interactions at play (Reid, Haugen, Gilgien, Kipp, & Smith, 2020). For example, turning closer to the gates with shorter radii dissipates more energy (Supej, 2008;Supej et al., 2011), which implies larger radius turns performed further from the gate might be preferable (Spörri, Kröll, Schwameder, & Müller, 2012;Spörri, Kröll, Schwameder, et al., 2018), albeit surmised from a few results measured in technical disciplines. Indeed, there can be differences induced by geomorphological characteristics of the course (e.g., steep vs. flat), which can vary between and within the behaviors of athletes [START_REF] Gilgien | Characterisation of skiers' mechanics, course setting and terrain geomorphology in world cup alpine skiing using global navigation satellite systems[END_REF]Supej & Holmberg, 2011).

Figure 7. Model of turning radius

The left panel shows a curved trajectory (black line with direction denoted by arrow) of an athlete performing a turn. The representation depicts 3 points along the trajectory (black circle with 'x') being fit with an arc segment (Pratt, 1987), which can then be used to determine the corresponding turn center (and subsequently turn radius) in space (turn angles displayed as ϴ 1 and ϴ 2 ). This depiction was adapted from Lind and Sanders (2004). The right panel shows the trajectory of an athlete performing giant slalom turns, with the coordinates (y, 'longitude'; x, 'latitude') of the center of the arc continuously fitted to the trajectory data (black 'x'). Note that some data are cropped from the graph to improve understanding, since radii trend toward infinity at turn-switch events.

Energy dissipation

In its most basic form, skiing is a story of energy conversion. In most sports, the velocity attained is a direct consequence of the energy production of the athlete (e.g., apply force vertically in jumping (Samozino, Morin, Hintzy, & Belli, 2010) or horizontally in sprinting [START_REF] Morin | Technical ability of force application as a determinant factor of sprint performance[END_REF]), and so is directly limited by athlete capacity. However, skiing is among a select group of sports in which the main engine for velocity is the conversion of potential energy (Ep) to kinetic energy (Ek) (e.g., downhill mountain biking). Consequently, athlete capacity is applied in managing energy conversion, and ultimately velocity, while respecting the course setting.

Athletes begin a ski run with a given Ep related to their absolute altitude and their BM.

They negotiate the ski course by either converting this energy into Ek or dissipating it via ski-snow and aerodynamic friction. The skier can modulate this conversion by positioning their center of mass (COM) and tactfully applying force to the snow via their boots, bindings, and skis (LeMaster, 2010), and potentially gain energy via positive muscle work (Meyer, 2012;Supej et al., 2011). Numerous factors influence the ski-snow interaction, including the ski materials and the snow hardness [START_REF] Nachbauer | Friction between ski and snow[END_REF]. These factors will only be discussed where they expressly affect biomechanical and performative constraints.

The capacity to minimize energy dissipation, as the change in mechanical energy per unit of altitude, has been used to describe performance in skiing research. Notably, since the Ep is simple to estimate (Ep=mass•gravity•altitude), and Ek is determined from the time derivative of the center of gravity's trajectory determined via positional data (Ek=mass(velocity 2 )/2), mechanical energy (Emech) can be calculated as:

Eq. 2

𝐸 mech = 𝐸 k + 𝐸 p and 'specific mechanical energy' (emech, as Emech relative to BM) (Supej, 2008) as Eq. 3

𝑒 mech = 𝑣 2 2 ⁄ + 𝑔𝑧 emech features in research as both a means of viewing the rapid evolution of performance relative to specific turns (differential of emech (Supej, 2008)) and for examining the distinct energy behavior in specific parts of the course by accounting for preceding performance (i.e., the difference in emech per turn, normalized to turn/section entry velocity [vin] (Supej et al., 2011)):

Eq. 4

∆𝑒 mech 𝑣 in ⁄ = ∆𝐸 mech 𝑚 • 𝑣 in
Subsequently, the best turn is performed with the highest entry velocity and with the lowest energy dissipation due to efficient management of snow and aerodynamic friction forces (e.g., decreased skidding (Supej, 2008), more aerodynamic pose (Supej et al., 2013), and more curved trajectories associated with 'carving' (Supej & Cernigoj, 2006)). Notably, a limitation of ∆emech/vin is that it does not encompass the entrance and exit orientation of the skier, which can conceivably be very important to characterizing success during a specific turn.

Based on the few studies researching this phenomenon, the maintenance of speed (i.e., a more positive ∆emech/vin) is more predictive of overall performance than trajectory in both technical events (Spörri, Kröll, Schwameder, et al., 2018;Supej et al., 2011), and provides more insight into sectional behaviors than measurements like timing which are strongly dependent on the preceding section. However, investigations into these characteristics are typically performed over relatively homogenous slopes, with small sample sizes, and brief sampling windows. As such, there is no clear consensus nor information from the other disciplines. Moreover, a higher overall (i.e., a full course) performance can feasibly include seemingly negative turn characteristics or energy behaviors. Performance within a turn or section is partially dependent on those before it (Supej et al., 2011), which means that a section with poor performance might be preferential if it avoids mistakes or results in disproportionately higher performance in subsequent sections. Additionally, several studies have recorded positive values of energy loss in skiing (i.e., less energy dissipation), suggesting that some energy can be regained (Reid, 2010;Supej, 2008;Supej & Holmberg, 2010) via work performed by muscles at opportune moments during the turning cycle [START_REF] Meyer | 3D model reconstruction and analysis of athlete performing giant slalom[END_REF][START_REF] Reid | Force and energy characteristics in competitive slalom[END_REF]Supej & Holmberg, 2010). Combined with differences in the tactical, technical, and physical strengths of athletes, these factors might explain the considerable variation observed in sectional values among otherwise similar athletes (Supej & Cernigoj, 2006).

While coaches and athletes might select preferential tactics based on the skier profile, the answer is not merely adopting a singular approach throughout a course. Since many factors influence skiing performance, including external (slope relief (Falda-Buscaiot, Hintzy, Rougier, Lacouture, & Coulmy, 2017; Supej, Hebert-Losier, & Holmberg, 2015), gate placement (Supej & Cernigoj, 2006), or snow conditions [START_REF] Gilgien | Characterization of course and terrain and their effect on skier speed in World Cup alpine ski racing[END_REF]) and internal factors (e.g., the individual capacity of the athlete), athletes must be adaptive. Nevertheless, athletes possessing the physical and technical capabilities to effectively manipulate and ultimately minimize energy loss while performing maximally within the constraints of a marked course will be at an advantage (Spörri, Kröll, Schwameder, & Müller, 2012;Supej et al., 2011;Supej et al., 2013).

The velocity barrier

The roots of maximizing turn velocity are complicated (i.e., the speed-trajectory tradeoff (Spörri, Kröll, Schwameder, & Müller, 2016;Spörri, Kröll, Schwameder, et al., 2018)).

However, the ability to attain and maintain a high velocity is limited by technical and tactical abilities (Supej & Holmberg, 2019), and logically the physical competency of the athlete. For example, the ability to carve (characterized by turning the skis on edge, rather than skidding and dissipating energy) is associated with greater velocity gain and enhanced performance (Spörri, Kröll, Schwameder, & Müller, 2012;Supej, 2008;Supej & Holmberg, 2011;Supej et al., 2013).

As discussed previously, in skiing the center of mass velocity attained is a consequence of the management of energy conversion instead of being directly dependent on the energy production of the athlete. As such, while in other sports it is rare for an athlete to attain a greater velocity than they can otherwise produce, in skiing it is possible to attain velocities the surpass the capabilities of the athlete simply by avoiding energy dissipation. Consequently, while maximizing velocity would appear globally beneficial, above a certain level athletes cannot ski effectively and are at risk of mistakes or injury (Supej et al., 2011); this concept is termed the 'velocity barrier.' Since maximizing velocity while respecting this barrier is probably critical to performance, and the barrier is subsequently limited by a threshold in capability, clarifying this mechanism might play a role in enhancing performance. Since velocity capability is not an inherent property of the human body, the velocity barrier is probably a result of intertwining external unmodifiable factors (e.g., course setting and snow quality) and internal physiological systems (e.g., physical, perceptual, trajectory targeting, and psychological). While it is difficult to assume the weighted contribution of each and their interactions, we will focus on the physical sphere for the following discussion.

In this thesis, we will attempt to provide a broader view of the contribution of trajectory and velocity maximization in giant-slalom performance and provide information regarding the occurrence and importance of the velocity barrier.

FORCE PRODUCTION AND PERFORMANCE

In its most basic form, successfully negotiating a course requires targeted force application. In skiing, the main forces acting on the skier are aerodynamic friction force, gravity, and ground reaction forces (i.e., snow-reaction forces [SRF]; see Figure 8). While the contribution of other external forces might play a role in some disciplines (e.g., minimizing aerodynamic drag is a dominant factor in speed events (Hebert-Losier et al., 2014)), the primary controllable mechanism of skiing is the production of force onto the snow to change SRF (LeMaster, 2010). Nevertheless, the interplay of force output and skiing performance is complicated. While it is impossible to ski without the capability to generate enough force and appropriately apply it to the snow, force applied at a given moment can serve to improve or worsen the instantaneous performance of a skier (Supej & Holmberg, 2019).

Figure 8. External forces while skiing

Fair and Fg correspond to air drag and force due to gravity. Ff is displayed here acting along the base of the skis, opposite to the direction of travel. SRF is represented here as the resultant of the force acting on each limb independently, which can shift depending on the situation. vcom is the resulting vector (dashed grey arrow) of the center of mass (black circle) velocity. Adapted from Reid (2010).

Aerodynamic drag and friction force

Due to the high speeds attained in ski racing, aerodynamic drag has been proposed as potentially linked to performance [START_REF] Barelle | Experimental model of the aerodynamic drag coefficient in alpine skiing[END_REF][START_REF] Luethi | The influence of aerodynamic and anthropometric factors on speed in skiing[END_REF]Supej et al., 2013;[START_REF] Watanabe | Postural changes and aerodynamic forces in alpine skiing[END_REF]. Moreover, the magnitude of drag is modifiable via technology (e.g., suits and low drag helmets) and training to adapt more aerodynamically efficient postures while skiing [START_REF] Meyer | Aerodynamic drag modeling of alpine skiers performing giant slalom turns[END_REF][START_REF] Watanabe | Postural changes and aerodynamic forces in alpine skiing[END_REF], 1978). The latter of these factors primarily involves adopting a crouched stance to reduce frontal area, often during postural training, but is partially dependent on athlete anthropometrics [START_REF] Meyer | Aerodynamic drag modeling of alpine skiers performing giant slalom turns[END_REF]. These approaches attract justified interest in the speed events [START_REF] Barelle | Experimental model of the aerodynamic drag coefficient in alpine skiing[END_REF] since velocities are much more significant. However, in the technical disciplines attempting to minimize air drag at the risk of other technical faculties is probably ill-advised (Supej et al., 2013) since aerodynamic drag contributes much less to energy dissipation compared to ski friction (Gilgien, Kröll, Spörri, Crivelli, & Müller, 2018).

Ski-snow friction is dependent on numerous factors, including the actual skiing approach (e.g., skiing straight, carving, or skidding) and the interaction between the ski material and snow surface (i.e., the unique interaction of compressed ice/snow molecules at various temperatures generating liquid and quasi-liquid layering) [START_REF] Colbeck | A review of the friction of snow skis[END_REF].

The complexity of modeling the friction behavior of skis concerning various trajectory and kinematic factors in realistic racing environments render it challenging to study. In general, the simplest way to model friction is as the product of the force applied and the shearing characteristics of the two surfaces in contact (the coefficient of friction [μ],

defined as the ratio between the force normal to the surface, and that experienced in friction force). Modern skis use low-friction waxed-bases, which exhibit very low friction during sliding in laboratory settings (μ<0.01), and considerable friction during carving and skidding (μ=0.45) [START_REF] Nachbauer | Friction between ski and snow[END_REF], owing mostly to the gliding vs. cutting or shearing mechanisms of the ski bases and edges, respectively. As such, during a ski turn, the most dissipation due to friction probably occurs during the 'steering' phase (see Figure 9), where the skis are at a high edging angle (i.e., carving through the snow or skidding) with large amounts of force applied normal to the ski (i.e., increased force normal to the ski = greater friction force). Similarly, energy can be purposefully dissipated (or otherwise) by 'skidding,' where force is applied to turn the skis in so that their orientation (the ski axis) diverges from the tangential of the trajectory (Müller & Schwameder, 2003).

Figure 9. Turning phases

Depiction of the phases of turning. Image Ron [START_REF] Lemaster | Images of World-Class Skiing[END_REF], overlay Matthew Cross.

Force and maximizing velocity

As discussed in previous sections, the center of mass velocity in skiing is predominantly a product of energy conversion rather than the positive contribution of work produced by the body. Consequently, force is produced to induce changes in SRFs, shift the velocity vector, and change the trajectory (i.e., turn). In a basic sense, turns with higher speeds and smaller turn radii present greater SRFs than slower turns with larger radii (i.e., radial force [Fr] = velocity 2 /radius). In techniques like carving, where the direction of the skis is in alignment with their trajectory, the proportion of SRFs directly acting to turn the athlete (i.e., acting perpendicular to the ski edging angle) is theoretically maximized. Large forces can also be experienced due to momentary increases in snowski friction, which can be a tactful decision to dissipate energy and reduce velocity to benefit later performance, or due to a mistake (Supej et al., 2011).

From a theoretical perspective, athletes who can produce greater force (and notably Fr)

can turn with a tighter radius while maintaining a high velocity or turn at a higher velocity with a given radius (Nakazato, Scheiber, & Müller, 2011) without dissipating energy. Conversely, those unable to produce and control high levels of force output compromise their ability to maintain high velocity levels or select preferable trajectories.

The latter athletes may choose strategies to disperse the built-up kinetic energy and reduce velocity by increasing friction (e.g., skidding) or choosing a less optimal line.

Following this reasoning, athletes with an enhanced ski-specific force-production capacity might conceivably possess a raised 'velocity barrier' compared to their counterparts and an associated increased capability to perform under control at higher speeds. The reasonable terminus of such a model is higher or lower overall course performance, and logically higher force output should be associated with better skiing.

However, as with most skiing science, the answer is more complicated.

Lack of consensus on the relevance of force production

The current consensus is that the timing and event-specific application (i.e., turn initiation) of force during skiing is determinant, with higher acute force output aligned with poor choices of turning and braking movements (Supej & Holmberg, 2019). Using an inverse dynamics model applied to the COM, Supej et al. (2011) showed that SRF magnitude did not differentiate between better or worse World-cup slalom athletes.

Instead, acutely high values during turns (radius <15 m) represented elevated momentary energy dissipation across the cohort (r=-0.50, p<.001). In some circumstances, SRF timing and application can distinguish fast and slow turns, whereas absolute magnitude does not (Nakazato et al., 2011). In a small homogenous sample, Reid (2010) reported a strong association between turn time and greater average SRFs applied in the direction of travel during a single 10 m slalom turn, but not when gate distance was increased to 13 m, with similar overall magnitudes for both courses.

However, several measurement techniques (e.g., direct vs. indirect force), methodological approaches (e.g., high-level athletes performing race-pace trials (Supej & Holmberg, 2011) vs. recreational athletes performing free-ski turns (Nakazato et al., 2011)), and different capture windows (e.g., 1-2 turns vs. course) complicate synthesizing findings. Notably, the extrapolation of a minor representation of the course to generalized performance is problematic, given the reasons discussed in Section 2.2.3 (Supej & Cernigoj, 2006), and competition courses are comprised of various external constraints that can vary substantially turn-by-turn (e.g., high and low inclination sections). Since the athlete who performs well over the entire course is the victor, there is value in drawing conclusions from a more extensive breadth of the course.

To our knowledge, no research has theorized force output as a potential explanation for an elevated 'velocity barrier' and performance. An overarching aim of this thesis is to provide more information regarding the relationships between force output and performance and indirectly test the premise of force production contributing to the velocity barrier.

FORCE-PRODUCTION CHARACTERISTICS

The external forces acting on the athlete during performance play a considerable role in dictating the physical demands. In skiing, the external force characteristics are irregular compared to other popular sports, which results in similarly unique muscular demands on athletes (Turnbull et al., 2009). Typically, researchers collect force-output data to understand better the physical load athletes experience for improving athlete safety and conditioning (Gilgien, Kröll, et al., 2018), changes in kinetics with technology (e.g., ski geometry [START_REF] Kröll | Effect of ski geometry on aggressive ski behaviour and visual aesthetics: equipment designed to reduce risk of severe traumatic knee injuries in alpine giant slalom ski racing[END_REF]) or course structure (e.g., gate offset [START_REF] Spörri | Course setting as a prevention measure for overuse injuries of the back in alpine ski racing: A kinematic and kinetic study of giant slalom and slalom[END_REF]), or understanding different technical approaches (Meyer, 2012;Reid et al., 2020;[START_REF] Supej | Modelling and simulation of two competition slalom techniques[END_REF]. While most studies feature holistic discussion and recommendations, few have expressly measured forces to understand better how athletic physical conditioning can be improved (Gilgien, Kröll, et al., 2018;Kröll, Spörri, Kandler, et al., 2015). This section will focus on narrating the current stance on force-output characteristics, emphasizing the impact of these demands on the athletic profile of skiers.

The kinetics of force output in skiing is relatively consistent and tied to the turning behaviors of the athlete. The most precise way of presenting these data are in turn phases and total force output (i.e., the summed reaction force on COM): transition as the 'lowest'

force output (i.e., the 'troughs,' associated with turn-switch moment), initiation of the turn increasing force, the 'steering' phase (sometimes called the 'turning' or 'control' phase, see (see Figure 9)) representing elevated and peak force output, followed by completion and transition to the next turn. Depending on the discipline and technical approach, forces may even be zero during the transition phase, where the athlete substantially unweights the skis or 'jumps' from one turn to another (Falda-Buscaiot et al., 2017;Reid, 2010;Supej & Cernigoj, 2006;Supej et al., 2002;[START_REF] Vaverka | Kinetic analysis of ski turns based on measured ground reaction forces[END_REF]. These phases correspond with force-time data that approximately follow a sine-pattern (see Figure 10), although the specific nature of each discipline changes the lengths of each phase of the force-time data observed (e.g., more prolonged and irregular force-time traces in speed disciplines (Gilgien, Kröll, et al., 2018)).

Figure 10. Force output determined from COM, comparing skiing disciplines

Data presented are for averaged total ground reaction force from a single turn for giant slalom and slalom (normalized to the average turn duration for each discipline). The turning figure above each graphic displays the relative phase for visual clarification, with the black line representing the mean and the dashed line representing the upper and lower 95% confidence intervals. The grayed area represents the latter half of the 'direction change' phase (i.e., the control phase occurring after the gate). Figure adapted (cropped and compressed) from [START_REF] Spörri | Course setting as a prevention measure for overuse injuries of the back in alpine ski racing: A kinematic and kinetic study of giant slalom and slalom[END_REF].

Magnitudes

The force output required by athletes during turning is quite substantial and constitutes both elevated average forces (i.e., high force over relatively long and extended periods)

and is punctuated by instantaneous peaks from snow-surface irregularities or mistakes.

The latter of these factors is somewhat difficult to measure since it requires direct measurement at the ski-snow interface and moderate filtering regimes (Nakazato et al., 2011), rather than more typical modeling of force output from kinematic data [START_REF] Brodie | Fusion motion capture: A prototype system using inertial measurement units and GPS for the biomechanical analysis of ski racing[END_REF][START_REF] Gilgien | Determination of external forces in alpine skiing using a differential global navigation satellite system[END_REF]Meyer et al., 2012;Reid, 2010;Supej et al., 2013). In general, information is sparse due to barriers to data collections (i.e., limited capture windows) with particularly little data on the speed disciplines (Supej & Holmberg, 2019). For example, in technical disciplines turn averaged values of between ~1.5 and 1.8 BW and peak values of ~1.9 to 2.3 BW are regularly presented (Gilgien, Kröll, et al., 2018;[START_REF] Gilgien | Determination of external forces in alpine skiing using a differential global navigation satellite system[END_REF]Spörri, Kröll, Gilgien, & Müller, 2016), although some authors have presented much higher values in SL (e.g., averages of 2-3 BW (Supej et al., 2011) and peaks in the vicinity of 3.5 (Reid, 2010) to 5

BW (Supej et al., 2002)). Measurements from pressure insoles tend to be higher than those calculated from COM kinematics, with average values of 1.75 to 1.95 BW per turn and up to 3.15 BW for maximum force [START_REF] Kröll | Effect of ski geometry on aggressive ski behaviour and visual aesthetics: equipment designed to reduce risk of severe traumatic knee injuries in alpine giant slalom ski racing[END_REF]Kröll, Spörri, Kandler, et al., 2015). Notably, force is applied during consistent (e.g., >92.8% of turn duration in GS (Gilgien, Kröll, et al., 2018)) loading and unloading turn patterns of the lower limbs [START_REF] Kröll | Effect of ski geometry on aggressive ski behaviour and visual aesthetics: equipment designed to reduce risk of severe traumatic knee injuries in alpine giant slalom ski racing[END_REF]Reid, 2010). Only Gilgien, Kröll, et al. (2018) have compared the force data of both disciplines and found average forces congruent with that previously reported for technical athletes (~1.5 BW for GS) and lower overall forces for both SG (1.4 BW) and DH (1.2 BW). However, as discussed at length by the researchers (Gilgien, Kröll, et al., 2018), due to much longer turn durations and overall run times, the physical loads (i.e., mechanical impulse) are much higher in the speed disciplines (124, 153, and 173 kBWs for GS, SG and DH, respectively). These factors have compelling implications for the physical conditioning of athletes and are discussed in greater detail in the proceeding sections.

In skiing, the limbs act somewhat independently, with the outside limb during the turn being the one that is most involved in force production [START_REF] Müller | Skiing with carving skis: What is new?[END_REF]Müller & Schwameder, 2003). Kinematic data on the subject typically supports different external conditions experienced during turning for each limb (Alhammoud, Hansen, Meyer, Hautier, & Morel, 2020;Berg, Eiken, & Tesch, 1995;Kröll, Spörri, Fasel, Schwameder, & Müller, 2015;Kröll, Spörri, Kandler, et al., 2015). However, due to assessment difficulties, the individual contribution of each limb to force production has been rarely studied (Nakazato et al., 2011). Kröll, Spörri, Kandler, et al. (2015) showed that the outside limb force production was 1.3 and 1.9 times higher than the inside limb for SL and GS, respectively. [START_REF] Falda-Buscaiot | Influence of slope steepness, foot position and turn phase on plantar pressure distribution during giant slalom alpine ski racing[END_REF] showed that the balance of the limbs (25 to 75%, inside to outside limb during the steering phase) did not substantially change with different slope conditions. The outside limb typically receives the most attention, with the inside limb being more responsible for technical factors such as balance and COM orientation (e.g., a 'supporting role' [START_REF] Falda-Buscaiot | Influence of slope steepness, foot position and turn phase on plantar pressure distribution during giant slalom alpine ski racing[END_REF]). However, since the force produced by the inside limb is still substantial, it should receive specific consideration in conditioning regimes (Kröll, Spörri, Fasel, et al., 2015;Kröll, Spörri, Kandler, et al., 2015). The contribution of each limb to force production across the different disciplines (e.g., see Figure 11) mediated by different kinematic conditions (discussed below) is a topic of further interest to practitioners and researchers.

Joint kinematics

Since turn times, course times, and velocities are different between the events, patent differences exist in forces expression. Technical events exhibit rhythmic and alternate patterns of extension and flexion of the lower limbs (~1.8 and 2.9 s for a full turn cycle of SL and GS, respectively (Alhammoud et al., 2020)). In contrast, speed events feature much slower movement cycling times (~4.0 and 5.0 s for SG and DH, respectively) and angular velocities (Alhammoud et al., 2020). In technical disciplines, athletes are almost consistently turning (e.g., in 92.8% of course in GS), with similar values in SG (79.4% of course, albeit at much slower turn-cycling), but only 54.8% of the course time is spent turning in DH (Gilgien, Kröll, et al., 2018). Before the modernization of skiing technique and introduction of carving skis, Berg and Eiken (1999) reported distinct 'stepped' changes in average angular velocity between skiing events (~69, 34 and 17°/s, for SL, GS, Spörri, Kandler, et al. (2015).

and SG, respectively) and similarly different load-bearing angles of the outside knee (more extension and less range for technical vs. speed disciplines) (Turnbull et al., 2009).

More recent detailed analyses (Alhammoud et al., 2020;Kröll, Spörri, Fasel, et al., 2015;Kröll, Spörri, Kandler, et al., 2015) have reported higher angular velocities across the events for the outside leg when using the same phase separation as Berg, in which SL appears to have drastically high angular velocities than the other events (i.e., at the knee, concentric, SL=79 °/s, GS, SG, and DH= 36-48 °/s; eccentric, SL=80 °/s, GS, SG, and DH= 32-40 °/s). In their large study, Alhammoud et al. (2020) showed the maximum knee angle, presumably associated with load bearing, was higher than that presented by Berg and Eiken (1999) (127 to 132° vs. 96 to 114°, for maximum angle of outside knee across the disciplines). Kröll and colleagues (2015;2015) presenting even higher maximum knee angle values in technical events (132 and 138° for SL and GS, respectively), which corresponded to an approximate plateau (i.e., ±10°) during which the highest forces were produced.

Peak degrees of flexion typically decrease during an event [START_REF] Fasel | Three-dimensional body and centre of mass kinematics in alpine ski racing using differential GNSS and inertial sensors[END_REF], which is likely a cause of fatigue impairing the capability to hold high levels of force at extended lengths (i.e., 'compression' of the lower-limb leg spring). In addition to updated information regarding the importance and discipline-specific role of the inside leg (i.e., different minimum angles and high SRF (Kröll, Spörri, Kandler, et al., 2015)), the values extracted at the hip were similarly disparate (both load-bearing and angular speeds). Compared to previous research, the presence and prevalence of relatively stable knee angles during the operative part of the turn is noteworthy (i.e., anecdotally associated with the highest SRF (Kröll, Spörri, Kandler, et al., 2015)) and increased considerably in both relative and absolute duration in the most 'speed' oriented discipline (Alhammoud et al., 2020); the implications of this so-called 'quasiisometric' phase are discussed in the following sections. The sole study (Alhammoud et al., 2020) that examined kinematic actions at the hip recorded drastically different actions occurring between disciplines (outside leg, ~60 to 80% of total turn spent at stable angles for SPEED, compared to ~11 to 34% in TECH); contextualizing these differences, the authors classified the disciplines into categories of 'nearly symmetric' (SL and DH) and 'high asymmetry' (GS and SG) based on the actions of the inside and outside limbs (see Figure 12). These differences are probably a product of lengthened turn-cycles and a non-negligible duration of the course spent in aerodynamic tucked positions in speed events (16 and 37%, for SG, and DH, respectively (Gilgien, Kröll, et al., 2018)) in the aim of reducing frontal area and energy dissipation due to drag [START_REF] Barelle | Experimental model of the aerodynamic drag coefficient in alpine skiing[END_REF]Supej et al., 2013) (technical athletes maintain a relatively upright posture, and SL athletes must 'punch' gates out of the way during turns).

Muscle actions and activation

Before interpreting these data, it is essential to remember that muscle actions are inferred from angular joint movement. However, musculotendinous unit lengthening or shortening can occur in both contractile and tendinous elements and be somewhat separate from that angular change occurring at the corresponding joints [START_REF] Minetti | Concentric, isometric and eccentric contractions: Which dominates Alpine skiing?[END_REF].

Subsequently, the true prevalence of various muscular actions in skiing needs confirmation. Unfortunately, while more portable versions of ultrasound echography technology might provide hope for more accurate measurements in the future, at present, there are no other means of inferring contraction modes in skiing. Further research is needed to clarify these points.

Data regarding the actual nature of contractile function in skiing is almost impossible to collect, and the few papers that present such information instead infer conclusions from joint-angle data. Seminal research by Berg and colleagues (Berg & Eiken, 1999;Berg et al., 1995) inferred contractile events from knee angle and EMG and concluded that there was approximately a 2:1 ratio (~1.0 vs. 0.5 s in GS) between eccentric and concentric activity, respectively (i.e., the angle was continually changing). In combination with the logical connection to managing the conversion (and dissipation) of energy while descending the mountain [START_REF] Behm | The role of instability with resistance training[END_REF]Turnbull et al., 2009), the results of Berg and colleagues (Berg & Eiken, 1999;Berg et al., 1995) shaped the view of muscle actions in skiing research. Subsequently, relevant skiing literature has mostly agreed on the predominance of eccentric activity (Turnbull et al., 2009). Joint-angle data in skiing are rare, and it was not until recently that updated information was available (Alhammoud et al., 2020;Kröll, Spörri, Fasel, et al., 2015;Kröll, Spörri, Kandler, et al., 2015). These updated studies highlighted the concerns of earlier commentary that the evolving and advancing nature of ski racing has likely resulted in changes in muscular actions. For example, in their piece on updated 'techniques' in skiing (i.e., parallel vs.

carving technique), Müller and Schwameder (2003) presented pre-publication data in which the majority of the steering phase during carving was performed at relatively stable knee angles (~125 to 135°) and during the highest SRF (implications for contractile modes were not discussed). Notably, Alhammoud et al. (2020) presented much lower ranges of motion for the outside and dominant limb than the original studies by Berg and colleagues (1999;[START_REF] Tesch | Aspects on muscle properties and use in competitive alpine skiing[END_REF] and a much shorter eccentric contraction duration (almost half that of Berg).

An essential difference in these new data is the confirmation of a dominant 'quasiisometric' contractile mode of the involved mono-articulate musculature [START_REF] Hintermeister | Muscle activity in slalom and giant slalom skiing[END_REF]. Similar to Müller and Schwameder (2003), the most considerable force is produced at relatively stable knee angles (Alhammoud et al., 2020;Kröll, Spörri, Fasel, et al., 2015;Kröll, Spörri, Kandler, et al., 2015) and for substantial relative durations of the turn phase (e.g., at the knee, >34% for GS and SPEED, and ~17% for SL [START_REF] Alhammoud | Contribution à l'analyse de l'activité neuromusculaire des skieurs alpins d'élite lors de tests isocinétiques et en conditions réelles d'entraînement[END_REF]). Compared to more traditional styles of skiing, the new 'carving' approach appears to be characterized by a more pronounced co-loading of the inside limb (Müller & Schwameder, 2003), albeit with different contractile modes per discipline [START_REF] Alhammoud | Contribution à l'analyse de l'activité neuromusculaire des skieurs alpins d'élite lors de tests isocinétiques et en conditions réelles d'entraînement[END_REF] and with different functions of the involved musculature (e.g., biarticular rectus femoris at stable lengths in recreational skiing) [START_REF] Kröll | Quadriceps muscle function during recreational alpine skiing[END_REF]. Lastly, while it appears eccentric and quasi-isometric contractile conditions are dominant, both concentric capabilities and elastic muscular properties are involved in skiing.

Interestingly, there are theories that the skier may be able to contribute some positive energy [START_REF] Reid | Force and energy characteristics in competitive slalom[END_REF]Supej, 2008;Supej & Holmberg, 2010) during the descent as a product of adequately utilizing the elastic and contractile elements of the muscles during distinct turning events (Supej & Holmberg, 2010). Although not well studied, Meyer (2012) presented data to support this phenomenon, which was subsequently attributed to the utilization of specific contraction modes during the latter part of the steering phase, or by explicitly reorienting COM. One theory is that the turn can be modeled like a playground swing [START_REF] Mote | Accelerations induced by body motions during snow skiing[END_REF], where the athlete 'pumps' when the radial forces are most significant and then flexes the lower limbs when the forces subside (or by utilizing aft and fore movements during the early and late turn phases, respectively [START_REF] Wirkus | How to pump a swing[END_REF]). Another theory suggests extending and orienting the center of mass towards the turn center during turn initiation [START_REF] Takahashi | Basic ski theory and acceleration during ski turn[END_REF]. Finally, when a turn is modeled as an inverted pendulum, the skier can manipulate COM velocity by momentarily extending or compressing the body to change the moment of inertia from the turn center. While the amount of energy generated is relatively minimal (1.5% gravitational energy available), these approaches can theoretically be discriminant for speed maintenance in situations which would otherwise induce speed loss, and could nonetheless be a deciding factor in performance at the highest level. However, at this stage little is known regarding their exact prevalence, nor whether the limiting factors to these approaches are more reliant on physical or technical aspects. In any case, with the advent of ever-improving technology reducing the barriers to the exact measurement of skiing biomechanical motion, it is an exciting avenue for future research.

Activation patterns can be measured while skiing using portable surface EMG systems [START_REF] Kröll | Quadriceps muscle function during recreational alpine skiing[END_REF]. The data can then be normalized to that collected during a maximum contraction (i.e., MVC) to infer contractile magnitudes of involved musculature during various events. Early research into high levels skiers reported dominant knee extensor musculature that was notably biased towards the outer-limb are consistent throughout turns, and performed close to or even greatly exceeding MVC (Berg et al., 1995;Hintermeister, Lange, O'connor, Dillman, & Steadman, 1997;[START_REF] Hintermeister | Muscle activity in slalom and giant slalom skiing[END_REF]Hintermeister, O'Connor, Lange, Dillman, & Steadman, 1997;[START_REF] Zeglinksi | Muscle activity in the slalom turn of alpine skiing and in-line skating[END_REF]. Aligned with angular kinematics (as described above), these early EMG data showed substantial activation during the 'eccentric' phase and drove much of the surrounding theories regarding its prevalence in later research and practice.

However, the adoption of carving skies and modern skiing approaches appears to have influenced how each individual limb is used (Müller & Schwameder, 2003), and feasibly this might affect the involvement of the contributing musculature. Notably, carving turns might result in 'co-loading' of the inside limb and coactivation of surrounding antagonist musculature [START_REF] Maxwell | Measurement of strength and loading variables on the knee during Alpine skiing[END_REF]), further implying the potential importance of a 'quasi-isometric' component in skiing (Müller & Schwameder, 2003).

While rare, recent evidence has shown that muscular activity increases with increasing slope angle [START_REF] Kröll | Quadriceps muscle function during recreational alpine skiing[END_REF] and is higher when using stiff race skies than more flexible substitutes [START_REF] Clarys | Ergonomic analyses of downhill skiing[END_REF]. In recreational skiers, [START_REF] Kröll | Quadriceps muscle function during recreational alpine skiing[END_REF] reported a dual action of the knee extensors crossing one and two joints (i.e., rectus femoris) where it acted as a knee extensor for the outside limb. While the rectus femoris was indeed co-loaded (i.e., for the inside limb), it acted instead as a hip flexor. Moreover, while knee extensors crossing only one joint (e.g., vastus lateralis) still appear strongly activated for the outside limb [START_REF] Falda-Buscaiot | Comparison of muscle activation pattern between alpine skiing and snowboarding[END_REF], their activity diminishes for the inside limb [START_REF] Kröll | Quadriceps muscle function during recreational alpine skiing[END_REF]. It is difficult to form a consensus regarding the weighted importance of individual muscular involvement since the results are dependent on the phase, limb, discipline, 'approach' (i.e., carving vs. parallel technique) [START_REF] Kröll | Quadriceps muscle function during recreational alpine skiing[END_REF]Müller & Schwameder, 2003). For example, the mean EMG amplitude of 65-67% MVC was reported by [START_REF] Clarys | Ergonomic analyses of downhill skiing[END_REF] across two slalom courses. However, while anterior tibialis and rectus femoris were consistently the highest and lowest activated, respectively, the other musculature around the knee and hip ranged in their output across the two courses (58-71% MVC). In any case, while early studies were performed almost exclusively on high-level athletes (Berg et al., 1995), it is difficult to transfer the results of recent studies using recreational athletes and semi-controlled turns to high-level and discipline-specific performance.

Very recently, Alhammoud (2019) collated surface EMG data from the lower limb musculature across a large number of training runs (253) from national level skiers across all the major disciplines. Angular kinematics were recorded simultaneously (data published elsewhere (Alhammoud et al., 2020)), providing a valuable dataset characterizing the lower-limb behavior of the muscle-tendon units in the skiing environment. Using a statistical parametric mapping approach, the authors observed that all disciplines displayed different EMG patterns, although the two speed events were much more similar than the other events. SL showed symmetrical and narrow EMG peaks across a turn phase (inside-outside limbs) as a cause of shorter more abrupt turn cycles, with all other disciplines exhibiting somewhat asymmetrical and broad peaks. While some differences existed per muscle and per limb (inside vs. outside), the technical disciplines tended to be biphasic, whereas the speed disciplines were monophasic. Notably, EMG activity peaked during the steering phase around gate crossing, which was of similar magnitude across the disciplines, and generally within the period associated with the lowest angular speeds or the quasi-isometric phase.

Interestingly, the highest angular velocities were associated with the lowest activity levelspotentially further inferring the importance of low-velocity and isometric strength across the disciplines. Regarding the current project, the work of Alhammoud ( 2019) was underway during the design and orientation of our aims and formed part of the rationale for not focusing on the collection of EMG from our methodological approach.

The occurrence of low extension velocity and isometric

MEASUREMENT

Overview and challenges to data collection

To understand the physical constraints a sport places on athletes, we must use valid measurement tools [START_REF] Atkinson | Selected issues in the design and analysis of sport performance research[END_REF]. Any devices utilized must be precise enough to provide accurate and repeatable measurements-optimally within the sporting environment to increase external validity. Unfortunately, the dynamic nature of skiing renders both aims challenging to meet. Foremost, the alpine nature of the sport means collection settings are rarely easily accessible, and any technology must withstand associated environmental extremes (e.g., low temperatures and icy conditions). Second, the dynamic nature of the sport necessitates the integration of technology that does not unduly affect the function of personalized skiing implements (i.e., ski/boot/binding interplay) and athletic expression. Third, the technology must be advanced enough to function correctly within the environment (e.g., onboard data storage and resistant materials) and collect useable and valid information (e.g., sufficient sampling frequency), among other internal validity factors. Various simulation studies exist of distinct skiing events [START_REF] Supej | Modelling and simulation of two competition slalom techniques[END_REF] or interactions between the skis and snow surface (Federolf, Roos, Lüthi, & Dual, 2010), but in general are very challenging when compared to those implemented in human locomotion and jumping. Some complications can be overcome (e.g., using heat packs or specialized technology to withstand the effects of otherwise damaging temperatures), but others present a more significant challenge (e.g., the narrowing of satellite triangulation due to steep surrounding terrain decreasing GPS accuracy (Gilgien, Spörri, Limpach, Geiger, & Müller, 2014)). From a practical perspective, since all phases of testing generally occur on the ski course, those wishing to perform such experiments must be proficient skiers.

While this seems logical and features as evidence of commitment to the sport and associated research, it nonetheless probably limits the pool of scientists who may otherwise engage in research. A result of these compounding factors is limited and practically complicated experimental setups, which often result in low sample sizes, small capture windows, and fundamentally limited technology.

Kinematics of the center of mass

Within the literature, researchers have used a variety of technologies to measure athlete kinematics. The most common kinematic assessment is time (course and sectional), which is simply provided by single or multi-cell beams set at specific points during the course (generally, FIS approved units like that used during competitions) (e.g., Supej & Holmberg, 2011). To provide more information regarding the actions of the skiers, more advanced technology is necessary.

Typically, camera setups build models of the skier's motion, which requires positioning a matrix of units and markers across the slope (Reid et al., 2020;Spörri, Kröll, Gilgien, et al., 2016;Spörri, Kröll, Schwameder, & Müller, 2012;Spörri, Kröll, Schwameder, et al., 2018;[START_REF] Spörri | Collecting kinematic data on a ski track with optoelectronic stereophotogrammetry: A methodological study assessing the feasibility of bringing the biomechanics lab to the field[END_REF]. As such, while these types of analyses provide crucial insight into biomechanical data (Reid et al., 2020), only small collection windows are feasible, which must be extrapolated to generalize performance over a much longer course. In some cases, specialized treadmills can be integrated with camera technology to solve small capture volumes imposed in the field (Fasel, Spörri, Schutz, Lorenzetti, & Aminian, 2017a, 2017b), since they effectively remove limitations associated with course length. Although, studies using ski treadmills center around using the 'carpet' as a specific modality to train and test, rather than supplant measurement on the field, due to the unique sliding characteristics and very low speeds (25 km/h) compared to ski races.

Until recently, few other options were available to measure athlete kinematics. However, there have been significant developments in wearable measurement technologies in recent years (Supej & Holmberg, 2019;Supej, Spörri, & Holmberg, 2020). Notably, increasingly accessible satellite navigation systems, which provide geospatial positioning via triangulation of signals transmitted from an array of satellites, have been used in skiing and substantially increased accessible capture volumes [START_REF] Fasel | Three-dimensional body and centre of mass kinematics in alpine ski racing using differential GNSS and inertial sensors[END_REF]Gilgien, Kröll, et al., 2018;Gilgien et al., 2014;[START_REF] Lachapelle | A high performance GNSSbased sensor for elite skier training[END_REF][START_REF] Naoto | A portable post-processed kinematic GNSS receiver for advanced ski measurements[END_REF][START_REF] Nemec | Skier's posture estimation using real time kinematics GNSS measurements[END_REF]Supej, 2010;Supej & Holmberg, 2011). The most common variants are global navigation satellite systems (GNSS), but there are several systems that differ in cost, setup simplicity, and data accuracy (Supej et al., 2020). A notable advancement is the advent of low-cost circuitry and open-source programs for differential GNSS and Real-Time Kinematic (RTK) systems (Valente, Momin, Grift, & Hansen, 2020), which could provide very accurate targeting solutions (~10 mm targeting precision) (Supej, 2010), albeit rarely tested in alpine skiing or with poor results (Gussiås, 2017). While the future is promising (Supej et al., 2020), researchers and practitioners should remain critical of GNSS since many factors can drastically reduce the accuracy and usability of the technology (Gilgien et al., 2014).

A limitation of GNSS is that the antenna is best placed higher on the body (e.g., the helmet), where it is relatively stable and has the highest chance of receiving satellite signals (Supej et al., 2020). Substantial efforts have been made in the research to computationally re-orient the antenna position to that approximating COM by fusing the data with complex multi-sensor models [START_REF] Brodie | Fusion motion capture: The biomechanics of alpine ski racing[END_REF][START_REF] Brodie | Fusion motion capture: A prototype system using inertial measurement units and GPS for the biomechanical analysis of ski racing[END_REF]Fasel, Lechot, Spörri, Müller, & Aminian, 2016;[START_REF] Spörri | Course setting as a prevention measure for overuse injuries of the back in alpine ski racing: A kinematic and kinetic study of giant slalom and slalom[END_REF] or implementing an inverse pendulum model with terrain modeling (Gilgien, Spörri, et al., 2015;Supej et al., 2013). However, there is some evidence that helmet attachment may suffice for approximating trajectory and energy behaviors (although the COM and the head diverge during the steering phase) [START_REF] Meyer | Estimating alpine skiers' energetics and turn radius using different morphological points[END_REF].

Moreover, the results suggest merely applying a unit to the hip accurately estimates data provided by the pendulum model.

Inertial movement units feature a range of sensors and can be synchronized and fused to produce a 3-dimensional athlete model [START_REF] Brodie | Fusion motion capture: The biomechanics of alpine ski racing[END_REF][START_REF] Brodie | Fusion motion capture: A prototype system using inertial measurement units and GPS for the biomechanical analysis of ski racing[END_REF][START_REF] Fasel | Three-dimensional body and centre of mass kinematics in alpine ski racing using differential GNSS and inertial sensors[END_REF]. Smaller variants of these systems have shown promise in detecting single-joint movement (e.g., lower back and trunk (Spörri, Kröll, Gilgien, et al., 2016))

and show promise for more elaborate inclusion into practice. Units can feasibly provide virtually unlimited 3-dimensional joint data at very high frequencies (e.g., 500 Hz (Fasel, Lechot, et al., 2016)), and can be used in integration with GPS to provide inclination/position of limbs in space in association with improved accuracy trajectory data [START_REF] Brodie | Fusion motion capture: The biomechanics of alpine ski racing[END_REF][START_REF] Brodie | Fusion motion capture: A prototype system using inertial measurement units and GPS for the biomechanical analysis of ski racing[END_REF]Fasel, Lechot, et al., 2016;Fasel et al., 2017a) via fusion and Kalman filtering [START_REF] Bergamini | Estimating orientation using magnetic and inertial sensors and different sensor fusion approaches: accuracy assessment in manual and locomotion tasks[END_REF]. Additional work for improving model accuracy has included the correction of positional data using periodic geographical 'anchor'

points in the form of powerful magnets placed at the base of gates (Fasel, Gilgien, Spörri, & Aminian, 2018). As a skier passes the gate, magnetometers in the IMUs pick up an inflection in the baseline magnetism, and these data provide distinct geographical points with which to correct drift in the positional data. Of course, this approach requires access to high strength magnets and aligning them within the course pre-testing.

One thrust of this thesis is to improve the knowledge of the integration of GNSS in alpine skiing by testing the capability to measure meaningful differences in key variables using a common sports GNSS unit and a custom-built RTK unit.

Kinetics

In alpine skiing, SRFs can be obtained in a variety of ways, but are generally: 1) inferred from either pressure insoles or force-sensors [START_REF] Falda-Buscaiot | Influence of slope steepness, foot position and turn phase on plantar pressure distribution during giant slalom alpine ski racing[END_REF][START_REF] Federolf | Impact of skier actions on the gliding times in alpine skiing[END_REF]Kröll, Spörri, Kandler, et al., 2015;[START_REF] Lüthi | Determination of forces in carving using three independent methods[END_REF][START_REF] Martínez | Comparison of the turn switch time points measured by portable force platforms and pressure insoles[END_REF][START_REF] Mote | The forces of skiing and their implication to injury[END_REF]Nakazato et al., 2011;[START_REF] Nakazato | Comparison between the force application point determined by portable force plate system and the center of pressure determined by pressure insole system during alpine skiing[END_REF][START_REF] Scott | Measurement of ski snowpressure profiles[END_REF]Spörri, Kröll, Gilgien, et al., 2016;Stricker, Scheiber, Lindenhofer, & Müller, 2010;[START_REF] Vaverka | Kinetic analysis of ski turns based on measured ground reaction forces[END_REF], or 2) estimated indirectly using an inverse dynamics approach from video or GNSS data in association with other methods (e.g., micro-technologies or surveying) [START_REF] Brodie | Fusion motion capture: A prototype system using inertial measurement units and GPS for the biomechanical analysis of ski racing[END_REF][START_REF] Gilgien | Determination of external forces in alpine skiing using a differential global navigation satellite system[END_REF]Meyer, 2012;[START_REF] Meyer | Aerodynamic drag modeling of alpine skiers performing giant slalom turns[END_REF]Reid, 2010;[START_REF] Reid | Force and energy characteristics in competitive slalom[END_REF]Spörri, Kröll, Gilgien, et al., 2016;Spörri, Kröll, Schwameder, et al., 2018;Supej et al., 2011;Supej et al., 2013;Supej et al., 2020). Among these methods, force platforms are the gold-standard in measuring kinetic data, since they provide a direct measurement of SRFs acting on each limb. However, difficulty integrating such technology into skiing practice has substantially limited studies utilizing this method. Moreover, until recently, measurement validity was degraded from designs that lacked optimal data capture capabilities due to technological limitations and were disruptive to skiing technique (e.g., increased clip-in height, weight, and modified ski rigidity). A recent system presented by [START_REF] Falda-Buscaiot | Development of a new 6-components force sensor design for biomechanical research in alpine skiing[END_REF] shows promise by addressing several of the confounding factors featured in traditional devices, even if it remains costly and relatively ungainly for athletes and researchers to utilize (e.g., require fixing directly to the boots; see Figure 13). Kinetic data can be estimated using models applied to kinematic data, where it can be separated into various subsets, including friction, SRFs, and aerodynamic drag at once (Gilgien, Kröll, et al., 2018;[START_REF] Gilgien | Determination of external forces in alpine skiing using a differential global navigation satellite system[END_REF]Reid, 2010;Supej et al., 2013). While subject to the limitations discussed above regarding the collection of kinematic data, when integrated with appropriate technologies, they provide a means of estimating the physical load on the athlete without unduly impacting their performance (i.e., only a small unit attached).

However, the force data derived from COM corresponds to the resultant SRF and so does not provide isolated force for each limb, nor detect distinct 'peaks' in force-time data that do not affect COM motion. As such, combining direct kinetic and kinematic tools might provide the best approach for quantifying interesting characteristics.

Figure 13. Two variants of ski mounted force plates

The left image shows a popular early design, used originally by Nakazato et al. (2011).

Each force plate weighs 0.9 kg and raises the clip-in height by 36 mm since each strain gauge is inserted between the bindings and the ski. On the right is a custom-designed system presented by Falda-Buscaiot et al. (2016). Each force plate comprises a cylindrical strain gauge that is the only connection point between two skeletonized aluminum frames: one connecting to the boot via screws and one that interacts with the binding. These customizations result in a standing height increase of only 8 mm, and approximately 1 kg added to each foot. While minor, the 'raised' strain gauges mean that the added load is more proximal than the earlier versions. Images adapted from [START_REF] Martínez | Comparison of the turn switch time points measured by portable force platforms and pressure insoles[END_REF] and Falda-Buscaiot et al. ( 2016) for left and right, respectively.

Interest in assessment off-snow

Assessments of skiing biomechanics on the field can provide precise information regarding the skier's force production and increase our knowledge about force output contribution to skiing performance. However, on-snow measurements do not necessarily clarify the degree to which athletic capacity (and notably force-production capacities) is a differentiating factor for performance. As such, there is substantial interest in assessing athlete's force capacities in laboratory and field tests informed by biomechanical data to understand better the physical characteristics underlying better or worse performers. While no such 'matched' assessments presently exist (i.e., physical profiles off-snow, compared to distinct discriminatory parameters on-snow), information exists regarding the physical profiles of skiers (Ferland & Comtois, 2018); the next section of this thesis (and subsequent sections of experimental work) will focus on this information.

FORCE-PRODUCTION CAPACITIES OF ALPINE SKIERS

PRELUDE

The following is a narrative account of force-capacity in skiers, divided into three sections focusing on 1) the physiological and mechanical basis of force production in human skeletal muscle and during movement, 2) essential variables representing the bounds of external force production and measurement methods (primarily in the lower limbs) , and 3) the current data and consensus of force capacity in skiers. While specific statements in this account are fully referenced, for brevity summarizing texts are regularly cited. Notable summary and commentary works can be found in [START_REF] Haff | Essentials of strength training and conditioning 4th[END_REF], Cormie andcolleagues (2011a, 2011b), Douglas andcolleagues (2017a, 2017b), Van Hooren and colleagues (2016;2017), [START_REF] Morin | Biomechanics of training and testing[END_REF], [START_REF] Cross | Methods of power-forcevelocity profiling during sprint running: A narrative review[END_REF], and Maffiuletti et al. (2016). Relevant reviews of the athletic profile of skiers are Hydren et al. (2013), White andJohnson (1993), Turnbull et al. (2009), Ferland andComtois (2018), andRaschner et al. (2013).

This section includes references to various works I contributed to during the tenure of this doctoral project, and during my previous academic qualifications:

Helms, E. R.

OVERVIEW

According to Newton's laws, force is applied to accelerate mass. Effective force application requires both physical and technical capacities [START_REF] Samozino | A simple method for measuring lower limb force, velocity and power capabilities during jumping[END_REF]. The former represents the general ability of the individual to produce mechanical energy, and the latter represents the faculty to apply a large proportion of this total capacity in a specific manner that contributes to sport-and context-specific performance. Physical capabilities are dictated by the limits of the body to perform work, dependent on a range of underlying and interacting neuromuscular, morphological, mechanical, and metabolic systems. Technical capacities encompass specific constraints of the targeted activity, which themselves represent specific motor patterning, involved musculature, and aspects involving segmental configuration and coordination. The differentiation between technical and physical is fundamental, since the balance between generalized physical capacity and the technical ability to apply this force per the sporting situation is incredibly important for success, and information regarding the predictive balance between these two capacities can provide invaluable insight into training and testing practices. A notable example of this in sprint running is the 'ratio of forces' (i.e., horizontal force/total force) [START_REF] Morin | Technical ability of force application as a determinant factor of sprint performance[END_REF], which provides a metric of the technical capability to apply force in such a way that accelerates the athlete. In practice, this ratio can subsequently be measured (Morin, Samozino, Murata, Cross, & Nagahara, 2019) and targeted for specific development [START_REF] Hicks | Improving mechanical effectiveness during sprint acceleration: Practical recommendations and guidelines[END_REF]. The same concept applies in alpine skiing, although there is considerably less research dictating the importance of force output in general, nor on the balance between specific force capacities and their technical derivatives on the field.

This thesis focuses on the macroscopic study of the force-production capacity of the lower limbs during mainly dynamic extension and static tasks, based on the literature discussed in the preceding sections. The following sections provide a narrative overview of the physiological and neuromuscular mechanisms underlying force production, field assessment methods, and the current force-profile of alpine skiers from direct measures of capacity. While the former are not explicitly addressed within the experimental content of this thesis, the latter form the basis for the selection and design of the subsequent methodological approaches. Where necessary, rationale for the thesis direction are provided at the end of their respective sections.

PHYSIOLOGICAL BASIS FOR FORCE PRODUCTION

Muscle force depends on the contractile elements of muscle tissue [START_REF] Gordon | The variation in isometric tension with sarcomere length in vertebrate muscle fibres[END_REF][START_REF] Huxley | Muscle structure and theories of contraction[END_REF][START_REF] Huxley | Proposed mechanism of force generation in striated muscle[END_REF][START_REF] Podolsky | Cross-bridge properties derived from muscle isotonic velocity transients[END_REF], applying tension to the skeleton [START_REF] Blix | Die länge und die spannung des muskels[END_REF][START_REF] Evans | The relation of length to tension development and heat production on contraction in muscle[END_REF][START_REF] Finni | Comparison of force-velocity relationships of vastus lateralis muscle in isokinetic and in stretch-shortening cycle exercises[END_REF][START_REF] Herzog | The three filament model of skeletal muscle stability and force production[END_REF][START_REF] Ichinose | In vivo estimation of contraction velocity of human vastus lateralis muscle during "isokinetic" action[END_REF][START_REF] Zajac | Muscle and tendon: Properties, models, scaling, and application to biomechanics and motor control[END_REF]. The transmission of internal to external force occurs via elastic tendons and fascicular tissues, which, when stretched (conceptually similar to an elastic band), contribute passively to tension. In this manner, force is measured externally at the extrema of the musculotendinous unit (i.e., MTU), and its magnitude is determined by several factors, including the size, alignment and positioning of muscle fibers (cross-sectional area, architecture, and 'pennation'), neural control elements, the length-tension and force-velocity characteristics of the muscle, and segmental dynamics.

The structural and neuromuscular basis for force production

The MTU is summarized by: 1) a contractile muscle component, 2) an elastic component in series with the contractile component, and 3) an elastic component parallel with the contractile component [START_REF] Hill | The mechanics of voluntary muscle[END_REF][START_REF] Weber | Muskelbewegung. Handwoterbuch der physiologie[END_REF]. Muscle force-production qualities are influenced by relative length-positioning and the speed at which the fibers are shortening [START_REF] Blix | Die länge und die spannung des muskels[END_REF][START_REF] Evans | The relation of length to tension development and heat production on contraction in muscle[END_REF][START_REF] Fenn | Muscular force at different speeds of shortening[END_REF][START_REF] Ritchie | The dynamics of muscular contraction[END_REF].

Skeletal striated muscle is organized into multiple bundles (fascicles) of fibers joined and run longitudinally to the muscle axis (see Figure 14). The substructure of fibers are myofibrils, which contain thin and thick protein filaments, called actin and myosin filaments, respectively. These filaments are juxtaposed in units (sarcomeres) and repeated in series, which result in a cylindrical shape. Sarcomeres are the smallest functional units responsible for muscle contraction.

Figure 14. Structure of skeletal muscle

In general, the active shortening action of the muscle is well summarized in the 'slidingfilament' model (see Figure 15), in which myosin 'heads' attach and form a cross-bridge between the myosin and actin filaments [START_REF] Gordon | The variation in isometric tension with sarcomere length in vertebrate muscle fibres[END_REF]. The myosin molecule subsequently pulls against the actin filaments [START_REF] Huxley | Muscle structure and theories of contraction[END_REF], which in turn pulls the Zdisk toward the center of the sarcomere. Finally, it detaches ready for reattachment at a new binding site [START_REF] Huxley | Muscle structure and theories of contraction[END_REF][START_REF] Huxley | Proposed mechanism of force generation in striated muscle[END_REF][START_REF] Podolsky | Cross-bridge properties derived from muscle isotonic velocity transients[END_REF]. This pulling movement results in the filaments 'sliding' parallel to one another and revealing new bindings sites for cross-bridge formation, with the result ultimately being muscle fiber shortening. Since these reactions occur on a minute scale, both the frequency and magnitude of cross-bridge formations must be very high for any measurable muscle displacement to occur. Reduced binding sites available for cross-bridge formation (in very extended or shortened muscle lengths) or the elements of the structure physically contacting each other (in significantly shortened lengths) impair filament sliding. In this manner, the magnitude of muscular force produced is dependent on the total number of crossbridges formed, with the best position for force production existing around the area with the most significant overlap between sliding filaments (i.e., the 'optimal' length). At its optimal length, a muscle will create the highest tension due to maximized myosin and actin binding-spots available [START_REF] Gordon | The variation in isometric tension with sarcomere length in vertebrate muscle fibres[END_REF]. Outside of the optimal range, the tension production is compromised (i.e., the length-tension relationship). As such, muscular force-production capacities are not only dependent on the relative position of actin and myosin filaments to each other but also the speed of muscle shortening. An inverse relationship between shortening speed and force production has been observed and attributed to intra-muscular fluid friction impeding filament sliding [START_REF] Hill | Mechanics of the contractile element of muscle[END_REF], and the lack of binding and rebinding capabilities of protein filaments with increasing speed [START_REF] Huxley | Muscle structure and theories of contraction[END_REF]. It is these factors that result in the typical force-velocity (Fv) relationship as it applies to individual muscles (see Figure 16). The Fv relationship in athletic movement will be discussed in later sections.

While the two-filament sliding-filament model well describes shortening and static muscle actions, it does not accurately represent lengthening contractions [START_REF] Douglas | Eccentric exercise: Physiological characteristics and acute responses[END_REF]. Notably, there is evidence for a third filament, titin, that actively resists muscle stretch by acting as a 'spring' that adapts its length and stiffness according to the surrounding contractile dynamics (Herzog, 2014). Titin's contribution to tension during lengthening muscle actions partially explains the higher force production observed in eccentric versus concentric muscle action.

Figure 16. Relationship between velocity, power, and force in skeletal muscle

Depicted here is the relationship between force and velocity in skeletal muscle, as initially determined by [START_REF] Hill | The heat of shortening and the dynamic constants of muscle[END_REF] in the sartorius muscle of a frog. In this simple depiction adapted from Cormie et al. (2011a), force, velocity, and power are relative to their maximum.

For contractile motion to occur, electrochemical impulses transmitted to the muscle fibers trigger complex biochemical reactions. These signals originate at the spinal cord and are transferred via motor neurons, which innervate multiple muscle fibers [START_REF] Haff | Essentials of strength training and conditioning 4th[END_REF]. At this level, the force-production capacity of a muscular unit is primarily dependent on 1) the number of units activated in each contraction, 2) the frequency of impulses transmission, and 3) the synchronicity with which units fire (Cormie et al., 2011a).

Muscle actions

Force production is influenced by the muscle actions involved, either in isolation or (more commonly) combined (see Figure 17). During a concentric contraction, the muscle shortens as a result of net positive force (i.e., produced force > opposing force) and positive mechanical work (force and displacement in the same direction). Cycling is a typical example of activity almost solely dependent on concentric contractions, but many everyday movements (e.g., walking) rely on net concentric work [START_REF] Devita | Muscles do more positive than negative work in human locomotion[END_REF]. In eccentric actions, the muscle force is less than that opposing it, and consequently, it lengthens. While perhaps its purest representation is during supramaximal resistance (i.e., the external resistive load supersedes maximum force production), eccentric actions are frequent in controlling motion and decelerating the body (e.g., the downward portion of a squat). In isometric actions, muscle force is balanced with that opposing it, and the length of the MTU remains constant. During dynamic sporting movement, some supporting musculature acts quasi-isometrically (notably the trunk) to stabilize the spine. In isometric actions, despite the lack of lengthchange (and thus zero work), energy is still expended as a product of continuously cycling cross-bridge formation to hold the muscle at a constant length [START_REF] Huxley | Muscle structure and theories of contraction[END_REF].

Note that isometric action measured at the MTU level can still involve some concentric action as the elastic components stretch and slack out, and MTU length change can also occur during isometric muscle actions (Van Hooren & Bosch, 2016).

The maximum force produced during concentric and isometric actions is typically less than eccentric actions [START_REF] Douglas | Eccentric exercise: Physiological characteristics and acute responses[END_REF]. The mechanisms underlying higher force production during eccentric contractions are attributed mainly to the involuntary 'breaking' of contractile protein bonds [START_REF] Douglas | Eccentric exercise: Physiological characteristics and acute responses[END_REF] and the unique contribution of titin to regulate muscle force [START_REF] Herzog | A new paradigm for muscle contraction[END_REF].

A result is that muscle lengthening can produce more mechanical work with less metabolic cost (Bigland- [START_REF] Bigland-Ritchie | Integrated electromyogram and oxygen uptake during positive and negative work[END_REF].

Time constraints of force production

From a macroscopic perspective, the maximal rate of force development (RFD) characterizes a range of underlying neuromuscular factors to develop force quickly. RFD is crucial in many sporting activities, and notably during explosive movements where the objective is to attain the highest velocity within the corresponding time-constraints (Maffiuletti et al., 2016). For example, during jumping the final velocity of the COM is dependent on the net work produced during the push-off. Accordingly, performance is enhanced (in this case, COM velocity and jump height) if force production during the entire push-off is as high as possible (Bobbert & van Zandwijk, 1999b The rapid development of force is reliant on several processes, termed stimulation, excitation, and contractile dynamics. These processes occur in series, and the step with the most extended delay likely has the most significant effect on RFD (Bobbert & van Zandwijk, 1999a). Broadly, stimulation, excitation, and contractile dynamics refer to: 1) building up muscle stimulation, 2) development of an active state (i.e., the relative number of free binding sites) per increased stimulation, and 3) the production of force (i.e., encompassing the various structural features of the musculotendinous unit), respectively (Bobbert & Casius, 2005;Bobbert, Gerritsen, Litjens, & Van Soest, 1996;Bobbert & van Zandwijk, 1999b). In general, contractile dynamics have received more attention in the research since they are easier to study and consequently are used to explain various mechanisms predominantly. A typical example is the difference in force production with and without countermovement, which is regularly attributed to elastic factors and the stretch shortening cycle (SSC; see below) (Van Hooren & Zolotarjova, 2017). In jumping, however, Bobbert and colleagues (2005;1996;1999a) reported that the primary explanation for the increased output was a product of increased stimulation, and subsequently, activation, built up during the countermovement phase. Specifically, an increased active state pre-concentric action allows force to be developed earlier in the push-off phase (i.e., concentric RFD) and was almost wholly explains differences in outcome performance. Consequently, improving the capacity to build up greater stimulation pre-contraction can enhance explosive performance.

An associated mechanism that has attracted recent interest is MTU slack (Van Hooren & Bosch, 2016;Van Hooren & Zolotarjova, 2017), which involves both activation and contractile dynamics as the delay between electromechanical processes and the recoil (i.e., catapult effect) of elastic elements. When a muscle is relaxed (without active or passive elastic force), the MTU can hang 'slack' from its attachments and insertions (Herbert et al., 2011;Herbert et al., 2015;[START_REF] Hug | Slack length of gastrocnemius medialis and Achilles tendon occurs at different ankle angles[END_REF].

Consequently, any slack must be taken up before force can be applied to the skeletal structure. The more the MTU is slack, the more time is needed to take up the slack and stiffen the unit. This period theoretically delays force production maxima to a greater degree than electrochemical processes (~6 vs. >100 ms, respectively) (Van Hooren & Bosch, 2016;Van Hooren & Zolotarjova, 2017). Unfortunately, it can be challenging to test the relative effect of various components in isolation since the build up of stimulation likely simultaneously reduces slack (Van Hooren & Zolotarjova, 2017).

Using the example of lower-limb ballistic performance, the contribution of these factors can be modelled by examining the difference in work production during jumping with and without countermovement. For example, with countermovement stimulation is increased and slack is reduced during the downward phase of the jump, and consequently force is transferred more quickly during the upward portion (Van Hooren & Zolotarjova, 2017). Conversely, in the SJ (i.e., without countermovement) the MTU is passively lengthened during the controlled downward and isometric phase, but less slack is taken up due to the lack of forces produced to decelerate COM. While somewhat unclear, increased and reduced slack is associated with compliance and stiffness, respectively [START_REF] Kubo | Elastic properties of muscle-tendon complex in long-distance runners[END_REF][START_REF] Kubo | Influence of elastic properties of tendon structures on jump performance in humans[END_REF]. Applying these factors to the common understanding of compliance and stiffness in jumping performance changes our perspective, which is discussed below regarding the SSC.

Theoretically, reducing slack pre-contraction onset (via increased stimulation, or otherwise) might improve RFD during explosive movement, and subsequently performance. With this in mind, the ability to build up stimulation and reduce slack might vary based on sporting code and playing level, which could subsequently provide valuable information for targeted training. A first step in elucidating the importance of these capacities in various contexts would be a better understanding of their contribution to augmenting force output at different movement velocities. Unfortunately, neither the effect of velocity, nor the wider association of these characteristics with performance is well researched.

The effect of velocity on the augmentation of force during countermovement, and

indirectly the effects of activation and slack, and its association with performance level of athletes will be explored in this thesis.

Stretch shortening cycle

The SSC phenomenon refers to a combination of mechanical and neurophysiological mechanisms that result in elevated work during a concentric contraction due to a previous forceful eccentric muscle action and is considered ubiquitous to explosive athletic movements. The SSC has three phases: 1) eccentric, during which loading quickly lengthens the MTU, the series elastic components store elastic energy, and the muscle spindles are stimulated; 2) a short static period between lengthening and shortening; and 3) concentric, which benefits from increased force production commonly attributed to reutilized stored elastic energy, increased muscular recruitment and increased firing rate to currently recruited musculature (e.g., via the 'Stretch reflex') (N.

J. [START_REF] Cronin | Triceps surae fascicle stretch is poorly correlated with short latency stretch reflex size[END_REF]. While the characteristics of each phase are essential in augmenting total work, should the amortization phase be too long, the stored energy dissipates as heat rather than being utilized during the following contraction.

Force production during the concentric phase of the CMJ (often measured indirectly via jump height) is almost universally acknowledged to be higher than SJ (Bobbert et al., 1996) and is commonly attributed to SSC mechanisms. Consequently, better performance in the CMJ relative to the SJ is positive, attributed to an increased capability to utilize the SSC. The prevailing perspective is that more compliant athletes utilize the SSC more (i.e., compliance = more 'elastic'), which is seemingly supported by inverse correlations between stiffness and performance augmentation via countermovement during jumping (r=-0.46, p<.05) [START_REF] Kubo | Influence of elastic properties of tendon structures on jump performance in humans[END_REF]. However, as decreased slack (i.e., acute or longitudinally increased stiffness) feasibly reduces the time to reach maximum force application (Van Hooren & Bosch, 2016), this interpretation relies on the supposed increased contribution of the SSC (i.e., via increased compliance) outweighing the negative influence of increased slack.

As discussed, the primary mechanisms associated with increased performance in the CMJ are a higher active state (and less slack), allowing more work production during the jump (Bobbert & Casius, 2005). For example, while the stretch reflex might aid in increasing stimulation, evidence for its contribution during jumping is inconsistent due to two factors: 1) it is unclear whether the dominant musculature acting at each of the involved joints lengthens at high enough velocities for the stretch reflex to be activated [START_REF] Kyröläinen | Stretch reflex responses following mechanical stimulation in power-and endurance-trained athletes[END_REF]Van Hooren & Zolotarjova, 2017), and, additionally, 2) active lengthening must occur for the reflex to be activated, and there is evidence to suggest that quasi-isometric states characterize the typical countermovement phase [START_REF] Kopper | Stretch-shortening cycle characteristics during vertical jumps carried out with small and large range of motion[END_REF][START_REF] Kurokawa | Interaction between fascicles and tendinous structures during counter movement jumping investigated in vivo[END_REF]. At the same time, while energy can be stored during eccentric actions and reutilized (i.e., 'potentiation') [START_REF] Bosco | Store and recoil of elastic energy in slow and fast types of human skeletal muscles[END_REF], this mechanism has only been directly observed in distinct musculature and specific movement conditions (Van Hooren & Bosch, 2016;Van Hooren & Zolotarjova, 2017).

Moreover, during jumping it is unlikely that potentiation majorly contributes due to requiring active muscle lengthening (Bobbert & van Zandwijk, 1999b). In any case, the difference between CMJ and SJ is almost wholly explained in modeling by a higher active state, which renders the contribution of SSC components to increased performance ballistic lower-limb extensions negligible (Bobbert & Casius, 2005;Bobbert et al., 1996).

The force-velocity relationship

The rate of performing mechanical work can be expressed in the construct of power output, which is computationally equal to the combination of force and velocity.

Subsequently, the Fv and power-velocity (Pv) relationships characterize the ability to produce force and power at a range of movement velocities [START_REF] Hill | The heat of shortening and the dynamic constants of muscle[END_REF]. Maximum power (Pmax) can be reached under an optimal combination of force and velocity during a movement or contraction (Fopt and vopt, respectively). The capacity for work and power is dependent on the Fv characteristics of the contributing musculature, which in turn represent different and independent properties: the ability to develop very high levels of force and the ability to contract muscles or extend limbs at very high velocities. In other words, the capacity to move slowly under very high external constraints (i.e., high force at low velocities) is disassociated from the inverse capacity -to move fast under low mechanical constraints (i.e., low force at high velocities) (Jaric, 2015). Since these capabilities are different, assessing force-production capacities at only one velocity cannot provide complete information, and so assessing the spectrum of force production at various velocities can provide insight into performance via observation of the balance or imbalance in mechanical properties.

Fv relationships well describe the actions of single muscles, joints, and multi-joint movements. While the former two are hyperbolic [START_REF] Fenn | Muscular force at different speeds of shortening[END_REF], the latter has been described as quasi-linear in a variety of movements, including cycling (both upper and lower body) [START_REF] Driss | The measurement of maximal (anaerobic) power output on a cycle ergometer: A critical review[END_REF], sprint running (both on treadmill ergometers and over-ground (Cross et al., 2017)), and ballistic extensions (both upper [START_REF] Rahmani | A simple method for assessing upper-limb force-velocity profile in bench press[END_REF] and lower body (Jaric, 2015;[START_REF] Soriano | The optimal load for maximal power production during lower-body resistance exercises: A metaanalysis[END_REF]). Notably, the Fv relationship is consistent across both acyclic and cyclic movements, typically comprising of data collected across multiple trials with various external constraints or across a single trial during which the athlete performs repetitive cyclic movements to accelerate a mass (e.g., during cycling or sprinting) (Cross, Samozino, Brown, & Morin, 2018). The difference in the shape of the Fv relationship between multi and single-joint actions is a product of various interactions [START_REF] Alcazar | On the shape of the force-velocity relationship in skeletal muscles: The linear, the hyperbolic, and the doublehyperbolic[END_REF]Jaric, 2015). However, prominent evidence suggests that the primary cause is power 'buffering' due to segmental dynamics (Bobbert, 2012;[START_REF] Bobbert | The relationship between pedal force and crank angular velocity in sprint cycling[END_REF]. The linear Fv relationship developed during multi-joint movements (see Figure 18) can be viewed in the same way as that presented in Figure 17, with the force intercept of the graphic approximating the theoretical maximum dynamic force at zero velocity (similar, but not identical to maximum isometric force), and a superimposed 'negative' velocity axis representing eccentric force. Unfortunately, limited and contradictory information exists regarding the Fv characteristics of multi-joint movements in eccentric states [START_REF] Alcazar | On the shape of the force-velocity relationship in skeletal muscles: The linear, the hyperbolic, and the doublehyperbolic[END_REF]Douglas et al., 2017a).

The quasi-linear Fv relationship during multi-joint movements provides insight into maximum capacities not otherwise practically accessible (see Section 2.3.4.3). By examining the extrema of the relationship (i.e., the x-and y-axis intercepts of the quasilinear fit), the following variables can be extracted: the theoretical dynamic maximum Black circles indicate data points from five individual jumps, with the black lines corresponding to linear and polynomial regression lines for the Fv and Pv relationships, respectively. The y-and x-axis intercepts of the regression lines of the Fv correspond to the maximum capabilities to produce force at low and high extension velocities (F0 and v0), respectively. Also depicted by the dashed lines are intercepting points of maximum power (Pmax) on the y-and x-axis, which correspond to the optimal force (Fopt) and optimal velocity (vopt) for power production. Data presented are compiled in the squat jump using the methods depicted in the subsequent experimental sections. Note that the data shown here are from an 'optimized' athlete, who produces Pmax at bodyweight, and data points can be spread further to the right or left of the regression (force and velocity dominant, respectively).

force produced at null velocity (F0); the theoretical maximum extension velocity until which force can be produced (v0); and Pmax, as the peak of the quasi-parabolic relationship between power and velocity, or computationally as Pmax=(F0•v0)/4 (Samozino, Rejc, Di Prampero, Belli, & Morin, 2012;[START_REF] Vandewalle | Standard anaerobic exercise tests[END_REF]. This collection of variables is regularly reported in the literature and characterizes the mechanical limits of the neuromuscular system for maximum force-production capacities. These relationships are macroscopic and represent the summation of various interacting factors, including muscle mechanics (e.g., length-tension, intrinsic Fv properties, and RFD), segmental dynamics, muscle morphology (e.g., tendinous properties, cross-sectional area, fascicle length, and pennation angle), and neural mechanisms (e.g., coordinative aspects, firing frequency, motor unit recruitment, and synchronization) (Bobbert, 2012;Cormie et al., 2011a;Jaric, 2015).

Pmax attracts interest in sports research due to its association with various athletic tasks (J. [START_REF] Cronin | Challenges in understanding the influence of maximal power training on improving athletic performance[END_REF]. For example, Pmax developed by the lower limbs during the push-off phase in jumping is correlated with sprinting performance [START_REF] Sargeant | Optimal velocity for maximal short-term (anaerobic) power output in cycling[END_REF] and with height attained in vertical and inclined jumps (Samozino et al., 2014;Samozino et al., 2012). Describing push-off performance using power has received criticism since jump height directly relies on impulse (force×time) [START_REF] Knudson | Correcting the use of the term "power" in the strength and conditioning literature[END_REF][START_REF] Ruddock | Jumping depends on impulse not power[END_REF][START_REF] Winter | Jumping: Power or impulse[END_REF]. Even so, the use of power can be justified since impulse is not an intrinsic mechanical, neuromuscular property (unlike Pmax). Instead, impulse is an externally measured mechanical output dependent on the context in which neuromuscular capacity is expressed (Samozino et al., 2012).

Across individuals, the same Pmax can be developed at a variety of combinations of underlying force expression, with the 'balance' of these capacities represented in the slope of the Fv relationship (i.e., SFv). Since ballistic performance is related to the level of power applied within the movement constraints (i.e., velocity or external load/resistance), SFv can influence performance independently from a change in maximum neuromuscular capacity. Samozino et al. (2012) validated a model of an individualized 'optimal' profile that would maximize push-off performance by correctly orienting the underlying mechanical capacities (F0 and v0) (i.e., maximize jump height at bodyweight [BW] with Pmax remaining constant). The further an athlete diverges from the optimized profile (SFvopt), represented in being oriented either towards force capacities at high or low velocities (i.e., force or velocity dominant, respectively; see Figure 19), the more substantial the reduction in their ballistic push-off performance at BW (Samozino et al., 2014). The concept of Fv profile optimization (Samozino et al., 2012) logically applies to explosive force production where external constraints dictate that power is developed at greater or lesser velocity. Accordingly, although more research is needed, there are circumstances where an athlete might benefit from adopting a more force-or velocity-dominant SFv than SFvopt. For example, in alpine skiing, force is produced primarily at much slower extension velocities than BW jumping (Alhammoud et al., 2020), and as such athletes might benefit from adopting a more force-dominant SFv compared to other sporting codes, or even compared to the individualized profile to maximize jump height.

The mechanical capacities underlying SFv can be developed via targeted training regimes (Jiménez-Reyes, Samozino, Brughelli, & Morin, 2017;Jiménez-Reyes, Samozino, & Morin, 2019;[START_REF] Simpson | Optimised force-velocity training during pre-season enhances physical performance in professional rugby league players[END_REF], with Morin and Samozino (2016) proposing a simple hierarchy of focus (see Figure 20). In general, low-level athletes will benefit from a generalized approach to develop mechanical capacity (i.e., Pmax), while higher-level athletes might benefit from targeting the development of the balance of underlying capacities to the specific sporting constraints (represented here in

SFv, but the same approach applies to other specificities). The timing and emphasis, according to this approach, is situational and under debate for many sports (e.g., crossover of physical to technical capacities).

Figure 19. Depiction of the optimal profile for maximizing jump performance

The image depicts two theoretical profiles relative to that which optimizes jump height for the same maximum power level ('BW optimal,' represented in the black dotted line) (Samozino et al., 2012). The grey line depicts force-dominance (F dominant; develop force at high speeds to maximize jump height), and the solid black line represents velocity-dominance (v dominant; develop force at low velocities to maximize jump height). The figure depicts the hierarchical approach to understanding the mechanical determinants of lower-limb push-off performance. Notably, the 'optimal' profile (*; as presented by Samozino et al. (2012)) typically refers to optimizing the balance of underlying Fv capacities (SFv) to maximize performance in 'unloaded' ballistic movement (moderate velocity conditions). However, feasibly optimal profiles exist for other unique scenarios (e.g., force production at speeds or in external resistive conditions that differ from unloaded jumping) and different sporting codes. Figure adapted from Morin and Samozino (2016), which initially included capacities vital to sprinting performance.

Strength endurance

Performance in repeated movements is directly related to the capacity to generate mechanical power and to sustain its production over time. The acute capacity for power relies on movement velocity, which is described by the Pv relationship (Bobbert, 2012;Jaric, 2015;Samozino et al., 2012). As presented above, the edge of the characteristic parabolic Pv curve represents 'maximum' capabilities, with the peak corresponding to the absolute maximum capacity for power (i.e., Pmax (Alcazar et al., 2017;Jaric, 2015)).

Everything under the edge of the Pv curve symbolizes submaximal power output (characterized by <100%Pmax) as varying combinations of force production at different velocities.

The ability to maintain power output over time depends on exercise intensity (%Pmax).

This interaction is well described by the power-time relationship (Pt; see Figure 21), which represents the entire spectrum of strength-endurance performance (i.e., endurance capacities), typically assessed as the maximum time a %Pmax can be maintained. The curvilinear Pt relationship levels off around an asymptote at which output can theoretically be sustained indefinitely (albeit, unpredictably), termed the critical power (Monod & Scherrer, 1965). Above critical power, the volume of work that can be performed by an individual is fixed (W ') [START_REF] Sreedhara | A survey of mathematical models of human performance using power and energy[END_REF], with the time to expend it contingent on %Pmax [START_REF] Poole | Critical power: An important fatigue threshold in exercise physiology[END_REF][START_REF] Skiba | Modeling the expenditure and reconstitution of work capacity above critical power[END_REF].

Figure 21. Typical power-velocity and power-time relationships

The figure depicts a typical power-velocity (left panel) and power-time (right panel) relationship, with the latter displaying endurance capacities (W', and filled-in box) as they correspond to a single assessment condition (denoted by the intersection between W ' and the power-time curve as a small circle) and critical power (dashed line).

The acute mechanical capacity for power (characterized by Pv) influences strengthendurance capacity (characterized by Pt) and differs between athletes. In general, there are three main methods through which an athlete might have superior strengthendurance performance: 1) possessing a higher Pmax for the same critical power, 2) possessing a higher critical power for the same Pmax, and 3) possessing a 'flatter' Pt profile with constant Pmax and critical power. Unfortunately, the former two capacities are independent and challenging to attain highly developed levels simultaneously. So different combinations and profiles can exist across athletes. For example, athletes in sports requiring acute explosive efforts (e.g., weightlifting and sprinting) typically exhibit lower critical power values than those who require longer duration outputs (e.g., long-distance runners) [START_REF] Vandewalle | Standard anaerobic exercise tests[END_REF][START_REF] Vuorimaa | Comparison of three maximal anaerobic running test protocols in marathon runners, middle-distance runners and sprinters[END_REF]. As such, differences exist within and between sports in strength endurance capacities due to different Pmax, critical power, and Pt profiles that feasibly influence performance (see Figure 22).

Figure 22. The strength-endurance capacity of two athletes expressed in threedimensions

A depiction of the power-velocity-endurance relationships in two athletes who display different power-velocity and -time characteristics. The graphic here represents data in three dimensions, as a compilation of that presented in Figure 21, with strength endurance shown at the same extension velocity for both athletes. Athlete A is depicted by black lines and exhibits a higher capacity for explosive force output (e.g., a sprinter); athlete B is represented by grey lines (and transparent grey shading for the strengthendurance relationship) and exhibits a lower capacity for explosive force, but higher endurance capacity (e.g., marathon runner). Adapted from Rivière (2020).

As displayed in Figure 22 and documented in the literature, there are observable differences in strength endurance capacity of athletes with different maximum power output characteristics [START_REF] Dekerle | Determination of critical power from a single test[END_REF]

EVALUATION OF THE FORCE-CAPACITY OF THE LOWER LIMBS

Since the expression of force can change drastically between movements and sports, and capacities in different force conditions are not necessarily connected, it is crucial to target and assess specific capabilities validly and reliably [START_REF] Hopkins | Measures of reliability in sports medicine and science[END_REF]. Validity refers to both the internal ability of the movement/testing to measure that targeted (e.g., Pmax), and the underlying capabilities to that externally exhibited or proposed as specific to performance (e.g., to DH skiing, as opposed to SL skiing, or more broadly sprint running). Moreover, a test must provide variables with low enough error to detect worthwhile changes in athlete capacity if it is to be valuable and applicable to the field.

However, if a test is widely adopted, perhaps the most critical factor is its practicality.

For example, specialized sprint running treadmills provide a practically unparalleled assessment of horizontal force-production characteristics, yet, because few practitioners have access to such equipment, more practical field methods have been developed and widely adopted (Cross et al., 2019). In the following section, we will briefly outline the current stance on assessing external force production of the lower limbs in different muscle actions using field methods.

Dynamic force production 2.3.4.1.1. Jump height and maximum power

Vertical jumps are probably the most frequently used measurements of lower-limb maximal neuromuscular output due to their relative simplicity, accessibility, habitual use by many athletes, and proven reliability (e.g., intersession, intra-class correlation

[ICC]=0.91-0.94 and coefficient of variation [CV]=2.9-3.3% [START_REF] Markovic | Reliability and factorial validity of squat and countermovement jump tests[END_REF]; intrasession, ICC=0.87-0.95 and CV=4.1-6.6% [START_REF] Moir | Intersession reliability of vertical jump height in women and men[END_REF]).

The CMJ (i.e., a jump performed with a swift downward movement preceding the upward push-off) and SJ (i.e., performed from a static half-squat position, following a brief pause) are the two most common jump variants. These jumps are used to test the capacity of the system to perform work during the concentric phase of a ballistic lowerlimb push-off, and the difference between them can provide further information regarding the contribution of countermovement mechanisms (see Section 2.3.3.3.2) (J. [START_REF] Cronin | Challenges in understanding the influence of maximal power training on improving athletic performance[END_REF]. Drop jumps are a variant of the CMJ, in which the downward phase of the jump is overloaded by having the athlete drop from a pre-set height and swiftly perform an explosive upward movement after landing (cueing can change, depending on the objectives of the test [START_REF] Haff | Essentials of strength training and conditioning 4th[END_REF]). The most common outcome measure of performance is the displacement of the center of mass during the flight phase, which can be obtained using a host of different technologies (e.g., jump mats, linear-position transducers, and even video-based cell-phone applications). Jump height is used to approximate Pmax and has been associated with various measures of functional performance (e.g., CMJ height vs. sprinting acceleration, r=0. 6-0.72, p<.01 (Wisloff, Castagna, Helgerud, Jones, & Hoff, 2004)). Unfortunately, jump height alone provides neither force nor velocity values, and even if it correlates with power, output can vary based on the mass of the individual and the push-off distance (hpo) (Samozino et al., 2012). Consequently, jump height in isolation cannot be used as an accurate index of Pmax and is limited in its explanatory power on athlete mechanical capacity (Morin, Jiménez-Reyes, Brughelli, & Samozino, 2019).

Fortunately, force data can be measured during jumping either directly via force platforms or indirectly estimated via inverse dynamics as a function of jump height and various anthropometric measurements. While force plates are undoubtedly the gold standard for assessing force-output characteristics, they are expensive and often ungainly for field measurements. Moreover, accurately representing phase-specific force production (e.g., during push-off) is dependent on the various detection criteria applied to the force-time data [START_REF] Mcmahon | Understanding the key phases of the countermovement jump force-time curve[END_REF], which change in their efficacy depending on the jumping conditions and the measurement objectives (Perez-Castilla, Rojas, & Garcia-Ramos, 2019). While there are several affordable field alternatives to force plates, they vary in their accuracy and comparability. An example of the problems arising from methodological and technical biases is the physical data published on alpine skiers (Ferland & Comtois, 2018), where club skiers present markedly higher jump height data than elite skiers assumedly attributed to the former using the 'jump-and-reach' test (i.e., 'Vertec,' in which performance is partially dependent on technique and upper-body flexibility) vs. the latter elite athletes using jump mat technology.

Several formulae use simple inputs to estimate force-capacity during jumping [START_REF] Mcmaster | A brief review of strength and ballistic assessment methodologies in sport[END_REF]. A notable mention is [START_REF] Bosco | A simple method for measurement of mechanical power in jumping[END_REF], who developed a validated method to calculate power over several jumping repetitions. Samozino, Morin, Hintzy, and Belli (2008) later developed a 'simple' method that uses inverse dynamics to estimate average power, force, and velocity data over a single extension, using measurements of body-mass, jump height, and push-off distance (see Figure 23). Notably, the accurate measurement of jump height, and any subsequent calculations applied to these data, relies on the precise measurement of flight time, and push-off distance. Consequently, factors such as standardization of takeoff and landing technique (i.e., extended lower limbs and in plantar flexion), and the depth of the starting position for the jump, are important to precise measurement [START_REF] Samozino | A simple method for measuring lower limb force, velocity and power capabilities during jumping[END_REF].

The simple method is valid against force-plate measurements (-3.2 to -9.3% bias, r=0.88 to 0.98, CV=3.7 to 13.3%, for force, velocity, and power variables) and slightly more reliable than the gold-standard method (e.g., intra-session CV=2.7, 6.5 and 8.6%, for force, velocity and power, respectively, ICC=0.97-0.99) [START_REF] Garcia-Ramos | Force-velocity relationship in the countermovement jump exercise assessed by different measurement methods[END_REF]Giroux, Rabita, Chollet, & Guilhem, 2015). Consequently, the combination of validity and accessibility of the method has seen it used in numerous research pieces (Morin & Samozino, 2016), including profiling the upper limbs [START_REF] Rahmani | A simple method for assessing upper-limb force-velocity profile in bench press[END_REF], and within strength-endurance assessments (Rivière, Peyrot, Cross, Messonnier, & Samozino, 2020b). Notably, the equations have been integrated into cell phone applications, which significantly increase the access to many practitioners and researchers [START_REF] Balsalobre-Fernandez | The validity and reliability of an iPhone app for measuring vertical jump performance[END_REF][START_REF] Sharp | Using smartphones for jump diagnostics[END_REF].

Figure 23. Measurement of push-off distance for calculation of average force

The image depicts the measurement of push-off distance (hpo) and height (h) during a loaded jump, using the practical landmark of the greater-trochanter (expressed as the encircled '×'). These data can be subsequently integrated with simple validated calculations (Samozino et al., 2008) to assess the force capacity of the lower limbs. Note that this same approach can apply to other ballistic movements, such as bench throw [START_REF] Rahmani | A simple method for assessing upper-limb force-velocity profile in bench press[END_REF]. Adapted from Samozino et al. (2008).

Unfortunately, while measuring power during jumping is arguably more useful than jump height alone, the output from a single jump only represents the maximum neuromuscular capability of the athlete in one velocity condition (i.e., around the middle of the Fv relationship). As such, this may not match the total maximum neuromuscular output of the athlete (Morin, Jiménez-Reyes, et al., 2019), and it does not provide information into the balance of underlying mechanical capacity for force production at different velocities. Not only do single jumps provide limited diagnostic details for the targeted development of athlete characteristics, but they also lack specific information regarding capacity at high or low velocities crucial for success for some codes.

Maximal strength

In the field, the most common method of assessing the maximum dynamic force of the lower limbs is the 1-repetition maximum test (1RM), which represents the absolute load at which an athlete can perform a single extension (e.g., a full-squat). There are several methodological approaches to this test [START_REF] Haff | Essentials of strength training and conditioning 4th[END_REF], all of which share an incremental increase in loading until a specific cut-off-typically determined via volitional failure or otherwise per a subjective rating of exhaustion. 1RM can be directly quantified as the load at which a final full repetition was performed (i.e., the load preceding failure), or via a calibration equation where multiple repetitions are performed [START_REF] Haff | Essentials of strength training and conditioning 4th[END_REF]. Of the many studies directly testing 1RM reliability (e.g., N=32, according to the systematic review of [START_REF] Grgic | Test-retest reliability of the one-repetition maximum (1RM) strength assessment: A systematic review[END_REF]) most have reported good numbers (intra-session, 92% of ICC values ≥0.80, CV=0.5 to 12.1%). The benefit of 1RM tests is their incredible accessibility since only loading and safety equipment are necessary to have an accurate measurement of maximum strength.

In general, 1RM appears to be an excellent measure of the capacity for strength (dependent on force production at low speeds) [START_REF] Grgic | Test-retest reliability of the one-repetition maximum (1RM) strength assessment: A systematic review[END_REF] during the concentric phase due to movement differences and lack of maximum ballistic intent. In any case, while a practical and potentially valuable measure of high force output, these results highlight that 1RM is slightly affected by velocity qualities.

Force-velocity profiling during ballistic push-offs

Variants of lower-limb ballistic extensions, such as jumping (Jaric, 2015;[START_REF] Soriano | The optimal load for maximal power production during lower-body resistance exercises: A metaanalysis[END_REF], are regularly integrated with a multi-trial approach to Fv profiling to characterize the limits of the body to produce power and force at high and low velocities. The interest in this approach is that it provides an overview of the capacity to perform work in the absence of technical constraints, and at different velocities which provides insight into the balance in underlying capacities to subsequently direct training progression. The capacity for maximal dynamic strength is represented in F0, which is determined in the theoretical absence of velocity (unlike 1RM). The capacity to produce force at high speeds is expressed in v0. The latter is particularly notable since common assessments targeting 'high velocity' capacity (e.g., unloaded CMJ) are far from the maximums that can be reached by the lower limbs during extension (i.e., in a 'balanced profile', 50% v0; e.g., see Figure 18). In the same manner that assessing maximum dynamic force output in 1RM is limited since it is dependent (in part) on velocity capacities (Rivière et al., 2017), valuable insight into the maximum velocity capacities of the lower-limbs is improbable during movements that are dependent on force production in moderate velocity conditions [START_REF] Soriano | The optimal load for maximal power production during lower-body resistance exercises: A metaanalysis[END_REF]. In jumping the Fv relationship can be compiled from peak data, or that averaged across the entire push-off phase [START_REF] Garcia-Ramos | Assessment of leg muscles mechanical capacities: Which jump, loading, and variable type provide the most reliable outcomes?[END_REF]. While the former presents potentially higher reliability (potentially due to being independent of movement onset detection protocols), peak values correspond to that developed during a single instant at potentially varying MTU positions and joint angles (based on unpublished work from our lab). Consequently, the latter corresponds to a more standardized marker of maximum capacity, and might be more relevant to sporting performance [START_REF] Samozino | A simple method for measuring lower limb force, velocity and power capabilities during jumping[END_REF].

To create an Fv profile requires force and velocity data compiled from multiple ballistic extensions at a range of loading conditions. Although theoretically one 'perfect' jump at

two disparate loads provides the information necessary to characterize the extremes of the Fv relationship [START_REF] Jaric | Two-load method for distinguishing between muscle force, velocity, and power-producing capacities[END_REF], more loads increase the possibility of correcting for physiological variability and attaining an accurate profile (albeit balanced with the negative effects of fatigue). With this in mind, a range of five different conditions is recommended (see Figure 24), beginning at body-mass and equally spaced until the athlete can produce a maximum jump height of ~100 mm (since below this height reliability is reduced [START_REF] Perez-Castilla | Evaluation of muscle mechanical capacities through the two-load method: Optimization of the load selection[END_REF][START_REF] Perez-Castilla | Assessment of loaded squat jump height with a free-weight barbell and smith machine: Comparison of the takeoff velocity and flight time procedures[END_REF]). There are some techniques to improving the quality of the outcome information, such as using the fit of the linear relationship to exclude outliers (e.g., remove the worst of five unique points) (Fessl, Fritz, & Kröll, 2020). A variety of technologies can provide the necessary data, each of which features their limitations (discussed in the previous section). When using forceplatforms, the data can be extracted directly from the force-time curve to determine averaged values during the push-off phase (Giroux et al., 2015;Samozino et al., 2008). In this fashion, potentially greater breadths of the Fv relationship (i.e., via heavier loads) can be examined, since variability induced by landing techniques is irrelevant since force is extracted directly from the push-off phase. Otherwise, inverse dynamics models can provide an accurate profile, which is dependent on the accuracy of the surrounding measurements (e.g., jump height and push-off distance) (Samozino et al., 2008).

Fv profiling can be applied to both the SJ and CMJ in isolation (Jiménez-Reyes, (Samozino et al., 2008) to force plates for calculating mechanical variables. They also compared an imposed 90° starting knee angle against that self-selected by the athletes and profiling the Fv relationship using all collected points vs. only two. The results reconfirmed the The image shows an athlete having performed multiple loaded jumps (black circles with a white fill), with well-balanced underlying Fv characteristics for maximizing jump height (i.e., lightest loading condition [body-mass] is the furthest point to the right). The grey area represents mechanical conditions with loading conditions less than bodyweight, so not easily accessible for testing without a system to provide assistance. Nevertheless, the extrapolation of the regression line to the furthest intercept (maximum theoretical velocity) has shown to provide acceptable error rates for testing practice. Ramos et al., 2019;Giroux et al., 2015). Moreover, in this comparison, the authors conclude that the simple method provides the best measure of validity and reliability compared to the gold standard force-plate method (Giroux et al., 2015).

The main limitation of Fv profiling is that it requires multiple jumps to be performed in non-fatigued states (i.e., with appropriate rest), and consequently requires time to assess.

While arguably providing more valuable insight into force capacity at a range of movement velocities for the same relative time as other tests (e.g., 1RM) it may remain difficult to schedule in sports with minimal testing and conditioning time (e.g., alpine skiing [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF]). However, the success of two-load Fv profiling (Fessl et al., 2020;Garcia-Ramos, Perez-Castilla, & Jaric, 2018;Janicijevic, Knezevic, Mirkov, Perez-Castilla, Petrovic, Samozino, et al., 2019;[START_REF] Jaric | Two-load method for distinguishing between muscle force, velocity, and power-producing capacities[END_REF][START_REF] Kröll | Assessing vertical forcevelocity profiles: Are two considered loads under specific circumstances enough[END_REF][START_REF] Sarabon | Force-velocity profile during vertical jump cannot be assessed using only bodyweight jump and isometric maximal voluntary contraction tasks[END_REF]) and decreasing error using the average of multiple trials (i.e., 2-3 trials at two loads vs. 1-2 trials at five loads) [START_REF] Hopkins | Measures of reliability in sports medicine and science[END_REF] show promise for improving the integration of the method into the field.

One criticism of this approach is its perceived lack of movement specificity to codes that do not strictly include ballistic push-offs. For example, explosive triple-extension of the lower limbs is central to jumping, but not recommended during skiing due to the potential for a loss of contact with the snow surface (Patterson, Raschner, & Platzer, 2009). However, a strength of Fv profiling during jumping is its capability to provide a view of the neuromuscular output of the body with relatively few external or technical constraints. Accordingly, the mechanical characteristics expressed during jumping are also relevant to sports in which the underlying physical capacity for force production at various extension velocities are interesting (e.g., alpine skiing), even if they do not strictly involve jumping. While other factors regarding the specific modality of assessment attract criticism (e.g., assessment of only force produced during the concentric phase [START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF]), Fv profiling using ballistic push-offs provides a controlled means of assessing the neuromuscular expression of dynamic force in more relevant conditions than otherwise possible (i.e., force production at very low extension velocities). Moreover, as discussed within this section, the typical approach to developing a profile is simple, fast, standardized, and reliable to a comparable or better degree to that provided by other alternatives.

For these reasons, Fv profiling was selected in the experimental approach of this thesis. In this manner, we were able to detect the capacity of skiers to produce dynamic force at high, moderate, and low velocities in a single test and test the contributions of factors underlying countermovement by comparing Fv characteristics in SJ and CMJ.

Multi-joint isometric force and rate of force development Maximum isometric force production capabilities are commonly assessed in the field using either the isometric mid-thigh pull (IMTP) or the isometric squat (Brady, Harrison, & Comyns, 2018). Both involve the athlete taking up a relatively upright position, similar to: 1) the most powerful position during a snatch or clean weightlifting movement (i.e.,

'the second pull'; typically prescribed within a range of motion at each joint (Comfort et al., 2019)), or 2) approximating a quarter squat in the isometric squat (note: the same joint angles can be followed [START_REF] Brady | A comparison of the isometric midthigh pull and isometric squat: Intraday reliability, usefulness, and the magnitude of difference between tests[END_REF] performed with a force plate, CV=9.2%, ICC=0.88]) for improving the accessibility and portability of the test. The significant difference between the assessments is the involvement of the upper body in the IMTP, which does not appear to differentiate between male athletes. However, in females, there is a large difference (isometric squat peak force +29%, p<.045). As such, the isometric squat might provide superior profiling of lower-limb force, though still dependent on the capability to transfer large amounts of tension through the vertebral column to the bar.

Both the isometric squat and the IMTP provide insight into maximum force-capacities at a perceivably lower risk, more reliable, and accessible assessment modality than other conventional alternatives (Brady, Harrison, & Comyns, 2018;[START_REF] Brady | A comparison of the isometric midthigh pull and isometric squat: Intraday reliability, usefulness, and the magnitude of difference between tests[END_REF]Comfort et al., 2019;[START_REF] De Witt | Isometric midthigh pull reliability and relationship to deadlift one repetition maximum[END_REF][START_REF] Deweese | The midthigh pull: Proper application and progressions of a weightlifting movement derivative[END_REF][START_REF] Haff | A comparison of methods for determining the rate of force development during isometric midthigh clean pulls[END_REF], albeit during different muscle actions (i.e.,isometric vs. dynamic [1RM]). Moreover, isometric force measured in these manners correlates with several measures of dynamic force output (e.g., jumping and weightlifting) and more practical performance measures (e.g., sprint cycling and throwing) [START_REF] Lum | The relationship between isometric forcetime characteristics and dynamic performance: A systematic review[END_REF]. While less data is available on the reliability of the isometric squat than the IMTP, both exhibit typically excellent reliability for maximum force measurements (ICC=0.92-0.99, CV=1. 7-4.3 (Brady, Harrison, & Comyns, 2018)). More recently, reliability values for maximum force produced on a isometric squat dynamometer (i.e., using force-plates, but with lashings in place of the more typical rigid fixed-bar setup) were acceptable across different fixed knee angle positions (90, 120 and 150°, where 180° is full extension of the knee; ICC=0.90 to 0.95, and CV=1.6 to 8.3%) although the results favored the deeper knee angle [START_REF] Sarabon | Force-velocity profile during vertical jump cannot be assessed using only bodyweight jump and isometric maximal voluntary contraction tasks[END_REF].

The instruction provided to the athletes is essential in gaining valid data [START_REF] De Witt | Isometric midthigh pull reliability and relationship to deadlift one repetition maximum[END_REF]. The most common instruction is a variant of 'pull as hard and as fast as possible' (Brady, Harrison, & Comyns, 2018), which is rationalized to collect both peak force capacity and RFD (Comfort et al., 2019). As such, providing the data acquisition frequency is high enough (~1000 Hz) (Maffiuletti et al., 2016), it is possible to calculate lower-limb multi-joint RFD during isometric field tests. Detection of movement onset is crucial to providing useable results, and the approaches used in the literature vary from manual 'expert selection' to algorithmic threshold detection protocols (e.g., 5 SD of stable BW = onset threshold) (Dos'Santos, Thomas, [START_REF] Dos'santos | Relationships between isometric force-time characteristics and dynamic performance[END_REF]Haff et al., 2015;Maffiuletti et al., 2016). Typically, peak RFD values suffer from inflated error and poor reliability (i.e., ICC<0.8 and CV>10%, and values as high as CV=18% (Brady, Harrison, & Comyns, 2018)), but by increasing the sampling window and using an averaged approach the error rate can be reduced within more useable ranges (Brady, Harrison, & Comyns, 2018). For example, [START_REF] Brady | A comparison of the isometric midthigh pull and isometric squat: Intraday reliability, usefulness, and the magnitude of difference between tests[END_REF] reported intra-day reliability values of ICC=0.89 to 0.91, and CV=9.6 to 9.9% for RFD averaged over the initial 200 and 250 ms in both IMTP and isometric squat tests. Since extended epochs from pull initiation rely, to increasing degrees, on peak-force capacities and muscle Fv properties (Maffiuletti et al., 2016), whether these results provide a discrete view of neuromuscular output compared to peak force is unclear (L. L. [START_REF] Andersen | Influence of maximal muscle strength and intrinsic muscle contractile properties on contractile rate of force development[END_REF].

A significant limitation of isometric assessments like the IMTP and isometric squat is that the force capacity is mainly dependent on the individualized length-tension relationships of the musculature at each involved joint. Consequently, while the measurements appear an excellent index of overall isometric force capacity, they may not be directly relevant to performance in other joint ranges. However, while the range in the IMTP is limited by practical factors (i.e., the bar contacting the limbs), using the isometric squat to assess angle specific force could provide insight into specific sporting tasks (e.g., in skiing, for the inside vs. outside limbs (Alhammoud et al., 2020)).

Moreover, recent evidence regarding the potential of the method to be used unilaterally and measure asymmetries could be valuable in return to sports practice, notably in sports, which feature elevated necessity for isometric force (C. [START_REF] Bishop | A novel approach for athlete profiling: The unilateral dynamic strength index[END_REF]Hart et al., 2012). The integration of these types of assessments into practice is interesting for future researchers.

The high reliability and practicality of the IMTP, in corroboration with evidence suggesting isometric force output and RFD might be a discriminating factor in alpine skiing performance [START_REF] Alhammoud | Contribution à l'analyse de l'activité neuromusculaire des skieurs alpins d'élite lors de tests isocinétiques et en conditions réelles d'entraînement[END_REF], drove the inclusion of this assessment in this thesis.

Eccentric force

The assessment of eccentric force in the lower limbs is complicated. In the first instance, since the maximum output of the muscles in eccentric actions is considerably higher than during dynamic or isometric actions [START_REF] Douglas | Eccentric exercise: Physiological characteristics and acute responses[END_REF], practically it requires dynamic supra-maximal loading to place the athlete in 'negative' mechanical conditions.

Several machines can measure eccentric force output [START_REF] Tinwala | Eccentric strength training[END_REF]; however, these cannot be strictly considered field methods. While it is possible to supramaximally load athletes in isoinertial movements (e.g., the squat), it is practically complicated, time-consuming, and potentially risky since assistance is needed to return the bar to the zero position.

Arguably the most valid field measurement technique uses the back-squat, during which the athlete is placed under increasing isoinertial loading and required to descend under a fixed movement velocity (dictated via metronome or other feedback) [START_REF] Douglas | Reactive and eccentric strength contribute to stiffness regulation during maximum velocity sprinting in team sport athletes and highly trained sprinters[END_REF][START_REF] Hollander | Maximal eccentric and concentric strength discrepancies between young men and women for dynamic resistance exercise[END_REF][START_REF] Spiteri | Contribution of strength characteristics to change of direction and agility performance in female basketball athletes[END_REF]. Maximum eccentric strength (i.e., eccentric 1RM) is determined as the load at which failure to control the descent is observed, either subjectively reported or objectively via deviation from a set velocity. For example, [START_REF] Douglas | Reactive and eccentric strength contribute to stiffness regulation during maximum velocity sprinting in team sport athletes and highly trained sprinters[END_REF] used a specialized smith machine which measured instantaneous and phase-specific movement velocity. These data were displayed in real-time to assist athletes in cueing their descent and provided precise cutoff criteria for detecting maximum eccentric strength (2-SD above targeted velocity during lower 2/3 of movement).

Another method uses a custom-built leg press machine (Harden et al., 2018) fitted with a system that provides automated pneumatic assistance during the concentric phase. The system features a selection of controllable factors that allow individualization and subsequently control (via visual and audible feedback) of movement amplitude during eccentric, isometric and concentric tests. During the eccentric test, the athlete lowers the load across a distance corresponding to between pre-set knee angles (10 to 90°) over 5 s.

Timing is cued using a programmable strip of lights along the path of the leg-press carriage that incrementally 'light up' to indicate the distance that should be attained per unit of time. Failure, and accordingly 1RM, are determined when the athlete cannot follow the light-cued descent. This approach is reliable (ICC=0.93, CV=3.0%, and smallest worthwhile change=2.9%) (Harden et al., 2018), can be used for training, and can detect worthwhile changes in athlete strength (Harden et al., 2020). Moreover, both this system, and that presented by [START_REF] Douglas | Reactive and eccentric strength contribute to stiffness regulation during maximum velocity sprinting in team sport athletes and highly trained sprinters[END_REF], can directly collect kinetic data via the integration of force-collecting technologies.

While the systems presented above are custom-built, similar data might be feasible from a variety of portable technologies (e.g., linear-position transducers) and more common strength and conditioning equipment (albeit more complicated to set up and control the loading). In any case, field methods currently assess eccentric capacity at an absolute velocity (e.g., approximately 30°/s at the knee [START_REF] Douglas | Reactive and eccentric strength contribute to stiffness regulation during maximum velocity sprinting in team sport athletes and highly trained sprinters[END_REF]). Whether one velocity condition provides sufficient information regarding specific maximal capacities is unclear [START_REF] Reeves | Behavior of human muscle fascicles during shortening and lengthening contractions in vivo[END_REF] since Fv data compiled during multi-joint eccentric actions is limited [START_REF] Douglas | Eccentric exercise: Physiological characteristics and acute responses[END_REF].

Some work has compiled an Fv profile using the data collected drop jumps by varying box heights (i.e., to vary the force and velocity data collected via force-plates during landing) and compiling the averaged velocity and force data expressed over the eccentric phase [START_REF] Moir | Using drop jumps and jump squats to assess eccentric and concentric force-velocity characteristics[END_REF]. While interesting, the relevance of such an approach to practice is unclear, since eccentric muscle actions may not occur during some drop jumps [START_REF] Kopper | Stretch-shortening cycle characteristics during vertical jumps carried out with small and large range of motion[END_REF], and the results are heavily dependent on the instructions of the task. Moreover, while the force-intercept of the eccentric Fv relationship (i.e., eccentric F0), likely supersedes that produced during concentric actions, that reported by [START_REF] Moir | Using drop jumps and jump squats to assess eccentric and concentric force-velocity characteristics[END_REF] was effectively equal to gravity.

Consequently, more research on the topic is necessary.

Strength-endurance during ballistic push-offs

Repeated ballistic jumps are a popular method of assessing specific strength endurance in research [START_REF] Bosco | Evaluation and planning of conditioning training for alpine skiers[END_REF]Bosco, Cotelli, Bonomi, Mognoni, & Roi, 1994;[START_REF] Breil | Block training periodization in alpine skiing: effects of 11-day HIT on VO2max and performance[END_REF]Emeterio & Gonzalez-Badillo, 2010;[START_REF] Nikolopoulos | Fitness characteristics of a Greek national alpine skiing team: correlation with racing performance[END_REF][START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF]Patterson, Raschner, & Platzer, 2014;[START_REF] Tesch | Muscle glycogen depletion and lactate concentration during downhill skiing[END_REF]White & Johnson, 1991) since they offer a simple means of controlling various factors to improve the specificity of the testing parameters (i.e., the underlying mechanical conditions of the test). Bosco and colleagues (Bosco et al., 1994;[START_REF] Bosco | A simple method for measurement of mechanical power in jumping[END_REF] popularized the method of measuring repeated jumps with their 30-60 s protocols. However, several variations exist which integrate sport-specific movements (e.g., jumping laterally on and off a box for maximum repetitions (Raschner et al., 2013)), adapting the performance target (i.e., maximum repetitions vs. maximum output over specific repetitions), timing, or mechanical conditions (via loading) in the aim of targeting specific endurance parameters [START_REF] Cular | Validity and Reliability of the 30-s Continuous Jump for Anaerobic Power and Capacity Assessment in Combat Sport[END_REF][START_REF] Fry | Kansas squat test: a reliable indicator of short-term anaerobic power[END_REF][START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF]Patterson et al., 2014).

In general, these tests have been shown to exhibit acceptable reliability for central outcome measures (ICC=0.87 to 0.99 (Bosco et al., 1994;[START_REF] Cular | Validity and Reliability of the 30-s Continuous Jump for Anaerobic Power and Capacity Assessment in Combat Sport[END_REF][START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF]Patterson et al., 2014;Raschner et al., 2013)).

Per the other push-off oriented assessments discussed in this section, several technologies can be integrated with these tests (e.g., force plates (Patterson et al., 2014) or contact mats (Emeterio & Gonzalez-Badillo, 2010)). The data reported are either expressed as average output during assessment (total, or for specific time periods) or fatigue indexes where the decrement in output is calculated relative to the average performance (e.g., as the difference between the first and last jumps, expressed relative to the maximum or mean value [START_REF] Cular | Validity and Reliability of the 30-s Continuous Jump for Anaerobic Power and Capacity Assessment in Combat Sport[END_REF][START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF] intent each repetition, both the relative intensity of the exercise (i.e., the %Pmax) and the mechanical conditions vary throughout the test (i.e., the Fv condition, as speed decreases). In the former instance, the results are rather dependent on the athlete's capacity to present maximum effort and can be affected by various factors such as cueing effort. A more pertinent approach might be to assess strength-endurance using a threshold approach where the athlete performs repetitions in which both RFv is standardized, and the power relative to the maximal power at this specific RFv (i.e., the %Pmax, per the v conditions, also called the 'power reserve'). Unfortunately, until very recently [START_REF] Rivière | Effet des conditions mécaniques d'exercice sur les capacités de production de force des membres inférieurs lors d'extensions acycliques uniques et répétées[END_REF]Rivière et al., 2020b), no such test exists in practice to our knowledge.

As such, the present variants of strength-endurance testing in ballistic jumps appear to be obscured by either differing exercise intensity relative to the individual's maximum capacity and a potential interplay with variation in the specific Fv conditions of the tests.

Nevertheless, current testing examples are widely used (e.g., reportedly for over ten years by the Austrian Ski Federation (Patterson et al., 2014), and historically with elite Italian skiers [START_REF] Bosco | Evaluation and planning of conditioning training for alpine skiers[END_REF]) and shown sensitive enough to detect changes in athletes physiological state during training cycles. Whether the data provided are a result of valid and relevant strength endurance properties requires more information.

In accordance with the results of co-authored work discussed later in this work [START_REF] Rivière | Effet des conditions mécaniques d'exercice sur les capacités de production de force des membres inférieurs lors d'extensions acycliques uniques et répétées[END_REF], an aim of this thesis was to design and implement a ski-specific strength-endurance test that controls for underlying mechanical conditions.

FORCE CAPACITY IN ALPINE SKIERS

Overview By nature, force expression in skiing is a combination of both physical and technical capacities. Since specific physical capabilities explain some proportion of performance, enhanced specific force-production capacities might be vital for skiers (Hydren et al., 2013;Turnbull et al., 2009). Consequently, there is interest in understanding the forcecapacities associated with better skiing in the aim of preparing athletes for the rigors of competition. However, the literature on the topic is convoluted, and no clear consensus exists regarding skiing specific muscular capacities, or even the relevance of physiological assessments outside of evaluating athlete adaptations from training interventions [START_REF] Bacharach | Intermediate and long-term anaerobic performance of elite Alpine skiers[END_REF].

Note that the skiing literature consists of publications from a range of source material, but in the following section, preference has been to rely on works that have undergone peer-review and publication in scholarly journals. Various other sources are referenced directly where relevant (e.g., thesis works, ski-coaching publications), but this was not performed exclusively (due to difficulties of accessing work in older publications, low quality of articles, and non-English language publications).

The current lack of consensus

A variety of investigators have attempted to quantify the determinant capacities of skiers (Ferland & Comtois, 2018) and, accordingly, design tests to better monitor them (Raschner et al., 2013). In general, the multifaceted nature of ski racing is presented as the most pertinent factor to consider in performance profiling and conditioning (Turnbull et al., 2009), which is reflected in the variety of tests used that measure force at high and low speeds across a broad range of motion, coordination, and stability (R. E. [START_REF] Andersen | An onsite test battery to evaluate giant slalom skiing performance[END_REF]Gilgien, Kröll, et al., 2018;Hydren et al., 2013;[START_REF] Maffiuletti | Is aerobic power really critical for success in alpine skiing?[END_REF]Neumayr et al., 2003;[START_REF] Polat | An examination of respiratory and metabolic demands of alpine skiing[END_REF]. Unfortunately, as described below, there are two main problems with the current stance of the literature.

Firstly, in tandem with the aging on-snow investigations, attempts to profile skiers span >40 years in the scientific literature; not only has skiing increased in professionalism during this period (i.e., increased access to standardized strength and conditioning (Hydren et al., 2013)), but there have been several rule and equipment changes that have markedly changed skiing style, biomechanical factors, and the overall performative landscape (Müller & Schwameder, 2003). Secondly, there have been limited links between on-and off-field force production in skiing research, mainly as a product of lacking on-snow data concerning athlete performative capacities to orient conditioning for performance enhancement (Gilgien, Kröll, et al., 2018;Kröll, Spörri, Kandler, et al., 2015).

Tests providing physiological data on skiers typically exist as part of batteries developed to offer a comprehensive view of physical capacities (S. L. [START_REF] Brown | Characteristics of national divisional and club male alpine ski racers[END_REF]Raschner et al., 2013;White & Johnson, 1991[START_REF] Zajac | Muscle coordination of movement: a perspective[END_REF]. These batteries, and the tests within them, often meet the objective of providing a generalist view of neuromuscular function but are arguably disconnected from skiing specific force qualities (see Figure 25). As discussed in Section 2.2, a synthesis of recent kinetic and kinematic data confirms that skiers produce force primarily during slow muscle actions (Alhammoud et al., 2020;Kröll, Spörri, Kandler, et al., 2015) and at high magnitudes (Gilgien, Kröll, et al., 2018;Kröll, Spörri, Kandler, et al., 2015). However, popular (Ferland & Comtois, 2018) and recommended [START_REF] Pritchard | Fitness testing parameters for alpine ski racing[END_REF] assessments in the literature mainly feature force production at moderate velocities (e.g., BW jumps), and arguably non-specific movement patterns (e.g., sprint cycling or shuttle runs). Curiously, at one stage, the United States Ski Federation even included short and medium-distance sprint running tests (40 and 400 m, respectively) as part of their ski-specific battery to assess explosive power and endurance (i.e., the 'Medals Test' (White & Johnson, 1993)). In the same manner, very recently Pritchard (2020) recommended the shuttle run as a means of assessing the aerobic fitness of ski athletes. While the soundness of these test can be argued, the relevance of results obtained from them to skiing is a separate factor.

In general, understanding the physical profile of skiers, and subsequently providing specific and useful testing regimes for athletes, is complicated by the current state of the literature. While some notable examples exist of specific tests (Raschner et al., 2013), published research on the subject is incomplete and would benefit from further investigation. Nevertheless, while often conflicting, there is a variety of evidence to substantiate positive relationships between various physical parameters and ski performance metrics (R. E. [START_REF] Andersen | An onsite test battery to evaluate giant slalom skiing performance[END_REF]Emeterio & Gonzalez-Badillo, 2010;Haymes & Dickinson, 1980;[START_REF] Miura | Maximum anaerobic power in adult alpine ski racers[END_REF][START_REF] Müller | Specific fitness training and testing in competitive sports[END_REF][START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF]Song, 1982;[START_REF] Vermeulen | Event-specific body characteristics of elite alpine skiers in relation to international rankings[END_REF][START_REF] Moritz Von Duvillard | Relationship of anaerobic performance tests to competitive alpine skiing events[END_REF].

The following sections will provide a summary of the current data on the subject.

Force at moderate-high velocities

Historically, force produced at high velocities and explosivity has been viewed as fundamental to skiers, and specifically integral in reactive movements and tactical positioning on the course (Turnbull et al., 2009). Subsequently, most tests of alpine skiers involve some measure of jump testing (e.g., single to multiple repetitions, single and The figure depicts the mechanical spectrum of force-capacity of the lower limbs at different extension velocities. While anecdotal, the figure estimates the more common conditions experienced during skiing, which constitute force produced in low-velocity conditions, with the magnitudes of expression being somewhat close to maximum output. The solid black line represents maximum neuromuscular output, with the area below the line representing all submaximal conditions. The black dashed line corresponding to the separator between mechanical conditions less than BW (to the right, towards the velocity intercept) and that greater than BW. The color of the shading denotes the frequency of mechanical conditions experienced, with darker shading corresponding to conditions experienced more frequently. Data were based on a compilation of reports of force output (Gilgien, Kröll, et al., 2018;[START_REF] Spörri | Course setting as a prevention measure for overuse injuries of the back in alpine ski racing: A kinematic and kinetic study of giant slalom and slalom[END_REF]Supej & Cernigoj, 2006;Supej et al., 2011;Supej et al., 2002) and angular kinematics (Alhammoud et al., 2020;Berg & Eiken, 1999;Berg et al., 1995;Kröll, Spörri, Kandler, et al., 2015) from on-snow assessments.

double leg, unloaded to loaded, and vertical to horizontal or lateral) (R. E. [START_REF] Andersen | An onsite test battery to evaluate giant slalom skiing performance[END_REF]Ferland & Comtois, 2018;Turnbull et al., 2009;White & Johnson, 1991[START_REF] Zajac | Muscle coordination of movement: a perspective[END_REF] shown to separate lower-level athletes from their higher-level counterparts while failing to discriminate between national-and elite-level athletes [START_REF] Reid | Validity of sportspecific field tests for elite and developing alpine ski racers[END_REF]. In addition to the age of these results complicating their current relevance, several tests in the battery can be criticized due to a lack of association with the underlying physiological qualities they purport to measure [START_REF] Jasmin | Applicability of the hexagonal obstacle test as a measure of anaerobic endurance for alpine skiers[END_REF]. Notably, change of direction and agility likely underscores performance in these more complicated jumping tasks (e.g., the hexagon obstacle test), and test-specific motor patterning and learning effects may confound associations with athlete level [START_REF] Nimphius | Change of direction and agility tests[END_REF].

Variants of maximum effort unloaded SJ and CMJs feature regularly in both skiing research (Ferland & Comtois, 2018) and various published testing batteries (Hydren et al., 2013;[START_REF] Pritchard | Fitness testing parameters for alpine ski racing[END_REF]Raschner et al., 2013). For example, a recent multi-cohort study of elite Norwegian athletes [START_REF] Haugen | Countermovement jump height in national team athletes of various sports: a framework for practitioners and scientists[END_REF] showed that the CMJ scores from alpine skiers (male, N=25; female, N=29) were elevated compared to other winter sports, endurance sports, most teams sports and the majority of strength and power sports measured (superseded by 'explosive' athletics events). Surprisingly robust associations between vertical jump and performance measures can be found (e.g., r=-0.86, for an average of 5 vertical jumps and skiing course time (R. E. [START_REF] Andersen | An onsite test battery to evaluate giant slalom skiing performance[END_REF]), but these results are far from consistent across different disciplines, sexes, and in updated works (Emeterio & Gonzalez-Badillo, 2010;Haymes & Dickinson, 1980;Jordan et al., 2018;[START_REF] Klika | Predicting skiing performance in 14-18 year old competitive alpine skiers[END_REF][START_REF] Moritz Von Duvillard | Relationship of anaerobic performance tests to competitive alpine skiing events[END_REF]. In general, updated data are limited and difficult to summarize due to disparities in assessment protocols and non-interchangeable technologies (e.g., 'Vertec' vs. force-platform) (Ferland & Comtois, 2018;Turnbull et al., 2009).

von [START_REF] Moritz Von Duvillard | Relationship of anaerobic performance tests to competitive alpine skiing events[END_REF] reported correlations between highest jump height (assumedly CMJ, but not stated) and performance (national 'United States Ski and Snowboard Association' scores) in all disciplines (r=-0.43 to -0.60) and relationships between the average of 5 consecutive jumps (r=-0.44 to -0.63) for disciplines excluding SG (r=-0.39). Both S. L. [START_REF] Brown | Characteristics of national divisional and club male alpine ski racers[END_REF] and White and Johnson (1991) reported absolute power during the vertical jump separated different athlete levels, yet normalized values provided less descriptive value (i.e., unable to discriminate between higher-level athletes). Emeterio and Gonzalez-Badillo (2010) showed associations between CMJ performance and ranking in males (rs=0.67-0.69, p<.004), albeit in youth athletes and with strong interactions with muscle mass (rs=0.57-0.70, p<.021). However, Jordan et al. (2018) reported no clear differentiation between youth and elite athletes in concentric jump measures (height, peak or mean power), although elite athletes displayed greater net-impulse during the eccentric phase. Most recently, Fessl et al.

(2020) performed an Fv profiling approach in SJ with a sample of alpine athletes, including a sample of 'elite' youth alpine skiers (N=9), in the aim of detecting differences and the efficacy of a reduced number of jumps. When compared to cross-country and ski jump athletes from similar performative levels, the young alpine skiers produced greater maximum velocity and maximum power per unit of body-mass (i.e., force at very high and moderate velocities, respectively) than the latter (p=.004) and former disciplines (p=.039), respectively. Another multi-sport study of Norwegian elite athletes (Haugen, Breitschadel, & Seiler, 2019) reported skiers presented comparable horizontal Fv profiles (i.e., during sprinting acceleration) to the median of the large group of power and team sports; although, the relevance of these data to the slow and largely orthogonal force production that dominates skiing outside is questionable at best. Some authors studying skiing kinetics [START_REF] Hintermeister | Muscle activity in slalom and giant slalom skiing[END_REF] have remarked on similarities between the force build-up during a skiing turn and the push-off in jumping, with the caveat of the slow movement speeds of the latter being a distinguishing factor.

As discussed in the previous sections, unloaded jumping is a practical and reliable means of assessing neuromuscular function. However, depending on the individual, jumping output exists somewhere around the middle of the force-velocity (Fv) relationship [START_REF] Soriano | The optimal load for maximal power production during lower-body resistance exercises: A metaanalysis[END_REF]. On the one hand, despite being an index of neuromuscular output, jump height is not necessarily a good predictor of the maximal power output of the lower limbs (Morin, Jiménez-Reyes, et al., 2019). On the other hand, even if it does track maximum power capabilities relatively well, the mechanical specificity of BW jumping to skiing is questionable since the expression of force is at markedly higher extension velocities (angular velocity of the knee for a 0.36 m jump is ~300°/s assuming moderate amplitude with 0.3 s push-off). In other words, jump height is a macroscopic index of dynamic force-production capacity in moderate velocity conditions and lacks discriminating information regarding the contribution of force at high and low velocities. These factors might explain the lack of consensus regarding this measurement in skiing research, such as inconsistent results (Ferland & Comtois, 2018), and even inverse relationships between performance and jump height in GS skiers (e.g., standing [lower=better] vs. jump height, r=0.64 (Haymes & Dickinson, 1980)).

Force at low velocities, in dynamic, isometric and eccentric conditions

A relatively common suggestion is that improving the maximum strength of an athlete might feasibly allow more significant work to be performed due to a lower relative intensity (Turnbull et al., 2009) and improved metabolic efficiency [START_REF] Foster | Evidence for restricted muscle blood flow during speed skating[END_REF][START_REF] Rundell | Compromised oxygen uptake in speed skaters during treadmill in-line skating[END_REF][START_REF] Szmedra | Hemoglobin/myoglobin oxygen desaturation during Alpine skiing[END_REF]. There are early reports of impressive maximum force capabilities in elite skiers (R. E. Andersen & Montgomery, 1988), including references to early textbooks that present associations with performance before the popularization of strength training [START_REF] Tesch | Aspects on muscle properties and use in competitive alpine skiing[END_REF]. Nonetheless, there is surprisingly little data on the subject. Strength assessments in the literature are typically implemented either in single-joint isometric or isokinetic dynamometers, with a few updated values from multi-joint and field strength tests using 1RM. Despite the historical interest in eccentric strength associated with the seminal research by Berg and colleagues (1999;[START_REF] Tesch | Aspects on muscle properties and use in competitive alpine skiing[END_REF], little research has strictly examined these capabilities, probably due to the practical difficulties in its assessment (see Section 2.3.4.5). A consequence of these factors is a sparse body of research that typically uses open chain (e.g., isokinetic dynamometry) and impractical technology, which at worst limits the ecological validity of the results and at best limits their practicality for field application.

Probably the strongest correlation between force production measures and skiing performance was reported on a specialized eccentric cycling ergometer, where the deviation from a targeted 'moderate load' torque during a long bout of exercise (20 min) was very strongly related to SL world ranking (r=0.89 to 0.93; discussed by Hoppeler (2016) regarding a German textbook and conference abstract). These results might provide strength to the premise that the modulation of force in eccentric modalities could be pertinent to performance in the tech discipline, or more generally for ski athletes. Unfortunately, few methods of assessing and training eccentric strength exist, and those that do typically require specialized ergometry. Other research that has quantified eccentric force production has typically failed to differentiate performance or disciplines, albeit using peak eccentric force in isokinetic measurements of the quads and hamstrings via isokinetic dynamometry (Alhammoud et al., 2019).

There is a variety of evidence to suggest skiers possess elevated force in isometric and slow-velocity isokinetic movements, albeit arising from studies performed >20 years ago. For example, alpine skiers showed significantly greater isometric strength of the knee extensors compared to other alpine disciplines (cross-country/Nordic) (Haymes & Dickinson, 1980), and comparative to some other sports [START_REF] Thorstensson | Muscle strength and fiber composition in athletes and sedentary men[END_REF]. Old reports from isokinetic dynamometry show torque at low but not high velocities separated club and national athletes (30 vs. 180 °/s, respectively) (S. L. [START_REF] Brown | Characteristics of national divisional and club male alpine ski racers[END_REF]. On the other hand, torque normalized to BW could not differentiate between 'high speed' athletes (e.g., sprinters) at event low angular velocities at the knee (e.g., 15-60) [START_REF] Thorstensson | Muscle strength and fiber composition in athletes and sedentary men[END_REF]. Moreover, maintenance of isokinetic torque (repetitions until 50% decrement in peak output) was correlated with performance (SL, r=-0.78 to -0.8; GS, r=-0.75) (Haymes & Dickinson, 1980). More recent examples were unable to differentiate between speed and technical specialists when measured using an isokinetic dynamometer (60-180 °/s), nor were they associated with performance (Alhammoud et al., 2019;Neumayr et al., 2003).

In an early master's thesis (R. E. [START_REF] Andersen | An onsite test battery to evaluate giant slalom skiing performance[END_REF], 1RM strength and skiing performance were correlated (SL, r=0.63, GS r=0.66 for USSA points). More recently, Emeterio and Gonzalez-Badillo (2010) showed the 1RM correlated to the skiing ranking of young males (rs=0.59, p=.017) but not females. However, in both cases some proportion of the results were probably attributed to variance in overall conditioning and factors associated with maturation, since they were young (15-19 years), and similar associations in these age groups have been observed with non-specific measurements athleticism (e.g., 'zig-zag' run) (Heikkinen, 2003). In an early anecdotal report of the practices of high-level Norwegian skiers, Refsnes (1999) reported impressive normative values from their alpine skiing squad, with females and males from their European Cup group (B-level) required to possess strength in the deep-squat of >2.2 and >2.5xBM in the deep squat, respectively. Interestingly, no other reports of dynamic multi-joint strength exist in the published literature for skiers.

In their cohort of young skiers Fessl et al. (2020) extracted the maximum lower-limb dynamic force capacity of young winter-sport athletes via Fv profiling, and showed that alpine skiers produced greater relative values and a more force-dominant profile than ski jumpers (both p=.004). Surprisingly, there was no clear difference in maximum force capacity when compared to cross-country skiers. However, since the alpine athletes possessed greater body-mass (9 kg heavier; 13.6%), presumably their absolute capacity for force production far exceeded their endurance counterparts. These values are understandably lower than those reported in World-cup speed discipline skiers by [START_REF] Rahmani | Force/velocity and power/velocity relationships in squat exercise[END_REF], however unfortunately little similar research exists in winter sports athletes to compare their values with. In any case, the values presented by Fessl et al. (2020) are comparable to a range of adult world-class athletes (e.g., Olympic and European championship-level BMX/track cyclists) (Giroux et al., 2016), with those reported by [START_REF] Rahmani | Force/velocity and power/velocity relationships in squat exercise[END_REF] superseding them.

More research is needed. Since the updated data evidence a dominant quasi-static (assumed isometric) action of the primary load-bearing limb (Kröll, Spörri, Kandler, et al., 2015), the assessment of lower limb isometric force might be a valuable addition to testing batteries in addition to (or in place of) challenging assessments of eccentric force production [START_REF] Pritchard | Fitness testing parameters for alpine ski racing[END_REF]. This factor, in association with multi-joint field tests of lower-limb force capacity, should help clarify the lack of consensus on the topic.

This information supported the decision to assess both maximum isometric force, and force production at a range of dynamic velocities in this thesis.

Strength-endurance

Anaerobic power is considered central to skiing performance [START_REF] Gross | High intensity training and energy production during 90-second box jump in junior alpine skiers[END_REF][START_REF] Polat | An examination of respiratory and metabolic demands of alpine skiing[END_REF][START_REF] Veicsteinas | Energy cost of and energy sources for alpine skiing in top athletes[END_REF][START_REF] Vogt | Physiological profile and training requirements of alpine skier[END_REF], and as such, tests targeting its assessment are used in skiers.

Utilized tests mainly include Wingate variants (Ferland & Comtois, 2018), the repeated jump [START_REF] Bosco | Evaluation and planning of conditioning training for alpine skiers[END_REF]Patterson et al., 2014), and other 'agility' style jump tests [START_REF] Reid | Validity of sportspecific field tests for elite and developing alpine ski racers[END_REF] (the latter are discussed above).

In general, the results from cycle ergometry assessment are challenging to synthesize.

For example, peak and mean power (r=0.66 and 0.73) via a 60 s Wingate correlated with GS performance in young athletes (R. E. [START_REF] Andersen | An onsite test battery to evaluate giant slalom skiing performance[END_REF]. Similarly, mean power was associated with performance in another group of male youth athletes (rs=0.55, p<.05), but not females (Emeterio & Gonzalez-Badillo, 2010). Song (1982) reported mean power correlated with DH ranking in youth athletes, but not GS. However, in the same publication, unspecific measures were very strongly correlated, perhaps showing athletes were still developing (e.g., grip strength r=-0.60 to -0.81). It is even more difficult to gain clarity for higher-level athletes. For example, various correlations between mean and minimum power and points in SL and GS have been observed for more extended duration tests (90 vs. 30 s; both only for females), but not during consecutive years [START_REF] Bacharach | Intermediate and long-term anaerobic performance of elite Alpine skiers[END_REF]. Furthermore, measures of decrement in capacity (either expressed as average work performed or the decrement in performance) show some efficacy, but not peak anaerobic power (White & Johnson, 1991). Since data are sparse and often feature small sample sizes (e.g., <10 [START_REF] Bacharach | Intermediate and long-term anaerobic performance of elite Alpine skiers[END_REF]Song, 1982)), more research is needed utilizing specific tests.

The most common tests of strength-endurance are performed in moderate velocity conditions. Emeterio and Gonzalez-Badillo (2010) reported moderate correlations between ranking and average BW jump height over 30 s in males (rs=0.59, p=.021), but not females. However, like other publications, these results were in youth athletes, and strong associations were simultaneously observed with muscle mass (rs =0.71, p=.003). In any case, jumping in moderate velocity conditions is unlikely to provide a specific assessment of the mechanical conditions experienced during skiing for reasons already discussed. A notable recent difference is the tests developed by Patterson and colleagues [START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF]Patterson et al., 2014), who modified the test originally proposed by [START_REF] Bosco | A simple method for measurement of mechanical power in jumping[END_REF] by loading the athletes (20 or 40% BW, for females and males, respectively) to be more skiing specific. While reliable and able to distinguish between capabilities measured over a training period (Patterson et al., 2014) and several seasons [START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF], the test was only associated with performative level in one of the four seasons during which the study occurred. Part of the results might be explained by a low sample size (N=10), or limitations associated with the standardization of the test to mechanical capacities of individual athletes altering the conditions under which each athlete performed (notably, RFv; discussed in Section 2. 3.4.6).

In any case, more information is sorely needed on the topic, and the experimental studies performed within this thesis work attempt to address this.

CONCLUSIONS

At present, a clear consensus of important force-production characteristics for skiers is impossible. However, the overall lack of data, and limitations of that presented, should not be interpreted as evidence for the absence of critical qualities for skiers. Undeniably, no single physiological factor can determine a good skier; however, by integrating new technology and understanding of neuromuscular constraints assessments in field tests, valuable insight might be gained into physical profiles for enhancing the targeted development of skiers. Notably, using methods to detect indexes of force-production capacities at different velocities underlying performance (i.e., the force at high and low velocities, maximal power output) could provide a more holistic view of skiing athletes.

Moreover, methods to assess the production of force at lower velocities (e.g., Fv

profiling, maximum theoretical force [F0]) or at null velocities (maximum isometric force) might provide novel information to aid in understanding the muscular profiles of ski athletes from varying disciplines. These methods, paired with appropriate sample sizes and robust methodological processes, should provide more clarity on the subject.

Furthermore, to understand the relevance of these factors in high-level skiers it is important to test these hypotheses in the appropriate population to avoid biases associated with youth and maturation, and to avoid overly heterogenous samples in which correlation analyses can be confounded.

Each of these factors are considered within the design of the methodology of the experimental thesis body, and explicitly discussed where appropriate.

THESIS AIMS

The specific aims of this thesis were to:

1) Explore the association between force production and giant-slalom skiing performance, via;

EXPERIMENTAL THEME 1: FORCE OUTPUT

the contribution of force magnitude and orientation to turn performance, and 4) characterize the contribution of the inside and outside limbs to force production. Skiers

PRELUDE

Before we profile skiers in their physical capacity for force, we must first understand force output in skiing and its importance for skiing performance. To our knowledge, there is little research that has measured force output in skiing and even fewer that has attempted to classify the impact of distinct force output characteristics with performance. Those that have done so have typically adopted turn-by-turn approaches, INTRODUCTION

In alpine ski racing athletes must negotiate a demanding course under variable constraints including event specific gate setups, challenging terrain, snow and weather conditions. Podium places are often separated by mere fractions of a second, which highlights the importance of pursuing small improvements in performance. An enhanced understanding of the contributors to this complex sport should provide a basis to better prepare athletes, and consequently produce worthwhile advancements in technique and conditioning.

Determining which capabilities separate high-level skiers from their lower-level counterparts is challenging. Skiing motion is essentially a result of utilizing the potential energy possessed at the top of the course by converting it into either kinetic energy (Ek)

or dissipating it (via ski-snow and aerodynamic friction) within the trajectory limits imposed by gates. An athlete who possesses the physical and technical capabilities necessary to effectively manipulate and ultimately minimize overall energy loss while negotiating the course is at an advantage (Spörri, Kröll, Schwameder, & Müller, 2012;Supej et al., 2011;Supej et al., 2013). Consequently, probably the most concise description of skiing performance is selecting the most direct trajectory allowed by the course and environment while minimizing energy losses at high speeds (Hebert-Losier et al., 2014).

In its most basic form, to turn and successfully negotiate a course, athletes must apply force onto the snow via their ski-specific (LeMaster, 2010). While other external forces contribute in some disciplines (e.g., minimizing aerodynamic drag in speed events (Gilgien, Kröll, et al., 2018)), the primary changeable mechanism of skiing is the production of force onto the snow, which induces snow-reaction forces (SRF) associated to changes in skier motion or as a product of changes in the ski-snow interaction (i.e., energy dissipation). The interplay of force output and skiing performance is complex, and while it is impossible to ski effectively without appropriate force generation and application capabilities, force applied at a given moment can serve to improve or worsen the instantaneous performance of a skier (Hebert-Losier et al., 2014). For these reasons, force output has attracted interest in applied research (Gilgien, Kröll, et al., 2018;Kröll, Spörri, Kandler, et al., 2015) and conditioning practice (Hydren et al., 2013).

While our understanding of skiing biomechanics has advanced considerably (Supej & Ogrin, 2019), the physical, technical, and tactical determinants of modern skiing performance remain mostly unclear. In racing, the ruling structure dictates 'macroscopic performance' as the shortest time between the course start and finish while adhering to the course boundaries (Fédération Internationale de Ski, 2020a). Course performance comprises multiple distinct but interrelated sections, in which there are intertwining approaches to minimizing time: 1) selecting an advantageous and more direct route between gates, or 2) preferencing a longer trajectory that enables higher speeds to be attained or maintained (depending on the characteristics upon entering the section) (Hebert-Losier et al., 2014). While the former approach is intuitive, as the distance traveled by the athlete is reduced, the ensuing tighter turns can result in more energy dissipation (Supej et al., 2011). The latter approach is typically associated with a longer path traveled between gates (Spörri, Kröll, Amesberger, Blake, & Müller, 2012;Supej et al., 2011), but this detractor can be overcome if enough velocity is gained within the section or maintained (i.e., less energy dissipated) (Spörri, Kröll, Schwameder, & Müller, 2012;Supej, 2008;Supej et al., 2011;Supej et al., 2013). Moreover, a higher sectional velocity directly influences performance in coming turns, which can be an advantage not apparent within the turn itself (provided the additional velocity can be managed effectively).

In slalom and giant-slalom (GS) there is some evidence that strategies enabling an elevated turn velocity appear preferable to a more direct route between gates (Federolf, 2012). Summarizing the recent stance on the approach, Spörri, Kröll, Schwameder, et al. (2018) suggest beginning turns earlier (Spörri, Kröll, Schwameder, & Müller, 2012;Supej, 2008), smoothly applying force (Supej, 2008), and 'carving' the skis (i.e., rather than skidding) (Spörri, Kröll, Schwameder, & Müller, 2012;Supej, 2008;Supej et al., 2011;Supej et al., 2013) as strategies to elevate velocity and performance in technical skiing disciplines. Unfortunately, our understanding of this phenomenon is drawn from a small pool of studies featuring specific and constrained external conditions. As such, it is possible that different results might be observed in other disciplines, and across course characteristics (Gilgien et al., 2020;[START_REF] Gilgien | Characterization of course and terrain and their effect on skier speed in World Cup alpine ski racing[END_REF]. In any case, attaining and maintaining high sectional velocities is limited by course constraints (Supej & Holmberg, 2010), technique (Supej et al., 2002), tactical approaches (Supej & Holmberg, 2019), and probably the physical competency of the athlete.

According to Newton's laws of motion, turns performed at higher velocities and/or with smaller turn radii (r) require elevated radial force output compared to slower and straighter turns (i.e., radial force [Fr]=velocity 2 /r). On the one hand, the same Fr can theoretically be observed in various situations, per the tactical approach to the turn mediated by the characteristics at entry (notably, entry velocity (Supej et al., 2011)). For example, two sections might display inversely proportionate velocity and turn radii (i.e., higher velocity and lower radius, and the inverse) and display similar force, and dissipation characteristics. On the other hand, athletes possessing an elevated capability to generate Fr might turn tighter at a given velocity or turn at a higher velocity with a given turn radius without needing to dissipate unnecessary additional energy. This ability to maximize Fr is well represented in the 'carving' technique, where anecdotally a large proportion of force being produced is directly turning the athlete along a curved trajectory (i.e., acting perpendicular to the tangential direction of the ski trajectory; Fr).

In carving, a large proportion of the turning phase is performed with the skis on edge and penetrating the snow surface, without a substantial lateral skidding component and associated minimal dissipation of energy (LeMaster, 2010). Reid et al. (2020) describe the phenomenon well, where carving is characterized by a reduced 'attack angle' between the longitudinal axis of the ski, and the velocity vector of its center. Practically, increased the attack angle results in skidding, with the inverse presenting the appearance of all points of the ski edge 'carving' through the same point on the snow. The interplay between carving and skidding is complicated, with some proportion of the turn inevitably being performed in conditions of skidding, and being mediated by a host of other factors such as the interaction between the environment and the ski geometry (Reid, 2010). Albeit a simplification, carving represents the most obvious way of attaining a greater velocity without unnecessary dissipation of energy (Spörri, Kröll, Schwameder, & Müller, 2012;Supej, 2008;Supej et al., 2011;Supej et al., 2013), provided the conditions permit it. However, athletes might deviate from carving in certain situations as a tactical choice (e.g., skidding to dissipate energy and avoid mistakes), or as a product of adopting a more direct trajectory, spending longer in the fall-line, and turning with a smaller radius (Reid, 2010). Nevertheless, without a capability to produce and control high levels of Fr athletes might reduce their strategic options, with the result being on average a lesser performance than otherwise possible from choosing strategies to disperse energy or a less optimal line.

While in numerous sport movements (e.g., sprint running, cycling or jumping) the maximal velocity is related to the highest kinetic work the athlete can produce, skiing velocity is a result of efficiently managing the transformation of energy (Supej & Holmberg, 2019). Consequently, maximal velocity corresponds to the highest value at which the athlete can ski while respecting the trajectory limits imposed by gates and without losing control and risking injury; this phenomenon is widely known as the 'velocity barrier' (Supej et al., 2011). While not widely researched, this barrier is likely the result of intertwining unmodifiable factors (e.g., course setting and snow quality), and physiological and psychological systems (e.g., perceptual, trajectory targeting).

Since it appears that the main mechanism behind skiing is the manipulation of SRFs, conceivably athletes with enhanced force output (notably Fr) might possess, ceteris paribus, a raised 'barrier' compared to their counterparts. Consequently, an elevated velocity barrier should be associated with elevated control at higher velocities, and a model terminus of better course performance. In other words, increasing athlete forceoutput capability is one theoretical means of improving performance during turns made at the limits of athletic ability. Assuming generating elevated Fr is important to ski-racing performance, the two main approaches to improving this variable would be increasing the total magnitude of force applied to the snow or applying a greater proportion of total capacity in the radial direction. In any case, at present the differentiation between total force output and that applied radially is unclear.

There is no consensus on the relevance of various force-output characteristics to performance, other than the timing and event-specific application of force being of higher importance than non-descript output (Hebert-Losier et al., 2014). For example, Supej et al. (2011) showed that slalom skiing SRF magnitudes did not clearly differentiate between athletes but rather acutely high values during turns were associated with high energy dissipation across the cohort. In a small homogenous sample, Reid (2010) reported a strong association between turn time and SRFs acting to 'drive' the athlete during a single 10 m slalom turn, but not when gate distance was increased to 13 m.

Furthermore, athletes who adopt a 'carving' technique, as opposed to a more traditional technique with shorter trajectories, ski faster but with non-dissimilar SRF (Nakazato et al., 2011;Supej et al., 2002). One explanation is that since forces can be produced, and SRFs induced, in favor of or against athlete performance (broadly, to optimally turn, or to dissipate energy), force applied in the correct manner (i.e., elevated Fr) is probably of greater importance than total output in less advantageous techniques (i.e., elevated energy loss).

There is relatively little information regarding the technical and physical parameters underlying SRF output in skiing, and a wide variety of measurement techniques (direct vs. indirect force measurement) and methodological approaches (high-level athletes performing race-pace trials (Supej & Holmberg, 2011) vs. recreational athletes performing free-ski turns (Nakazato et al., 2011)) render synthesizing findings challenging. Moreover, a commonly acknowledged limitation is the extrapolation of a minor representation of the course (e.g., 1-2 turns) to generalized course performance (Spörri, Kröll, Schwameder, & Müller, 2012). Sectional times in ski racing are notoriously variable (e.g., ~10% in high-level athletes) (Supej & Cernigoj, 2006), and competition courses are comprised of external constraints that can vary substantially turn-by-turn (e.g., high-and low-inclination sections), which highlights the value in concluding a more extensive breadth of the course.

In alpine skiing, SRF can be estimated in a variety of means: 1) estimating output via pressure insoles (Kröll, Spörri, Kandler, et al., 2015) or using specialized force platforms (Nakazato et al., 2011), and 2) using an inverse dynamics approach via video (Supej et al., 2011) or global navigation satellite systems (GNSS) (Gilgien, Kröll, et al., 2018) in combination with other micro-technologies (Spörri, Kröll, Schwameder, et al., 2018).

Force platforms remain the gold-standard method, but difficulty integrating such technology into skiing practice has substantially limited their implementation in research. Furthermore, until recently, technology lacked optimal data capture capabilities (e.g., low sample frequencies) and typically featured somewhat invasive designs (e.g., increased clip-in height, weight, and modifications to the rigidity of the ski) that inevitably degraded measurement validity. Moreover, while the biomechanical analysis in alpine skiing appears in the published literature in the 1980s (Hebert-Losier et al., 2014), modifications to the ruling structures, slope preparation, and ski-binding technology mean that the biomechanical environment in which the athletes perform has changed markedly (Müller & Schwameder, 2003). Consequently, despite a recent thrust in ski-research efforts coinciding with the development of portable technologies (e.g., high frequency portable low-cost inertial units), there is still a paucity of published information on the subject (Supej & Holmberg, 2019). Ski-force-platform systems have benefited from similar technological advances (Falda-Buscaiot et al., 2016), but an inability to determine the snow referential complicates separating the proportion of force output applied effectively during a turn (i.e., Fr). While Fr can be computationally separated from total force when measured from an inverse dynamics model applied to center of mass (COM) kinematics, the total SRF might not exactly track that produced by the limbs in isolation. Consequently, a combination of approaches might represent the best means of providing a holistic view of SRF output characteristics in skiing.

The aims of the present study were to: 1) clarify the association between skiing performance and optimizing trajectories and maximizing velocity, 2) test the importance of radial force in skiing performance, and 3) further explore the importance of force magnitude and orientation of force output in skiing turn performance. To this end, we measured force output and positional data using a combination of recently validated skispecialized force plates (Falda-Buscaiot et al., 2016) and a sports GNSS system on highlevel skiers performing a race-paced short GS course. Based on previous research, we hypothesized that performance would be well predicted by a capability to minimize energy dissipation to the detriment of path length, associated with increased radial force output. We further predicted that radial force would be primarily determined by both the capability to produce force and orient it effectively radially. Lastly, provided the total force produced by the lower limbs is a limiting factor for orienting force radially, we assume that athletes who presented greater total force would do so by producing more force to both the outside and inside limbs. Equipment and course characteristics

MATERIALS AND METHODS

Participants and protocol

Course setting and environmental monitoring

Throughout experimentation, snow quality (hardness, crystalline structure, and temperature) was monitored, as well as environmental conditions (temperature, wind, and visibility). The average temperature was ~1°C, with the nights preceding testing having temperatures low enough to freeze snow on the course. The course setting was initially performed by a high-level ski federation coach, adhering to a GS setup: 18 gates, ~25° slope relief (see Figure 27). Netting poles were placed along the periphery of the slope, which remained in place throughout the study, to corroborate gate positioning.

They were measured with at least two external poles and the gates preceding them.

Where necessary, measurements were made to additional immoveable points (pylons and ski-track mountings). As such, for each point, we were able to triangulate the initial position and corroborate using both external and internal points, and accurately replicate the course setting throughout experimentation.

Figure 27. Course representation

Depicted is a skier (not to scale, for clarity) traversing the course setup. ×, gates; grey line, athlete trajectory through analyzed gates (expanded for clarity); dashed lines represent the separation of the various analysis sections (speed, overspeed, and flat), with the approximate section characteristics (i.e., latitude and altitude) displayed in the corresponding axes (y-and z-axis, respectively). Note: since no course mapping was performed, section characteristics represent the average value between the turn-switches demarcating the beginning and end of each section, across all athletes and trials.

Ski equipment

For each trial, skiers were equipped with the same pair of race skis (model: LAB X-RACE GS, Salomon, Annecy, France; radius: 30 m; length: 1.93 m) and bindings (model: X19

LAB, Salomon, Annecy, France). A ski technician prepared the bases and edges of the skis before each experimental day. The skis featured a binding plate fabricated to accommodate the elongated clip-in length resulting from the sensor attachment (+60 mm). Athletes wore a selection of race model ski boots (model: X LAB+ 140 WC, Salomon, Annecy, France), provided in 1 size (10 mm) increments between sizes 24.5 and 28.5. Where preferred, the use of personal boot-liners and tongues was allowed.

Athletes used personal race suits (or were supplied with the appropriately sized suit), and other International Ski Federation (FIS) approved race clothing and protective gear (e.g., helmet, goggles, and back protectors).

Positional measurement

Athletes were equipped with a portable (~20 g) sports GNSS (model: Stadium tracker, Mac-Lloyd Sport, Paris, France) mounted in a small hip-bag attached at approximately the height of the COM (L5 vertebrae). The GNSS collected positional data from both Russian (GLONASS) and American (GPS) satellite constellation systems and featured a 9-axis accelerometer and IMU system (18 and 100 Hz, respectively; end data down sampled to 10 Hz). Data were collected using the manufacturer supplied software, which featured a fusion algorithm designed to improve positioning accuracy by combining satellite-derived data with that from the inertial sensors [START_REF] Brodie | Fusion motion capture: A prototype system using inertial measurement units and GPS for the biomechanical analysis of ski racing[END_REF]Fasel, Spörri, & Aminian, 2016;Gloersen, Kocbach, & Gilgien, 2018).

The time between the start and end of the run was measured using an FIS approved wireless system (model: 'Basic wireless solution,' Tag Heuer, La Chaux-de-Fonds, Switzerland), comprising of a starting-gate trigger and a dual-beam photo-voltaic cell set at approximately thigh height at the final gate in the course. For redundancy and data corroboration, two cameras (model: Hero 5, GoPro, San Mateo, USA) were used to record each skier: one operated by a researcher filming gates 6 through 9, and the second held by another researcher who followed the skier at approximately 5-10 m. Both cameras were affixed to handheld stabilizers (model: G5, FeiyuTech, Guilin, China).

Cameras were manually time-synchronized with each trial by filming part of the calibration process.

GNSS validity and reliability

GNSS units are widely used in sports science literature (Gloersen et al., 2018). While they can provide useful data regarding a variety of relevant metrics for skiing performance practically and efficiently (Supej et al., 2020), accuracy is system dependent and highly variable (Gilgien et al., 2014). To test the accuracy of our system and methodological approach, we performed two separate analyses: 1) a quasi-validity study, in which we compared key variables from the system against a criterion Real-Time Kinematic (RTK) system (see Section 3.2), and 2) a test of intra-athlete reliability, where key kinematic variables were compared in athletes who completed two maximum effort trials of the current testing protocol (N=6). Lastly, as a strategy to reduce the potential error associated with our units, we selected an analysis approach that examined only turnaveraged data that was subsequently further averaged over a minimum of three turns (Hopkins, Marshall, Batterham, & Hanin, 2009).

Force measurement

A custom-designed force collection system was used in this study to provide 3dimensional SRFs and moments (Falda-Buscaiot et al., 2016). The system (model: ISkiSet, Sensix, Poitiers, France; see Figure 28) comprised of two cylindrical force sensors per boot, which themselves included six full-bridge strain gauges. Each sensor was secured between two routed aluminum brackets: one formed to fit either the front or rear of a race designed alpine sole (ISO: 5355) and one formed to interact with either the front or rear of a typical race binding. Each force sensor was affixed between these two brackets to create a floating frame, where the sensors are the only point of connection between the skier and the ski. Briefly, the units were initially designed to meet the limitations of previous systems; primarily, excessive weight (~4 kg in previous designs vs. ~1.2 kg in current), and significantly raised clip-in points (up to 40 mm in previous designs vs. 6 mm in the current). The units were connected by cable to a small hip-mounted acquisition card (model: Jam Ingénierie, Chambery, France), which was equipped with a synchronized inertial unit (model: LSM9DS1, STMicroelectronics, Geneva, Switzerland). Raw output, acceleration, and gyroscopic movement were amplified and recorded at an amplitude of 200 Hz. Each set of boots underwent a lab-based calibration procedure (details explained in Falda-Buscaiot, 2017) to provide an accurate estimate of force and torque on and around the x-axis, y-axis, and z-axis (anteroposterior, mediolateral, and vertical, respectively). The result was a selection of boot-specific calibration matrices that were applied (model: MATLAB 2019B, Mathworks, MA, USA)

to the raw amplitude signal from the force. The raw voltage provided by the sensors was converted into force units using the appropriate calibration matrix per boot size.

Figure 28. Force plate device

Visible are the specialized force-plate devices used to collect the primary SRF data in this study. The novelty of these devices in contrast to previous designs is that the circular strain gauges are situated at the front and rear of the boots, where they are affixed between two 'floating' metal brackets as the only point of connection between the skier and the ski. This shift in the placement of the strain gauges enabled clip in height to be minimized, and the mass to be reoriented more distally compared to previous iterations. Each force plate could provide force and moments in the three axes (mediolateral=x, anteroposterior=y, normal=z), but only resultant forces were examined in this study. 3.1.4.3.1. Calibration,synchronization,

filtering and turn selection processes

During the calibration procedures, athletes collected trials while balancing on each ski;

the raised force plate was 'zeroed,' with the other plate collecting athlete BM. These files were saved for later use in normalizing variables to BM, which corresponds to total system mass, including all clothing and technology equipped during the skiing trial (i.e., athlete tare BM, plus the normalized mass of the skis, force plates, boots, and personal equipment). Pre-and post-trial athletes performed a strong double limbed jump on their skis; this was to provide a clear spike on force and acceleration signals (from both the GNSS and the force-plate acquisition card) to synchronize data streams.

Force data were then combined to create a resultant value for each limb and zeroed. Data from the GNSS were resampled to match the force plates (i.e., from 10 to 200 Hz) using cubic spline interpolation and then smoothed using 2 nd order Savitzky-Golay filter with a window of 201 frames. Force plate and GNSS data were synchronized using algorithmic cross-correlation applied around the impulses created from the athlete's jumping motion (100 frames either side of detected peaks from the on-board accelerometers of the GNSS and force-plate acquisition card). The filtering frequency for force and positional data was first approximated based on previous research [START_REF] Fasel | IMU-and GNSS-based turn switch detection in alpine ski racing[END_REF]Stricker et al., 2010), and then confirmed via fast-Fourier transformation, and manual observation of the Power spectral density, to remove higher frequency domain data not relevant to our analyses (e.g., vibration (Spörri, Kröll, Fasel, Aminian, & Müller, 2017)). Subsequently, the force and positional data were filtered using 2 nd order low-pass Butterworth at 8 and 1.5 Hz, respectively.

From this point, the synchronized and filtered data-streams were separated into distinct turns using the point of inflection in the trajectory (Adelsberger, Aufdenblatten, Gilgien, & Tröster, 2014). These turn-switch events were determined by searching for the point of sign change (+ to -, or vice-versa) on the triple derived trajectory data (Delhaye, Cross, Bowen, Samozino, & Hintzy, 2020). The fidelity of these turn-switch detection moments was corroborated using the method of Nakazato et al. (2011) applied to the SRF signals from each force plate. Briefly, the summated and filtered (low-pass 1 Hz Butterworth) vertical SRF signal was processed through two peak-finding algorithms to detect peak SRFs (the approximate apex of each turn) and the minimum value in the valleys between each peak (the 'unweighting,' signaling the turn-switch). The points extracted from the latter algorithm were overlaid with those from the inflection point method, confirmed, and the final temporal markers (from the inflection method) were used to cut the synchronized force and positional data into distinct matrices corresponding to each turn.

14 turns (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) were selected for final analysis, representing athletes having attained reasonable speed (i.e., stopped pushing with poles and skating to accelerate) to the turn directly preceding the final gate.

Section selection

From the total analyzed turns, two main steps of analysis were chosen: 1) 'course' averaged variables, where the average performance over the total analyzed turns was considered as a single coherent value for testing our hypotheses, and 2) 'sectional' averaged variables, where the course was separated into distinct typical sections known by ski practitioners, each characterized by the specific relief of the course and basic kinematic data (i.e., velocity and turn time): a section with the intent of gaining speed (Section 1: 'speed,' turns 3-5 and 15-16), a steep section where athletes managed speed that potentially was at risk of exceeding their 'velocity barrier' (Section 2: 'overspeed,' turns 6-10), and a flat section where athletes maintained speed (Section 3: 'flat,' turns [11][12][13][14]. The distinction was made separately by different experimenters possessing experience in high-level ski coaching.

Parameter computation

For each force platform, the three force components were combined into resultant force: Eq. 5

𝐹 res i = √𝐹 x 2 + 𝐹 y 2 + 𝐹 z
z axes of each ski referential. The magnitude of the total force produced by both limbs onto the snow (F) was obtained by the sum of the magnitudes of Fout and Fins and considered as the same magnitude as the resultant SRF applied to the COM. While the true magnitude of resultant SRF is unknown, due to the impossibility of detecting the orientation of each ski in space (i.e., the true vector orientation for Fout and Fins), the error induced by any potential differences in SRF orientation at each ski on F is assumed to be minimal. The absolute difference between the limbs was calculated at each instant and expressed as a percentage of F:

Eq. 6

𝑑𝑖𝑓𝑓 = |(𝐹 out -𝐹 ins )| 𝐹 ⁄
From this point, the following variables were calculated for each turn: average F (Ftot), average diff (Fdiff), peak values for F (Fmax) and for the outside and inside limbs (Fmaxout and Fmaxins, respectively). For data provided from the GNSS unit the following turn variables were calculated: velocity at the entry (vin) and averaged (vavg), and the cumulated displacement per turn (L, as the trajectory based performance parameter (Spörri, Kröll, Schwameder, et al., 2018), for use in the analysis model described later).

Turn radii (r) were calculated by fitting three consecutive points of the trajectory (at its native frequency of 10 Hz, up sampled to 200 Hz [i.e., 60 consecutive points]) with an arc segment (Pratt, 1987). Radial force (Fr) was computed by summing the centripetal force and the component of the bodyweight (i.e., BW in N) acting on the radial direction of the turn when angle of the slope ≠0 (Jentschura & Fahrbach, 2004):

Eq. 7 𝐹 r = 𝑣 2 𝑟 ± 𝑔 sin 𝛼 cos 𝛽
with α equal to slope relief, and β as the angle between the COM trajectory and that horizontal to the fall line (see Figure 30). Then, r and Fr were averaged over each turn.

The ratio of forces (RF) was expressed as the ratio between turn-averaged Fr and Ftot (see Figure 29). See Figure 31 for an example of the course averaged output of primary kinetic variables.

Figure 29. Depiction of the technical index of force application in skiing

Pictured is a skier inclining into a turn, applying force, and being acting on by reaction forces. The total magnitude of the resultant force is represented in Ftot, with that applied radially as Fr. The ratio of that applied radially to the total force-production of the athlete represents an index of technical capability, based on previous research from cycling and sprinting [START_REF] Morin | Technical ability of force application as a determinant factor of sprint performance[END_REF]. The higher the ratio, the more efficient the athlete is in applying force in the radial direction.

The primary macroscopic performance factor in this study was total course time (T). In contextualizing sectional performance, we used the change in specific mechanical energy for the turn, normalized to the velocity at turn entry (vin) as a velocity-based parameter (Spörri, Kröll, Schwameder, et al., 2018) and as the index of performance for the turn (∆emech⁄vin (Supej & Holmberg, 2011)):

Eq. 8

∆𝑒 mech 𝑣 in ⁄ = ∆(𝑣 2 2 ⁄ + 𝑔 • 𝑧) 𝑣 in ⁄
where z corresponds to the altitude and ∆ the change between two turn-switches (i.e., the beginning and end of a turn). ∆emech/vin provides a valuable method of accounting for the influence of the performance of previous turns (Spörri, Kröll, Schwameder, et al., 2018;Supej, 2008;Supej et al., 2011), and has been used to describe the within-turn performance of a range of athletes: a higher ∆emech/vin (commonly, the 'less negative', or even positive in some cases) is interpreted as less energy dissipated or more energy produced (if any) since the value is negative when energy is dissipated (Supej, 2008;Supej et al., 2011).

Statistical analysis

Statistical analyses were performed using JASP (version: 0.11.1, JASP Team, Amsterdam, Netherlands). T initially violated the assumption of distribution normality (Shapiro-Wilk score, p=.04), which, after a further inspection, was due to an outlier in the dataset.

While the data appeared congruent with the other scores and consistent with video observations, data from this athlete were removed due to the sensitivity of the subsequent models to outliers (final N=15).

In the first instance, key variables (turn time [Tturn], vin, ∆emech/vin, L, Fr, RF, Ftot, Fout, Fins, Fdiff, Fmax, Fmaxout, and Fmaxins) were compared between sections using repeated measures

ANOVAs with Holm posthoc tests, and Cohen's d for the magnitude of difference. To characterize the determinant nature of force production, we developed a stepped analysis procedure (Figure 32) to be applied to all datasets: course, speed, overspeed, and flat. The model consisted of two primary statistical approaches: Bivariate The strength of Pearson's correlations was interpreted using threshold values of r<0.1, 0.3, 0.5, and 0.8 to represent trivial, small (minor), moderate, large (strong), and very large (very strong) effects, respectively (Hopkins et al., 2009). For Cohen's d threshold values for qualitative interpretation of effects were d<0.2, 0.2, 0.5, and 0.8 as trivial, small (minor), moderate, large (strong), and very large (very strong) effects, respectively. The alpha value for all tests was a=.05.

Sensitivity analyses were performed using the sample size estimation software (G*Power [START_REF] Faul | Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses[END_REF]), to determine the approximate threshold of detectable effect for each statistical model and associated sample size (see Figure 33).

Figure 32. Modular outline of data-analysis applied to all sectional datasets

'Multiple regression' models (continuous lines) feature stepwise entry criteria, and 'Correlation' models (dashed lines) are Pearson's product-moment correlation tests.

RESULTS

For the reliability in course level kinematic data, the systematic variability was <2.1%, and the random variability was CV<2.86% for all variables except for ∆emech/vin (CV=4.95%). For sectional data, systematic variability was 0.3-4.6%, and the intra-athlete variability was CV=1.3-5.7% for all variables except for ∆emech/vin, which ranged from

Figure 33. Sample size plot

The two contour plots presented here depict the sensitivity of the utilized statistical models to detect effects, with a Type 1 error rate of α=.05 and 80% power. Plot A relates to the various multiple regression models and shows that with N=15, we can reasonably detect moderate or large effects (R 2 ≥0.45). Plot B relates to the Pearson's correlations and indicates large effects can be reasonably detected (r≥0.62). Note that both effects are quite considerable, which should be considered in interpreting our results.

CV=6.4-9.21%. For the validity comparison with the RTK system, the bias between the systems for 'sectional' turn groupings was -1.0-1.4%, agreement of r=0.69-0.97, and CV of 1.2-3.3% for Tturn, vin, L, and Fr (for ∆emech/vin, bias=-1.3%, r=0.82, and CV=9.1%). For full methodological details and results of both 'sectional' and 'turn-by-turn' analyses, see Section 3.2. The repeated-measures ANOVAs showed sectional effects in all variables except for RF, Fout, and Fdiff (Table 1). 2). L did not significantly improve the model in any case. In the flat section, no combination of variable models predicted T.

Level 2 -Relationships between course and sectional performance parameters and radial force

Fr produced throughout the course and in speed and overspeed sections was negatively correlated with T, and positively correlated with section-specific ∆emech/vin (see Table 3).

In the case of the flat section, Fr was related to T, but not with ∆emech/vin. Grey background denotes no clear prediction of independent variable; Course, data averaged over total analysis window (14 turns); CI, confidence interval; 1. Speed, turn averaged data from speed section; 2. Overspeed, turn averaged data from overspeed section; 3. Flat, turn averaged data from flat section; T, time in seconds between start and finish of course; Fr, radial force; ∆emech/vin, change in specific mechanical energy normalized to entry velocity of each turn; Note: all variables with the exception of T are averaged per the relevant section.

DISCUSSION

This study showed that the GS course performance of experienced to World Cup level skiers is explained better by an ability to minimize the dissipation of energy per section, rather than the distance traveled. This same finding was generally applicable within distinct sections of the course, except for a flat section in which neither normalized speed energy dissipation nor trajectory parameters could clearly distinguish athletes. Radial force output was strongly or very strongly related to course performance and strongly related to less energy dissipation in most sections. Elevated production of radial force was explained firstly by a higher capacity to produce total force, and secondly, by a greater ability to apply a more substantial proportion of this force in the radial direction.

Greater force production capability was linked to an increased capacity to generate force to the outside ski, and subsequently to apply force to the inside ski (i.e., a reduced difference between the limbs). In general, each of our hypotheses were confirmed, but were contextualized stronger, weaker, or even absent relationships in specific sections;

notably, the course performance was predicted by neither trajectory nor speed performance parameters in the flat section, and performance within this section (energy dissipation) was not predicted by radial force production.

In general, our findings support other analyses in GS (Spörri, Kröll, Schwameder, et al., 2018) that preference methods of attaining and maintaining velocity while minimizing energy loss (e.g., carving (Spörri, Kröll, Schwameder, & Müller, 2012;Supej, 2008;Supej et al., 2011;Supej et al., 2013)), rather than aiming to reduce path length [START_REF] Spörri | Perceived key injury risk factors in World Cup alpine ski racing--an explorative qualitative study with expert stakeholders[END_REF]Supej et al., 2011). Sectional ∆emech/vin over the course, and in speed and overspeed sections, explained a substantial proportion of variance in T (R 2 =0.46-0.67, p<.003), whereas L did not. This might suggest better athletes possess enhanced perceptual, technical, and physical capabilities and adopt variable turn strategies that enable them to minimize energy dissipation over a series of turns rather than a distinct, shorter or longer approach (e.g., a mixture of short and long turn strategies among higher and lower performing athletes). The lack of clear association between speed and trajectory parameters in the flat section might highlight that these variables do not represent the best measure of performance in this section or that different strategies in this section can be associated with similar performances. Notably, the lower relief of this flat section and energy production behaviors of the athletes could feasibly reduce the predictive ability of ∆emech/vin (Meyer, 2012). Another explanation might be that performance might be more clearly predicted by 'determinant' parts of the course (Supej, 2008;Supej & Holmberg, 2019) that stress technical and physical athletic limits. However, this is rather difficult to prove in practice, since each variable with which this hypothesis might be tested features its own intricacies. For example, while ∆emech/vin appears to be a good sectional performance predictor, the minorly weakened relationship between sectional ∆emech/vin and T in the overspeed section is probably a consequence of athletes adopting purposeful dissipation (e.g., following the delayed gate (Supej & Holmberg, 2010)) to avoid mistakes by dissipating energy to benefit later turns (Supej et al., 2011). Such a tactic would create a 'negative' result in the turn or section in which the dissipation occurred (in our analyses, weaken the negative correlation) but produce a net positive effect on overall performance. Lastly, ∆emech/vin is sensitive to computational and methodological errors, albeit at apparently acceptable levels in our analyses (i.e., CV<10%), and the associated decreased reliability of this variable might have prevented the detection of otherwise significant interesting effects.

In general, there were strong to very strong associations between lower course times and greater Fr. Although there is little empirical data on Fr in skiing, our findings are congruent with evidence that performance is determined mainly by attaining a high average velocity (Hebert-Losier et al., 2014), and carving represents the theoretical optimal approach to skiing at speed while minimizing ski-snow friction (Müller & Schwameder, 2003). Logically it should follow that athletes exhibiting greater Fr would likewise minimize energy dissipation (i.e., a less negative ∆emech/vin); however, this was not the case in all sections. While a clear and substantial relationship existed between elevated Fr and ∆emech/vin over the course and in speed and overspeed sections, this relationship was unclear in the flat section, which might suggest more considerable variability in the technique adopted to generate Fr (e.g., energy gain). Likewise, the relationship observed between Fr and ∆emech/vin in the steep overspeed section (moderate strength), might suggest tactfully shedding some speed by deviating from carving (as explained above) and circumspectly maintain or even increase Fr in later turns (observed in conserved strong relationship between Fr and T in overspeed section). In any case, athletes who developed high levels of sectional Fr were likely to attain faster course times, and thus logically would present a higher 'velocity barrier'.

In all sections, the combination of total force-output magnitude (Ftot) and the capability to apply a larger proportion of that output in the radial direction (RF) significantly predicted Fr. On average, ~68% of Ftot was applied radially, with much greater values observed in overspeed and flat compared to the speed section. In this case, RF represents a ratio of 'mechanical effectiveness' in which better athletes theoretically apply a greater proportion of their total output efficiently (i.e., higher proportion of Ftot radially). A similar model exists in sprint running and cycling, where it provides an enhanced understanding of acceleration performance determinants and orienting training goals [START_REF] Morin | Technical ability of force application as a determinant factor of sprint performance[END_REF]. Similarly to sprint running, in skiing both 'physical' (Ftot) and 'technical' (RF) capabilities contribute to force applied effectively (Fr), but interestingly the variance explained by each variable was changeable depending on the sectional window. In the speed section, Ftot had much greater explanatory power than RF (R 2 =0.64 and 0.36, respectively). One possibility is that in the speed section (and at various times throughout the course), better athletes generated force in response to targeted dissipation, transient and random vibrations (Supej & Ogrin, 2019) that might otherwise disrupt the motion of less capable skiers to maintain optimal skiing technique (and generate high levels of Fr). In contrast, in the flat section Fr was much more strongly predicted by RF than Ftot (R 2 =0.60 vs. 0.39, respectively), which might highlight the reduced necessity for targeted dissipation with athletes further from their velocity ceilings; the substantially lower ∆emech/vin in this section strengthens this theory, and it is possible that athletes performed positive muscular work and gained additional energy, which served to both partly compensate energy dissipation and to elevate Fr. Several studies have recorded positive values of energy change in skiing, suggesting that some energy was regained (Meyer, 2012;Reid, 2010;Supej, 2008;Supej & Holmberg, 2010) during rhythmic turns. However, in the overspeed section and over the complete course, Ftot and RF were quite balanced in their contributions to elevated radial force (e.g., course, R 2 =0.50 and 0.49, respectively). These findings have interesting implications for practice since in general better athletes both technically orient a larger proportion of force to perform at preferable trajectories and speeds (i.e., elevate carving, as a product of improved Fr) and display generally enhanced force output on the skis. However, since the absolute physical aptitude of the skiers were not measured in this study (instead, the ability to exhibit output within the constraints of skiing), it is unclear whether force output on the skis (radial or otherwise) represents or are limited by: 1) maximum athletic capacity, 2) maximum athletic capacity mediated by various constraints (technique, tactic), or 3) a combination of these and other factors. Evidence of near-maximal muscular activation during skiing [START_REF] Alhammoud | Contribution à l'analyse de l'activité neuromusculaire des skieurs alpins d'élite lors de tests isocinétiques et en conditions réelles d'entraînement[END_REF]Berg & Eiken, 1999) and enhanced physical capacity for force in skiers (Hydren et al., 2013) would support the theory of physical capability being a determinant factor, but further evidence is needed.

Athletes produced force at approximately a 2:1 ratio between the outside and inside limbs. While greater force applied to the outside limb was hierarchically the strongest predictor of global force output in all sections (p<.001), a strong inverse relationship with the difference between limbs was observed (p<.001) in all sections. Specifically, a globally higher total force output was explained by a higher force output of the outside limb and an associated more balanced application of force between the limbs (i.e., disproportionately higher contribution of the inside limb). These findings were further corroborated with individual correlations between force produced to both the inside and outside limbs (Fins and Fout, respectively) and sectional Ftot, without relationship between the limbs. There are several possible explanations for this finding, each of which assumes a relationship between total force and carving (Müller & Schwameder, 2003) (tested in Level 3). Two scenarios represent better performance (i.e., a higher Fr): tighter turns (i.e., lower radius and shorter trajectory), and turns performed at higher speeds. In the preceding example, a skier aiming to reduce their turn radius must first increase the edging angle of the ski (Federolf et al., 2010). In this aim, athletes incline laterally towards the center of the turn, while simultaneously applying force at an increasing edging angle to bend and carve the skis through the snow, resulting in a tighter radius (Müller & Schwameder, 2003). The capability to turn with tighter radii depends on the capability to produce forces to the mechanically advantageous outside limb at a biomechanically unique position. Increasing the edging angle requires inclining the upper body towards the turn center, where some application of force to the inside ski is needed to maintain control and dynamic balance [START_REF] Lemaster | Systematic use of the inside skin in carved turns[END_REF]. However, evidence showing supra-maximal (i.e., greater than the maximum voluntary isometric contraction) levels of activation (Berg et al., 1995) indicates turns that require very high levels of force may supersede single-limb force-production capabilities. In circumstances where athletes must produce more force than possible via the outside limb, there is no other option than to apply a proportion of force using the other limb (or to disperse energy). In any case, this finding highlights the necessity of conditioned force output for the inside limb, which is notable given the disparate knee and hip angles at which these forces are produced between the two limbs (Alhammoud et al., 2020;Kröll, Spörri, Kandler, et al., 2015). In physical conditioning, high-level athletes might focus on the development of force application at angles of the knee/hip complex relevant to the outside ski and the inside ski (~-20° for the inside limb, using a non-carving approach (Berg et al., 1995) and -34° in recent literature (Kröll, Spörri, Kandler, et al., 2015)). Such an approach should elevate the force production of the lower limbs in total (i.e., increase Ftot) and allow for more flexibility in performing turns that require both greater force application in general and an enhanced contribution of the inside limb (i.e., more balanced force profile).

Limitations

Athletes were required to wear a variety of relatively unfamiliar equipment, which may have affected their performance. While steps were taken to resolve this factor (e.g., familiarization), athletes may not have performed at their peak. The methodological approach of averaging multiple turns was chosen to reduce error (Hopkins et al., 2009), provide a more macroscopic view of performance, and to highlight the capability of detecting important differences in performance using sports GNSS. While our results

support the conclusions of more detailed analyses (Spörri, Kröll, Schwameder, et al., 2018), including those from other disciplines (Supej, 2008;Supej & Holmberg, 2010;Supej et al., 2011), turn-by-turn analyses afforded by higher accuracy positional devices (e.g., low-cost RTK) would aid in further contextualizing the relationship between force output and performance in skiing. While in this study, carving is considered the 'optimal' technique, there are instances in which athletes deviate from this approach and prefer other strategies. These instances might result in a more beneficial overall performance for the athlete (Hebert-Losier et al., 2014;Supej & Holmberg, 2019), but are not directly considered in our model. Moreover, while advanced athletes may possess the physical and technical qualities to incline the ski and carve at a variety of turn speeds and radii (Müller & Schwameder, 2003), there are practical limitations to the ability: the geometry of the ski (i.e., the radius of the side-cut), ski-snow interaction [START_REF] Federolf | Deformation of snow during a carved ski turn[END_REF], and the lateral inclination imposed by the boots (Müller & Schwameder, 2003).

CONCLUSIONS

Our results support other analyses that better GS performances are predicted by lower energy dissipation at higher speeds. Higher radial forces are related to performance and are determined by both total force production and an enhanced ability to orient a greater proportion radially. The contribution between production and orientation of force varies depending on course characteristics. Athletes who apply more force (and potentially perform better) adopt techniques that elevate total force output via the outside limb and, subsequently, a proportionally higher contribution of the inside limb. These results strengthen the evidence for enhanced force-output capacities in ski racers and might provoke conditioning focus for the inside limb. While both 'technical' and 'physical'

force qualities appear determinant in GS skiing, we cannot conclude whether the athletes were truly exhibiting their physical limits; further detailed analyses, including crossexamination of off-snow tests of physical output, should help clarify these points.

Increased force-output capacity, in combination with adopting techniques to improve force application effectiveness (RF) on the skis, should raise radial force capacity (e.g., carving) and allow athletes greater physical and technical freedom to select advantageous trajectories on-piste. Lastly, these results may be context, technology, or athlete-specific, and should be tested in greater depth. Notably, testing whether similar results are observed across the other skiing disciplines, and using other slope setups, would provide a more encapsulating view of force output and performance for researchers and practitioners.

VALIDITY OF TURN-AVERAGED KINEMATICS IN ALPINE SKIING USING A LOW-COST REAL-TIME KINEMATIC (RTK) SYSTEM

ABSTRACT English

The advent of increasingly accessible global navigation satellite systems (GNSS) has exciting implications for alpine skiing research and practice. The aims of the study were to test the validity and reliability of a low-cost Real-Time Kinematic (RTK) system to be subsequently used as a criterion measure to validate a sports GNSS for detecting macroscopic turn-averaged and sectional performance variables in skiing. Two experiments were performed, consisting of: 1) attaching an RTK system to a mountain coaster which ran along a repeatable track four times in an alpine environment, and 2)

both the RTK (criterion) and a sports GNSS attached to skiers on a set giant-slalom course. For the former experiment, the validity and reliability of the system were tested by computing the systematic and random error, respectively, against a digitized ground track. For the latter experiment, the validity of the GNSS was assessed for velocity, path length, radial force, and energy dissipation, across individual turns and turns collapsed into sections (four turns), using absolute bias, correlation, and typical error (CV%)

statistics in comparison to the 'criterion' RTK system. The mountain coaster experiment revealed minimal random error and variability in longitude (0.023±0.0075 m) and altitude (0.19±0.066 m). The moderate systematic error and variability (mean=0.431-0.697 m, standard deviation=0.616-0.366 m) were due to limitations in the digitized ground plan and an offset between the rails and the attachment of the antenna, which was exacerbated while turning (due to the sled inclining towards the turn centers). For the skiing test, data were typically low bias (<1.5% for all variables, except energy dissipation [4.5%]), with moderate to very strong agreement in all variables. In general, variability was low (CV<5%) except for radial force and energy dissipation when considering individual turn analysis (7.0 and 12.9%, respectively). Adopting a sectional approach substantially improved agreement and error, all representing strong or very strong agreement except radial force (moderate) and all CV<9.1%. These results evidence the accuracy of a low-cost RTK unit in ski-similar conditions and support a turnaveraged approach to detect worthwhile differences in various performance variables using common sports positional units.

PRELUDE

This chapter has a methodological focus and experimentally falls within the purview of the previous one, although chronologically occurred afterward. This chapter includes two experiments that validate a low-cost high-accuracy global positioning system in the first instance and subsequently use this unit as a criterion device to test the accuracy of a typical sports unit (the one used in the previous study) to detect worthwhile differences in skiing performance metrics. Specifically, a relatively unique, albeit macroscopic approach is adopted to bolster the data collected in our previous study and to provide information regarding the use of more accessible technologies for skiing trajectory measurements. Note: while unfortunate, the low-cost RTK presented in this chapter was not used as the primary means of detecting positional data in the previous on-snow experiments (i.e., see Chapter 3.1) due to the simple fact that the system had not yet been developed and tested at that stage of the thesis. Instead, its development was driven in tandem to testing further and hopefully strengthening our methodological approach, and for implementation in later studies (subsequently canceled, due to seasonal interruptions).

Co-authored works associated with this section

INTRODUCTION

In alpine skiing, trajectory measurements are valuable for biomechanics research and for practitioners to provide valuable feedback to athletes. Unfortunately, the complex alpine nature of skiing represents a challenge in providing such data. Several accurate capture methods exist (e.g., motion capture), but their complexity often results in brief capture windows (1-3 turns). Global navigation satellite systems (GNSS) can feasibly provide various important metrics for performance, ranging from merely time and velocity data to more sensitive parameters such as a change in mechanical energy (Supej et al., 2020).

The ongoing development of GNSS technology and the increased accessibility provides exciting possibilities for their integration into alpine skiing research and practice.

While the consensus leans in favor of the usefulness of GNSS devices in alpine skiing (Supej et al., 2020), the field of technology falling under this general moniker is broad and variable. For example, multiband units operate on several satellite systems (e.g., American 'GPS', Russian 'GLONASS,' and Chinese 'BeiDou'), provide more positioning possibilities, and consequently tend to be more accurate than their older counterparts [START_REF] Jackson | Comparing global positioning system (GPS) and global navigation satellite system (GNSS) measures of team sport movements[END_REF]. Some modern systems combine positional data from satellites and that collected via inertial measurement units to corroborate and correct movement at high frequencies and further improve positioning [START_REF] Brodie | Fusion motion capture: The biomechanics of alpine ski racing[END_REF]. Other approaches use data collected from a stationary unit ('basestation') to correct random error in the signal of a moving unit ('rover') (e.g., differential

GNSS [dGNSS]

). Typically, GNSS units rely on 'code-based' positioning, which corroborates the 3-dimensional position of the receiver based on the delay in code (Pseudo Random Code) received from each satellite by the antenna. The gold standard is Real-Time Kinematic (RTK) systems, which use a 'carrier-based' ranging technique in combination with corrections from a base-station unit to improve positioning accuracy (see Figure 34) drastically. These units are widely used commercially and have been implemented in sports, including alpine skiing (Gussiås, 2017;Supej et al., 2020).

Unfortunately, the cost and ungainly nature of RTK units have typically hindered their integration into the research and regular performance monitoring. Given the value of the information they provide, information on utilizing the results from different types of technology in alpine skiing is interesting and worthwhile.

Figure 34. RTK in skiing

A practical illustration of the integration of RTK into skiing practice. In addition to utilizing different signal processing that drastically increases accuracy, random error is measured in a stationary base station ('BASE'), which is then corrected to the signal measured by the measurement unit ('ROVER') for a final position of improved accuracy ('TRUE POSITION'). Various satellite systems utilized by the RTK system are also pictured. Note, the system used in this research is BeiDou 'ready' but does not currently function on this system.

TURN-AVERAGED KINEMATICS IN SKIING: RTK & GNSS 123

The skiing literature features a host of interesting biomechanical parameters that can be measured using GNSS technologies. The most obvious of which is instantaneous position paired with time on a given course, separated into various temporal markers (e.g., section times or position relative to a gate). These basic parameters can be enhanced with information regarding the athlete's velocity, sectional energy behaviors (e.g., loss in mechanical energy normalized to entry velocity [∆emech/vin] (Supej, 2008)), and various force parameters [START_REF] Gilgien | Determination of external forces in alpine skiing using a differential global navigation satellite system[END_REF]. While values of <0.1 m are deemed acceptable for trajectory in high-level athletes (Supej et al., 2020), there is limited information regarding the smallest-worthwhile differences across important variables and skiing cohorts considering both device accuracy and athlete variability.

While the technology is broad and continually evolving, manufacturers typically quote positional errors at ~1 m in modern typical GNSS units, although errors of up to 4.5 m have been reported in favorable conditions with single satellite positioning [START_REF] Gilgien | Characterisation of skiers' mechanics, course setting and terrain geomorphology in world cup alpine skiing using global navigation satellite systems[END_REF]. At face value, RTK systems are far more accurate than basic GNSS units (i.e., <0.01 m error (Supej, 2010)), with dGNSS similarly providing impressive accuracy during skiing trials (i.e., ~0.04 m (Gilgien et al., 2014)). Typically, very high-quality units are used for research (Supej, 2010), and while low-cost versions of these technologies exist (notably, RTK kit-set units (Takasu & Yasuda, 2009;Valente et al., 2020)), earlier variations have shown concerning error rates in alpine skiing (Gussiås, 2017).

Most error rates are calculated based on instantaneous trajectory measures, as the deviation from a high-end criterion device, and rarely on performance metrics. This is logical since most variables derived from the same potentially erroneous signal will feature inflated inaccuracies. Nevertheless, feasibly a more 'macroscopic' approach using turn-or section-averaged data could reduce error rates (e.g., four 'trials' halves the error (Hopkins et al., 2009)) and potentially reduce concerns associated with systematic bias or 'false fix' data. Moreover, a lack of discriminative capability for elite athletes does not necessarily degrade situational efficacy to lower-level counterparts. Recent sports devices appear acceptable in cross-country skiing (Gloersen et al., 2018), and the accessibility of similar accessible GNSS units is of interest to many practitioners and researchers. Regardless, there are still concerns around the ability of typical units to provide accurate and reliable enough data to detect worthwhile differences in performance metrics in the notoriously challenging alpine skiing.

This study aimed to test the validity of a sports GNSS device to measure various performance parameters in alpine skiing. To this end, we performed two experiments:

1) a validity and reliability study for our custom compiled 'low-cost' Real-Time Kinematic (RTK) on a known and repeatable trajectory against ground-plot information, and; 2) a criterion validity comparison between the RTK system and a sports GNSS system for individual turns, and multiple turns collapsed into 'sectional' averages.

METHODS

. Mountain coaster experiment

An RTK unit was fixed to a mountain coaster rail system that circulated throughout an overcast morning of experimentation (see Figure 35). The rail system was at a French ski resort (Saint François Longchamp, France; altitude ~1700 m) and consisted of a ~996 m track that turned back and forth alongside a ski slope. A two-seated sled circulated around the course at a velocity controlled by the riders (via a braking system). The sled path was practically immovable, comprising of a central metal rail and two adjoining parallel rails.

The RTK antenna was placed atop a padded seat at the rear of the sled, and the electronics in a small bag affixed to the bottom of the seat. A base station was affixed to the roof of a vehicle positioned in an unobstructed location near the course bottom. We performed four separate trials in the morning over three hours in overcast metrological conditions. Each run had different velocity traces (and time) due to non-normalized braking patterns by the operators. The mountain coaster was selected for this test for three interrelated reasons: 1) it provided a quasi-identical trajectory across multiple runs, which significantly improved the ease with which numerous trials could be compared for reliability without biological error; 2) it shares key similarities to skiing, including a mountainous environment, similar speeds and loss of elevation, and quasi-similar alternating turning styles, and; 3) while unable to access a higher quality reference system against which to validate the system, we were provided with a digital highresolution ground-track document that allowed digitization for overlay and comparison.

Figure 35. Illustration of mountain coaster sled setup

Depiction of the mountain coaster sled, upon which the RTK antenna was fixed (dashed circle). The stylized black lines represent the track on which the sled ran and was approximated in the digitized plans provided and used for our validity comparisons.

Skiing experiment

Athletes performed two trials of a marked giant-slalom course while equipped with the custom-built RTK and a sports GNSS. The experimental collection was performed during the final stages of the habitual training practice, and as such, the athletes were already familiar with the course, warmed-up, and ready for maximum effort skiing.

Athletes performed 1-2 race-paced runs, after which various performance metrics were derived from turn-by-turn and turns grouped into sections and then compared to test the validity of the sports GNSS. Athletes provided written informed consent, and the operational procedures were approved by the ethics board of the University Savoie Mont Blanc and were aligned with the World Medical Association (Declaration of Helsinki).

The athletes were female regional-level skiers (N=4; age, 19±1 yr). Testing occurred on hard groomed snow and during stable environmental conditions (~1 hr, during the morning). A federation coach set brush gates to model a giant-slalom setup (20 gates) on a moderate-grade consistent slope (~17° relief). Athletes used their personal boots and ski gear and equipment (e.g., helmet, goggles, and back protectors). Athletes were equipped with two distinct systems that provided positional data: 1) a sports GNSS system (model: Stadium tracker, Mac-Lloyd Sport, Paris, France), and 2) a custom-built RTK system (as the 'criterion' measure).

Two 'rover' RTK units were worn by athletes during the testing period in a small backpack, with the antenna attached to the helmet in the same manner as the sports

GNSS. An identical unit was used as a base/reference station fixed to a tripod on a flat open area above the testing site and remained stationary and unobstructed throughout the testing procedures.

Equipment

For both experiments, positioning was provided by low-cost RTK (see Figure 36)

compatible GNSS unit/s built from the following componentry: a high-fidelity antenna For the skiing experiment, an additional sports GNSS system provided positional data from the Russian (GLONASS) and American (GPS) satellite systems at a down-sampled rate of 10 Hz fused with data from an onboard inertial measurement unit (Gloersen et al., 2018). The units were lightweight (~20 g per unit) and were attached to the helmet using commercial Velcro.

Trials were also recorded by video to corroborate data where necessary (camera model: Hero 5, GoPro, San Mateo, USA; stabilizer model: G5, FeiyuTech, Guilin, China), which was held by a researcher who skied behind the athlete at a safe distance.

Data analysis

For each experiment, rather than providing 'real-time' feedback, the data from the RTK rovers and base station were extracted and analyzed post-operatively using programs from the RTKLIB (version: 2.4.3 b33) directory (Takasu & Yasuda, 2009). The separate Clockwise from top: battery pack, RTK compatible receiver, portable computer system, and a high-fidelity antenna.

navigational data acquired from the rover and base station were combined to provide kinematic positioning solutions, with an elevation mask of 20° to exclude low-strength satellites. Where used, the sports GNSS data were downloaded using the manufacturersupplied software. From this point, the results were processed using MATLAB (model:

R2019b, Mathworks Inc., Natick, Massachusetts, USA).

Mountain coaster data

The downhill portion of the run was separated from the entire course for analysis, just after the carriage release for the first run (i.e., just after the first low-speed turn). The rationale for this decision was that the beginning, uphill and straight portions of the course beginning were covered and impaired signal acquisition, in addition to comprising mostly slow or stationary periods of motion. Just before the downhill portion, the RTK system transitioned to a fixed solution. Data were synchronized at a distinct geographical point and zeroed in all axis. The raw, unfiltered data were used for comparisons.

A reference ground track was generated from the information obtained from the building plans. Specifically, distinct data regarding the measurement scale and the center axis of the sled track was extracted using the image digitization plugin in MATLAB. Due to the lack of exact geographic positioning, the resulting longitudelatitude data for the ground track was rotated to fit the overlaid trajectories of the RTK system using cross-correlation. Note: the plans from which the ground track was digitized were preliminary building plans which did not necessarily represent the exact dimensions of the finished structure and represented the center of the rails upon which the sled ran (i.e., the RTK antenna was ~1.5 m above the rails, and the rails ranged from <1 m from the ground to >3 m). As such, this comparison features several limitations, which we will discuss in the interpretations of the results.

Skiing data

Positional data (longitude, latitude, and altitude) were smoothed (11 frame Savitzky-Golay) and then low-pass filtered (1 Hz second-order Butterworth). The files were initially cut before and after the trial using velocity-time data (as just before the athlete began the trial, until after they braked and came to a stop following the final gate). From this stage, individual turns were extracted using the point of inflection in the triple derived latitude positional data (Adelsberger et al., 2014) as distinct turn-switch events (i.e., the end of one turn and the beginning of the proceeding turn). Turns during which the RTK system did not provide the most accurate outcome solution (i.e., 'float' rather than 'fixed' = four turns in total) were excluded from the analysis for both units. The final data selected for analysis consisted of 16-17 turns per athlete (total of 93 turns), depending on the 'tactical' approach to the first and last turn cycles (e.g., early skidding on the last turn was excluded).

Parameter computation for the mountain coaster

For the RTK validity test, only longitude, latitude, and altitude were extracted for comparison across different runs. No other variables were extracted, mostly due to different operator speeds across runs voiding the possibility of assessing other interesting variable sets (e.g., energy behaviors). Moreover, the aim here was to test the accuracy of the raw positional data provided by the RTK system from which all the other variables will be computed during skiing. The difference in longitude and altitude data from the 'criterion' digitized ground track in m were computed along latitude position for each of the four trials.

Parameter computation for skiing

Per each distinct data-stream, for each turn, the following variables were computed:

turn-entry and averaged velocity (vin and vavg, respectively), cumulated displacement (L) (Spörri, Kröll, Schwameder, et al., 2018)), average radial force (Jentschura & Fahrbach, 2004), and the difference in specific mechanical energy normalized to the velocity at turn entry (∆emech⁄vin (Supej & Holmberg, 2011)). The computation of these variables are discussed in detail in the previous chapter (see Chapter 3.1).

Two distinct data analysis approaches were employed to test the validity of the devices:

1) data from all possible turns were individually compared between the units (e.g., L turn 1 for each athlete, GNSS vs. RTK), and; 2) data from each athlete (16 turns, with the first turn excluded where necessary) were grouped into four consecutive turns, averaged and then compared in the same manner (e.g., L averaged across turns 1-4 for each athlete, GNSS vs. RTK).

Statistical analysis

For the mountain coaster, we adopted a simplified approach to detecting systematic and random error and variability to measure validity and reliability, respectively. Precisely, along each dimension of longitude (i.e., on each point of the trajectory), the mean and standard deviation of the difference of the trajectory of the four runs between RTK and reference digitized ground track data for altitude and longitude were calculated.

Subsequently, the mean and standard deviation over the entire run of the mean difference (across the four runs) between RTK and ground track trajectory represented the systematic error and its variability across the entire run, respectively. These two indexes were used to assess the 'validity' of the RTK system in comparison to the 'reference' ground track data. To represent the random error of the RTK units and its variability across the entire run, the mean and standard deviation of the standard deviation (across the four runs) between RTK and ground track trajectory were similarly calculated across the entire run. These two later indexes were used to assess the reliability of the RTK system across the four runs.

Descriptive data are presented as means±standard deviation. For the skiing experiment, the RTK and GNSS data were compared using bias, Pearson's correlations, and typical error. Overall bias between the methods was assessed using the mean difference between the practical (GNSS) and that from the criterion (RTK) and reported in raw units ±95% confidence intervals. The strength of agreement between the two measures was assessed using Pearson's correlation coefficient (r) on the log-transformed data, and threshold values of 0.3, 0.5, 0.7, 0.9 to represent weak, moderate, strong, very strong agreement, respectively (Hopkins et al., 2009). Typical error of estimate as a percentage (CV%) provided a measure of error magnitude. All individual turns were analyzed in the first instance, and then the analysis was repeated on the 'grouped' turns for all athletes.

RESULTS

Mountain coaster

The mean systematic error compared to the ground track in longitude data was 0.

Skiing experiment

Full descriptive data and results are presented in Table 6, with plots of the bias ±95% The purpose here is to show that the graphic displays four separate trajectories (black lines) alongside the digitized ground path of the coaster (dashed line).

Sectional data understandably shared similar bias scores to turn-by-turn analyses (<1.4%). However, agreement was substantially improved, with all but Fr representing strong or very strong agreement (moderate agreement for Fr). Similarly, error was markedly reduced by adopting a sectional approach, with all variables CV<9.1%.

DISCUSSION

On the one hand, despite systematic error in our measurements (not associated with the RTK system), we can infer validity and excellent reliability in the low-cost RTK device in these testing conditions. On the other hand, in this brief investigation, a typical sports GNSS unit provided sufficient estimates of several key performance parameters in ski racing. Surprisingly the values provided from turn-by-turn analyses generally appear very acceptable and adopting a 'sectional' approach markedly reduced systematic and random error. As such, practitioners and researchers might benefit from adopting a sectional approach in their analyses and athlete feedback, particularly when examining variables such as ∆emech/vin and Fr, which are valuable in contextualizing skiing performance but suffer from inflated computational errors (albeit within acceptable 134 CHAPTER 3. THEME 1: FORCE OUTPUT bounds compared to other sports science measurements). Such an approach could feasibly allow the use of relatively standard sports GNSS technology into alpine skiing practice and research, albeit requiring post-processing and considering the remaining error of some variables.

While at face value, the mountain coaster validity data appear relatively poor, there are several explanations for these results. Namely, the RTK antenna position was above that inferred from the ground track of the coaster, and along the track the rails were set to pivot the coaster back and forth. As such, this pivoting created an offset in the longitudelatitude position between the top of the sled (i.e., the antenna position) and the ground track. This pivoting typically occurred during turning (i.e., to offset Fr) and probably explains the characteristic tracking of the RTK trajectory inside each turn (see the explicit and repeated offsets in Figure 37). Moreover, since the digitized plan was not final, presumably there are some minor differences between our plot and that finalized on the course. Lastly, the accuracy of our digitization was constrained by the quality of the document provided (specifically, line 'fineness'), which resulted in some estimation granularity. For these reasons, we can reasonably assume that the systematic errors observed between RTK and the ground track were due to the latter not precisely describing the actual coaster trajectory, notably during turns where the higher systematic errors were observed. Consequently, considering the very high reliability of the RTK system, we can infer the validity of the RTK system, even if a validation using a true criterion trajectory is needed.

Notably, the results from our mountain coaster experiment depict low levels of random error and variability in both altitude and longitude data. Moreover, we theorize that these error rates are inflated due to the integration of error along another axis as a byproduct of data normalization. Specifically, while higher random error in altitude was expected (Gilgien et al., 2014), the necessity of normalization for comparisons compounded error via that induced in the longitude-latitude plane. In any case, these results are encouraging for the integration of similar technologies into alpine skiing practice, given the similar characteristics under which this experiment was performed (e.g., alpine environment, similar speeds, and trajectory characteristics). Nevertheless, some concerns still exist regarding the capability of such units to detect appropriate targeting solutions in various environments, since a concern with such 'low-cost' units is their disposition to fail to find a fixed solution or detect a 'false' fix (Gilgien et al., 2014;Gussiås, 2017). More research using similar updated technology-notably integrating higher quality antennae and higher sampling frequencies in congruence with previous investigators' concerns (Gussiås, 2017)-is warranted.

The core kinematic variables detected from the sports GNSS displayed low turn-by-turn bias and acceptable TE overall compared to our criterion measurement in regional-level skiers. The base variable of T had negligible bias between the methods (<0.01 s).

However, since T represents the time between trajectory inflection for each athlete (i.e., a representation of the technical approach of each athlete rather than the more traditional 'timing split' between two standardized geographical points), the actual practical utility of this variable is probably limited. Nevertheless, the difference in turn time helps clarify where subsequent errors in the signal arise (Gilgien et al., 2014). In the first instance, some inflated error can be expected due to the low sampling frequency of each unit (i.e., a minimum difference of 0.1 s). Moreover, errors in determining the turn-switch moment affect the subsequent turn (e.g., turn 1=+0.1 s, turn 2=-0.1 s); this is a further argument for averaging several turns or trials to minimize this error when adopting the same turnswitch detection approach. Both velocity measures had negligible bias between the units and approximately 0.5 and 0.6 m/s of error. Similar results were observed in cumulated path length (L), albeit with slightly inflated error, probably as a partial result of the turncutting technique. The overall error of ±1.32 m is considerably larger than the values presented for worthwhile differences in high-level athletes (Supej et al., 2020), albeit based on different measures of the trajectory. Understandably, the more computationally complex variables exhibited inflated error scores. Slightly higher Fr scores were observed when measured from the sports GNSS, with moderate agreement and large error (0.54 N/kg). The agreement and error from ∆emech/vin were the worst of the variables calculated (moderate agreement and very large error, respectively). While the smallest worthwhile difference for various cohorts is not well known, clearly caution is necessary when assessing these variables in turn-by-turn via low-cost GNSS.

Nevertheless, there may be some applications in lower-level athletes as a coaching feedback tool.

When implementing a sectional/averaged approach, there were drastic reductions in error. In the first instance, the reduced difference between the methods in turn-time (70% error reduction) supports this approach as a means of accounting for problems caused by consecutive offsets in turn detection. As an example of this correction, the typical error of L was drastically reduced to 0.56 m. The error of all other variables followed suit, albeit with the agreement maintaining or slightly worsening (potentially caused by reduced and more heterogenous datapoints). In any case, these results support the use of a 'sectional' approach to reduce error in sports GNSS units or, indeed, to improve the capability to detect small and worthwhile changes in higher-level athletes with more advanced technologies (Hopkins et al., 2009). While the slope in this study was separated into nondescript 'sections' of consecutively grouped turns, feasibly, this approach could be applied to sections with distinct geomorphological or technical characteristics (as performed in the previous chapter). Providing similar performance outcomes for distinct sections (e.g., steep vs. flat) could viably provide coaches and athletes with valuable information with which to contextualize the regular feedback received by expert eyes and video [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF]. Moreover, such an approach might allow the greater implementation of monitoring since our results support the capability of relatively low-cost units to provide valid measures of a variety of variables. Of course, these findings should be tempered with an acknowledgment that GNSS units are still at risk for several confounding factors (e.g., signal obstruction due to rocky over-cropping)

that should be considered when implementing into practice.

Limitations

While used to validate the system used in the subsequent criterion validation of the sports GNSS, the experiment featured the following limitations: It was performed on a different mountain, persistent lack of 'time-synced' criterion device, lack of 'snow' surface (i.e., which can complicate positioning), and problems with the comparison to the digitized ground-track and the actual trajectory of the sled. Regarding the latter point, we digitized the ground plan from a high-resolution document provided by the ski station and created an XYZ plan of the mountain coaster ground track. However, the plan was a building layout and may not have represented the coaster as it was finalized in the environment. Moreover, the plan was for the central axis of the coaster track (and more accurately the vertical projection of the track to the ground), and the antenna was fixed approximately ~1.5 m from the rails (and potentially 2-3 m above the ground in some places). Moreover, as discussed above, during the turns the track dips and inclines the sled towards the turn center or otherwise to enhance the experience of the rider.

These limitations in the comparison explain, in part, the differences we observed between the highly repeatable RTK trajectory and that provided by the digitized ground plan. Nevertheless, validation against a true high-quality positional technology or a more accurate known ground-track would provide a clearer picture of the device validity.

For the skiing experiment, both units were attached to the head, which is distinct from the center of mass trajectory. While an attachment point closer to the COM would have been preferable to increase the interest in several variables (Supej et al., 2020), the helmet was chosen here for practicality (i.e., difficulty attaching both units in a small space without compromising the safety of the athlete) and for the likelihood of providing clear satellite coverage for both units. Moreover, there is some evidence to suggest the bias introduced by such an approach is relatively minimal and systematic [START_REF] Meyer | Estimating alpine skiers' energetics and turn radius using different morphological points[END_REF]. The present study aimed to test the validity of GNSS signal to obtain key variables for skiing performance, but not to study and interpret these variables per se. While we acknowledge different signal strength is possible with different attachment points (Supej et al., 2020), our results support the agreement between sports GNSS and criterion measures when the raw signal is good.

CONCLUSIONS

Sufficiently accurate performance data can be measured from sports GNSS units, particularly when paired with a 'sectional' approach to analyzing presenting data. While acceptable, error associated with force and energy behaviors was still present and should be considered when interpreting study results. Our results evidence typical GNSS exhibit inflated error compared to more accurate tools and measurements but remain a possible alternative to assessing performance metrics in research and practice when integrated with analytical approaches to improve accuracy.

EXPERIMENTAL THEME 2: FORCE CAPACITY

LOWER-LIMB FORCE-PRODUCTION CAPACITIES IN ALPINE SKI DISCIPLINES: EVIDENCE OF THE IMPORTANCE OF FORCE-DOMINANT PROFILES

ABSTRACT English

Specific force capacities might be a limiting factor for alpine skiing performance, yet there is little consensus on the capabilities in question, and whether they differ between disciplines. We aimed to test the effect of discipline (speed and technical) and seasonal performance level (international standings) on lower-limb force-production capacity.

We assessed dynamic force-production capacity at extremely low and high velocities (via force-velocity relationships in squat jump), maximum isometric force, and rate of force development (via mid-thigh pull). Differences in disciplines were assessed via a general linear model controlling for athlete standings and an interaction effect between standings and discipline. The relationship between force -production parameters and performance per discipline was further explored using Pearson's correlations. Raw unloaded jump height did not differentiate disciplines, and only absolute power was higher in speed athletes (ω 2 =0. While robust associations were observed between performance and maximum isometric force in speed (r=-0.88, p<.001), there was only a trend for moderately higher absolute isometric force in better technical athletes (r=-0.49, p=.052). Both alpine skiing disciplines display a preponderance for dynamic force output at low velocities, and maximum isometric force was particularly consequential in speed athletes. There was a complete lack of predictive quality for moderate velocity conditions (maximum power and jump height) in either discipline. These results strengthen the evidence for emphasizing the development and testing of isometric force and dynamic strength at low velocities in ski athletes.

Français

Pour bien skier, les athlètes doivent produire des niveaux de force élevés afin de tourner tout en réduisant la perte d'énergie. Par conséquent, les capacités de production de force des membres inférieurs peuvent être un facteur limitant pour les performances en ski.

PRELUDE

In the previous chapters, we showed that force-output characteristics are a discriminating factor on the skis. Notably, better athletes apply higher forces to turn, and greater forces in general, aligned with overall higher course speeds. Having proven that force output is indeed vital on the snow, the next step is to characterize the force-capacity et al., 2009). Force expression differs for each event and discipline (Gilgien, Kröll, et al., 2018) as a result of distinct performative constraints. For example, where TECH events are characterized by more frequent and rhythmic turns (~1.8 and 2.9 s for SL and GS, respectively), SPEED features considerably slower movement cycling (~4.0 and 5.0 s for SG and DH, respectively) (Alhammoud et al., 2020) Discipline comparisons are rare, but average turn-by-turn forces appear higher in TECH compared to SPEED, yet longer turn, and course durations result in much greater physical loads (i.e., impulse) in SPEED vs.

TECH (DH>SG>GS) (Gilgien, Kröll, et al., 2018). Moreover, while the duration and magnitude of force output are notable, in both disciplines, peak values far exceed turnaverages (e.g., in TECH, 1.74 to 1.95 × BW vs. 3.15 × BW for peak force (Kröll, Spörri, Kandler, et al., 2015)). Although acute instances of force production could represent mistakes or energy dissipation (necessary or otherwise) (Supej et al., 2011), a capacity for both average and peak force appears essential. However, while elevated force production on-snow is a product of enhanced physical and technical capabilities, the interplay between that expressed during skiing and that possessed by the athlete offsnow is a priori unclear. More specifically, we might pose the question: to what extent is the force developed during skiing limited by specific capacities?

The terminus of long arcing turns is rhythmic extension-flexion (loading-unloading) patterns of the lower limbs and uniquely slow and long contraction cycles. Even the most frequent turn cycling event (SL, ~0.9 s) exhibits markedly slower angular velocities of the lower limbs compared to common sports such as sprint running (e.g., average of outside knee turning phase of <80 °/s (Alhammoud et al., 2020;Berg & Eiken, 1999;Kröll, Spörri, Kandler, et al., 2015) at the knee vs. average backward leg swing velocity of 664 °/s (Miyashiro, Nagahara, Yamamoto, & Nishijima, 2019)). While the general trend for low-velocity-high-force muscle actions is maintained across disciplines, research generally corroborates distinct 'stepped' changes in average angular velocity across events (knee and hip, SPEED<TECH) in parallel with turn duration (SPEED>TECH) (Alhammoud et al., 2020;Berg & Eiken, 1999;Kröll, Spörri, Kandler, et al., 2015). The associated contractile modes is a fundamental topic, albeit rarely studied explicitly, with eccentric modalities historically attracting disproportionate attention in the literature (e.g., seminal research by Berg and colleagues (Berg & Eiken, 1999;Berg et al., 1995)).

However, recent evidence implies the highest force is produced during a pronounced quasi-isometric phase of the extended outside limb (i.e., knee, ~128 to 138 °) (Alhammoud et al., 2020;Kröll, Spörri, Kandler, et al., 2015) for substantial durations during turning (e.g., % of turn for outside limb: knee, ~11% for SL and 34 to 42% for GS and SPEED; hip, ~27 to 55% in TECH and ~60 to 81% for SPEED) (Alhammoud et al., 2020). As such, high force produced at low velocities and in quasi-isometric conditions appears a dominant function of modern ski turns (Kröll, Spörri, Kandler, et al., 2015), performed close to or even exceeding maximum voluntary contraction [START_REF] Alhammoud | Contribution à l'analyse de l'activité neuromusculaire des skieurs alpins d'élite lors de tests isocinétiques et en conditions réelles d'entraînement[END_REF]Berg et al., 1995). These factors should feature in assessments of skiers' muscular capacities.

While challenging to synthesize, there is a variety of evidence to suggest positive relationships between various force qualities and ski performance metrics (R. E. Andersen & Montgomery, 1988;Ferland & Comtois, 2018;Hydren et al., 2013;Turnbull et al., 2009;White & Johnson, 1993). Notably, variants of maximum effort BW squat jumps (SJ) and countermovement jumps (CMJ) feature prominently in skiing research (Ferland & Comtois, 2018) and in various published testing batteries [START_REF] Haugen | Countermovement jump height in national team athletes of various sports: a framework for practitioners and scientists[END_REF]Hydren et al., 2013;Raschner et al., 2013;Refsnes, 1999), albeit utilizing varying methodological approaches and non-interchangeable technologies (e.g., 'vertec' vs.

force-platforms). While bodyweight (BW) jumps are a practical and reliable means of assessing neuromuscular function, force is expressed at markedly greater extension velocities compared to skiing (average velocity = ~300 °/s with moderate amplitude, 0.36 m jump height [h] and with 0.3 s push-off). Moreover, since h and maximum power (Pmax) are macroscopic indexes of dynamic force production in approximately the center of the force-velocity (Fv) relationship, they lack data discriminating force at high and low velocities. These factors might partially explain the mixed results in the literature using these types of assessments (Ferland & Comtois, 2018), such as inverse relationships between skiing performance in high-level skiers (GS standing [lower=better] vs. h, r=0.64) (Haymes & Dickinson, 1980), or non-different scores between young and elite athletes (Jordan et al., 2018). Consequently, more specific measurements might provide insight into capacities discriminating alpine ski racers.

While skiers are viewed as 'force-dominant' (i.e., high-force-low-velocity on the Fv spectrum) (Hydren et al., 2013), the literature targeting the assessment of these capacities is limited and aging. Studies using isokinetic dynamometry have remarked on the impressive force-capacities of skiers, at least in respect to other sporting codes and recreational individuals (R. E. Andersen & Montgomery, 1988). Some older works show torque at low, not high velocities (30 vs. 180 °/s, respectively), separated club and national athletes (White & Johnson, 1993). However, more recent investigations were unable to differentiate between speed and technical specialists, nor were they associated with performance (Alhammoud et al., 2019;Neumayr et al., 2003). While the high isometric output of skiers is typically lauded, the little research that has adapted such testing into practice has almost exclusively used isolated joint assessments (R. E. Andersen & Montgomery, 1988;Turnbull et al., 2009;White & Johnson, 1993). Two notable exceptions are (Berg et al., 1995) [START_REF] Bosco | Evaluation and planning of conditioning training for alpine skiers[END_REF]Bosco et al., 1994;Fessl et al., 2020;Patterson et al., 2009Patterson et al., , 2014)), albeit with mixed results.

For example, in national-level junior skiers average power produced during loaded SJs at 40% BW was only correlated with skiing performance during the last of four consecutive years of monitoring (attributed to accrued physical development finally 'matching' technical efficiency) (Patterson et al., 2014). Following earlier methodological works in skiing [START_REF] Rahmani | Force/velocity and power/velocity relationships in squat exercise[END_REF], a recent example compiled a range of loaded-jump performance to create a force-velocity (Fv) profile of elite youth skiers and was able to differentiate between other alpine sports (i.e., greater relative maximum power than cross-country skiers, and a more force-dominant profile than ski-jumping) (Fessl et al., 2020). Little other research has directly attempted to quantify ski-specific force production in recent research, and a more detailed analysis of force output capacities of skiers might provide clarity surrounding the relevance of specific capacities and performance characteristics.

The specific force-production capacities underlying skiing disciplines, or performance in general, remain unclear. As such, this study aimed to: 1) test the effect of disciplines in lower limb force-production capacities, and; 2) test whether the latter were related to performance during the subsequent season. To that end, we implemented a protocol including methods to assess the dynamic production of force at extremely low and high velocities (via Fv relationship) and maximum isometric force in an attempt to provide novel information on the specific force production of skiers at different lower limb extension velocities and contraction modalities. Based on the state of the literature regarding the on-snow qualities from each discipline, we hypothesized that SPEED athletes would display higher force production at lower extension velocities and in isometric qualities, and these qualities would be emphasized in higher-level athletes. standing=93.1±59. 3 [range=1-194]). This indicator was selected as that closest to the profiling, including a relatively balanced opportunity for athletes from all events to score updated FIS points before substantial worldwide interruptions to the racing schedule due to the novel coronavirus pandemic, COVID-19.

METHODS

Participants and experimental design

Skiers' force-production capacities were tested through 2 different assessments: Fv profile in SJ from multiple loaded jumps to assess dynamic muscle output, and isometric mid-thigh pull (IMTP) to obtain maximal isometric force and rate of force development.

All athletes were competitive at the time of testing and free of any musculoskeletal injuries that would impair their ability to participate in the testing to the fullest of their Warwickshire, England) provided resistance. The location of the setup was not changed during the testing implementation (i.e., the same room and equipment). For the SJ depth, athletes were initially set at a 90° knee angle and then allowed to adjust from this position based on the objective of jumping as high as possible with and without external load (Janicijevic, Knezevic, Mirkov, Perez-Castilla, Petrovic, & Garcia-Ramos, 2019;Janicijevic, Knezevic, Mirkov, Perez-Castilla, Petrovic, Samozino, et al., 2019). Once selected, the safety supports of the power rack were set to this height, and where necessary, thin rubber wedges were stacked on the safety-bars to adjust to the rack height at a higher resolution (~10 mm). Limb length was measured from the head of the greater trochanter to the most distal point of the fully extended limb and plantarflexed foot, and push-off distance (hpo) was computed as the difference between limb length and the vertical distance between greater trochanter and floor in their starting position in the squat rack (Samozino et al., 2008).

For each SJ, the athletes slowly descended until the bar lightly contacted the rack supports, after which they raised the bar slightly (i.e., to their measured position), paused for 3 s, and jumped upwards with maximum intent. All parts of this procedure were verbally cued by the researcher (i.e., 'SQUAT!' and '3, 2, 1, GO!'). Athletes performed two trials/repetitions at each load, separated by approximately ~15 sec. The final number of sets was determined by whether trials were deemed unfit for analysis via immediate observation (e.g., poor jump technique) or unrealistic via preliminary assessment of the Fv relationship (i.e., R 2 <0.90 and outlier analysis)-described below.

Jump height (h) for all loads was measured using an optical gate system (model:

OptoJump Next, Microgate, Bolzano-Bozen, Italy) placed inside the footprint of the squat rack and operated by the researcher adjacent to the setup (see Figure 41). This equipment has been previously shown to be a valid and reliable means of measuring jump height [START_REF] Glatthorn | Validity and reliability of Optojump photoelectric cells for estimating vertical jump height[END_REF], using basic physics principles. Data were collected using manufacturer software and exported in raw format for analysis.

Figure 41. Representation of athlete squat-jump setup

The picture shows a high-level ski athlete in the bottom position of the squat before push-off and after touching the bar against the rack supports and raising the bar (to their pre-set measured position). The optical gates are visible within the rack footprint (operated via laptop outside the view of the picture).

Isometric mid-thigh pull

Athletes performed maximal isometric mid-thigh pull using a portable mid-thigh pull platform consisted of an Olympic lifting bar with its ends and bearings removed (7.5 kg), attached to a rigid platform via a heavy-duty chain (see Figure 42). Similar portable systems have been shown to provide valid and reliable force measurement when compared to force plates (James et al., 2017;Urquhart et al., 2018). Athletes were instructed to set themselves in a position where they felt comfortable to present maximum effort (i.e., like that of the second pull of the 'clean-pull' movement, commonly used by alpine skiers (Hydren et al., 2013), and other athletes). Where necessary, athlete starting position was adjusted to be within the ranges specified in the literature (i.e., 125-145° knee and 140-150° hip) (Comfort et al., 2019), while allowing individual technique. Athletes were instructed on the objective of 'pulling as hard and as fast as possible' for each trial, and provided with the following verbal cues: to take up a stable position and to apply pretension and remove slack from the system ('position!'), a verbal countdown from three, and then an immediate and aggressive pull until the researcher halted the trial ('PULL, PULL, PULL, PULL … STOP'). The athletes performed two submaximal trials of these procedures, which included viewing the force-time trace post-trial to improve internal cueing. Athletes rested for 3 min and then performed two maximum effort ~5 s trials separated by 5 min. In the case of two mistrials (Comfort et al., 2019), an additional was performed.

During each trial, force-time data was measured continuously at 1000 Hz using a portable strain gauge system consisting of a custom-designed acquisition unit, comprising of an S-beam load cell (Model: 1000 kN S-Beam Load cell, Meltrons Millennium Mechatronics, Auckland, NZ) between two heavy-duty stainless-steel rings.

Pull height was adjusted using a carabiner linked through the appropriate chain length, and a turnbuckle mounted through the center of the platform. This system is similar to that presented in recent research (Dobbin et al., 2018;James et al., 2017;Till et al., 2018), which aids in the accessibility and portability of isometric force, given the cost and ungainly nature of force-plate systems. Note that the capability of this system to measure rate of force development (RFD) data is not well tested, and will be discussed in the limitations section.

During each trial, athletes applied pretension to the system to aid in correct positioning (Comfort et al., 2019) and to minimize problems with system slack (e.g., peaks in forcetime data due to the chain 'snapping' taught). This preload value was individualized but monitored to ensure values were not unreasonably high or low. To ensure the variability in preload values did not clearly or substantially interact with our results [START_REF] Haff | Force-time dependent characteristics of dynamic and isometric muscle actions[END_REF], we tested the relationship between the preload values, maximum force, and RFD (29 trials; 436±200 N).

Figure 42. Representation of isometric mid-thigh pull platform

The image depicts a high-level ski athlete in the approximate starting position for the onset of a maximal pull. Visible is the bar (competition Olympic bar core), wireless strain gauge system, and lashing system comprising a chain, carabiners, and a turnbuckle mounted to the base. The base platform comprised two parallel steel girders, connected by a metal plate (in the shape of a widened 'H'; reinforced, due to early variations of the design being prone to flexing under high tensile loads). Two pieces of grip-taped particleboard were bolted to the top of the platform. Not pictured: grip straps, which were permitted when grip was a limiting factor in the test.

Data Analysis

Jumping Force-velocity relationship

Mechanical output of the lower limbs can be estimated using a selection of validated equations (described at length elsewhere (Giroux et al., 2015;Samozino et al., 2008))

applied to the jump height and anthropometric measurements of an athlete. For each jump, average force (F), velocity (v), and power (P) during the push-off phase were calculated using jump height (h) for jumps with the highest jump height per loading condition:

Eq. 9

𝐹 = 𝑚 tot • 𝑔 • ( ℎ ℎ po ⁄ + 1)
Eq. 10

𝑣 = √ 𝑔 • ℎ 2 ⁄
Eq. 11

𝑃 = 𝑚 tot • 𝑔 • ( ℎ ℎ po ⁄ + 1) • √ 𝑔 • ℎ 2 ⁄
with mtot as the total system mass (sum of body-mass and any external load present [e.g., bar, load, and bar clips]), g gravity ( 9.81 m/s). For each subject, individual force-velocity (Fv) relationships were compiled from various F and v data from 5-6 loading conditions using linear least-squares regression. The x-and y-axis intercepts of the linear relationship defined the maximum theoretical force and velocity capability of the athlete (F0 and v0, respectively). SFv was obtained as the slope of the Fv regression, and maximum power (Pmax) was subsequently computed (Samozino et al., 2012) as Eq. 12 the initiation of force production determined using manual selection (see Figure 43).

𝑃 𝑚𝑎𝑥 = 𝐹 0 • 𝑣 0 4 ⁄ 4
While algorithmic pull-initiation detection is typically recommended (Comfort et al., 2019), the lack of BW signal (i.e., preload only) rendered manual detection preferable (Maffiuletti et al., 2016). Any data showing countermovement was removed. Maximum (RFDmax) and 'average' (RFDavg) values were assessed as the maximum of a 50 ms moving average window, and the average value between 0 and 200 ms, respectively, of the timederivative of the force signal. The maximum isometric force was determined as the maximum of a 500 ms moving-average window of the force signal (Fmax). Averaged values were selected to both improve reliability and to increase specificity to critical periods of force application in skiing (e.g., turn initiation (Alhammoud et al., 2020;Kröll, Spörri, Fasel, et al., 2015;Kröll, Spörri, Kandler, et al., 2015)). Operator reliability was tested by analyzing 60 randomized trials, three times, each separated by 2 to 3 days, with the repeatability for variables dependent on initiation detection deemed acceptable for subsequent analysis (raw typical-error value of 1.37 N/s/kg and a quasi-perfect intraclass correlation [ICC>0.99]).

Statistical analysis

Statistical procedures were performed using JASP (version: 0.11.1, JASP Team, Amsterdam, Netherlands). Differences between the technical and speed disciplines were assessed via a general linear model which controlled for both the effect of athlete performance (i.e., the standings from their best event) on the dependent variable as a covariate while allowing for non-parallel regression lines per group (i.e., an interaction effect between performance and discipline within the model, 'group×covariate') (Leppink, 2018). While a small to moderate interaction effect was only observed in three variables (absolute F0 and relative and absolute Fmax), we believe this approach provides a more accurate analytical model of the data than an ANCOVA and subsequently enhances our interpretation of the strength of the relationship between the dependent variable and performance in each cohort. The main effects of discipline and performance on the dependent variables (h, Pmax, SFv, F0, v0, Fmax, RFDmax, RFDavg), and interaction effect, were reported using omega-squared (ω 2 ). Athlete age voided the assumption of normality (Sharpiro-Wilk=0.73-0.83, p<.005), and so was unable to be entered into the linear model. Instead, discipline effects were tested using a non-parametric Mann-Whitney U test (U, rank-biserial correlation [rrb]).The threshold values for qualitative interpretation of effect magnitude were ω 2 <0.01, 0.01, 0.06, and 0.14 as trivial, small, moderate, large, and very large, respectively. The difference and confidence intervals of comparison at the mean of each level were calculated using contrasts and presented to provide further information on the likelihood and direction of each effect (since ω 2 is directionless).

To further explore the effect of performance for each discipline, distinct Pearson's correlational analyses (two-tailed) were performed between performance (disciplinespecific standing) and the variety of force-capacity variables (r [lower confidence interval; upper confidence interval], and p). A Spearman's rank correlation coefficient (rs) was used to test associations between age and performance in the place of the parametric analyses. The strength of agreement was interpreted using values of r, or rs<0.1, 0.3, 0.5, and 0.8, as thresholds for trivial, small, moderate, large, and very large, respectively (Hopkins et al., 2009).

Where relevant, descriptive statistics presented as means±standard deviations, or median(interquartile range), with the alpha value for all tests at a=.05, with a<.1 considered as a trend towards a clear inference. Sensitivity analyses were performed using the sample size estimation software (G*Power [START_REF] Faul | Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses[END_REF]) to determine the approximate threshold of detectable effect for each statistical model and associated sample size (see Figure 44).

RESULTS

Normative data and linear-model analysis results for group comparisons of dynamic and isometric force measurements, including model effects with performance, can be found in Figure 45 and Table 7. Pairwise correlations between standing and dynamic and isometric force output are presented in Figure 46 and Figure 47, respectively. -1.97(-17.5;13.6) trivial 0.39 large *** 0.01 small # , p<0.1; * , p<0.05; ** , p<0.01; *** , p<0.001; N, number of athletes; SD, standard deviation; diff, difference in raw units; CI, 95% confidence intervals; ω 2 , omega-squared effect size; cells demarcated with a '-' correspond to effects practically equal to zero (<0.001); h, unloaded squat jump height; m, meters; Pmax, maximal power; W, watt; W/kg, watt per kilogram; SFv, Slope of the linear force-velocity relationship; Ns/m, Newton seconds per meter; F0, maximal theoretical force; N, newtons; N/kg, newtons per kilogram; v0, maximal theoretical velocity; m/s, meters per second; Fmax, maximum isometric force; RFDmax, maximum rate of force development; N/s. Newtons per second; N/s/kg, Newtons per second per kilogram; RFDavg, average rate of force development; qualitative thresholds for the magnitude of omega squared effect sizes ω 2 <0.01, 0.01, 0.06, and 0.14, as trivial, small, moderate, large, and very large.

Figure 46. Pairwise correlations between variables of dynamic output and performance

Data correspond to the mean Pearson's correlation (diamond), with the error bars the 95% confidence intervals (including qualitative thresholds for interpretation on the x-axis; '+,' positive; '-,' negative). TECH (black, hollow diamond) and SPEED (grey, solid diamond) skiers. Variable pairs are: h, unloaded squat jump height; Pmax, maximal power; SFv, Slope of the linear force-velocity relationship; F0, maximal theoretical force; v0, maximal theoretical velocity; variable units are provided only to differentiate absolute variables (e.g., W, for watts) from their allometrically scaled counterparts (e.g., W/kg, for watts per kilogram of body mass).

Figure 47. Pairwise correlations between variables of isometric force output and performance

Data correspond to the mean Pearson's correlation (diamond), with the error bars the 95% confidence intervals (including qualitative thresholds for interpretation on the x-axis; '+,' positive; '-,' negative). TECH (black, hollow diamond) and SPEED (grey, solid diamond) skiers. Variable pairs are: Fmax, maximum isometric force; RFDmax, the maximum rate of force development; RFDavg, the average rate of force development; variable units are provided only to differentiate absolute variables (e.g., N, for Newtons) from their allometrically scaled counterparts (e.g., N/kg, for Newtons per kilogram of body mass).

SPEED athletes were heavier than TECH (+6.7 [-2.53;10.83] There were large correlations between performance and a more negative SFv in both SPEED (r=0.67 [0.22;0.89], p=.008), and TECH (r=0.60[0.17;0.84], p=.011). This forcedominant profile was corroborated by strong associations for absolute F0 in both disciplines (SPEED, r=-0.79 [-0.93;-0.46], p=.001; TECH, r=-0.57 [-0.83;-0.13]

DISCUSSION

In general, our results support the 'force-dominant' nature of skiers. SPEED athletes displayed higher absolute maximum force-production capacities in both dynamic and isometric modes compared to TECH athletes, which might be associated with the extended quasi-isometric muscle actions and greater masses in their discipline. Alpine skiing performance was associated with a muscular profile dominated by elevated isometric force, dynamic force capacity at low velocities, and the capacity to develop force quickly. As such, maximum force output, rather than maximum power production, appears to match high-level skiers' needs.

One of the strengths of this research is a broad athlete sample, which included athletes from C group national representation to world number 1 in their respective event.

Surprisingly robust associations between athlete age and standings showed that higherranked athletes were both heavier and older. These results can be explained by three results may be simply a product of a long-term structural conditioning approach towards attaining strength rather than depicting a direct length between force capacities and performance. In any case, both longitudinal athlete development data, and expanded analyses using a larger pool of elite-level athletes, would clarify these points.

SPEED athletes were much heavier than their TECH counterparts. This is not a novel observation (e.g., see [START_REF] Vermeulen | Event-specific body characteristics of elite alpine skiers in relation to international rankings[END_REF]), but serves to support the theories above regarding the accrual of muscle mass. The relevance of momentum in the sport (LeMaster, 2010), and the long term implications of impulse during skiing practice (notably in SPEED (Gilgien, Kröll, et al., 2018;[START_REF] Gilgien | The training of olympic alpine ski racers[END_REF]), could feasibly result in athletes gaining additional mass (generally, or active, respectively) and explain our results. While it might be better to possess greater relative force capacities (as a product of increased capacity, or decreased BW), since the force produced due to radial acceleration during turning would be lower (i.e., ability to turn with greater speed, for a given turn radius and maximum force output), greater BW probably has an overall positive (or at least a less negative) effect on performance for a given speed due to more substantial momentum. In any case, the answer is undoubtedly more complicated than merely older and bigger athletes being dominant: for instance, the highest-ranked skier in our sample was slightly younger than the group means. Longitudinal data of athlete development should help clarify these points.

The unloaded jump data presented in this study are roughly congruent with published normative values on alpine skiers (excluding that using non-similar assessment modalities) (Ferland & Comtois, 2018). For example, h and average power output in our group are similar to that reported for a recent mixed-sex cohort of elite skiers (Jordan et al., 2018). The only other recorded SJ performances for skiers (Bosco et al., 1994) exceed the athletes in this study, which might be explained by a broader cohort (i.e., national to international athletes vs. international only in Bosco et al. (1994)), different assessment techniques (e.g., contact mat), or other factors relating to the training history of the athletes. In our cohort, there were no differences between disciplines nor any interaction with performance for unloaded jump measures. This result is notable since the literature widely reports jump measures for ski athletes (despite mixed results across disciplines and sexes) (R. E. [START_REF] Andersen | An on-site test battery to evaluate giant slalom skiing performance[END_REF]Emeterio & Gonzalez-Badillo, 2010;Haymes & Dickinson, 1980). Since h is an index of neuromuscular capacity normalized to BM [START_REF] Markovic | Effects of sprint and plyometric training on muscle function and athletic performance[END_REF], it is unsurprising that while absolute Pmax differentiated skiers (SPEED moderately greater), relative values did not. Similarly, there was a total lack of association between Pmax and performance. The lack of discriminatory ability of lower-limb force-production capacity at moderate velocities in higher-level skiers has been shown elsewhere (e.g., Haymes & Dickinson, 1980), although in development athletes the measure appears useful (Hydren et al., 2013;Song, 1982); this might point to the fact that the development of non-specific physical capabilities (i.e., general, neuromuscular output and muscle mass) may benefit lowerlevel athletes, until the point of diminishing returns are met, and more specific training is necessary. In any case, while unloaded jumps are undoubtedly a practical assessment of lower-limb output (e.g., for tracking athlete training adaptations (Morin & Samozino, 2016) or return to sports practices (Jordan et al., 2018)), our results challenge the use of these and similar tests of maximum neuromuscular output at moderate velocities to infer core force-capacity data for high-level alpine skiers (Ferland & Comtois, 2018;Turnbull et al., 2009).

Ski athletes displayed a baseline preponderance for dynamic force production at low velocities. For example, compared to a cohort of track and field athletes (Jiménez-Reyes et al., 2014), skiers produced considerably higher F0 in both absolute and relative means, albeit with a lower Pmax assumedly due to diminishing force output at higher velocities (i.e., a lower v0). Interestingly, when converting F0 to 1-repetition maximum (Rivière et al., 2017), our data are slightly lower than older anecdotal reports of the minimal level expected of B-level athletes and above (TECH, 2.15±0.29 × BW; SPEED, 2.26±0.35 × BW, vs. >2.5 × BW), and perhaps even lower due to bias induced by different squat depths (i.e., approximately 'half-squat' in our data vs. deep-squat depth in the report) (Refsnes, 1999). Moreover, mean relative F0 values are comparable to young elite Austrian skiers (C-level), albeit our group presumably possessing much higher absolute force capabilities from higher BW (+4.5 and +10.9 kg for group means), and the 'pause' before the concentric phase in the SJ being much shorter for the youth group (Fessl et al., 2020).

Our F0 values are slightly lower than ~20-year-old data from the French world-cup SPEED squad (-5 N/kg, for the group mean of SPEED) [START_REF] Rahmani | Force/velocity and power/velocity relationships in squat exercise[END_REF], although this could be partially explained by our more variable cohort (i.e., A, B, and C national squads). Moreover, presumably because our group was heavier (+ 5 kg) the difference might be smaller in absolute values (unreported in the manuscript). When comparing the disciplines, absolute F0 was much greater in SPEED athletes, but there were no apparent differences when scaled to BM. These results are interesting since field measurements regularly show turn-averaged and peak force output inferred from a measurement of COM are greatest in TECH (Supej & Holmberg, 2019). One explanation could be that SPEED athletes spend more significant absolute time in conditions of high load (>1.5 × BW), which results in much higher impulse (Gilgien, Kröll, et al., 2018), and feasibly could lead to enhanced conditional adaptations. Furthermore, forces during ski turns are regularly allometrically scaled to BW (Gilgien, Kröll, et al., 2018;Supej et al., 2011), which might further explain the large difference observed in absolute force in our cohort of SPEED skiers since they generally weigh more than technical athletes [START_REF] Vermeulen | Event-specific body characteristics of elite alpine skiers in relation to international rankings[END_REF]. In any case, in both disciplines, an absolute force-dominant profile (i.e., more negative SFv) was associated with performance. However, while the association between performance and SFv was similar in magnitude for each discipline (r=0.60 to 0.67), this was a product of the comparatively higher predictive quality of elevated force output at low velocities in SPEED (i.e., F0, see Figure 46), and both higher force-production capacities at lower velocities and reduced force production at high velocities in TECH athletes (i.e., v0, see Figure 46). As such, while SPEED athletes appear to benefit from a profile that is simply oriented towards high force/low velocities, TECH athletes would benefit from a more homogenous and balanced nature of force output across the Fv spectrum. The reliance on gaining and maintaining velocity against dissipating factors (e.g., aerodynamic drag) is essential in SPEED (Gilgien, Kröll, et al., 2018;Hebert-Losier et al., 2014), and the necessity for increased active mass and impulse (and subsequently momentum), might explain our results.

Both the absolute and (notably) relative Fmax values are among the highest presented in normative data (e.g., similar to high-level track cyclists and collegiate weightlifters) (Brady, Harrison, & Comyns, 2018). Unfortunately, there is little information on the maximum force output of skiers outside of that using isokinetic dynamometry (Alhammoud et al., 2020;Neumayr et al., 2003), although data presented in an early study by Haymes and Dickinson (1980) using modified isometric leg-extension and that by Berg et al. (1995) using an isometric leg press in World Cup skiers (2897 ± 708 N)

roughly match our study when accounting for the diverse nature of our cohort (2930±369 N for Haymes vs. upper quartile of TECH=3138 N, corresponding to the 'elite' athletes).

In contrast to maximum dynamic force, our Fmax values are considerably higher and less variable than historic reports from the French SPEED squad (38±6 vs 32±8 N/kg, respectively) by [START_REF] Rahmani | Force/velocity and power/velocity relationships in squat exercise[END_REF]. Two notable differences compared to this older dataset are the mean differences in output and the association between force production in dynamic and isometric actions. In the former instance, where there was no difference in our dataset (p=0.228 to 0.254), dynamic force was much higher than isometric force in the older dataset (+23%, p<0.001). In the latter instance, where [START_REF] Rahmani | Force/velocity and power/velocity relationships in squat exercise[END_REF] reported no association between the two variables, when performing a paired Pearson's correlation we observe moderate to strong associations between the two (absolute, r=0.76 [0.54;0.88], p<.001; relative, r=0.48 [0.14;0.72], p=0.008; see Figure 48). As Rahmani et al. ( 2001) themselves note, their results are likely mostly explained by the standardized position for the test being outside of the optimal force-length position (i.e., 90° vs. 125 to 145° at the knee, for [START_REF] Rahmani | Force/velocity and power/velocity relationships in squat exercise[END_REF] and our data, respectively). In any case, presumably, had the skiers in the study selected their preferred position for maximum force production, they would have provided similar values to dynamic maximum force (i.e., F0), and to those produced by our athletes. Recent work comparing the Fv characteristics compiled using multiple jumps and using isometric force produced during a squat set at different knee angles supports this theory [START_REF] Sarabon | Force-velocity profile during vertical jump cannot be assessed using only bodyweight jump and isometric maximal voluntary contraction tasks[END_REF].

Nevertheless, some of the difference between the old and new French team results might be indicative of unique adaptations caused the dominant quasi-isometric action in modern skiing. Moreover, similar or slightly lower scores observed in our more recent cohort serve to support the validity of the associations between these capacities in better athletes, instead of them simply being a result of an increased professionalization of strength and conditioning focus over time (Hydren et al., 2013). Graphic displays the association between maximum force produced in dynamic movement (i.e., as theoretical maximum force, extracted from the Fv relationship in squat jump; y-axes) and that produced in isometric movement (i.e., as assessed during a 500 ms window, during the isometric mid-thigh pull; x-axes). Graphic 'A' corresponds to absolute data, and graphic 'B' presents data normalized to bodyweight.

SPEED athletes produced much greater Fmax in both absolute and relative terms, which could be a product of discipline-specific adaptations due to the greatly elongated and high load quasi-isometric phases during turning and substantially elevated impulse during ski runs compared to TECH (Alhammoud et al., 2020;[START_REF] Gilgien | The training of olympic alpine ski racers[END_REF]Kröll, Spörri, Kandler, et al., 2015). Moreover, in straight phases, SPEED athletes adopt a tucked position to minimize air drag (16-37% of turn duration) (Gilgien, Kröll, et al., 2018), which increases the time spent in isometric modes at the hip (Alhammoud et al., 2020) and is probably the primary cause of quasi-constant muscular activity (>40% MVC)

versus the variable contraction mode activation patterns in TECH (sine pattern, ~15-75% MVC) (Alhammoud et al., 2020). The importance of high isometric force capacity for SPEED was further corroborated by robust relationships with performance. On the other hand, only a trend (p=.052) for a moderate association between absolute Fmax was

FORCE-PRODUCTION CAPACITIES IN SKI DISCIPLINES

observed in TECH congruent with shorter quasi-isometric phases during turning compared to SPEED (Alhammoud et al., 2020). Consequently, while isometric force output is likely still crucial in TECH athletes, the capability to produce force dynamically appears of greater importance (albeit at very low velocities).

Similarly to Fmax, both RFDmax and RFDavg were substantial compared to the reported normative values in the literature (Brady, Harrison, & Comyns, 2018). In general, RFD did not separate SPEED and TECH athletes (a trend for minorly greater RFDavg in SPEED). However, in both disciplines, all RFD measures except one (RFDmax scaled to BM for SPEED) displayed moderate to very-strong associations with performance. The capability to apply force with finesse is known anecdotally to be determinant for skiing (Hebert-Losier et al., 2014;Turnbull et al., 2009), both for application in turning events (e.g., turn initiation and turn-switch) and the essential capacity to dampen very high levels of force as a product of transient vibrations and course irregularities. In the first instance, a necessity for quick application of force could explain the strong associations with RFDmax and RFDavg and performance [START_REF] Keränen | FIS-ranking and carving turn force production profile[END_REF].

While initially, one might surmise SPEED athletes require less RFD due to slower turn cycling elongating turn events (Alhammoud et al., 2020), we found similar or stronger correlations than TECH. This result might suggest a requirement for enhanced RFD in both disciplines-for example, in response to significant deviations in athletes' lower limbs while traversing the slope at high velocities in DH [START_REF] Ducret | Analysis of downhill ski performance using GPS and grounding force recording[END_REF]). An overall enhanced neuromuscular profile might explain some proportion of this result for SPEED athletes since the association between RFD and Fmax is increasingly prevalent following contractile initiation (i.e., >75 ms (Maffiuletti et al., 2016)). Still, the substantial relationships between RFDmax and RFDavg and performance without a clear association with Fmax in TECH weakens this interpretation.

In any case, our results support the discriminative nature of RFD in ski athletes from both disciplines, with a slight bias of maximum 'early-phase' output in TECH athletes, and 'late phase' output in SPEED athletes. Lastly, our device's validity for testing RFD

has not yet been tested, and lower quality systems have exhibited poor results. As such, although our unit features several improvements that should enhance the measurement validity of RFD (discussed below), these factors should temper the interpretations of our findings here.

Although there is limited information on the longitudinal effects of ski training on physiological adaptations, we assume the differences observed here are a product of the chronic unique demands of alpine skiing-and more specifically, disciplines-on the athletes. Consequently, we believe our results indicate the existence of specific force capacities underlying the needs of skiing disciplines and performative levels. More broadly, our results might support more direct associations between specific physical qualities and performance in the SPEED disciplines, compared to the more technically variable TECH discipline. Since effectively applying force in skiing is related to physical capacity and technical abilities, targeted enhancement of specific force production capacities is one means of enhancing performance. For example, improving specific athletic capacity might feasibly allow athletes to work at a lower relative percentage of their maximum, becoming more metabolically efficient and suffer fewer consequences of sustained skiing activity (Turnbull et al., 2009). Another possibility is that an athlete with enhanced capacity can produce additional output when needed, avoid mistakes (e.g., skidding to dissipate energy), and subsequently gain valuable time. In any case, the relationship is likely more complicated, and further research should investigate and clarify the association between specific physical capacities and force production on the snow.

Possibility for spurious correlations

It is important to note that older athletes were more highly ranked (rs=-0.81 to -0.83; p<.001), and age and training history were quasi-perfectly associated, since in our cohort, these variables are near perfectly correlated due to the athlete sample beginning structured weight training at the same stage (i.e., in ski schools). Consequently, a concern is that the association between force production capacities and performance might be a spurious correlation caused by higher-performing athletes being older and possessing a more substantial training history (i.e., longer accrued adaptations from strength and conditioning). Evidently, some proportion of our results can be explained partially by the long-term accrual of strength, the nationalized focuses on conditioning, and other factors that skew the dispersion of older athletes towards higher rankings (partially discussed in the opening paragraphs of this section). Unfortunately, it is not easy to separate the effects of age and training history from the analyses. The only way to fully answer this question would be to perform a multi-site data collection to separate the 'cultural' approaches to conditioning.

We further tested potential interactions by including age and maximum force capacity (F0) in a multiple regression model to predict performance (see Of course, it is non-sensical that for most athletes, solely increasing force-production will elevate skiing performance (except in cases where force is truly limiting an athlete).

Similarly, it is illogical that performance might be increased only by aging. Instead, these results are likely a mixture of accrued strength training and longitudinal adaptations brought on by skiing practice, and thus indicate a need for specific underlying force capacities in tandem with the development of surrounding technical, tactical, physiological, and other capacities that come with experience in the sport.

Limitations

A common but notable limitation with this research is the possibility that the results we observed are related to the geographical approaches of the talent development and coaching practices of the athletes (i.e., French national team). A multi-site data collection involving athletes from multiple countries would help elucidate associations between various physical characteristics and performance. While outside of the purview of this work, such an investigation might help isolate confounding nation-specific approaches to conditioning that might otherwise result in interpretations of performance association (Maffiuletti, Jordan, Spring, Impellizzeri, & Bizzini, 2009). Similarly, provided with a large enough sample separating athletes into their specific events or multi-event specialists would provide a clearer view of specific performance characteristics underlying athletic profiles.

Ski athletes are known to display a disproportionately stronger lower body than other sporting codes (Hydren et al., 2013), and consequently, upper-body strength may have limited force production in the IMTP. Accordingly, the isometric squat might provide a valid alternative for future research (Brady, Harrison, & Comyns, 2018;[START_REF] Brady | A comparison of the isometric midthigh pull and isometric squat: Intraday reliability, usefulness, and the magnitude of difference between tests[END_REF]. Moreover, such an approach could allow simple assessment of unilateral force output (Brady, Harrison, & Comyns, 2018) and modulation of knee angle, both of which might provide unique information for skiers. The assessments used in this research were bilateral, and while technique dependent (Müller & Schwameder, 2003), in skiing, the limbs act somewhat independently with the outside leg generating the majority of force (outside:inside, ~2:1 ratio), often in a different manner to the inside limb (Alhammoud et al., 2020;Kröll, Spörri, Kandler, et al., 2015). While there are concerns regarding complexity and thus reduced feasibility for integration into a team environment, there might be interest in assessing the dynamic and isometric output of individual limbs in future ski research.

Our portable IMTP system was selected to improve the accessibility of isometric assessments, given the cost and ungainly nature of force-plate systems. However, while similar setups provide accurate Fmax with some systematic bias (Dobbin et al., 2018;James et al., 2017;Till et al., 2018;Urquhart et al., 2018), the one report of RFD validity that exists depicts poor agreement compared to fixed-bar force-plate systems (James et al., 2017). Our unit and setup overcome several critical limitations of previous designs that feasibly improve RFD accuracy (e.g., rigid base-plate [wood vs. reinforced steel], high sampling frequency [<100 vs. 1000 Hz], and rigid tether [material lashing strap vs.

hardened metal chain]), and might be considered a different assessment than the criterion solution since the bar is moveable. Nevertheless, our RFD results should be interpreted with these factors in mind.

Lastly, our results do not assess other vital capacities, such as force production maintenance over multiple repetitions (Turnbull et al., 2009). As such, while complicated to measure, future research should attempt the integration of these specific parameters further into tests of strength-endurance capacity.

CONCLUSIONS

Our results show that the better skiers are those who possess a higher capacity for specific force production, and accordingly, individual force-production capacities of the neuromuscular system might be a limiting factor of force output-and performanceduring skiing. Specifically, skiing disciplines differ based on the level of force production but share an overall strong association between force-capacity at low velocities, isometric force, the ability to build up force quickly, and performance level. As such, ski athletes might benefit from focusing on developing muscular capacity for high force at low velocities and isometric properties for ski racers. This strengthens the evidence for emphasizing the training and testing of isometric force and dynamic strength at low velocities in place of more common physical output tests (e.g., unloaded countermovement jumps) in ski athletes.

Practical applications

• Both alpine skiing disciplines display a preponderance for dynamic force output at low contraction velocities, with a complete lack of predictive quality of maximum power conditions (e.g., Pmax and unloaded jumps). The elevated force output observed in these cohorts and the general association between high force capacity and performance may point to the need for dynamic capacity at low velocities in skiers.

• SPEED athletes displayed robust relationships between performance and dynamic low-speed, isometric, and both maximum and average RFD-notably in absolute conditions. Developing high quasi-isometric capacity in SPEED athletes, in tandem with accumulating active mass, is probably advisable.

• For TECH athletes, the associations between force production and performance were weaker than those observed in SPEED. Absolute dynamic force at low velocities and maximum isometric force in absolute displayed moderate strength associations, albeit only a trend for significance for the latter capacity. Both maximum and average-absolute and relative-RFD similarly predictive. As such, while on-snow performance in TECH is probably more determined by 'technical' aspects than SPEED, developing specific force capacities might be worthwhile.

• These results do not preclude the necessity for a well-developed baseline of generalized muscular capacity. Notably, developmental athletes might focus on the accumulation of active mass and generalized neuromuscular capabilities, after which shifting focus to enhancing force production at low velocities and RFD. Welldeveloped athletes (i.e., sufficient Pmax and v0) may see diminishing returns on nonspecific capacity development.

• Similar batteries utilized in this research might be considered for implementation since they enable the precise measurement of apparently skiing-relevant muscular parameters. Moreover, they represent simple, practical, yet valid measurement tools and computational approaches able to be easily integrated as part of routine testing and monitoring performance in remote locations.

THE EFFECT OF COUNTERMOVEMENT ON FORCE PRODUCTION DEPENDS ON EXTENSION VELOCITY: A STUDY OF ALPINE SKIERS & SPRINTERS 4.2.1. ABSTRACT English

In jumping, countermovement increases the force produced during the following concentric phase and consequently increases performance. There is little information on whether this augmented force is velocity specific, nor the degree to which this varies between athletes. We used a force-velocity (Fv) profiling approach in high-level skiers (N=23) and sprinters (N=30) to detect inter-athlete differences in countermovement effect at different speeds and to further test for differences between sporting groups and performance levels. Countermovement ratios (CR) were computed between Fv variables obtained from squat jumps and countermovement jumps: Jump height (CRh), maximum power (CRP), maximum theoretical force (CRF), and maximum theoretical velocity (CRv). or CRh,p>.05). Countermovement effect appears to be both velocity and sports specific and may be associated with performance in some codes (e.g., 33% skier standing explained by higher maximum force and lower CRF). Notably, while countermovement effect was not associated with performance at any speed for sprinters, better skiers might benefit from training the mechanisms underlying force production without countermovement at low speeds in tandem to an overall increase in maximum force production capabilities.

Français

PRELUDE

In the previous chapters, we showed that force-output characteristics appear essential in skiing and that better skiers exhibit specific and elevated force-capacities; notably, high force at low speeds and isometric force (importance dependent on the discipline). To provide further insight, we investigated whether adding countermovement provided further descriptive efficacy regarding skiing-specific force capacities during explosive lower-limb extension. Consequently, we were interested in whether specific countermovement characteristics (i.e., how countermovement adapts force production across the force-velocity profile) provided any additional information to the noncountermovement performance measurements presented in the preceding chapter.

Moreover, to our knowledge, little research has directly examined the effect of countermovement on force production at different extension velocities. To fortify our investigation, we performed the same tests on a group of high-level sprinters.

Comparison of the two mechanically disparate groups (i.e., characteristically high-force skiers vs. high-velocity sprinters) allowed the further contextualization of skiers' forceproduction capacities and a novel means of testing the velocity, sport, and performancelevel interactions on countermovement effect.

Co-authored works associated with this section

INTRODUCTION

Lower limb explosivity and contextual power output are central physical components in many sports. While there are several assessment methods, jumping is a practical means of measuring lower limb explosivity. The two most common jump variants are the countermovement jump (CMJ) and squat jump (SJ), which differ based on the presence or lack of a swift downward motion directly preceding the upward propulsive phase, respectively. Both can provide a reliable assessment of the neuromuscular function for power output (Cormie et al., 2011a). However, since humans naturally opt for implementing some magnitude of countermovement in ballistic movements, the CMJ arguably provides a more specific measure of typical sporting performance (van Zandwijk, [START_REF] Van Zandwijk | From twitch to tetanus: Performance of excitation dynamics optimized for a twitch in predicting tetanic muscle forces[END_REF]. Nevertheless, the differences between the SJ and CMJ, and more broadly the capability to produce force with and without countermovement, are interesting for exploring contextual performance, notably for application in situations that allow little or no countermovement (e.g., a sprint-block start or turning during skiing).

Lower-limb power output is almost universally acknowledged to be higher with countermovement than without (Bobbert & Casius, 2005;Van Hooren & Zolotarjova, 2017), with a larger difference traditionally attributed to an enhanced 'utilization' of mechanisms underlying the countermovement phase [START_REF] Young | Relationship between strength qualities and sprinting performance[END_REF]. Of the mechanisms presumably responsible for this performance augmentation, several rely on the active lengthening of muscle fibers (i.e., eccentric contraction) during the downward portion of the movement (e.g., residual force enhancement [START_REF] Herzog | Residual force enhancement in skeletal muscle[END_REF]). However, although there is negative joint movement during countermovement, it is not necessarily a priori clear that jumps of typical amplitudes result in active muscle fiber lengthening (Van Hooren & Zolotarjova, 2017). Similarly, while the stretch reflex mechanism might provide some force augmentation, it requires both lengthening and lengthening at speeds unlikely to be reached during jumping.

Furthermore, any additional activation resulting from the reflex is probably negligible given motor units are already near-maximally activated (Kubo et al., 2007;McBride, Casius (2005) showed that the differences in jump performance with and without countermovement were largely preserved without accounting for either mechanism.

Similarly, the utilization of elastic energy stored during the countermovement phase might provide some benefit, but probably only in small magnitudes that become more apparent at higher movement velocities and during smaller amplitudes.

In their recent review, Van Hooren and Zolotarjova (2017) highlighted that the principal explanation for an augmented performance in the CMJ compared to the SJ can be The effect of countermovement on lower-limb force production is commonly assessed in jumping as a 'countermovement ratio' (CR) between h or the power developed during the concentric propulsive phases of a CMJ and SJ (e.g., McGuigan et al., 2006). Several variations exist (McGuigan et al., 2006;Pruyn, Watsford, & Murphy, 2016;Tufano et al., 2013), which have been implemented in the interest of better understanding the contributors to explosive performance within and across various sports. For example, McGuigan et al. (2006) showed that CRs varied across sports (e.g., greater in soccer than softball for males and females), and early reports by Komi (1984) show that 'jumping' disciplines (notably, ski jumping) displayed larger CRs (as CMJ-SJ, in h and work) than runners or physical education students. These results are interesting, given the rationale above, since a larger CR is not necessarily beneficial and might reflect an inability to produce force without countermovement via an inability to build up stimulation, more compliant musculature (i.e., lower stiffness (Pruyn et al., 2016)), non-beneficial forcelength-velocity characteristics, or other factors. While complicated by varying ratios across sporting disciplines, this perspective is tangentially supported by better athletes not universally exhibiting higher countermovement effects (Van Hooren & Zolotarjova, 2017).

CRs are almost exclusively measured in bodyweight (BW) jumping, using h or power expressed during the concentric portion of the jump (McGuigan et al., 2006). While undoubtedly practical and arguably relevant to some sporting situations (e.g., strong correlations between CMJ performance and sprinting (J. B. [START_REF] Cronin | Strength and power predictors of sports speed[END_REF]), this approach only quantifies the countermovement effect in a single distinct (intermediate)

force-velocity (Fv) condition and does not represent performance in other mechanical states (Samozino, 2018a). Moreover, even if h at BW is associated with force production in approximately the middle of the Fv spectrum, and consequently a 'macroscopic' view of countermovement effect, it might not accurately represent maximal power capabilities (Morin, Jiménez-Reyes, et al., 2019). The methodological impact of this problem was partially illustrated in considerable inter-athlete variation in CRs observed by using h vs.

peak power developed during the jumps as the underlying variable (McGuigan et al., 2006). However, perhaps the main limitation of a BW-only approach is that it might not be pertinent for sports or sporting situations that rely on performance in more distinct mechanical conditions. Specifically, since the balance in Fv capacities is independent of maximum power (Samozino et al., 2014), and various sports and sporting circumstances display distinct mechanical characteristics (Giroux et al., 2016), we might expect the expression of countermovement to vary similarly according to the mechanical condition (Samozino et al., 2014). Consequently, exploring the effect of countermovement at different movement velocities would seem pertinent to understand the expression of force in broader conditions since assessment in a single velocity condition may mask underlying CR differences at high or low speeds.

Unfortunately, there is limited data on the interaction between velocity and countermovement effect, which is constrained to averaged data lacking individual variability. The Fv profile compiled from multiple loaded jumps in both SJ (Jiménez-Reyes, Samozino, Pareja-Blanco, et al., 2017) and CMJ (Samozino et al., 2012) provides a valid (Samozino et al., 2010) and relatively simple means of assessing force expression per movement velocity, and the effect of countermovement separate from the movement itself. Few studies have compiled Fv profiles from SJ and CMJ movements together (Cuk et al., 2014;Cuk et al., 2016;Jiménez-Reyes et al., 2014;[START_REF] Sarabon | Force-velocity profile during vertical jump cannot be assessed using only bodyweight jump and isometric maximal voluntary contraction tasks[END_REF]. Jiménez-Reyes et al. ( 2014) compared the intra-individual mechanical profiles of high-level track and field athletes and observed globally increased mechanical capacity with a countermovement. On average, the group elevated Pmax was a product of the Fv relationship being shifted to the 'right' (i.e., both maximum theoretical force [F0] and velocity [v0] increased). However, disproportionately higher increases in F0 vs. v0 (i.e., force at low vs. high velocities, respectively) were reported with countermovement. The authors interpreted the results as being due to a higher active state per the effect of increased loading on the countermovement phase (i.e., more substantial augmentation of maximum force capabilities) and the decreasing influence of neural and mechanical mechanisms with increasing speeds. These interpretations are plausible but inverted from the current understanding of the interplay between the jumps: a more significant countermovement difference infers an underdeveloped capability to produce force during the SJ (Van Hooren & Zolotarjova, 2017). In any case, these factors strengthen the theory that CRs might vary based on the mechanical conditions and thus illustrate the need to test the hypothesis further.

Plausibly, since the sporting background and performative level can generate unique Fv profiles (Giroux et al., 2016), they might similarly induce intra-individual differences in the mechanisms underlying the effect of countermovement. For example, while many sports are dominated by force applied in high-velocity conditions (e.g., 664°/s backward leg swing velocity in sprinting (Miyashiro et al., 2019)), alpine skiing is dominated by slow flexion-extension patterns of the lower limbs (e.g., <86°/s at the knee for the concentric phase (Alhammoud et al., 2020)) at high force output and for extended durations (e.g., an impulse of 124 to 173kBWs (Gilgien, Kröll, et al., 2018)). These factors challenge the relevance of assessments that solely examine force production and potentially countermovement effect in 'moderate' Fv conditions (see Figure 49).

Moreover, a more detailed examination of potential relationships between performance level and countermovement effects per movement velocity could serve to deepen our understanding and provide unique and novel information on the mechanisms underlying countermovement augmentation for sports specific training purposes. For the skier (BM=90 kg; dashed line), data corresponds to the course averaged output per limb (inside=grey, outside=black; solid line) from one turn as measured by specialized force plates from a raw dataset [START_REF] Cross | Force output in giant-slalom skiing: A practical model of force application effectiveness[END_REF], showing both feet independently. For the sprinter (BM=72 kg, solid lines), foot strikes (i.e., impulse followed by flight time and subsequent impulse of opposite limb) 2-7 of a maximum sprint are displayed (limb 1=black, limb 2=grey), as measured by in-ground force plates from a raw dataset (Morin, Samozino, et al., 2019). While not displayed on this graph, the speed at which these forces are produced is very different, with very slow and very fast angular velocities of the lower limbs for skiing and sprinting, respectively.

In this chapter, we aimed to: 1) further examine the influence of velocity on the effect of countermovement using a 'ratioed' approach with Fv profiling; 2) explore interindividual variability on these factors, notably within distinct athlete populations (alpine skiers and track and field athletes), and; 3) test whether the expression of explosive capacity and the effect of countermovement contribute to sport-specific performance.

These aims assume a baseline difference between the sporting cohorts, so a tertiary aim of the project was to differentiate between the two sports in mechanical profiles. We hypothesized that the effect of countermovement would be independent at high and low velocities and that differences would likely exist between athlete groups and performative levels.

METHODS

Participants and study design

In this study, we recruited a range of male alpine skiers (N=23) and a cohort of track and field athletes (N=30) as a point of comparison. Our rationale for testing our aims in this population was that the two disciplines anecdotally represent opposite ends of the mechanical spectrum. Consequently, while yet untested, these mechanically distinct cohorts present a unique means to test the variance of CRs across sports and with performance.

All athletes were high-level (national-international representatives), accustomed to the testing procedure with a history of resistance training and testing protocols, and free of any musculoskeletal injuries that might impact their capacity to perform maximally.

The skiers hailed from both speed (super giant and downhill, N=11) and technical

Procedures

Pre-session body mass (BM) and lower-limb length were measured, followed by a ~20 min dynamic warm-up. The athletes then selected their preferred squat depth and performed loaded SJ and CMJs while aiming to produce the highest jump height to compile Fv relationships (Morin & Samozino, 2016). Athletes wore regular exercise attire and trainers or Olympic lifting shoes for the testing procedures. Olympic lifting bars and bumper plates. Loading magnitude was selected per preexisting rationale to provide a span of loading broad enough to compile an accurate Fv profile (Morin & Samozino, 2016).

Athletes performed consecutive SJ and CMJ movements per loading condition. For SJ, athletes descended with the bar slowly to their individualized and pre-set depth (i.e., slightly above the rack supports or lightly touching the elastic bands), rested isometrically for 3 s (verbally cued), and then jumped upwards with maximum ballistic effort. For CMJ, the same process was followed except without strict cueing and allowing countermovement (i.e., no pause). For each loading condition, one to two trials were performed with small intra-repetition rest, and 3 to 5 min passive rest was allowed between movement type and subsequent loading increase. Jump height data were measured using optical gates (model: OptoJump Next, Microgate, Bolzano-Bozen, Italy)

and calculations based on fundamental physics (Asmussen & Bonde-Petersen, 1974). h data was monitored throughout, and loading was adjusted where necessary to a final value of four to six unique data points. Data were entered in real-time to compile a preliminary Fv relationship to identify irregular jumps via the linear regression line (in addition to other disqualifying points, such as stumbling, irregular hpo, or other abnormal movements as visually assessed). Five to seven sets were completed in total, which allowed for the repetition of one or two jumps according to their accuracy, as judged by the linear Fv profile.

Overall performance index

Athletes for both sporting codes were provided a performance ranking to test subsequent hypotheses around the importance of mechanical variables and the CR in their sport. For the skiers, the performance metric was their current best-event world standing, per the 9 th annual list issued by the International Ski Federation. For the sprinters, we used their best competitive performance in the 100 m for the season.

Athletes who did not compete in the 100 m were omitted from the corresponding analyses. Data from the jump with the highest jump height (h) per loading parameter were used to calculate the average force (F), power (P), and velocity (v) over the push-off phase using a validated method (Giroux et al., 2015;Samozino et al., 2008). Briefly, the method used fundamental Newtonian physics applied to the raw h data, in combination with the total mass of loading condition (BM + external load; mtot) and the measurements of hpo:

Eq. 13

𝐹 = 𝑚 tot • 𝑔 • ( ℎ ℎ po ⁄ + 1)
Eq. 14

𝑣 = √ 𝑔 • ℎ 2 ⁄
Eq. 15

𝑃 = 𝑚 tot • 𝑔 • ( ℎ ℎ po ⁄ + 1) • √ 𝑔 • ℎ 2 ⁄
Both SJ and CMJ Fv and Pv relationships were fit with least-squares regressions for each athlete. The theoretical limits of the athlete force-production capacities at extremely low and high velocities (F0 and v0, respectively) were extrapolated as intercept between the curve and each axis and were used to compute maximum power (Pmax=F0•v0/4). The slope of the Fv relationship represented the balance in mechanical capabilities (SFv) and was further characterized by expressing it as a percentage of the 'optimal profile' per BW (Fvimb; >100% is force dominant, <100% is velocity dominant) (Samozino et al., 2014;Samozino et al., 2012).

Countermovement ratio

CR (CMJ/SJ) were computed in the first instance using BW h from each movement (CRh)

and subsequently using variables from the Fv relationship to obtain CR at different velocities: CRP for Pmax, CRF for F0, and CRv for v0 (i.e., at intermediate, extremely low, and extremely high velocities, respectively). Each of the variables is graphically represented in Figure 50.

Statistical analysis

Statistical analyses were performed using the open-source software JASP (version: 0.12, JASP Team, Amsterdam, Netherlands). Descriptive statistics are presented as means±standard deviation or median(interquartile range [IQR]) where explicitly stated.

To test initial differences between force production in CMJ and SJ, data (h, Pmax, SFv, F0, v0

for both movements) from skiers and sprinters were pooled and analyzed using Wilcoxon's signed-rank paired samples tests after data from 4/5 variables were found to be non-normal (Shapiro-Wilk, W=0.875-0.955, p<.001-.045). Data were reported using the Hodges-Lehmann estimate and the rank-biserial correlation (rrb) to provide effect magnitude. Otherwise, Spearman's rho (rs, p-value) nonparametric correlations were performed on the pooled CR data to test for associations between CRs at low and high velocities (i.e., CRF vs. CRv, respectively).

Figure 50. Force-and power-velocity relationships compiled from multiple jumps with and without countermovement

Black and grey lines correspond to the force-and power-velocity relationships with and without countermovement, respectively. CRP and CRh correspond to ratios between with and without countermovement in maximum power (Pmax, as the peak of the parabolic power velocity relationship) and jump height (i.e., both existing in moderate velocity conditions); CRF and CRv the ratios between with and without countermovement for maximum theoretical force and velocity (F0 and v0, as the x-and y-axis intercepts of the linear force-velocity relationship and corresponding to very low-and very high-velocity conditions, respectively), respectively. Each '×' corresponds to the 'best-case' scenario when implementing ratios on unloaded jumping movementsthat the jumps correspond to the peak of the power-velocity relationship (i.e., perfectly tracks maximum power, and the athlete is perfectly balanced for lower-limb explosivity (Samozino et al., 2014)). The oval corresponds to an approximate band of error when using jump height as an indicator of maximum power capacity since it depends on the maximum power and balance between force and velocity capacities (Morin, Jiménez-Reyes, et al., 2019).

Differences between sport disciplines in BM, h, and key Fv variables in the SJ (Pmax, SFv, F0, v0, and Fvimb) were assessed using independent T-tests and the Welch's unequal variances T-test where necessary (i.e., p<.05 in Levene's test). Cohen's effect sizes using the pooled standard deviation were used to provide a measure of effect magnitude. For CRs, both the assumption of normality and equality of variances were violated (Shapiro-Wilk and Levene's, respectively, p<.05), and therefore the nonparametric Mann-Whitney U test was used in place of the parametric independent tests. Results were reported as the median difference between the two groups (Hodges-Lehmann estimate) and associated effect magnitude (rrb).

To assess the potential contribution of mechanical capacity and CRs in performance, we performed sport-distinct multiple regression analyses. Each cohort was analyzed separately, with world standings and the fastest 100 m time as performance (i.e., the dependent variable) in skiers and sprinters, respectively. Sports-specific performance was entered in the model as the dependent, with each CR 'matched' with the corresponding Fv variable in CMJ as the two independent variables (e.g., CRF and CMJ F0). Some sprinters did not officially perform in the 100 m (e.g., hurdlers, long jumpers, or 400 m specialists), which resulted in a smaller dataset for these analyses (N=19).

Following the reduction, data met the pre-requisite assumptions for regression analyses, except for CMJ Pmax, which was slightly skewed due to two powerful and high performing athletes. Log-transforming the dataset improved normality (Shapiro-Wilk, W=0.921 p=.117) but did not substantially change our results. Therefore, the analysis was performed on the 'non-normal' dataset for continuity. For each model, the following statistics were reported: standardized β, F, model R 2 [adjusted], and p-value.

The threshold values for qualitative interpretation of effect magnitudes were as follows:

d<0.2, 0.2, 0.5, 0.8, and 1.2; r, rs, and rrb<0.1, 0.1, 0.3, 0.5, and 0.8; as trivial, small, moderate, large, and very large, respectively (Hopkins et al., 2009;Sawilowsky, 2009). The alpha value for all tests was .05, with .1 considered a trend.

Sensitivity analyses were performed using the sample size estimation software (G*Power [START_REF] Faul | Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses[END_REF]) to determine the approximate threshold of detectable effect for each statistical model and associated sample size (see Figure 51).

Figure 51. Sample size plots

The four contour plots presented here depict the sensitivity of the utilized statistical models to detect effects, with a Type 1 error rate of α=0.05 and 80% power. Plots A and B relate to the Wilcoxon paired-samples and Mann-Whitney U tests and illustrate that N=53 can reasonably detect small to moderate effects (rrb=0.24 and 0.38), respectively. Plot C relates to the Independent T-tests and indicates that with a total N=53 moderate-large effects can be reasonably detected (Cohen's d=0.79). Plot D relates to the multiple regression and indicates that for both samples (skiers, N=23; sprinters, N=19), we can reasonably detect moderate effects (R 2 =0.33 and 0.38, respectively).

RESULTS

h, Pmax, F0, v0 were all very strongly increased by countermovement. Increased interindividual variability resulted in unclear effects on SFv (see Table 9). A strong negative association (rs=-0.735, p<.001) was observed between CRF (median=1.091 [0.333]) and CRv (median=1.058[0.413]) (see Figure 52 and Table 10).

Skiers and sprinters differed in several key mechanical variables, with sprinters having lower h, Pmax, v0, and a more negative SFv (Table 11, Figure 53). Skiers were much heavier, had a higher relative value of SFvopt%, and there was a trend for skiers displaying moderately higher absolute F0. No clear differences were observed in relative F0. There were moderate to large differences between skiers and sprinters for CRv (median=1.17 [0.413] CR, 'countermovement ratio' as countermovement-jump performance/squat-jump performance; CRh, the ratio between jump height in countermovement jump versus squat jump; CRP, the ratio between maximum power determined from the peak of the power-velocity relationship in countermovement jump versus squat jump; CRF, the ratio between maximum theoretical force determined force-velocity relationship in countermovement jump versus squat jump; CRv, the ratio between maximum theoretical velocity determined force-velocity relationship in countermovement jump versus squat jump; U, Mann-Whitney U test; CI, confidence intervals (95%); IQR, interquartile range.

CHAPTER 4. THEME 2: FORCE CAPACITIES

Figure 52. Comparison between sports and pooled correlation results for countermovement ratios

The graphic displays the median and interquartile ranges for countermovement ratios between key force-velocity capacities: intercepts of the force-velocity relationships (F0 and v0, respectively), maximum power output (Pmax), and jump height (h). Boxplots are median and quartiles, with white filled boxes representing skiers and grey sprinters. ' × ' represents the mean and circles data from individual athletes (except where values significantly overlap). The dashed line represents a balance/equality between squat-and countermovement-jump output, with values above the line (i.e., >1) representing a higher value with a countermovement and vice-versa. Comparisons between sport codes in the respective mechanical quality are displayed as Mann-Whitney test (U) and rank biserial correlation (rrb). Pairwise differences between mechanical capacities (F0 vs. v0) for the pooled athlete data are presented in Spearman's rho (rs). **p-value<.01, ***p-value<.001. m, meters; Pmax, maximal power; W, watt; W/kg, watt per kg; SFv, Slope of the linear force-velocity relationship; Ns/m, Newton seconds per meter; Ns/m, Newton seconds per meter per kilogram; F0, maximal theoretical force; N, newtons; N/kg, newtons per kilograms; v0, maximal theoretical velocity; m/s, meters per second. Fvimb, the imbalance between the current profile and the optimal for maximizing jump height at body mass.

Figure 53. Sports comparison in force-capacities determined from the squat jump

The data are the median (solid black line) and interquartile ranges (black dotted lines) of each cohort (skiers, top; sprinters, bottom). x-axes are normalized.

In skiing, force (F0 and CRF) and velocity (v0 and CRv) multiple regression models were related to performance (see Table 12). However, only in the former case did both variables contribute to the model. In the latter case, the model prediction was weaker and mostly due to a strong positive relationship with v0 (i.e., inverses proportionate with performance) and no clear predictive quality with CRv. In the sprinters, only the model including Pmax and CRP, was related to performance, without a significant contribution of CRP. stand. β, beta-weight in standardized units; F, F test; df, degrees of freedom; Pmax, maximal power; CRP, ratio between maximum power determined from the peak of the power-velocity relationship in countermovement jump versus squat jump; F0, maximal theoretical force; CRF, ratio between maximum theoretical force determined force-velocity relationship in countermovement jump versus squat jump; v0, maximal theoretical velocity;

CRv, ratio between maximum theoretical velocity determined force-velocity relationship in countermovement jump versus squat jump.

DISCUSSION

Skiers and sprinters displayed some key differences in the expression of forceproduction characteristics. According to the mean data, dynamic lower-limb forceoutput characteristics were augmented by countermovement. Countermovement effect in conditions common to research (i.e., in moderate conditions, around maximum power) did not differentiate sporting codes. However, the expression of countermovement effect appeared to differ across movement velocities and sporting groups, which led to marked differences at high and low extension velocities.

Specifically, at lower velocities, the countermovement effect was small for skiers, with much greater variability at high velocities, whereas sprinters exhibited the inverse characteristics (a larger effect of countermovement at low velocities vs. high velocities).

Similarly, countermovement effect might vary with performance, with better skiers possessing greater force output and a smaller countermovement effect at low velocities, albeit lacking association at any velocity and 100 m performance in sprinters. These results highlight a necessity to examine countermovement effect in conditions relevant to the sport, and have interesting, albeit complex, implications for training.

Unsurprisingly, given the different underlying performative features of each sport, skiers and sprinters varied in key lower-limb mechanical characteristics in the SJ. In the first instance, despite an average SFv far from optimal (Samozino et al., 2012), sprinters exhibited a much greater h (+0.101 m for sprinters vs. skiers) due to higher relative Pmax than skiers. Skiers presented a much more force-oriented profile (closer to their 'optimal,' 87 vs. 65%, where 100% optimizes h), which was particularly notable in absolute conditions (i.e., non-normalized to BW) and led to skiers displaying a trend for moderately greater output in conditions of absolute F0 (unclear differences in relative F0)

and much lower v0 than sprinters. While somewhat difficult to compare due to the substantial differences in force-production techniques (e.g., orthogonal vs. horizontal in skiing vs. sprinting, respectively), sport-specific differences in mechanical profiles might be due to skiers regularly performing high force (Gilgien, Kröll, et al., 2018) at extremely slow angular velocities of the lower limbs (Alhammoud et al., 2020) contrasting the rapid and elevated force output of sprinters at very high angular velocities. Moreover, skiers exhibit peak torque at larger joint flexion angles in key musculature at the knee (Alhammoud et al., 2019) when compared to other athletes (S. R. Brown, Brughelli, Griffiths, & Cronin, 2014), which might support elevated force production in the initial portion of a jump (i.e., at low angular velocities similar to that assessed in isokinetic dynamometry [60°/s]) versus sprinters who mostly produce force at greater lengths of dominant musculature (e.g., hamstrings) and high contractile velocities. While both cohorts of athletes were relatively well matched in performative capabilities within their sport codes (national and international representatives), the sprinters generally appeared to exhibit elevated explosive force-production capacities. This could be explained by physicality playing a more direct role in performance in sprinting, rather than being mediated by substantial environmental and equipment constraints as in ski racing.

In the first instance, h in unloaded conditions and Pmax were augmented via countermovement (+0.068 m and +415 W [17.2 and 17.5%], respectively). This finding is in congruence with the literature, which overwhelmingly supports increased mechanical output with countermovement in various sporting codes (Bobbert & Casius, 2005;Bobbert et al., 1996;[START_REF] Bobbert | Why do people jump the way they do?[END_REF]McGuigan et al., 2006;[START_REF] Zajac | Muscle coordination of movement: a perspective[END_REF]including in skiers (Jordan et al., 2018) and in sprinters (Jiménez-Reyes et al., 2014).

Moreover, the magnitude of augmentation of h are in line with previously reported values (e.g., CRh = 1.03-1.17 for various sports (McGuigan et al., 2006)). The anecdotal agreement between CRh and CRP is unremarkable, given the underlying mechanical association between the two measurements (at least for group comparisons) (Morin, Jiménez-Reyes, et al., 2019).

When examining the changes in the Fv relationships with countermovement, we observed an overall shift upwards and to the right, consistent with previous reports (Bosco & Komi, 1979;Jiménez-Reyes et al., 2014). Accordingly, both force at low and high velocities was increased (i.e., CR >1), while the slope of the Fv relationship (i.e., SFv) did not change on average. However, substantial variability in SFv, and the underlying augmentation at each extreme of the Fv profile (CRF and CRv), signified individuality in the effect of countermovement on distinct mechanical capabilities (see Figure 54).

Moreover, an inverse relationship between CRF and CRv suggests that the effect of countermovement is not necessarily the same at different extension velocities of the lower limbs between athletes. Mechanisms underlying the difference between CMJ and SJ might differ based on the mechanical condition relative to the athletes' capabilities, and athletes displaying a particularly elevated CRF or CRv were lacking development in the mechanisms underlying performance in the opposing capacity (or vice versa).

Nevertheless, while associated, the considerable unexplained variance between the CRF and CRv (rs 2 =46%) suggests the countermovement effect provides different information regarding lower-limb force production capabilities at the extremes of the Fv relationship (i.e., expression at one end of the relationship, cannot be predicted by the other).

Consequently, even if correlated here, we can reasonably assume that CRF and CRv are two independent indexes. Consequently, assessing the countermovement effect at one velocity provides only a partial view of the phenomenon, which may not be observed at other velocities.

Figure 54. Variability in the change in force-velocity profile with countermovement

The graphic displays the change in mechanical capacity with countermovement, as expressed in the slope of the force-velocity relationship (i.e., SFv) assessed with (CMJ) and without (SJ) countermovement. The light grey ' × ' represent datapoints from individuals, with the adjoining grey lines linking the two movements -should countermovement provide no effect on the balance in mechanical capacity the grey line linking the two profiles should be flat. The black outlined diamonds and adjoining black lines correspond to the mean data, which can be observed as 'no change' on average, but with large inter-individual variability.

We observed a strong negative association between SJ force at low and high velocities and the corresponding CR (r=-0.464 to -0.509, p<.001), indicating lower F0 and v0 amplified countermovement effect. One explanation could be that athletes with lower F0

have poorer coordination at low speeds (and vice versa), which in turn influences the timing of muscular activation patterns, reduces the capability to build up an active state pre-concentric phase, and reduces performance in the SJ [START_REF] Bobbert | Effects of muscle strengthening on vertical jump height: A simulation study[END_REF]Bobbert & van Zandwijk, 1999b;[START_REF] Prokopow | The effects of changes in the timing of muscle activation on jump height: A simulation study[END_REF]. This provides support to the theory that individuals unable to build up a high active state before muscle shortening without countermovement (per reduced coordinative capability, or otherwise) may still perform adequately with countermovement since they can build up stimulation during the downward phase (Van Hooren & Zolotarjova, 2017).

As such, a large countermovement effect appears partly related to poor SJ rather than good CMJ abilities. In the same vain assessing mechanical capacity only in CMJ might hide impairments in relevant capacities at the corresponding extension velocity (e.g., rate of force development).

While baseline Fv data differentiated sporting codes, the increase in Pmax or h via countermovement did not differ between skiers and sprinters. However, aligning with the independence of the balance in Fv properties and power output observed in our correlation results (see Table 10), each cohort responded differently in the augmentation of force across the Fv relationship. This is important since without considering the velocity effect on CR, one might conclude a lack of discriminative capability, or perhaps that skiers and sprinters shared similar abilities to 'utilize' the countermovement as a force/power amplifier (including the various underlying mechanisms) (Bobbert & Casius, 2005;Van Hooren & Zolotarjova, 2017). Skiers presented a lower CRF, and sprinters had a lower CRv, which is concordant with the general force and velocity dominant performative nature of skiers and sprinters, respectively, and smaller differences between SJ and CMJ (i.e., a lower CR) being potentially beneficial (Van Hooren & Zolotarjova, 2017). Specifically: 1) skiers are more force dominant and therefore displayed a lower augmentation of force at low velocities with countermovement, and; 2) sprinters are more velocity dominant and coincidingly exhibited a lower augmentation of force at high velocities with countermovement.

Low extension velocities increase the relative time to build up stimulation in the SJ, while elevated external load stiffens the tendon, resulting in slower shortening velocities and hence higher force potential of muscle fibers [START_REF] Fletcher | Running economy from a muscle energetics perspective[END_REF]. Since the absolute extension time is much greater in high-force-low-velocity conditions, the effect of maximum-voluntary force and non-elastic characteristics of the muscle may play a more significant role in the work produced (Maffiuletti et al., 2016) than at higher speeds (e.g., BW jumps). Both factors might explain the reduced CRF values observed in the skiers, who notoriously exhibit large impulses (Gilgien, Kröll, et al., 2018) in very slow or quasi-isometric contractile conditions (Alhammoud et al., 2020;Berg & Eiken, 1999;Kröll, Spörri, Kandler, et al., 2015) during ski competition and training. Moreover, since concentric actions in skiing are preceded by low-force (around turn-switch (Kröll, Spörri, Kandler, et al., 2015)) and relatively low activation [START_REF] Alhammoud | Contribution à l'analyse de l'activité neuromusculaire des skieurs alpins d'élite lors de tests isocinétiques et en conditions réelles d'entraînement[END_REF]Berg & Eiken, 1999). Consequently, these distinct stimuli might have resulted in adaptations that benefit increased activation against large external loads and at low velocities more than adaptations that improve rapid force production (i.e., rate of force development (Maffiuletti et al., 2016)). Other potential explanations for differences in CRF could be large inertial loads necessitated by the assessment interacting with the general familiarity and capability of the athletes with high loads (i.e., benefiting skiers), kinematic differences, or reduced coordinative capabilities during the concentric phase (i.e., worsening sprinters performance). While the extended contractile time reduces the relative importance of several factors, these factors could feasibly explain some of the intra-sport differences observed.

At the velocity end of the Fv spectrum, shorter propulsive phases likely increase the relative effect of muscle activation (i.e., the lag to reach maximal active state) and contraction dynamics (i.e., the lag in the application of force to the bone due to nonaligned or compliant musculature, also referred to as muscle slack) on the difference between jumps. Notably, these phenomena are encompassed within the well-known construct of rate-of-force development (Maffiuletti et al., 2016). The duration of the contraction dynamics is associated with tendon stiffness (Kubo et al., 2007), which might partially explain the lower ratios in a 'stiffer' sprint cohort (Pruyn et al., 2016) ). In the same manner, where increased stiffness might be an explanation for the lower CRv values in sprinters (Pruyn et al., 2016), assumedly, the inverse explanation (i.e., compliant musculature) could explain the inflated values in skiers. Moreover, it is plausible that while skiers may be proficient in building up stimulation at low extension velocities (although, assumedly decreased relative importance could mask its effect), they might lack coordinative abilities to correctly time muscular activations at high speeds in the SJ (Bobbert & van Zandwijk, 1999b) leading to greater CRv values.

In addition to our results indicating that countermovement effect appears to be dependent on velocity and might vary based on the sport (per their integral mechanical characteristics), the sport-distinct multiple regression analyses show that they might also vary based on performance. Notably, better-ranked skiers exhibited both greater force output at low velocities (i.e., F0) and a lower CRF (33% variance), highlighting that both the capability to develop maximum force and to minimize countermovement effect at low speeds are essential. The association between higher F0 and lower CRF and performance is in line with our interpretations regarding the adaptations from the prevalent high force, low velocity, non-countermovement, but continuously activated states during skiing (Berg & Eiken, 1999). As CRF is an index of force production at low velocities directly preceded by elevated external constraints, it might be a valuable measure for skiers in the future. For sprinters, while a model containing Pmax and CRP explained 30% of the variance in 100 m season-best time, CRP did not improve the model (p>.05). In the same manner, better skiers exhibited lower force production at high velocity (v0), albeit without the predictive contribution of CRv (20% variance). Assumedly this result is reminiscent of the increased variability expected in v0 values (e.g., coefficient of variation, 14 vs. 5% for v0 vs. F0, respectively (Giroux et al., 2015)), or athletes with high F0 possessing low v0. In any case, the predictive quality of both higher F0 and lower CRF is in line with our interpretations regarding specific adaptions from skiing practice: ski athletes must perform the primary concentric phase without strict countermovement, and in conditions of unloading and relatively low activation (Alhammoud et al., 2020).

These factors may point to the need to develop unique strategies to build up activation to be subsequently applied during a slow concentric and quasi-isometric phase (Patterson et al., 2009). CRF may quantitatively represent this capacity, but this should be examined in greater detail. As such, in support of the surrounding literature (Van Hooren & Zolotarjova, 2017), we cannot confirm an overall trend for CRs and performance level, but rather that in distinct sporting scenarios (e.g., for specific sports, at specific extension velocities) they might provide discriminative information for monitoring and potentially training implementation.

Limitations

CR variants have acceptable reliability (Tufano et al., 2013)

CONCLUSION

The effect of countermovement on force-production appears to vary across the Fv spectrum within and between sports. However, no clear conclusions could be drawn regarding sport-specific countermovement characteristics in conditions common to the literature. These factors emphasize the interest in assessing a broader range of force output-countermovement, or at least ensuring specific velocity bands are targeted, to ensure characterization of sports with unique mechanical profiles. A larger increase from countermovement does not appear to be globally beneficial for athletes, with athletes from mechanically disparate codes tending to show smaller ratios at extension velocities characteristic of their sport (i.e., skiers displaying a tendency towards smaller differences at low velocities and sprinters smaller at high velocities). These factors were further emphasized by some associations with performance, albeit not globally. Future research might aim to integrate more complex measurements and modeling using multi-joint movements (e.g., jumping) and Fv profiling to better understand the mechanisms underlying performance and the expression of countermovement effect across sports and movement velocities. In general, more work is needed on the subject, preferably combined with other tests of athlete capacity, stiffness, and perhaps even muscle structure or length-tension capacities to elucidate underlying mechanisms. Such research would enable a more holistic view of countermovement effect as it pertains to sporting performance and provide a better view of possibilities for monitoring performance and targeted training implementation.

PRACTICAL IMPLICATIONS

• Countermovement generally augmented performance but disparities in CR across the Fv spectrum between and within the two sports highlight the potential value in individualized CR assessment over the entire velocity spectrum (notably, within sports with unique mechanical performance profiles). Differences between athlete groups were unclear in conditions around maximum power, which further emphasizes the interest in assessing a broader range of force-output countermovement capabilities in various athlete groups. Otherwise, assessing the effect of countermovement in only one velocity condition could mask potentially important differences in other velocity conditions.

• There is a lack of evidence that a bigger difference between force production with and without countermovement is beneficial for athletes. Notably, skiers displayed smaller differences at low velocities, while sprinters possessed the inverse trend and displayed smaller differences at high velocities. These traits may reflect an enhanced capability to build up activation with large inertial loads in skiers, greater tendon stiffness and ability to quickly increase muscle activation in sprinters, and unique force-velocity and force-length capacities in both cohorts.

• Our results suggest sport disciplines might display unique CR at various sportsspecific velocities, which in turn may be trainable. Notably, an inverse relationship between CRF and performance in skiers suggests athlete might benefit from training the mechanisms underlying force production without countermovement at low speeds in tandem to an overall increase in maximum force-production capabilities.

No clear association between countermovement expression and performative level in sprinters existed, however smaller differences at high speeds might be weighted in individualized training progressions.

• Future research is needed on the subject, preferably combined with other tests of athlete capacity, stiffness, and perhaps even muscle structure or length-tension capacities to better understand the reasons for differences underlying CR expression (e.g., global rate of force development).

STRENGTH-ENDURANCE ASSESSMENT IN ALPINE SKIERS: DOES TARGETING SPECIFIC FORCE-VELOCITY CONDITIONS & INTENSITY CHANGE OUR VIEW? 4.3.1. ABSTRACT English

In the sport of alpine skiing, athletes must perform repeated muscular efforts representing alternating turns on a steep course as quickly as possible. Logically, strength endurance draws attention in physical profiling, yet the current stance of its importance is complicated by limitations in methodological design and aging results.

The aim of this study was to explore the importance of strength endurance in high-level alpine skiers using a protocol designed to both: 1) control and target the specific mechanical demands of the sport, and; 2) individualize the testing conditions to skiers' capacities. To this end, the lower-limb force-velocity qualities of 23 national-level skiers from both ski disciplines (N=12 technical and N=11 speed) were tested, after which they performed a recently developed repeated squat jump strength-endurance test. The test was based on very recent research from our group and designed to be as ski-specific as possible-characterized by athletes performing repeated controlled squat-jump repetitions at a set relative intensity (80%) of maximum output, and in high-force lowvelocity ratios (imposed via external loading and a target jump height) individualized per their lower-limb mechanical characteristics. Performance was quantified as maximum repetitions and mechanical work accumulated until exhaustion. Discipline differences were tested using a general linear model, controlling for performance and variation in the testing conditions, and associations with performance were assessed using multiple regression, with maximum force capacity and endurance (total accumulated work) as independent variables. Technical athletes performed more repetitions (F (1,18)

PRELUDE

In the previous chapters, we showed that force output is essential and appears linked with distinct and elevated force capacities. High force in isometric conditions, force at low extension speeds, an ability to build up force quickly and without countermovement are predominant in high-level skiers and may render them distinct compared to other sporting cohorts. However, skiing is characterized by the repetition of force output over many turns. Consequently, if better athletes exhibit specific maximum force output capabilities, logically a capability to perform multiple repetitions at high outputs might enhance our view of high performance. However, like the surrounding body of research, the literature concerning strength endurance is relatively limited and generally does not thoroughly consider skiing-specific force output. Recent collaborative projects have provided promising evidence that a more targeted and valid assessment of strength endurance in skiers might be possible by controlling the relative test intensity and implementing individualized skiing-specific mechanical conditions. As such, the general aims of this chapter were to summarize recently co-authored research on strength endurance, design a ski-specific testing protocol that controls potentially confounding factors, and subsequently test whether it could discriminate between disciplines or performance levels.

Co-authored works associated with this section

INTRODUCTION

In the sport of alpine skiing, athletes must perform repeated muscular efforts representing alternating turns on a steep course aiming to finish as quickly as possible.

While different skiing events present distinct course constraints and require different force-application characteristics (Gilgien, Kröll, et al., 2018), slow rhythmic flexion and extension of the limbs at high levels of force (Alhammoud et al., 2020;Kröll, Spörri, Kandler, et al., 2015) render skiing unique compared to many other sports. The ability to generate high levels of force over a course, and throughout various sections, is associated with better performance (see Chapter 3.1), and so it logically follows that advanced athletes should possess developed strength-endurance capacities.

Performance in repeated movements is directly related to the capacity for acute mechanical power and to maintain its production over time. The power-velocity (Pv) relationship (Bobbert, 2012;Jaric, 2015;Samozino et al., 2012) describes the capacity for power at varying movement velocities, with its edge representing 'maximum'

capabilities. The peak of the Pv relationship corresponds to the absolute capacity for power (Pmax; as a standard measure of maximum neuromuscular dynamic force production (Alcazar et al., 2017;Jaric, 2015)). Everything under the edge of the Pv curve represents submaximal power output (characterized by %Pmax) as varying combinations of force production at different speeds. Power output over time (Pt; see Figure 21) well describes strength-endurance performance and is typically represented in either the maximum time a certain %Pmax condition can be maintained or by using various fatigue indexes (e.g., mean power produced during maximum protocol).

Different combinations of force and velocity output (i.e., RFv, as the ratio of force and velocity parameters to maximum capacities) can result in the same %Pmax and change the characteristics under which repeated movements are performed (e.g., at high speeds and low force, or low speeds and high force). Until recently, the effect of changing RFv was relatively unknown, since in common tests using cycle ergometry movement frequency and velocity cannot be separated (i.e., the faster the athlete pedals [increased movement frequency], the more velocity oriented the RFv), rendering examination of each effect in isolation impossible (frequency of movement changes both rest and contraction numbers (Broxterman et al., 2014;Enoka & Stuart, 1992)). Moreover, for the same %Pmax, a change in RFv can drastically effect the effort relative to maximum capacities (i.e., the mechanical reserve; as %Pmaxv; see Chapter 2.3), and potentially strength-endurance performance (Sargeant, 1994(Sargeant, , 2007;;Zoladz, Rademaker, & Sargeant, 2000). For example, 80%Pmax can be sustained for some time in 'optimal' velocity conditions (i.e., at 50% maximum velocity; vopt, corresponding to 80%Pmaxv), but can only be performed once in very highforce or very high-velocity conditions since they represent the 'edges' of the Pv relationship (i.e., 100%Pmaxv; see Figure 55). The impact and interplay of %Pmaxv and RFv have been recently addressed by our research group (Rivière et al., 2020b).

Figure 55. Power-velocity graphic illustrating mechanical reserve

Illustrated are the maximum capacity of an athlete (black line on the edge of the powervelocity relationship, including maximum power; Pmax), with the dark grey dotted horizontal bar depicting 80%Pmax. The shaded grey area above the dotted line corresponds to the mechanical reserve in various test settings of 80%Pmax. In optimalvelocity conditions (vopt), the test settings represent a true decrement of mechanical capacity (i.e., marker '2', where 80%Pmax = 80%Pmaxv). However, as the velocity of the movement increases or decreases substantially, the mechanical reserve changes: markers '1' and '3' represent conditions where performance at lowand high-velocities (respectively) result in zero mechanical reserve (100%Pmaxv), and essentially no maintenance of power output. tested beforehand (Samozino et al., 2010)), and practically manipulated using external load and targeted jump height (i.e., the push-off velocity (Samozino et al., 2008)). By comparing performance in each condition, the relative contributions of underlying characteristics to performance were tested: different velocity conditions at set levels of %Pmax and %Pmaxv (separately), and at varying levels of %Pmax while controlling velocity.

Subsequently, the effects of %Pmax, %Pmaxv, and RFv on Nrep and Wtot were tested using regression analysis. The findings were that, on average, when controlling absolute movement speed, a large proportion (88.4%) of strength endurance was determined by mechanical reserve (i.e., %Pmaxv, as the position of the conditions relative to the edge of the Pv parabola). However, the underlying mechanical Fv condition still explained a significant proportion of variability (9.1%, corresponding to the variance explained by the low-or high-speed condition for the same %Pmaxv). In general, endurance performance was greater in conditions of lower %Pmaxv (i.e., greater mechanical reserve) and in lower RFv (i.e., higher movement speeds, relative to maximum capacities).

Consequently, it appears that endurance capacity is partially dependent on the underlying mechanical conditions, characterized by RFv, albeit assuming our results apply to unexplored sections of the strength-endurance relationship (only two levels of %Pmaxv were studied). Consequently, strength endurance appears effected by forcevelocity conditions, with the result being a three dimensional strength-endurance profile (power-velocity-time; see Figure 56) rather than the more common two dimensional depiction (e.g., see Figure 21). Simply, assessment of strength endurance is related to the positioning of the underlying settings and therefore, assessment in only one speed, %Pmax, and %Pmaxv condition is likely insufficient.

The results of this initial study were expanded by assessing the contributors to interindividual differences in strength endurance performance. Specifically, our research group (Rivière, Peyrot, Cross, Messonnier, & Samozino, 2020a) sought to clarify whether performance in different velocity conditions was related and test the relative effect of generalized and specific strength-endurance qualities to endurance performance in different conditions. The project tested relationships between the different mechanical conditions at the same relative intensity (85%Pmaxv condition; i.e., horizontally across the Pv relationship), corresponding to three different velocity conditions, referred to here as 'low,' 'medium,' and 'high speed' (see Figure 57). Average strength endurance performance (quantified as the mean repetitions performed across the three different velocity conditions), and the 'expression' of endurance capacities across the three different velocity conditions (i.e., the Nreps at high velocity and high force). Only performances in moderate to high-speed conditions were correlated (r=0.695; p=.008),

with the more disparate markers (low vs. high speed) appearing to diverge in clarity and effect (r=0.231; p=.447). Consequently, strength endurance appears velocity specific, which should be considered within sports-specific tests and the interpretation of results.

Notably, testing strength endurance across distinct Fv conditions, or better over the entire spectrum of possible mechanical conditions, allows the compilation of a complete picture of force-velocity-endurance capabilities. Accordingly, it can be possible to detect athletes who present high strength endurance at rather low or at high velocities, and vice versa.

To summarize the current position, strength endurance appears to vary based on several factors that should be controlled to ensure the results are valid (see Figure 58). These factors include the individual physical attributes and capabilities of the athlete (the external performance construct), the constraints under which the capacities are being assessed (the testing parameters), and the interaction between the two levels. The first level consists of the individual strength-endurance qualities of the athlete, that likely vary between and within sporting codes. For example, alpine skiing is different from other sports in strength-endurance requirements, and the different skiing disciplines might exhibit further specificities (Hydren et al., 2013;Turnbull et al., 2009). Regarding the second level, the specificity of the assessment method is important (i.e., external validity, how similar is the test in general to the sporting construct [e.g., underlying musculature involved]), which encompasses the positioning of the underlying

Strength endurance in skiing

Due to its relatively short duration and high intensity (e.g., 45 sec to 3 min), skiing is generally assumed to be primarily dependent on anaerobic metabolism [START_REF] Gross | High intensity training and energy production during 90-second box jump in junior alpine skiers[END_REF][START_REF] Polat | An examination of respiratory and metabolic demands of alpine skiing[END_REF][START_REF] Veicsteinas | Energy cost of and energy sources for alpine skiing in top athletes[END_REF][START_REF] Vogt | Physiological profile and training requirements of alpine skier[END_REF]. Consequently, anaerobic power is universally acknowledged as important for skiing [START_REF] Ferguson | Limitations to performance during alpine skiing[END_REF] and is a widely proposed and monitored capability for performance (Patterson et al., 2014) and injury [START_REF] Spörri | Course setting and selected biomechanical variables related to injury risk in alpine ski racing: an explorative case study[END_REF]. Consequently, strength endurance in skiing is undoubtedly a crucial factor in performance. Researchers have attempted to characterize the metabolic systems underlying performance during skiing trials with some success (Turnbull et al., 2009), but this does not necessarily offer a practical solution to those wishing to assess and monitor specific capacities in athletes.

Notably, course characteristics and environment influence the expression of force and force-endurance capacities [START_REF] Falda-Buscaiot | Influence of slope steepness, foot position and turn phase on plantar pressure distribution during giant slalom alpine ski racing[END_REF][START_REF] Gilgien | Characterization of course and terrain and their effect on skier speed in World Cup alpine ski racing[END_REF], and are challenging to control. Moreover, even where such tests are possible, it is difficult to compare results from one course to another, and in any case, measurements on-snow represent a technical derivative of athletic performance and do not necessarily offer insight into true physical capabilities. Finally, such testing is costly and impracticalnotably during the off-season valid and reliable measurements of force-endurance can be used to guide training interventions.

Various laboratory and field-based anaerobic power tests have been used in skiers, including cycle ergometry (e.g., 'Wingate variants' (Ferland & Comtois, 2018)), and RSJ [START_REF] Bosco | Evaluation and planning of conditioning training for alpine skiers[END_REF]Patterson et al., 2014). For example, peak and mean power during a

Wingate test were correlated to performance in slalom and giant slalom (stronger in giant slalom) [START_REF] Nikolopoulos | Fitness characteristics of a Greek national alpine skiing team: correlation with racing performance[END_REF], with lower correlations in slalom attributed to the higher technical requirement in the discipline. While there is limited recent data, anaerobic cycle tests are known to generally differentiate between technical (TECH) and speed (SPEED) discipline skiers, with the former producing higher levels of peak power, and the latter producing greater average force in longer duration tests, and so a greater

Criticisms of previous models of strength-endurance assessment in skiers

Compared to more typical sporting circumstances, skiing represents a unique style of force production and endurance, which should influence measurement design.

Numerous skiing specific factors are nearly impossible to model in a controlled manner (e.g., ski technology and unstable surfaces), but the remaining reliable parameters should center on the assessment of underlying specific strength-endurance capacity. It is feasible to approximate involved muscles and muscle actions, mechanical reserve, movement frequency and duration, and the specific mechanical conditions of the exercise (Rivière et al., 2020a(Rivière et al., , 2020b)). Precisely, in skiing: 1) athletes must accurately modulate their output at or close to their maximum, rather than present maximum physical effort at each turn (although untested); 2) the frequency in most disciplines is slow (e.g., 0.6 Hz in giant slalom, see Chapter 2.2) and externally cued (gates), and; 3) the mechanical conditions are oriented towards force production at low velocities with an elongated quasi-isometric phase (Alhammoud et al., 2020). Simply, neither maximum jumping frequency within a given timeframe, nor assessment in moderate velocity conditions (e.g., bodyweight), are likely to represent skiing specific strength-endurance capacity (among other problems resulting from the design of such a test).

Cycling tests of anaerobic output are standard in the skiing literature (Ferland & Comtois, 2018). However, cycling is starkly dissimilar to skiing, with far higher angular velocities of the lower limbs in all-out tests (i.e., non-specific RFv) and divergent muscle actions (i.e., concentric only in cycling). Moreover, since Wingate tests are all-out, variability is induced due to varying movement frequency, RFv, and %Pmaxv. RSJ tests are a popular method of assessing specific strength endurance in alpine skiing athletes in research [START_REF] Bosco | Evaluation and planning of conditioning training for alpine skiers[END_REF]Bosco et al., 1994;[START_REF] Breil | Block training periodization in alpine skiing: effects of 11-day HIT on VO2max and performance[END_REF]Emeterio & Gonzalez-Badillo, 2010;[START_REF] Nikolopoulos | Fitness characteristics of a Greek national alpine skiing team: correlation with racing performance[END_REF]Patterson et al., 2009Patterson et al., , 2014;;[START_REF] Tesch | Muscle glycogen depletion and lactate concentration during downhill skiing[END_REF]White & Johnson, 1991) and in practice (Raschner et al., 2013), with the constraints of the test (e.g., closed chain, isoinertial load) justified as being more specific than other standard tests (Patterson et al., 2014). The seminal 'Bosco' repeated jump test [START_REF] Bosco | Evaluation and planning of conditioning training for alpine skiers[END_REF]Bosco et al., 1994) was a notable attempt to create a simple and more specific example of skiing practice. However, the test suffers from many limitations discussed in the above sections: non-fixed mechanical reserve, variable movement frequency, and mechanical conditions that are unlike skiing (e.g., the angular velocity of the knee during an unloaded jump is ~300 vs. <89°/s in skiing disciplines (Alhammoud et al., 2020)) and probably varies per individual (Rivière et al., 2020a). The lack of consensus from previous tests in the literature serves to support this theory [START_REF] Bosco | Evaluation and planning of conditioning training for alpine skiers[END_REF]Emeterio & Gonzalez-Badillo, 2010;[START_REF] Moritz Von Duvillard | Relationship of anaerobic performance tests to competitive alpine skiing events[END_REF]. Moreover, the current state of the literature may indicate that anaerobic endurance does not strongly differ among athletes of a certain level, or that the results are partially reminiscent of several limitations in methodological design.

More recently, Patterson and colleagues (2019;[START_REF] Gilgien | Characterisation of skiers' mechanics, course setting and terrain geomorphology in world cup alpine skiing using global navigation satellite systems[END_REF] presented an RSJ test that adopted a more specific approach by loading the athletes per unit of bodyweight (20 and 40% for females and males, respectively), and having the athlete perform jumps at a specific tempo. This test solves some limitations of previous iterations by targeting and controlling the tempo and placing the test in lower-velocity RFv conditions. However, while targeting force-dominant conditions via weighting athletes is commendable, loading selection based on bodyweight does not normalize the assessment per individualized mechanical conditions (i.e., %Pmaxv and RFv) (Morin, Jiménez-Reyes, et al., 2019). This means that athletes might perform the test in different mechanical conditions, which might bias performance, depending on the profile of the individual (Rivière et al., 2020a). Moreover, in longitudinal monitoring, performance changes might not be associated with strength endurance but instead be a product of a shift in underlying expression of force-velocity capacity (i.e., a more force or velocity-oriented profile, without a change in underlying strength-endurance capacity). As such, actual results might be obscured by either differing exercise intensity relative to the individual's maximum capacity or the interplay with the athlete's force-velocity balance.

Article placement and aims

A persistent problem with previous strength-endurance assessments is that neither %Pmaxv nor RFv are fixed-both of which affect strength endurance in isolation (Rivière et al., 2020b), are specific to the individual's mechanical profile, and performance in a particular condition only appears related to performance in similar conditions (Rivière et al., 2020a). The strength-endurance profile appears to be three-dimensional (see Figure 56), and in the best case, should be assessed as the 'volume' of the curve between acute Pv and Pt capacity. However, no such test exists in the literature at present (Rivière et al., 2020a). A single assessment could provide useful information into specific strengthendurance capacity, provided the underlying test settings (RFv and %Pmaxv) mimic sports performance and are controlled based on the individual's expression of Pv characteristics (Rivière et al., 2020a). In this manner, strength endurance is defined as the ability to maintain a given relative force and power production (i.e., a given 'fraction' of maximal capacities) instead of maintaining total output over time. While the latter might be more specific to the field (e.g., models the ability to maintain elevated force production during turning or over an entire run), there would be no possibility to distinguish the relative contributions of higher maximal capacities (inducing higher mechanical reserve for a given absolute power) from a higher ability to maintain power over time; we aimed to distinguish these two factors.

We developed an RSJ protocol designed to be skiing specific by manipulating the underlying %Pmaxv and RFv constraints and subsequently standardizing them to the mechanical capacities of each athlete. Using this test, the aims of this work were to: 1) attempt to differentiate between skiing disciplines (TECH and SPEED), and; 2) test the relationship between strength endurance measured via the test and performance. A tertiary aim of this work was to provide commentary on the practicalities associated with strength-endurance assessment into high-level sporting practice, with some information on the possible specificity of such a test to skiing and other sports. Considering the sportspecificities (i.e., duration, force production levels), we hypothesized that SPEED athletes should display a better capacity for strength endurance than TECH skiers and that maximum force and strength endurance would be associated with higher performance in both disciplines.

METHODS

Participants

A range of national-level ski athletes hailing from all focal disciplines participated in this research (male, N=23, age, 24±5 yr; body mass, 83±7 kg; FIS, 22±11 pts). Athletes were free from injuries that would impact their ability to participate and provided written consent. All operational procedures were performed following the University Savoie Mont Blanc and the World Medical Association (Declaration of Helsinki).

Study design

The testing presented was the last in a ~1.5 hr session, preceded by Fv profiling in squat jump and countermovement jump, and isometric mid-thigh pulls. The RSJ test followed ~30 mins of rest, which allowed sufficient recovery based on pilot data and measurements of pre-test blood-lactate levels (N=6, mean ~1.5 mmol/L).

The movements were universal and regularly used as part of conditioning; however, athletes were habituated to the RSJ procedures before the testing battery (described in detail below). The athletes' performance level was defined as their world-standing in their best event, as published in the 9 th annual list from the FIS. For comparisons between disciplines, athletes were separated into TECH or SPEED depending on which event the athlete was best ranked (e.g., lowest standing in downhill = SPEED). around a ~90° knee angle [START_REF] Garcia-Ramos | Force-velocity relationship in the countermovement jump exercise assessed by different measurement methods[END_REF]Janicijevic, Knezevic, Mirkov, Perez-Castilla, Petrovic, & Garcia-Ramos, 2019;Janicijevic, Knezevic, Mirkov, Perez-Castilla, Petrovic, Samozino, et al., 2019), and subsequently regulated using the safety supports of the power rack and thin rubber wedges where necessary. For each SJ, athletes slowly descended until the bar was slightly above the rack supports, paused with the load for 3 sec (verbally cued), and then jumped with maximum intent without countermovement. One or two jumps were performed at each load with ~15 sec rest, and 3 to 5 min passive rest was allowed between each load. Five or six sets were performed in total, with poor trials removed (i.e., those lacking good jumping technique, or unrealistic according to linear fit of the Fv profile) and the highest jumps from each load used for the final analyses.

Procedures

Endurance profile

Strength endurance was assessed using a variant of the RSJ protocol proposed and discussed at length by Rivière and colleagues (2020;2020a, 2020b). Since assumingly ballistic capacities (i.e., rate of force development) are still crucial for skiers (e.g., see

Chapter 3.1), we selected testing during an SJ since other squatting variants do not feature force output with maximum intent across the push-off period. Moreover, by requiring athletes to control the descent and pause in isometric contraction at the bottom of the squat, the muscle actions somewhat model those performed during skiing (Alhammoud et al., 2020): steering phase in the isometric pause, completion in the eccentric landing, transition in the flight time (i.e., period of low activation), and the turn initiation (and perhaps late steering phase (Kröll, Spörri, Kandler, et al., 2015)) in the concentric push-off. The order and length of each action can be challenged and are discussed later in this chapter.

During the test, the aim was to attain and maintain a targeted jump height of 0.10 m, under a loading condition that represented 80% of the maximal power that can be developed at the corresponding mean push-off velocity (80%Pmaxv; see Figure 59). The value of relative intensity (mechanical reserve) was determined from piloting, where athletes performed activity for roughly the duration of a TECH ski race (~1 min). While the duration was somewhat shorter than SPEED events, both the comparative aims of this investigation and the additional time to implement a separate testing protocol rendered the use of one assessment preferable (note: this limitation is discussed later in this chapter). This approach was chosen in place of dictating testing duration or Nrep due to the limitations inherent in all-out style tests (discussed in Section 4.3.3.3). Moreover, it was assumed that unlike such tests, a threshold assessment where athletes must regulate their output and finish in maximum conditions was assumed more ecologically valid to ski racing. The mechanical conditions of the test (i.e., RFv) were set via a targeted push-off velocity to ensure mechanical conditions like skiing (i.e., high force with low angular velocities at the knee/hip (Alhammoud et al., 2020)) within the constraints of test accuracy. Specifically: 1) the jump height was fixed at 0.7 m/s (corresponding to 0.10 m, as the lowest jump height athletes could reliably produce (Morin & Samozino, 2016)), and the external loading was selected to result in the appropriate mechanical reserve per the corresponding push-off velocity (80%Pmaxv).

Athletes self-regulated their effort aided by immediate feedback of jump height displayed on a screen set at eye level. Athletes performed jumps at an average frequency of 0.33±0.01 Hz, which represented 2.5 sec of quasi-isometric (i.e., eccentric followed by isometric) state between jumps after correcting for push-off and flight time (individualized per hpo). The movement was cued by a metronome, on the signal of which athletes jumped, landed (descended smoothly), and rested in an isometric position in the lowest position of the SJ until the proceeding beep (see Figure 60). The instruction was to maintain the targeted jump height (and so power) for as long as possible, within the performance constraints outlined. Athletes were monitored and encouraged throughout, and the test was ceased when a substantial drop in performance was observed (i.e., three jumps >5% below targeted height). Raw jump height and frequency data were extracted using the manufacturer software for treatment. Blood Jump height was measured via an optical system (model: OptoJump Next, Microgate, Bolzano-Bozen, Italy), placed within the footprint of the squat rack. These gates were placed inside the footprint of the squat rack and connected via cable to a laptop, operated by the researcher adjacent to the setup. The laptop was connected to an external screen placed on a platform directly in front of the athlete, which provided live measurements of jump height for feedback during the endurance test so athletes could regulate and cue their subsequent efforts. Jump height, contact, and flight time were exported via the manufacturer software in raw text format for analysis. Blood was drawn using a lancet, and lactate concentration was measured using a portable analyzer (model: Lactate Pro 2, LT-1730, Arkray, Kyoto, Japan).

. Jump analysis and force-velocity profiling

Using a validated method (Samozino et al., 2008) based on the calculation of lower-limb output using jump height, anthropometric measurements, and external loading conditions. During the push-off phase, average power (P), force (F), and velocity (v) were calculated as

Eq. 16

𝐹 = 𝑚 tot • 𝑔 • ( ℎ ℎ po ⁄ + 1)
Eq. 17

𝑣 = √ 𝑔 • ℎ 2 ⁄
Eq. 18

𝑃 = 𝑚 tot • 𝑔 • ( ℎ ℎ po ⁄ + 1) • √ 𝑔 • ℎ 2 ⁄
with mtot as the total mass (body mass [bm] + external load), and g gravity ( 9.81 m/s/s).

Subsequently, individualized Fv relationships were generated by fitting jump data with linear least-squared regressions. The maximum output of the lower limbs was characterized by the intercepts of the Fv relationship as maximum force (F0) and velocity (v0), and maximum power (Pmax) as Eq. 19

𝑃 max = 𝐹 0 • 𝑣 0 4 ⁄ 4.3.4.5.2

. Endurance profile

The computational approach for this method is explained at length elsewhere [START_REF] Rivière | Effet des conditions mécaniques d'exercice sur les capacités de production de force des membres inférieurs lors d'extensions acycliques uniques et répétées[END_REF]. Briefly, the targeted mechanical conditions for the RSJ protocol (practically, additional load, and the targeted jump height) were obtained using individualized Fv variables and applying fundamental laws of dynamics (Samozino et al., 2008). Since jump height was fixed (hRSJ=0.1 m), averaged push-off velocity for the endurance condition (vRSJ) can be estimated using Eq. 17, as equal to 0.70 m/s. Knowing the individual Pv relationships and following the calculation of Pmax, and the necessary decrement for the RSJ performance (PRSJ=80%Pmaxv), the external loading necessary to evoke the targeted mechanical conditions (mRSJ) can be calculated as:

Eq. 20

𝑚 RSJ = [ (𝑃 RSJ 𝑣 RSJ ⁄ ) 𝑔 • (ℎ RSJ ℎ po ⁄ ) + 1 ⁄ ] -𝑏𝑚
The individualized mechanical conditions for the testing were represented in the Fv ratio (RFv), calculated as:

Eq. 21

𝑅 𝐹𝑣 = (𝐹 RSJ 𝐹 0 ⁄ ) (𝑣 RSJ 𝑣 0 ⁄ )
with FRSJ representing the targeted force output per-repetition of the RSJ protocol, as calculated using Eq. 16, h as hRSJ, and mtot as bm+mRSJ.

Post-test, raw values (h, Hz, and time) were extracted and analyzed in Microsoft Excel (model: Microsoft Office 365, Microsoft, IBM, USA). Test completion (i.e., exhaustion and test cessation) was defined as an inability to perform three consecutive jumps above 95% of the targeted jump height [START_REF] Rivière | Effet des conditions mécaniques d'exercice sur les capacités de production de force des membres inférieurs lors d'extensions acycliques uniques et répétées[END_REF]. For each repetition of the test, mechanical variables were calculated using Eq. 16, Eq. 17, Eq. 18, and mechanical work per repetition (W) was calculated as:

Eq. 22

𝑊 = (𝑚 tot ) • (ℎ po + ℎ)
where each variable constitutes that determined during the RSJ test: mtot is equal to mRSJ+bm, and h is hRSJ. Strength-endurance performance was calculated as the total number of repetitions performed (Nrep) and the total cumulated work (Wtot=W•Nrep) performed by the athlete in the repetitions preceding cessation (in both absolute and normalized to body mass). The coefficient of variation of h (CVh) was calculated as a representation of the capability to repeat targeted muscular output in the given RFv conditions accurately.

Statistical analysis

Data were processed using the open-source statistical software JASP (version: 0.12, JASP Team, Amsterdam, Netherlands). Descriptive statistics are reported as means ± standard deviation.

Differences in discipline-specific strength endurance were assessed via a general linear model with standings, RFv, and the interaction between standing and discipline as covariates in the model (Leppink, 2018). Model effects were reported using omegasquared (ω 2 ), with contrasts to provide the difference and directionality of the comparisons between the disciplines.

To further explore the association between strength-endurance ability and performance for each discipline, two multiple regression models were performed with standing as the dependent variable and a model containing maximum capacity and strength endurance (F0 and Wtot). The regression analyses were performed on the full group and each cohort separately. For each model, standardized beta (β), F, model R 2 (adjusted), and p-value were reported. In addition, Spearman's rho (rs, p-value) non-parametric correlations were used to test the association with effort variability (CVh) and discipline-specific performance since there was a trend for voided normality (Shapiro-Wilk=0.865, p=.067).

Quantitative thresholds were applied to the various effect sizes to provide a qualitative interpretation of effect: ω 2 <0.01, 0.01, 0.06, and 0.14;and rs<0.1, 0.1, 0.3, 0.5, and 0.8 as trivial, small, moderate, and large, respectively (Hopkins et al., 2009). The alpha value for all tests was set at p=.05, with p<.1 considered as a trend towards a clear inference.

Sensitivity analyses were performed using the sample size estimation software (G*Power [START_REF] Faul | Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses[END_REF]) to determine the approximate threshold of detectable effect for each statistical model and associated sample size (see Figure 61).

Figure 61. Sample size plots

The two contour plots presented here depict the sensitivity of the utilized statistical models, with a Type 1 error rate of α=.05 and 80% power. Plot A exhibits that within the General Linear Model and N=23 we can reasonably detect a large effect (ω 2 =0.075); Plot B exhibits that within the group multiple regression model and N=23 we can reasonably detect R 2 >0.37. For the multiple regressions within TECH and SPEED, we can reasonably detect R 2 >0.6 and 0.64, respectively. Note that when separating the disciplines, the magnitude of effect needed to attain power is substantial.

RESULTS

On average, athletes performed 21±7 repetitions, which corresponded to a test length of 64±20 s of work performed, with a blood-lactate accumulation of 8.42±1.46 mmol/L. , p<.001; N, number of athletes; SD, standard deviation; diff, the difference in raw units; CI, 95% confidence intervals; ω 2 , omega-squared effect size; RFv, ratio of force-velocity conditions to maximum capacity during test; cells demarcated with a '-' correspond to effects of <0.001; Nrep, number of repetitions performed in test; Wtot, total cumulated work performed during protocol; J, joules; qualitative thresholds for the magnitude of omega squared effect sizes ω 2 <0.01, 0.01, 0.06, and 0.14 as trivial, small, moderate, large, and very large, respectively.

DISCUSSION

An RSJ protocol designed to target underlying conditions of skiing while controlling for confounding factors detected significant differences between disciplines and created models of absolute capacity and strength endurance that were associated with performance. Notably, maximum force-production capacity rather than strength endurance appears more associated with performance among high-level athletes.

However, when examining the various interactions between strength-endurance characteristics and standings, it is apparent that the results are somewhat indicative of limitations in methodological design and should be viewed critically. As such, while the methodological basis and justification for this study design were strong, its results evidence the critical need for further research to understand the appropriate strengthendurance capacities for skiing disciplines: Is one test sufficient to understand important determinant capacities, or are more complex designs necessary? The information associated with answering such a question would be invaluable and subsequently drive the design of more specific testing modalities for ski racers.

Discipline differences

There were differences in the test in Nrep and Wtot normalized to body mass, with SPEED athletes presenting lower values than TECH in both variables. However, in absolute Wtot, no clear differentiation between disciplines existed. In the first instance, the lower Nrep and relative Wtot is not entirely surprising since these variables do not directly account for the greater repetition-by-repetition work produced by SPEED athletes on average as a product of their overall greater force capacity. Moreover, in the models for both Nrep and relative Wtot there was a large-very large effect for performance, showing that better athletes performed fewer repetitions and less relative work, and a large interaction effect with discipline, indicating that effect was unequal for SPEED and TECH. Neither of these factors was observed for absolute Wtot, which accounts for the higher outputs of athletes. The implications of this are essential for interpreting test results and weighing various methodological interactions for future workboth are discussed in detail below.

As described in Chapter 4.1, better skiers from both cohorts possess greater maximum dynamic force-output capacities and an associated elevated and more 'force-oriented'

force-velocity profile. A consequence of higher-level athletes exhibiting greater forceproduction capacity at lower speeds is that they performed the RSJ test in conditions of higher force. Since velocity was fixed (i.e., per average push-off velocity), greater average force per-repetition resulted in greater power per-repetition, which was subsequently associated with shorter test duration (additional analyses, rs=-0.888, p<.001). The interindividual variability between capacity for power and strength endurance is well known, with athletes with dominant explosive capacities (e.g., sprinters) possessing both dominant power production and lower critical power than those specializing in events focusing on endurance [START_REF] Vandewalle | Standard anaerobic exercise tests[END_REF][START_REF] Vuorimaa | Comparison of three maximal anaerobic running test protocols in marathon runners, middle-distance runners and sprinters[END_REF]. It is a well-known phenomenon that athletes who produce higher average power output fatigue faster [START_REF] Lievens | Muscle fiber typology substantially influences time to recover from high-intensity exercise[END_REF], which can be interpreted as either powerful athletes typically possessing lesser endurance qualities, or more powerful athletes developing higher power during the test (in all-out or relative conditions) and consequently scoring lower in such tests. Both factors, but notably a greater capacity for power during the test, likely explain the reduced test duration in higher-level SPEED athletes and the non-discriminant nature of Wtot.

Test association with performance

In general, the linear regression models showed that the maximum capacity for force production explained a much greater proportion of performance than strength endurance. This was particularly emphasized in SPEED athletes, where a very large proportion of standings were explained by the model (73% variability explained), with essentially no contribution of strength endurance. While these findings should be tempered by limitations in the methodological approach, nevertheless information suggest that accruing large maximum capacity for maximum force production is of greater importance to high-level skiers than being able to maintain a given percentage of that maximal force for an extended period. Accordingly, the test assesses the capacity to maintain a relative percentage of maximum capacity (characterized by %Pmaxv); as such, athletes who possess a greater capacity for power production (and force production at low speeds, per the interaction between RFv and %Pmax) might still perform better on the field if the muscular output required from them is absolute (imposed by the setting of gates, or the interaction between the skis and snow). A greater maximal capacity induces a higher mechanical reserve for a given absolute force or power, and so a higher overall performance (or average force production) over time at this absolute intensity. In other words, two athletes with different F0 and the same strength-endurance capacity performing the same turn (at the same velocity) will do so at different levels of their %Pmaxv: in such a case, the athlete with a greater capacity for maximum dynamic force at low speeds would be at an advantage, due to performing with a higher mechanical reserve. Moreover, in the previous example, the athlete with the greater capacity can perform the turn at a higher velocity (i.e., at greater levels of force) for the same relative level of their mechanical reserve. In tandem with a more complete exploration of strength-endurance capacities, an idea for future tests might be to set athletes in absolute conditions relevant to that expected in the field-albeit the settings fo which currently lacking a strong empirical basis. In any case, a strength-endurance test in such a setting might better mimic on-field performance but would prevent the separation of the relative effects of a higher mechanical reserve (and so higher maximal capacities) from what is due to a higher ability to maintain a given fraction of this maximal capacity over time (which can be the exact definition of strength endurance).

At this time, the answer to such a problem is, unfortunately, unclear.

Another possible explanation is that despite indirectly controlling RFv via the velocity condition of the test (i.e., to represent the most force-dominant condition possible), there was variation in intra-athlete mechanical conditions of the test (RFv=2. 40±0.49, range=1.76-3.34). Notably, while group means of RFv were similar (2.36±0.57 vs. 2.44±0.41, for SPEED vs. TECH, respectively), the data were slightly skewed towards more forcedominant conditions in SPEED athletes (skewness=0.7 vs. -0.156 for SPEED vs. TECH, respectively). Consequently, the negative relationship between Nrep and standing can be explained, in part, by SPEED athletes with higher standings performing the test in greater RFv (rs=0.44, p=.037) (Rivière et al., 2020b). Notably, slight biases in RFv with more force oriented SFv would compound the imbalance caused by greater absolute maximum force capacities. This would lead to even greater power-per-repetition and amplify the hastened fatigue of higher-level athletes, even if the relative effect of RFv is relatively small compared to mismatches in mechanical reserve (i.e., 9 vs. 88% variance explained in strength-endurance performance, respectively). Instead, assuming a baseline level of anaerobic and aerobic capacities in conjunction with perhaps an acutely elevated force skiing events (e.g., 2.5 min for DH (Patterson et al., 2014)). In any case, while we had strong justification upon which to set only one condition for all athletes, the mechanical conditions expressed in this test may be positioned within the incorrect region of the strength-endurance profile for either or both disciplines. Since disparate regions of the strength-endurance profile are not related (athletes who perform better in one area are not necessarily those who perform better in another) (Rivière et al., 2020a), there is interest in a more encompassing view of strength-endurance performance in skiers. For example, this test does not provide information regarding the critical power of the athletes [START_REF] Poole | Critical power: An important fatigue threshold in exercise physiology[END_REF], and it is possible that aerobic capacities, rather than anaerobic capacities (or a combination of the two), might be a differentiating factor for skiing performance in the disciplines. As such, while outside the purview of this work, it would be interesting to investigate the design of discipline-specific testing protocols to provide a clearer and more specific picture of performance within each discipline.

Limitations and future perspectives

RSJs have several changeable constraints that can be manipulated to improve sports specificity (Rivière et al., 2020a(Rivière et al., , 2020b)). Several factors make them a good candidate for assessing skiers since they approximate skiing motion and key muscle-action similarities [START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF]Patterson et al., 2014). However, the movement and associated assessment method itself has three main limitations: 1) the lack of an emphasized loading during the isometric period at high angles (Alhammoud et al., 2020;Kröll, Spörri, Kandler, et al., 2015); 2) the lack of capability to assess RFv conditions <0.7 m/s; 3)

the balance and order of each 'jump event' is somewhat disconnected from that observed during skiing (e.g., the flight phase corresponds to turn-switch, yet lasts for a much shorter time than the low-activation period in skiing [START_REF] Alhammoud | Contribution à l'analyse de l'activité neuromusculaire des skieurs alpins d'élite lors de tests isocinétiques et en conditions réelles d'entraînement[END_REF]). Moreover, several limiting factors are associated with loaded jumping itself. Notably, skiers do not necessarily aim for explosive triple extension during turning [START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF], and overloading the lower limbs is performed via a barbell carried on the back. The latter case is notable due to its stark dissimilarity to skiing (i.e., loading constraints are experienced from the ground up), and may have induced error into our results; specifically, stronger athletes (notably, SPEED) presented very high F0 values and subsequently required very high loading to attain the mechanical conditions required for the testing. Despite normalization to Fv characteristics, the resulting assessment duration might have been a combination of lower-limb and upper-body strengthendurance characteristics. Unfortunately, these limitations are integral to the design of the RSJ test and might require the use of specialized ergometry if they are to be overcome. While it would undoubtedly decrease the practicality of such a test, there might be interest in the development of specialized testing ergometry for alpine skiing strength-endurance assessment, or integration of existing technologies into novel testing scenarios (e.g., the 1080 Quantum, or similar devices).

Since blood-lactate measurements were performed following the cued cessation of the test (after an evident decrement in capability and inability to attain the desired jump height), the measurement includes jumps that were not subsequently included as part of the test. This number is typically similar between athletes (~3 jumps) but can be neither avoided nor strictly standardized. As such, the blood-lactate readings include some error as a product of representing a minor amount of additional work performed by some athletes in conditions outside of that accounted for in the test.

During the test, athletes rested in an isometric position between each jump that was selfselected (around the desired angle, approximately 90° knee angle) (Janicijevic, Knezevic, Mirkov, Perez-Castilla, Petrovic, & Garcia-Ramos, 2019) as that which they felt most comfortable to maximize jump height. Consequently, the test may bias athletes who selected an angle that inadvertently put them in an advantageous kinematic position during the isometric phase (i.e., reduced moment arms at the knee and hip). Due to variability in the length-tension relationship, the best starting position to jump high is probably not the best position for every person to sustain isometric contraction for more extended periods [START_REF] Boyas | Influence of exercise intensity and joint angle on endurance time prediction of sustained submaximal isometric knee extensions[END_REF].

During the RSJ, athletes self-regulated their squat depth using the cues of lightly touching the rack and then raising slightly and staying in isometric contraction. While in all cases the method was standardized as much as possible, a better approach would be a non-rigid system the athletes could touch and then subsequently perform a squat jump without potential interference or assistance from contacting the racks. Notably, future researchers might consider integration with depth feedback, such as a linear position transducer or laser system (Fessl et al., 2020), where the athlete receives a clear signal when they reach the correct depth.

CONCLUSIONS

The schedules of skiers are notoriously limited [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF], highlighting the importance of valid and accurate assessments of athletic capability on which to orient training and monitor determinant capacities. We developed a specific testing protocol to improve the assessment of specific strength-endurance capacities for skiers. The subsequent protocol resulted in SPEED athletes performing shorter duration test and better-ranked athletes performing shorter durations than their lower-level counterparts.

When strength-endurance was presented as total cumulated work, there were unclear differences across disciplines and with performance. The most likely explanation for our results would appear to be the fact that better athletes typically performed the testing in conditions of greater absolute power, and the underlying mechanical settings were not representative of skiing performance (notably, SPEED). As such, our results rather evidence the complexity in assessing relevant strength-endurance capacity in alpine skiers and provide some evidence upon which future investigations might build to create more specific assessments for skiing performance assessment.

Lastly, while unlikely, it is possible that in this cohort of high-performing skiers'

anaerobic strength endurance as measured in RSJ is not a clear contributor to success.

While literature typically supports its importance (Hydren et al., 2013;Turnbull et al., 2009), predictive analyses on this topic often unveil complicated or seemingly nonpredictive results [START_REF] Nilsson | Aerobic variables for prediction of alpine skiing performance -a novel approach[END_REF][START_REF] Patterson | The 2 minute loaded repeated jump test: Longitudinal anaerobic testing in elite alpine ski racers[END_REF]Patterson et al., 2014)-although, as discussed early in this chapter these studies suffer from similar limitations. In any case, future research is needed to explore the bounds of this relationship, notably exploring the full three-dimensional nature of the strength-endurance relationship with the aim of better characterizing its determinant nature in alpine skiers.

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PERSPECTIVES, PRACTICAL APPLICATIONS, & CONCLUSIONS

5.1. PERSPECTIVES

SUMMARY OF THESIS TAKE-AWAYS

In context with the surrounding literature, this thesis provides answers (full or partial)

to the questions listed below. The answers here are simple and summarize the lengthy discussions and conclusions within each experimental chapter:

Is minimizing energy dissipation (i.e., maximizing speed) more important than path length to giant slalom skiing performance?

Broadly, yes. Confirming the findings of previous work, gaining and maintaining a high course speed exceeds the predictive quality of basic trajectory parameters. However, in some sections (i.e., flat), there appears to be no clear relationship between these factors and performance. Moreover, while used as a somewhat blanket finding for skiing, these analyses need repeating in other events (notably, super-giant slalom and downhill).

Are higher forces related to better skiing?

Yes. Better course performance, defined as either less energy dissipation during turns or course time, is ubiquitous with increased force production in the radial direction. High radial force production can be divided into general 'physical' capacity (higher total force developed by lower limbs onto the skis and snow), and an ability to apply a more significant proportion of that effectively (i.e., radially, technical effectiveness)-both are generally equally important. However, their hierarchy can change depending on the section of the course examined.

Is the balance between the limbs in force production meaningful for better skiing?

Probably. Synthesizing our findings with the surrounding literature, the balance between the limbs seems to vary as a function of the turn approach (increased radial force/acceleration, increased inclination, increased force applied to inside ski). However, to increase total force output, one first increases the output of the outside limb and then applies proportionately more to the inside limb. Feasibly, an athlete with a higher total 5.1. PERSPECTIVES force production expressed on the snow will ski better, and such an athlete might possess a better force-production capacity with the inside limb.

Do better skiers possess specific lower-limb force-capacities?

Yes. Higher-ranked skiers generally possess an absolute maximum force-oriented profile of the lower limbs. This disposition toward 'force-dominance' encompasses both dynamic force at low speeds, isometric force, and a capacity to develop force quickly.

Because these characteristics differentiate skiers from other sporting codes (e.g., sprinters), in addition to being increasingly prevalent with better and typically older skiers, we assume that they represent distinct longitudinal adaptations from the sport.

Notably, no 'moderate' velocity measurements (i.e., maximum power or jump height)

clearly separated better athletes from their counterparts.

Do skiers present different lower-limb force capacities compared to athletes from other sports?

Yes. Compared to sprinters, skiers present a lower-limb force profile oriented towards production at lower extension speeds. Absolute force capacity at low extension speeds, not relative or at moderate to high velocities, appear prevalent in skiers.

Do unique force capacities characterize alpine skiing disciplines?

Yes. Both disciplines demonstrate high-force muscular capacities, with sizeable intraathlete variability. Speed and technical skiers appear to differ primarily in their dependence on absolute dynamic and isometric force, with speed athletes possessing superior values across both qualities, but notably the latter. Technical athletes seem reliant on dynamic force output at low speeds, isometric force, and rate of force development (notably, without countermovement), which aligns with the faster and more cyclical turns observed in vivo. On the other hand, better speed athletes generally possess both elevated low-velocity and isometric force qualities, which is logical considering the possible long-term adaptations associated with both their skiing discipline and the coinciding event-specific strength training.

Does countermovement provide additional explanatory information on forceproduction capabilities for skiers?

Yes. The countermovement effect is velocity-and individual-dependent, and as such, profiling force production with and without countermovement can provide discriminatory information. Since it can differentiate different athletes (e.g., sprinters vs. skiers) and different performative levels, it might be interesting for profiling purposes.

Specifically, a smaller countermovement effect on force production at low speeds (higher force) in tandem with a greater overall maximum dynamic force capacity appears predictive of better skiers. Note that a high countermovement effect is instead the sign of a poor squat jump performance than a high countermovement jump ability: the smaller countermovement effect at low speed of skiers results from high forceproduction squat jump in these conditions.

Can we test skiing-specific strength-endurance capabilities, and do they differ between discipline and performance levels?

Probably, but more research is needed. It is possible to design and implement a highly standardized and specific testing protocol for skiing using repeated squat jumps by manipulating various parameters and underlying mechanical conditions. Our results might indicate that among high-level skiers, the differentiating factor was instead an absolute capacity for force production, rather than strength endurance (i.e., a capability to maintain a given % of maximal capacities). However, this thesis evidenced that more research is needed to characterize strength-endurance performance accurately and subsequently select the appropriate assessment parameters for disciplines. As such, while our findings indicate potential differences between disciplines and competitive levels, unfortunately, the design of our test had notable limitations that confound conclusions. As research associated with this project indicated, the relevance and specific assessment of strength-endurance parameters for skiers is a critical topic for future research.

SUGGESTIONS FOR FUTURE RESEARCH

The thesis has presented several questions and investigative avenues for future research:

• To what degree is an athlete limited by their force production while skiing in competition?

More specifically, is an athlete who presents higher force capacities (i.e., greater force during a targeted lab or field test) also producing a higher force during skiing? • What is the full power-velocity-endurance spectrum of skiing athletes from various skiing disciplines and events? Once the correct parameters are elucidated (i.e., from a threedimensional profile of power-velocity-endurance capacities), can we design a specific test battery to detect meaningful differences in strength endurance between athletes of different levels and from different cohorts?

• Do any of the variables above in this study provide value for injury prevention or return-tosport practices?

REFLECTIONS

As the results of several previous studies and practical evidence would support, the relationship between physical profiles and skiing performance is complicated. In this thesis, we detected several meaningful inferences regarding the influence of force output and capacity on performance, including acute and macroscopic views of performance and comparison between disciplines and other sports. Nevertheless, while scientific rigor dictates focusing on specific factors while controlling interactions, discoveries are inevitably reintegrated within a complex and multi-factorial environment. Further clarification of the importance of various force capacities for skiers (e.g., by performing on-and off-snow assessments on the same athletes), and subsequently training nestled within the competitive environment, would help ground these results in practice.

Technology

Technological constraints inevitably limited this project. Experimental Theme 1 features sport GNSS units as the primary technology for collecting trajectory data. Previous research has indicated promise for GNSS technology in the field of alpine skiing (Supej et al., 2020), albeit confounded by a host of factors that can reduce the usability of data (Gilgien et al., 2014). It was for these reasons that Experimental Theme 1 (Chapter 3) featured the comparison of the core GNSS to more advanced technology (Section 3.2).

While the results from this nested validity study were hopeful, the higher-level RTK system used as the criterion in these analyses has not been explicitly validated in alpine skiing. At the same time, while similar systems provide small error (Root Mean Square Error <5 mm) in rudimental analyses (Valente et al., 2020), more advanced systems provide very accurate measurements of skiers (Supej, 2010), and the quasi-validity comparison of our kit-set unit to a known ground-track plan on a repeatable track indicated validity might be expected, future research might consider the validation of similar low-cost RTK units in the field. Consequently, while a turn-averaged approach was adopted to account for potentially increased error, the kinematic data provided in Sections 3.1 and 3.2 should be interpreted with this in mind. Nevertheless, the potential for low-cost kitset RTK units to provide incredibly accurate trajectory profiling in skiing previously only accessible with incredibly complex and costly setups is encouraging for the future.

In this thesis, a portable mid-thigh pull device was used to measure maximum isometric force and rate of force development. In general, these types of devices are relatively contemporary, and consequently, there are few reports of their validity. Those that exist typically use simple designs (e.g., wooden base plates and 'crane scales' (Dobbin et al., 2018;Till et al., 2018)) or feature relatively low sampling rates (e.g., 100Hz (James et al., 2017)). In general, researchers have typically only examined maximum force, of which the results have been decisively positive (e.g., high agreement with criterion measurements, albeit with some systematic bias (Dobbin et al., 2018;James et al., 2017;Till et al., 2018)). However, rate of force development has either remained unreported (Dobbin et al., 2018;Till et al., 2018) or has not attained validity compared to force-plate systems (i.e., ICC≤0.7, CV≥8.8% (James et al., 2017)). While our system features several

PERSPECTIVES

clear improvements compared to previous designs (e.g., higher sampling rate and a nonelastic tethering system) and was implemented on higher-level athletes (national and international level strength-trained), we were unable to directly assess its validity for detecting rate of force development during the tenure of this project. Consequently, the rate of force development data presented in this thesis should be interpreted as preliminary until validation of this specific system is performed and published.

Characterization of performance

Following in the path of previous studies (Turnbull et al., 2009), FIS points (or standings, as determined by event-specific FIS points) were used to represent the competitive performance level of athletes. While FIS points invariably provide a valid measure of macroscopic athlete level, they encompass accrued performance across multiple seasons influenced by various factors (e.g., tactical decisions regarding race participation, other athletes participating in a given race, and starting order). For these reasons, FIS points and standings are not necessarily representative of the real and current athletic performance. Consequently, while efforts were made to ensure that the best data representing athlete conditions were taken (i.e., race data from the closest time-point to the field tests), the lack of a more direct measurement of 'on-snow' performance stands as a limitation of the results of this work. A more salient approach might be to directly assess athlete performance within the field, within the same epoch as assessing neuromuscular function. A few researchers have adopted this approach, using course time to represent performance (R. E. [START_REF] Andersen | An onsite test battery to evaluate giant slalom skiing performance[END_REF]. However, since time provides limited descriptive information regarding athlete performance intricacies (discussed in Sections 2.1 and 2.2), integration with more nuanced variables would invariably enhance analyses. Of note, the original aims of this thesis included such assessments, but pivotal disruptions in the athlete schedules during the 2019-2020 season caused by COVID-19 rendered it impossible.

Discipline bias and age

Performance in TECH and SPEED is quantified in basically the same way: macroscopically, as standings or FIS points, and within races, as time from start to finish of a course. However, where the course layout changes each event in TECH events (although the same slope may be used for recurrent years per specific races), in SPEED there is much less variation in course setting (as discussed in Section 2.1). Specifically, a combination of the global limit of courses able to hold full-length SPEED events (notably, DH) and course-setting regulations result in relatively consistent gate placements in SG and DH across the years. Ergo, older and more experienced athletes boast accrued slope familiarity compared to younger athletes with limited experience on the alpine skiing circuit. Moreover, even in the Europa Cup, athletes ski shortened and reduced difficulty versions of that on the World Cup circuit. Younger athletes (e.g., those primarily competing in FIS events) have little to no access to the slopes performed at the Europa and World Cup level.

Consequently, where one might argue that performance in TECH events relies more on technical and tactical flexibility (i.e., the capability to adapt to a new course structure), tactical capacities like imagery and memory are likely more imperative in SPEED events.

These are unique and immutable characteristics of alpine skiing and provide additional support to the use of more targeted 'performance' variables for future research. In any case, these factors do not discount the results of this thesis since both disciplines evidentially require a strong backbone of specific physical competencies on which to construct technical and tactical efficiency.

Athlete classification

Where necessary, the athletes in this study were collapsed into the broader classification of 'discipline' based on their highest-ranking event. However, distinct neuromuscular profiles may exist within disciplines (e.g., SL vs. GS and SG vs. DH). Furthermore, three

World-Cup athletes in this sample were classified in the French team system as multievent specialists and consequently competed across two or more events at a high level (although each was superior in a single event). Unfortunately, the sample sizes necessary for these types of analyses were impossible to meet, given the restricted number of highlevel athletes in the geographical proximity of this project. None-the-less, there is evidence to suggest that each event experiences unique biomechanical constraints during ski trials (Alhammoud et al., 2020;Gilgien, Kröll, et al., 2018), and examining event-and multi-event-specific neuromuscular profiles is a fascinating subject for future researchers.

PRACTICAL APPLICATIONS

TRAINING IMPLICATIONS

Increasing our understanding of alpine skiing and the requirements it places on athletes provides a more robust basis for implementing targeted assessment protocols and physical preparation regimes. The collective works of this thesis provided evidence that force production could limit performance on the snow and that skiers generally exhibit a unique neuromuscular profile compared to other sports. Moreover, this 'skiingspecific' profile appears to be exaggerated in better-ranked athletes and is different between the two main disciplines. Consequently, this thesis constitutes both novel and confirmatory information that might aid in orienting future practitioners and research efforts.

In general, the findings of this thesis support the development of dynamic force at low speeds, isometric force, and explosivity (RFD). Absolute capacity was typically determinant, rather than that produced per unit of body mass, which supports previous authors' work (Ferland & Comtois, 2018) in suggesting that additional mass can be positive in skiing provided it is balanced with the appropriate physical competency.

Since both muscle growth and maximum strength (here, interpreted as force at low speeds [i.e., skiing specific]) are determined mainly by training volume [START_REF] Grgic | Effect of resistance training frequency on gains in muscular strength: A systematic review and meta-analysis[END_REF], both factors should be considered in designing conditioning programs. With this in mind, greater workout lengths or increased workout frequency accrue higher training volume, which results in increased muscle mass (Schoenfeld, Ogborn, & Krieger, 2017) and strength [START_REF] Grgic | Effect of resistance training frequency on gains in muscular strength: A systematic review and meta-analysis[END_REF]. Since muscle growth appears comparable between high and low loads with equated training volume [START_REF] Schoenfeld | Strength and hypertrophy adaptations between low-vs. high-load resistance training: A systematic review and meta-analysis[END_REF], ski athletes can conceivably work in ski-specific bands of velocity (i.e., force at low extension velocities), and both increase muscle strength, attain a favorable recomposition towards active mass, and even increase RFD if performed with explosive intent [START_REF] Blazevich | Effects of resistance training movement pattern and velocity on isometric muscular rate of force development: A systematic review with meta-analysis and metaregression[END_REF]. Specific considerations for training are discussed below.

General perspectives

Even if not solely sufficient for creating a high-level ski racer, maximizing on-snow training is paramount to the development of ski athletes [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF]. Of 2019) reported that it was not until the 4 th consecutive season of tracking repeated jump capacity that correlations with performance were observed. While potentially a spurious correlation, the results were attributed to athletes having progressed their ski racing to a point where they might 'capitalize' on increased physiological and neuromuscular capacities. In any case, the relatively limited time in physical conditioning must be expended as precisely and efficiently as possible (Turnbull et al., 2009). Hopefully, the thesis results bolster this aim via an enhanced understanding of the muscular profile of skiing and that exhibited in high-level ski racers.

The sparsity-of-effects principle (i.e., the Pareto principle, popularized as the 80/20 rule (Pareto, 1964)) generalizes that across many models (initially, economics, but valid across numerous fields), the minority of causes explain the majority of the effects.

Presumably, this concept applies to the span of specific adaptations that can be reasonably accrued from time spent on athlete conditioning. Specifically, ensuring the fundamental principles of training are met, associated with a core understanding of the capacities necessary to the sport, might represent a small proportion of total training time but provide exaggerated positive effects on athlete profiles (see Figure 63).

Applying this perspective to skiing conditioning and integrating the findings of this thesis, we can assume that the 'core' physical profile of skiers centers on a capability to develop maximum dynamic and isometric force at low speeds (changeable importance, depending on the event), explosive capacity to develop force quickly, and presumably greater attainment of muscle mass. With this in mind, it would seem pertinent to ensure that these relatively simple factors are decisively attained within the broad spectrum of physical conditioning that ski athletes receive (Hydren et al., 2013).

Figure 63. The Pareto principle applied to training efficiency

The figure illustrates that core efficient training stimuli likely provide most of the beneficial sport-specific adaptations the athlete experiences. Note that this is a theoretical framework and does not strictly infer that in every situation, this model applies nor that the division is precisely 80/20%.

As presented by Helms, Morgan, and Valdez (2018), the lowest tier effect for strength and muscle gain is developing a program that an athlete will adopt and adhere to (see Figure 64). This is important to not overlook in programming since both monotonous and overly complicated training might provide unique benefits (and be attractive for coaches), yet their value is dependent on being adopted by the athlete. The following tiers are overall training volume and progression. While undoubtedly important, the top tier effects explain a comparatively smaller magnitude of adaptations and are somewhat dependent on a strong foundation of the lower tier principles. Of course, this perspective does not supplant the multi-factorial nature of skiing performance and physical competencies highlighted by many authors (Turnbull et al., 2009). Nor does it argue for dismissing the other '80%' of focus in off-snow conditioning that results in potentially comparatively minor perceivable gains; notably, 'exercise selection' is likely to play a more prominent role in sports where specific force production is a central part of the performance (e.g., development of specific bands of force production, per the results of this thesis). However, it does present a rationale for ensuring the core conditioning practices within ski conditioning are evidence-based to ensure the limited time available to develop core physical competencies is effective and not unduly influenced by integrating perceivably 'specific' training alterations (see Section 5. As discussed throughout this thesis (notably, Section 2.1), on-snow training features heavily in skiers' yearly schedule (see Figure 5). [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF]

Force-velocity based training

It is possible to target specific Fv qualities based on either deficiency in specific mechanical characteristics (Jiménez-Reyes, Samozino, Brughelli, et al., 2017;[START_REF] Jiménez-Reyes | Optimized training for jumping performance using the force-velocity imbalance: Individual adaptation kinetics[END_REF] or the development of specific characteristics. The simplest way of adapting this approach is by profiling an athlete in their Fv or load-velocity profile and subsequently targeting a specific band of velocity (i.e., velocity-based training). This 'velocity-based' approach has been integrated across various movements, but notably in sprinting [START_REF] Cahill | Sled-pull load-velocity profiling and implications for sprint training prescription in young male athletes[END_REF] and jumping (Jiménez-Reyes, Samozino, Brughelli, et al., 2017).

With training, it is possible to target and subsequently adapt the Fv profile in both jumping (Jiménez-Reyes, Samozino, Brughelli, et al., 2017;[START_REF] Simpson | Optimised force-velocity training during pre-season enhances physical performance in professional rugby league players[END_REF], and technical derivatives such as sprint running (Cahill, Oliver, Cronin, Clark, Cross, Lloyd, et al., 2020;Cahill, Oliver, Cronin, Clark, Cross, & Lloyd, 2020). For example, a recent article which prescribed training based on individual strengths and weakness in force output (as determined via SFvopt% (Samozino et al., 2014)) found it much more effective in 'balancing' the athletes force-capacities but also increased both their dynamic force and peak power more than traditional training [START_REF] Simpson | Optimised force-velocity training during pre-season enhances physical performance in professional rugby league players[END_REF]. Although the further an athlete is from their targeted profile the more time is needed to attain it [START_REF] Jiménez-Reyes | Optimized training for jumping performance using the force-velocity imbalance: Individual adaptation kinetics[END_REF], once attained, the balance in Fv characteristics appears relatively consistent during a short 'detraining' period. Although there have been some

mixed results indicating that the athletes' pre-training scores might influence adaptations in more technical derivatives [START_REF] Cross | Training at maximal power in resisted sprinting: Optimal load determination methodology and pilot results in team sport athletes[END_REF], adaptations in force output appear to be velocity specific. Consequently, integrating an Fv approach into testing and training for alpine skiers is encouraging, with the terminus being improved adaptations in dynamic force production at low speeds.

Eccentric, isometric and rate-of-force-development

A variety of studies have provided encouraging evidence regarding the beneficial nature of eccentric training (Douglas et al., 2017a;[START_REF] Schoenfeld | Hypertrophic effects of concentric vs. Eccentric muscle actions: A systematic review and meta-analysis[END_REF]. Even if eccentric force production may not be as central to skiing performance as once considered (according to a synthesis of recent on-snow data, see Section 2.2), eccentric training has compelling implications for skiers. Notably, eccentric exercise is substantially less metabolically taxing than concentric exercise when performed at the same intensity (Bigland- [START_REF] Bigland-Ritchie | Integrated electromyogram and oxygen uptake during positive and negative work[END_REF]. Vice versa, more volume can be accrued during eccentric vs. concentric exercise for the same metabolic consequences (albeit taxing for the neuromuscular system) [START_REF] Douglas | Eccentric exercise: Physiological characteristics and acute responses[END_REF]. When used with higher external loads associated with the relative intensity during concentric training, eccentric training appears superior for explosive force production and a variety of interesting muscle-tendon adaptations applicable for skiers (Douglas et al., 2017a).

Notably, while customized apparatus [START_REF] Douglas | Effects of accentuated eccentric loading on muscle properties, strength, power, and speed in resistance-trained rugby players[END_REF]Harden et al., 2020) or commercial alternatives [START_REF] Tinwala | Eccentric strength training[END_REF] are the best methods of training in eccentric modalities, several more accessible alternatives exist (e.g., partner-assisted squats, flywheel devices, or 'accentuated' methods) (Suchomel et al., 2019a[START_REF] Suchomel | Implementing eccentric resistance training-part 2: Practical recommendations[END_REF].

Similarly, the use of isometric training is noteworthy for developing specific characteristics for skiers. For example, isometric training at a range of intensities produces significant improvements in maximal force and even in muscular hypertrophy [START_REF] Oranchuk | Isometric training and long-term adaptations: Effects of muscle length, intensity, and intent: A systematic review[END_REF]. Moreover, positive adaptations in the musculotendinous unit have been observed following training, and when integrated with maximum ballistic intent, it can improve RFD [START_REF] Oranchuk | Isometric training and long-term adaptations: Effects of muscle length, intensity, and intent: A systematic review[END_REF]. Classically, fast movements have been deemed crucial to improving RFD, but adaptations in RFD via training performed at zero movement velocity challenges this view [START_REF] Tillin | Maximal and explosive strength training elicit distinct neuromuscular adaptations, specific to the training stimulus[END_REF]. More specifically, movements characterized by maximum movement intent (i.e., explosive) are central to improving RFD [START_REF] Alegre | Effects of dynamic resistance training on fascicle lengthand isometric strength[END_REF][START_REF] Cormie | Adaptations in athletic performance after ballistic power versus strength training[END_REF][START_REF] Oliveira | Effects of fast-velocity eccentric resistance training on early and late rate of force development[END_REF][START_REF] Van Cutsem | Changes in single motor unit behaviour contribute to the increase in contraction speed after dynamic training in humans[END_REF]. The fundamental nature of movement intent is intuitive given the epochs over which RFD is measured occur very quickly following force onset, which relies on muscular activation [START_REF] Blazevich | Effects of resistance training movement pattern and velocity on isometric muscular rate of force development: A systematic review with meta-analysis and metaregression[END_REF]. Consequently, isometric training, integrated with maximum ballistic intent, could be a notable addition to the development of specific force capacities for skiers.

Integration of 'ski-specific' constraints The inclusion of vibration and instability on training outcomes is challenging to study due to standardization difficulties. There is some evidence that low-frequency vibration results in acutely elevated neural activation, which potentially results in improvements in force and power output when integrated into conditioning [START_REF] Jordan | Vibration training: An overview of the area, training consequences, and future considerations[END_REF][START_REF] Lamont | Effects of adding whole body vibration to squat training on isometric force/time characteristics[END_REF], or at least non-detrimental effects using cogent protocols [START_REF] Wilcock | Vibration training: could it enhance the strength, power, or speed of athletes?[END_REF]. Adaptations appear to be partially dependent on how vibration is applied, with vertical oscillators much more effective for long-term adaptations (e.g., the passive-leg-press [START_REF] Liu | The effects of passive leg press training on jumping performance, speed, and muscle power[END_REF]) than oscillating platforms [START_REF] Marin | Effects of vibration training on muscle strength: a metaanalysis[END_REF]. Moreover, both the amplitude and frequency of vibrations affect the adaptations (i.e., trends for more significant effects observed with increased amplitudes and frequencies of those studied [START_REF] Marin | Effects of vibration training on muscle strength: a metaanalysis[END_REF]), but the optimal range for specific adaptations remains unclear. However, the evidence is far from conclusive as a product of lacking standardization, data inferred from singlemuscle studies, and most of the positive results are from untrained or recreational athletes [START_REF] Luo | The use of vibration training to enhance muscle strength and power[END_REF][START_REF] Wilcock | Vibration training: could it enhance the strength, power, or speed of athletes?[END_REF]. Nevertheless, when targeted to the appropriate frequency, it could provide an additional training stimulus for alpine skiing athletes [START_REF] Spörri | The use of body worn sensors for detecting the vibrations acting on the lower back in alpine ski racing[END_REF]Supej & Ogrin, 2019).

Instability training is theorized to develop the neuromuscular system via coordinative aspects, decreasing co-contractions, and improving task-specific motor patterning [START_REF] Behm | The role of instability with resistance training[END_REF]. Instability training is similarly challenging to qualify since it can refer to a wide range of movement integration (e.g., minor, double vs. single leg;

major, standard squat vs. a squat on a swiss ball). In its purest form, instability integrated via training unilaterally appears to increase activation of antagonist musculature (V. [START_REF] Andersen | Muscle activation and strength in squat and Bulgarian squat on stable and unstable surface[END_REF], which could be interesting for similarity during a skiing turn [START_REF] Hintermeister | Muscle activity in slalom and giant slalom skiing[END_REF]. However, some investigations have reported reduced muscular activation of the agonist (i.e., increasing the relative contribution of the antagonist) [START_REF] Mcbride | Isometric squat force output and muscle activity in stable and unstable conditions[END_REF], and almost all studies report impaired force production relative to the stable alternative (V. [START_REF] Andersen | Muscle activation and strength in squat and Bulgarian squat on stable and unstable surface[END_REF][START_REF] Behm | Muscle force and activation under stable and unstable conditions[END_REF][START_REF] Drinkwater | Effect of instability and resistance on unintentional squat-lifting kinetics[END_REF][START_REF] Mcbride | Isometric squat force output and muscle activity in stable and unstable conditions[END_REF].

Consequently, including instability reduces the total load that can be moved, which in turn reduces training volume (i.e., potentially compromising strength and muscle gains [START_REF] Grgic | Effect of resistance training frequency on gains in muscular strength: A systematic review and meta-analysis[END_REF]).

For example, while unilateral training might be expected to transfer better to sprinting, the results of a recent meta-analysis indicated that while the impact of 'velocity specific' better left to train and adapt during sports practice (i.e., on-snow sessions). For example, the development of a strong basis of force capacity at low speeds and in isometric states (see Section 4.1), to be honed on-snow, subsequently improving the 'technical application' of force and performance (see Section 3.1). In any case, echoing statements by [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF], the overarching crossover between physical conditioning and on-snow training is owed more focus in future research.

TESTING

Testing skiers

The effective individualization and orientation of training goals is dependent on the testing athletes and understanding their strengths and weaknesses relative to the sport.

For ski racers, full physical testing is performed approximately twice per year, at the beginning of the physical preparatory period and just before competition [START_REF] Gilgien | The training of olympic alpine ski racers[END_REF]Hydren et al., 2013;Raschner et al., 2013). As such, testing must be specific, valid, and reliable to ensure an accurate representation of athletic status. However, it is crucial to consider that when adapting from challenging neuromuscular stimuli, supercompensation can take up to four weeks to unveil itself (Jiménez-Reyes et al., 2019;

Morin, Capelo-Ramirez, Rodriguez-Perez, Cross, & Jiménez-Reyes, 2020). As such, the timing of athlete conditioning and rest around the testing must be considered when implementing tests, as either fatigue or other factors potentially mask the actual physiological status of the athlete. While challenging, practitioners might consider selecting a few low-impact tests to longitudinally monitor athlete progress (some suggestions below) to ensure accurate capture of the real condition and progression of the athlete.

Learnings from this thesis

To the best of our knowledge, several of the tests used are the first to be reported on alpine skiers and might be considered part of the longitudinal battery of testing athlete profiles. While confirmatory data is needed, this thesis's results provide a rationale for the assessment of specific force capacities.

The tests used in this thesis were selected based on their practicality when implemented with accessible technology and their validity despite their apparent simplicity.

Consequently, while each test requires regulation to provide accurate results, these tests can easily be integrated into routine monitoring practices-even in remote locations, such as ski stations. In its current form, the Fv and isometric testing can be performed over a ~1 hr period (depending on warm-up duration). Moreover, using fewer loading parameters in the Fv profiles (e.g., two loads vs. five) can substantially reduce assessment time [START_REF] Jaric | Two-load method for distinguishing between muscle force, velocity, and power-producing capacities[END_REF]. Furthermore, such an approach provides accurate information regarding mechanical capacity, provided steps are taken to reduce the error associated with fewer data points (e.g., an average of multiple jumps for one point) (Fessl et al., 2020;Garcia-Ramos & Jaric, 2018;[START_REF] Perez-Castilla | Evaluation of muscle mechanical capacities through the two-load method: Optimization of the load selection[END_REF]. The accuracy of Fv profiling methods is well supported when used with familiar athletes and in controlled conditions [START_REF] Garcia-Ramos | Force-velocity relationship in the countermovement jump exercise assessed by different measurement methods[END_REF]Giroux et al., 2015), and previously within youth and world-cup skiing populations (Fessl et al., 2020;[START_REF] Rahmani | Force/velocity and power/velocity relationships in squat exercise[END_REF]. However, conditions must be standardized, and lower-level or un-familiar athletes probably require extra attention to attain useable results.

Once familiarized, the repeated squat jump strength-endurance test lasts only 5-10 min, including a short 'practice' of ~5 jumps at the target jump height, carrying the targeted jump weight, and with the appropriate tempo and squat depth settings. One potential practical limitation is that results are dependent on the athlete having performed an

PRACTICAL APPLICATIONS

accurate and timely Fv profile preceding the test since these are used to set the parameters under which strength endurance is assessed directly. Consequently, this both stands as a limitation to recurrent testing since it is effectively 'added' to the Fv profiling duration (albeit relatively short) and inflates the possibility for error. In any case, as discussed in Section 4.3, more research is needed before the test can be trusted to provide relevant information. Notably, while only one power-velocity-endurance condition was examined in this thesis, there is real interest in the development of a 'three-dimensional' profile that characterizes the capabilities of skiers (in general) and individual athletes. Such an approach is yet to be published but could feasibly provide both a more encompassing and accurate view of strength endurance parameters for skiing performance-notably when paired with a more detailed view of force-velocitytime date extracted from skiing-and an improved platform on which to test individuals for monitoring and training purposes.

The usefulness of the isometric force assessments to ski practice is supported by this thesis and is in line with the historical assessment of isometric force in high-level skiers (Berg et al., 1995;[START_REF] Rahmani | Force/velocity and power/velocity relationships in squat exercise[END_REF]White & Johnson, 1993). Notably, the low error rates and ease of assessing isometric force highlights its usefulness in monitoring the development of critical physical characteristics in skiing training and potential performance parameters (Brady, Harrison, & Comyns, 2018). However, while the midthigh pull was implemented in this work, the disproportionate lower-body strength exhibited in ski athletes (Hydren et al., 2013) might have limited the capability of some athletes to provide a maximum measure of the lower limbs [START_REF] Brady | A comparison of the isometric midthigh pull and isometric squat: Intraday reliability, usefulness, and the magnitude of difference between tests[END_REF]. In this case, the isometric squat might provide a more valid method of detecting output-notably, in female populations. One additional benefit to using such isometric assessments (IMTP or isometric squat) is that the angles of the knee and hip can be set to profile angle-specific force [START_REF] Sarabon | Force-velocity profile during vertical jump cannot be assessed using only bodyweight jump and isometric maximal voluntary contraction tasks[END_REF] aligning with the disparate inside and outside limb (Kröll, Spörri, Fasel, et al., 2015;Kröll, Spörri, Kandler, et al., 2015). Furthermore, both the isometric mid-thigh pull and the isometric squat can be implemented unilaterally to assess asymmetries (potentially angle specific), which could provide added value for return to sport and injury prevention (C. [START_REF] Bishop | Unilateral isometric squat: Test reliability, interlimb asymmetries, and relationships with limb dominance[END_REF]Dos'Santos, Thomas, Jones, & Comfort, 2017). In any case, the integration of such a test into regular monitoring is likely valuable for future researchers and practitioners.

The Fv profile, RSJ, and the isometric pull/squat can be performed with relatively accessible technologies. In the former instance, provided controlled loading is available, a variety of technology can provide the prerequisite distance-time data. The most notable of which is the MyJump application [START_REF] Balsalobre-Fernandez | The validity and reliability of an iPhone app for measuring vertical jump performance[END_REF], which can provide a valid measurement of jump height (and subsequently Fv profiles with validated equations (Samozino et al., 2008)) for only ~10 EUR and a recent cellphone [START_REF] Stanton | Validity and intra-rater reliability of MyJump app on iPhone 6s in jump performance[END_REF]. To measure maximum isometric force, we used a custom-designed portable platform similar to those in recently published research (James et al., 2017). While our unit is not currently commercially available, similar straingauge units retail at 1000 EUR and can be easily attached to immovable objects (e.g., the base of a squat rack) in place of a customized platform. Where assessing RFD is not the goal, similar and accurate maximum force values are possible via much less costly options (e.g., simple 'crane' scales, ~30 EUR) (Urquhart et al., 2018). However, while certainly lower cost and more portable than force-plate alternatives, it features some potential limitations to the more traditional mid-thigh pull setup. As such, where forceplatform technologies are available (notably, with more cost-effective, portable, and valid variants increasingly available [START_REF] Peterson Silveira | Validity of a portable force platform for assessing biomechanical parameters in three different tasks[END_REF]) and the assessment location accommodates the corresponding setup, selectively using these types of technology might be preferable.

In any case, while providing a simple and accessible approach to assessment was an undercurrent of this project, more advanced measurement and analysis types (e.g., distinct analysis of force-time data analyzed from force-platforms (Jordan et al., 2018)) might provide more analytical ability. With the advent of ever progressing and accessible technologies, this is an exciting avenue for future research.

CONCLUSIONS

CONCLUSIONS

The overarching aim of this thesis was to clarify the characteristics and importance of force production in skiers. To meet this aim, the existing literature on both the importance of force output on the snow and the specific capacities exhibited by skiers in field and laboratory tests were examined. The subsequent narrative reviews (Chapter 2) indicated that force production was important, albeit the bounds of which unclear, and that this force was expressed in specific patterns: during slow muscular actions and at high magnitudes. The subsequent physical profiles of skiers tended to match these characteristics. However, in general, the literature was very sparse and featured relatively limited specific assessment of relative force-production capacities, considering the narrative woven through the skiing biomechanics data. A force-assessment model was developed based on these capacities, using field testing methodology to enhance its potential integration into practice. However, since no study in the literature clearly examined force-output characteristics and performance, the first objective was to clarify this relationship.

Subsequently, a group of skiers performed a skiing trial while equipped with various technologies to provide kinetic and kinematic data. The collected data were used to: 1) clarify the association between skiing performance and optimizing trajectories and maximizing velocity, and; 2) test the importance of radial force in giant-slalom skiing performance, and to characterize the contribution of force magnitude and orientation of force in turn performance (Chapter 3). The results showed that better athletes dissipated less energy and produced greater radial force, which was determined by both absolute magnitudes applied to the ski and an ability to apply it effectively. Having clarified the bounds of the importance of force production, high-level skiers were profiled using methods selected to target ski-specific force capacities. Information regarding athlete focal discipline, performance level, and force production were collected (Chapter 4): at high and low velocities, in isometric conditions, the capability to develop force quickly (Section 4.1), the effect of countermovement on force output (Section 4.2), and strength endurance (Section 4.3). Skiers generally: 1) displayed a unique capacity for absolute force at low velocities; 2) exhibited discipline-specific force profiles; 3) demonstrate elevated specific capacities in higher-level athletes, and; 4) probably exhibited different strength endurance profiles, requiring different testing parameters. The general discussion in Chapter 5 provided suggestions for integrating the results of this thesis into practice, including relating the findings to the realities associated with elite sports routines and argued for efficiency in training and testing approaches.

As several previous studies and practical evidence would support, the relationship between force output, broad athletic profiles, and skiing performance is complicated.

However, in this study, we were able to detect meaningful differences between disciplines, with several capacities being linked to performance. The studies in this thesis collectively draw attention to both the prevalence of force production at low speeds in high-level skiers and the lack of discriminating capability provided by force at moderate and high velocities (like those commonly used in the literature). We theorize that athletes with elevated determinant characteristics might have a performative advantage, which either provides a greater absolute capacity to apply during opportune moments or ski consistently at a lower relative intensity. Nevertheless, while these provide some valuable information on the relevance of specific capacities to ski disciplines and macroscopic performance parameters, the relationship between physical capacity to that applied on-snow in modern ski racing remains relatively untested. Hopefully, this work can provide value for future research and practice in the area.

BIBLIOGRAPHY

Introduction

In alpine skiing, an athlete must negotiate the course by managing the production and absorption of external forces. While aerodynamic forces have been shown to be predictive of performance in some disciplines (Hebert-Losier et al., 2014), ground reaction forces (GRFs) are the primary mechanism for skiing actions. For these reasons, force output in skiers has attracted interest in both applied research (Hebert-Losier et al., 2014) and conditioning practice (Hydren et al., 2013).

Logically, the amount of ground reaction forces produced during skiing is intrinsically related to the kinematic characteristics observed. That is, a turn performed at higher speeds and a tighter turn radius (i.e. radial force = velocity 2 /radius) will be associated with a greater GRF profile than slower and less aggressive turn tactics (assuming consistent body-weight [BW]). While force is often explained as the subsidiary variable in this equation (i.e. greater GRFs are a result of the speed and line choice), the inverse explanation holds interest for understanding performance for training athletes:

Athletes who can produce greater force (and notably radial force) can similarly turn with a smaller radius while maintaining a high velocity or turn at a higher velocity with a given radius (Nakazato et al., 2011). Certainly, an enhanced capacity for force production is generally accepted as a necessary physical component for ski athletes (Hydren et al., 2013;Turnbull et al., 2009). However, while some evidence suggests advanced athletes exhibit a greater ability to produce force [START_REF] Keranen | FIS-ranking and carving turn force production profile[END_REF], the relationship is likely more complicated (Supej et al., 2011). Data on the subject is rare, and often features limitations due to technology and the complex nature of collection in an alpine environment.

In alpine skiing, GRFs can be measured in a variety of means, but generally: 1) directly, either assuming output via pressure insoles [START_REF] Falda-Buscaiot | Influence of slope steepness, foot position and turn phase on plantar pressure distribution during giant slalom alpine ski racing[END_REF] or using specialized force platforms (Nakazato et al., 2011), and 2) indirectly using video (Supej et al., 2011) or GNSS in combination with other micro-technologies [START_REF] Sporri | The role of path length-and speed-related factors for the enhancement of section performance in alpine giant slalom[END_REF]. Clearly, among these methods force-platforms are the gold-standard in measuring kinetic activity, but the challenging alpine environment and difficulty integrating technology with skiing material has substantially limited studies utilizing this per boot, was used to gain GRF data. The units attached to a typical alpine racing boot, and subsequently clipped into a typical race binding; in this manner the sensor comprised the sole point of connection between the ski boot and the ski. The units were lighter (~1.2 kg) and mounted lower (2 mm) than traditional systems. The sensors were wired to an acquisition card (Jam Ingénierie, Chambery, France) carried in a small bag worn just above the iliac crest of the hips (approximating center of mass).

Raw voltage data was recorded and was subsequently converted into force using calibration files.

Cross M.R., Delhaye C., Bowen M., Coulmy N., Morin J.-B., Hintzy F., Samozino P.

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Science and Skiing VIII

A GNSS system (Stadium tracker, Mac-Lloyd Sport, Paris, France), provided positional and accelerometer collecting data at an output frequency of 10Hz. The data were collected using the manufacturer supplied software, featuring a fusion algorithm to improve positioning accuracy, and were exported in raw form for later processing.

Course time was collected using a photovoltaic system (Tag Heuer, La Chaux-de-Fonds, Switzerland), set at the starting-gate (typical FIS style trigger) and at the final gate in the course (dual-beam cell set at thigh height). Athletes wore a standardized selection of ski boots (X LAB+ 140 WC, Salomon, Annecy, France), in their respective size and with their own boot liners, and the same pair of waxed and edged race skis (LAB X-RACE GS, Salomon, Annecy, France; radius: 30m; length: 193 cm; bindings:

X19 LAB, Salomon, Annecy, France). Athletes wore FIS approved race suits and protective gear (e.g. helmet, goggles, and back protectors).

Following a warm-up and course familiarization, athletes performed a short calibration and synchronization procedure for the various sensors. 1 to 2 trials of the course were performed, interspersed with approximately 15 minutes of rest.

The synchronized force and positional data were separated into 14 turns by detecting the turn-switch moment as the inflexion point of the COM trajectory (Adelsberger et al., 2014). From this point the resultant force produced by the two limbs filtered using a 10Hz low-pass Butterworth filter. The data were expressed as multiples of bodyweight (BW) and summated to provide a total value of GRF for both limbs. Peak (Fpeak) and mean (Fmean) force were computed for each turn, and the absolute difference in mean force between limbs was calculated and expressed as a percentage of Fmean (Fdiff). The averaged velocity (vavg) and the cumulated distance (Traj) traveled were both calculated per turn from the raw positional data provided in the 3 axes. The final data were averaged (to provide course average values) for final analysis. All data processing were performed in MATLAB (Massachusetts, USA).

The mean data were entered into a correlation matrix to firstly test for their relationship to total course time (T), and secondly to examine the interrelationship between the nt (r; p<0.05). The strength of relationship was interpreted using values of 0.5, 0.7, 0.9, and 1.0, as thresholds for moderate, large, very large and nearly perfect, respectively (Hopkins et al., 2009).

Results

Full correlation results are presented in Table 1. The mean time to complete the course was 28.83 ± 1.22 s. Average velocity was nearly perfectly related to course time (p<0.001), where cumulated distance was not. Mean (1.70 ± 0.15 BW) and peak force (3.76 ± 0.42 BW) produced across the turn cycles had very large (p=0.004) and large (p=0.032) relationships with course time, respectively. The difference in output between limbs was 32 ± 7 % of Fmean and was not predictive of performance.

Discussion & conclusions

Our findings show that in a giant slalom course average velocity was of much greater predictive value than the trajectory chosen. While the predominance of velocity as a predictor of performance is probably a result of the conditions under which variables were measured (i.e. course and discipline), it is in agreement with research in giant slalom [START_REF] Sporri | The role of path length-and speed-related factors for the enhancement of section performance in alpine giant slalom[END_REF].

The average and peak GRFs measured in this study are substantial and, while it is difficult to compare values from different methodological approaches, technologies and courses, our magnitudes are generally congruent with the literature (Falda-Buscaiot et al., 2016;Nakazato et al., 2011). The peak forces observed in our study were typically higher than presented (e.g. Nakazato et al., 2011), which feasibly might represent differences in methodological approaches and a potentially more sensitive measurement techniques.

GRF output was split between the limbs in approximately a 2:1 ratio (outside to inside limb). While the outside limb takes precedence in the literature and coaching practice as the dominant and driving limb during the turn, the inside limb is still required to present substantial levels of force production (on average, 0.54 BW throughout the turn cycle). This is particularly notable given the disparate knee and hip angles at which these forces are produced (Turnbull et al., 2009), which might highlight an increased necessity to train force throughout the knee/hip complex at different angles.

Interestingly, while it is common to cue athletes to emphasize pressure on the outside ski, in our results there was no clear relationship between how the athletes presented the force between the two limbs and course time.

The large to very large correlations observed between the force developed by the present greater force production ability. While the relationship was clear (p<0.01) and substantial (52% of variability explained), the magnitude of unexplained variability between higher level performances. The similarly large unexplained variance between

Favg and vavg adds strength to the argument that the better skiers are those who possess enhanced technical and physical capability to orient their force output in the necessary direction (Hebert-Losier et al., 2014).

The ability to generate peak force was strongly related to better course performance.

This result can be partially explained by an associated generalized force output capability (i.e. athletes with high average force output, also present high peak force), but is nevertheless interesting given research typically presents an inverse relationship between higher peak force output and performance (Hebert-Losier et al., 2014).

Notably, while instantaneously high GRF output measured via inverse dynamics from center of mass is probably associated with dissipation of energy, force measured directly from the limbs could feasibly represent different mechanisms. Our GRF data do not match the characteristically smooth force-time data typically presented (see

Limitations

The study took place on a closed race course over the course of a 1-month period.

While weather conditions were monitored and controlled as closely as possible, variable meteorological conditions might have affected our results. Due to the nature of the study, athletes were required to wear and use non-habitual equipment (i.e. skis and boots). While athletes were familiarized and were fitted as well as possible to the equipment at hand, it is possible that performance was affected. This was unavoidable, given the nature of the study design, and controlled for in the nature of

Introduction

Biomechanical analyses of alpine skiing performance typically separate data into turns to define the cyclic motor abilities of the athlete. Detecting the beginning and end of a turn is a challenging task for researchers and mainly depends on the definition chosen and the technologies used. When aiming to detect the moment of switching from one turn to another, there are two main approaches: 1) consider the end of a turn at the beginning of the proceeding one (Approach 1), in which a ski run is strictly an alternation of right and left turns separated by a turn switch (TS) event, and 2) a straight-line transition period is considered between two turns, which defines the alternation between straight and turn phases as separate. These two approaches can be implemented on both kinetic and kinematic data signals.

-Approach 1 detects a TS when COM and ski trajectories cross paths (Supej & Nemec, 2003). This method requires a complex set up of 3D motion capture cameras and post processing.

Consequently, analyses of more than a few turns are difficult. COM and ski trajectory can also be estimated using inertial measurement units (IMU) and Global Navigation Satellite Systems (GNSS) (Fasel et al., 2016); these sensors are accurate but similarly require complex data processing. A less computationally demanding method of detecting the TS is to use GNSS data to determine the inflexion point (Trajinfl) of the COM trajectory (Adelsberger et al., 2014). Notably, this method is comparable to the gold-standard (lag <30 ms; [START_REF] Fasel | IMU and GNSS-Based Turn Switch Detection in Alpine Ski Racing[END_REF] and can provide data over much greater course lengths. Finally, kinematic data can be used to detect TS events via Approach 2; namely, the COM trajectory straight and turn phases can be separated when the turn radius of COM crosses 30m (Traj>30, Traj<30) (Spörri et al., 2012). These events correspond to the end or the beginning of substantial COM direction change, which can be subsequently linked to the beginning and the end of the turn phase.

While less common, TS events can be computed using kinetic data. The gold standard corresponding to Approach 1 defines TS as the minimum summated normal ground reaction force (nGRF) exhibited over a given turn cycle (Fmin; Nakazato et al., 2011).

As such, the TS phase is associated with a period when force applied to the skis is close to zero (i.e. an unweighting between turns), which is surrounded by large force application on the relevant outside ski (Schaff et al., 1996). Further to the specific TS moment, these data can also define distinct events within the turn phase (e.g. turn initiation) (Nakazato et al., 2011), and detecting the beginning and end of the nGRF on the outside ski (relevant to Approach 2) could be an interesting new method to define the beginning and end of a turn. Indeed, the outside ski supports higher nGRF during turn than inside ski and is mostly involved in direction change of the skier. The beginning of the force application of the outside limb induces bending of the ski [START_REF] Yoneyama | Ski Deflection Measurement during Skiing and Estimation of Ski Direction and Edge Angle[END_REF] and could be directly linked trajectory changes.

There are several methods and approaches to segment a ski run into turns.

Consequently, researchers or practitioners with access to multiple data streams lack guidance on which method or technology is optimal for a specific situation or aim.

Furthermore, there is sparse information regarding the link between kinetic and kinematic events at turn initiation. The aim of this study is to explore time difference between cutting turns methods and evaluate if clear relationships exist between kinematic and kinetic definitions of the beginning and the end of a turn.

Methods

Results

Time lag between the reference (Fmin) and the other methods are reported in Table 1. There were clear (P<0.001) differences between all methods, except between Trajinfl and Fbeg which

shown no statistical difference. The lag difference between these two events was 3.3 ms (± 12 ms). Assuming Trajinfl and Fbeg can be considered as a common event, the order of appearance during a turn was: Traj<30 and Trajinfl (and/or Fbeg) always last and second-to-last, respectively. Fend is logically consistently before Fmin, and the order of Traj>30 was variable (1 st (68 %), 2 nd (25 %) or 3 rd (7 %)).

Discussion and conclusion

The major result of this study was that time per turn shifted depending on the turn cutting method used. Kinetic TS events (Fmin) were always detected earlier than kinematic TS events (Trajinfl). Based on this finding, during direction the change period tra must be considered when integrating the methods into research and practice.

consequence of the manipulation of ground-reaction forces. While clearly logical, these findings serve to solidify the understanding of ski mechanics. Of interest to those progressing in the field of skiing biomechanics analysis, our results have important implications for analysis procedures. Namely, since the definition of the beginning and end of a ski turn (and underlying methodological design) provide clearly different results, the aim of the measurement will determine the technological and analytical approach implemented.

The reference kinetic method to cut turns (Fmin) does not occur concomitantly with kinematic events, so a turn cut with this method contains two trajectory direction changes. To cut turns including only one direction change we recommend using the beginning of force application on the external ski (FBeg). While Fbeg is presently found using manual selection, programmatic automatization could aid in reducing potential Lag between Traj<30 and Trajinfl (~20 % of turn time) corresponds to the values previously reported between Traj<30 and the kinematic gold standard (Spörri et al., 2012). Similarly, [START_REF] Fasel | IMU and GNSS-Based Turn Switch Detection in Alpine Ski Racing[END_REF] showed that Trajinfl is close to the kinematic gold standard. While in this study we only compared the difference in timing between the various methods, it seems clear that depending on the approach taken to separate a downhill run into distinct turns, different results might be observed in a variety of output variables (e.g. dissipation in mechanical energy) particularly over short analysis windows. Since the body of research features a variety of turn switch methods, careful selection and rationale of the method selected would aid in the future comparison of research findings.

Future researchers are encouraged to perform a deeper analysis of vGRF pattern to better clarify these findings, and the relationship between technical strategy and observed lag. Clearly, force output is of interest, given the inferred importance to kinematic events and some factors of performance.

INTRODUCTION

n alpine ski racing athletes must negotiate a demanding course under variable constraints including event specific gate setups, challenging terrain, snow and weather conditions. Podium places are often separated by mere fractions of a second, which highlights the importance of chasing small improvements in performance. Better understanding of the contributors to performance in this complex sport should provide a basis to better prepare athletes, and consequently produce worthwhile improvements in technique and conditioning.

Determining which capabilities separate high-level skiers from their lower-level counterparts is challenging. Skiing motion is essentially a result of utilizing the potential energy possessed at the start of the course, by converting this energy into either kinetic energy or dissipating it (via ski-snow and aerodynamic friction) within the trajectory limits imposed by gates. An athlete who possesses the physical and technical capabilities necessary to effectively manipulate and, ultimately, minimize energy loss within the marked course is at an advantage (1)(2)(3). In its most basic form, to turn and successfully negotiate a course, athletes must apply force onto the snow via their ski-specific equipment. While the contribution of other external forces might play a role in some disciplines (e.g., minimizing aerodynamic drag is a dominant factor in speed events ( 4)), the main changeable mechanism of skiing is the production of force onto the snow, which induces snow-reaction forces (SRF) associated to changes in skier motion or as a product of changes in the ski-snow interaction (i.e., changes in energy dissipation). The interplay of forceoutput with skiing performance is complex, and while it is impossible to ski effectively without a certain capability to generate and appropriately apply force to the snow, force applied at a given moment can serve to improve or worsen the instantaneous performance of a skier (5). For these reasons, force output in skiers has attracted interest in applied research (4) and conditioning practice (6).

While our understanding of skiing biomechanics has advanced considerably in recent years (7), the physical, technical, and tactical determinants of skiing performance remain largely unclear. Course performance (i.e., time) can be contextualized as comprising multiple distinct but interrelated sections, in which there are intertwining approaches to minimizing time: i) selecting an advantageous and more direct route between gates, or ii) preferencing a longer trajectory that enables greater speeds to be attained or maintained (depending on the characteristics upon entering the section) (5). While the former approach is intuitive, since the distance traveled by the athlete is reduced, the ensuing tighter turns might dissipate more energy (2). The latter approach is typically associated with a longer path between gates (2,8), but this detractor can be overcome if enough velocity is gained within the section or maintained (i.e., less energy dissipated) (1)(2)(3)9). Moreover, a greater sectional velocity directly influences performance in coming turns, which can be an advantage not clearly apparent within the turn itself (provided the additional velocity can be managed effectively). In slalom and giant-slalom (GS) there is some evidence to show that strategies enabling an elevated turn velocity appear preferable to a more direct route between gates (10). Summarizing the recent stance on the approach, Spörri, Kröll (11) suggest beginning turns earlier (3,9), and smoothly applying force ( 9) and 'carving' the skis (i.e., rather than skidding) (1)(2)(3)9) as strategies to elevate velocity and performance in technical skiing disciplines. Unfortunately, our understanding of this phenomenon is drawn from a small pool of studies featuring specific and constrained external conditions. As such, it is possible that different results might be observed across disciplines, and with different course characteristics (12,13). In any case, attaining and maintaining high sectional velocities is limited by course constraints (14), technique (15), tactical approaches ( 16), and the physical competency of the athlete.

According to Newton's laws of motion, turns performed at higher velocities and/or with smaller turn radii (r) require elevated radial force output compared to slower and straighter turns (i.e., radial force [Fr]=velocity 2 /r). On the one hand, the same Fr can theoretically be observed in various situations per the tactical approach to the turn mediated by the characteristics at entry (notably, entry velocity (2)). For example, two sections might display inversely proportionate velocity and turn radii (i.e., higher velocity and lower radius, and the inverse) and display similar force, and dissipation characteristics. On the other hand, athletes possessing an elevated capability to generate Fr might be able to turn tighter at a given velocity or turn at a higher velocity with a given turn radius without needing to dissipate unnecessary additional energy. This ability to maximize Fr is well represented in the 'carving' technique, where anecdotally a large proportion of force being produced is directly turning the athlete along a curved trajectory (i.e., acting perpendicular to the tangential direction of the ski trajectory; Fr). In carving, a large proportion of the turning phase is performed with the skis on edge and penetrating the snow surface, without a substantial lateral skidding component and associated minimal dissipation of energy (17). Reid,Haugen (18) describe the phenomenon well, where carving is characterized by a reduced 'attack angle' between the longitudinal axis of the ski, and the velocity vector of its center. Practically, increasing the attack angle results in skidding, with the inverse presenting the appearance of all points of the ski edge 'carving' through the same point on the snow. The interplay between carving and skidding is complicated, with some proportion of the turn inevitably being performed in conditions of skidding, and being mediated I Force in giant-slalom skiing 3 by a host of other factors such as the interaction between the environment and the ski geometry (19). Albeit a simplification, carving represents the most obvious way of attaining a greater velocity without unnecessary dissipation of energy (1)(2)(3)9), provided the conditions permit it. However, athletes might deviate from carving in certain situations as a tactical choice (e.g., skidding to dissipate energy and avoid mistakes), or as a product of adopting a more direct trajectory, spending longer in the fall-line, and turning with a smaller radius (19). Nevertheless, without a capability to produce and control high levels of Fr athletes might reduce their strategic options, with the result being, on average, a lesser performance than otherwise possible from choosing strategies to disperse energy or a less optimal line. While in numerous sport movements (e.g., sprint running, cycling, or jumping) the maximal velocity is related to the highest kinetic work the athlete can produce, skiing velocity is a result of efficiently managing the transformation of energy ( 16). Consequently, maximal velocity corresponds to the highest value at which the athlete can ski while respecting the trajectory limits imposed by gates and without losing control and risking injury; this phenomenon is widely known as the 'velocity barrier' (2). While not widely researched, this barrier is likely the result of intertwining unmodifiable factors (e.g., course setting and snow quality), and physiological and psychological systems (e.g., perceptual, trajectory targeting). Since it appears that the main mechanism behind skiing is the manipulation of SRF, conceivably athletes with enhanced force output (notably Fr) might possess, ceteris paribus, a raised 'barrier' compared to their counterparts and, consequently, elevated control at higher velocities, and a model terminus of better course performance. In other words, increasing athlete force output capability is one theoretical means of improving performance during turns made at the limits of athletic ability. Assuming generating elevated Fr is important to ski-racing performance, the two main approaches to improving this variable would be increasing the total magnitude of force applied to the snow or applying a greater proportion of total capacity in the radial direction. In any case, at present the differentiation between total force output and that applied radially is unclear.

There is no consensus on the predictive nature of various force-output characteristics, other than the timing and event specific application of force being of higher importance than non-descript output (5). For example, Supej, Kipp (2) showed that slalom skiing SRF magnitudes did not clearly differentiate between athletes but rather acutely high values during turns were associated with elevated energy dissipation across the cohort. In a small homogenous sample, Reid (19) reported a strong association between turn time and SRF during a single 10 m slalom turn, but not when gate distance was increased to 13 m. Furthermore, athletes who adopt a 'carving' technique, as opposed to a more traditional technique with shorter trajectories, ski faster but exhibit non-dissimilar average SRF (15,20). One interpretation is that while an enhanced capacity for total force output may be advantageous, what is more important is the way in which force is applied to the snow; notably, a greater proportion of force produced to carve the ski (i.e., elevated Fr) instead of total output in less advantageous techniques (i.e., elevated energy loss). There is relatively little information regarding the technical and physical parameters underlying SRF output in skiing, and a wide variety of measurement techniques (direct vs. indirect force measurement) and methodological approaches (high-level athletes performing race-pace trials ( 21) vs. recreational athletes performing free-ski turns ( 20)) render synthesizing findings challenging. Moreover, a common acknowledged limitation is the extrapolation of a minor representation of the course (e.g., 1-2 turns) to overall performance (3). Sectional times in ski racing are notoriously variable (e.g., ~10% in high-level athletes) (22) and competition courses are comprised of external constraints that can vary substantially turn-by-turn (e.g., high-and low-inclination sections), which highlights the value in drawing conclusions from a wider breadth of the course.

In alpine skiing, SRF can be estimated via pressure insoles (23) or specialized force platforms (20), and using inverse dynamics via video (2) or Global Navigation Satellite System (GNSS) (4) in combination with other micro-technologies (11). Force platforms remain the gold-standard method, but difficulty integrating such technology into skiing practice has substantially limited their implementation in research. Furthermore, until recently technology lacked optimal data capture capabilities (e.g., low sample frequencies) and typically featured somewhat invasive designs (e.g., increased clipin height, weight, and modifications to the rigidity of the ski) that inevitably degraded measurement validity. Moreover, while biomechanical analysis in alpine skiing appears in the published literature in the 1980s ( 5), modifications to the ruling structures, slope preparation, and ski-binding technology mean that the biomechanical environment in which the athletes perform has changed markedly (24). Consequently, despite a recent thrust in ski-research efforts coinciding with the development of portable technologies (e.g., high frequency, portable, low-cost inertial units), there is still a paucity of published information on the topic (16). Ski-forceplatform systems have benefited from similar technological advances (25), but an inability to determine the snow referential complicates separating the proportion of force output applied effectively during a turn (i.e., Fr). While Fr can be computationally separated from total force when measured from an inverse dynamics model applied to center of mass (COM) Force in giant-slalom skiing 4 kinematics, the total SRF might not exactly track that produced by the limbs in isolation. Consequently, a combination of approaches might represent the best means of providing a holistic view of SRF output characteristics in skiing.

The aims of the present study were to i) clarify the association between skiing performance and optimizing trajectories and/or maximizing velocity, ii) test the importance of Fr in skiing performance, and iii) further explore the importance of force magnitude and/or orientation of force-output in skiing turn performance. To this end, we measured force output and positional data using a combination of recently validated ski-specialized force plates (25) and a sports GNSS system on high-level skiers while they performed a race-paced short GS course. Based on previous research, our hypothesis was that performance would be well predicted by a capability to minimize energy dissipation, associated with elevated Fr output. We further predicted that Fr would be largely determined by both the capability to produce force and orient it radially. Lastly, provided the total force produced by the lower limbs is a limiting factor for Fr, we assumed that athletes who presented greater total force would do so by producing more force to both the outside and inside limbs.

MATERIALS AND METHODS

Participants and protocol

Alpine skiers with diverse backgrounds (N=16), training histories, and performance levels (i.e., ski monitors and club participants to current World Cup competitors) participated in this study (age 26±5 yr; stature 1.79±0.06 m; body mass [BM] 84.0±8.1 kg; course time [T] 29.14±1.60 s) over a 5-week period in winter. Athletes were devoid of any injuries that would affect their ability to participate fully in the testing. Before testing commenced, athletes were instructed on the testing procedures, allowed an opportunity to answer questions, and then provided written consent regarding their participation in the study. All operational procedures were completed within the ethical requirements of the Fédération Française de Ski and the Code of Ethics of the World Medical Association (Declaration of Helsinki), and approved by the ethics committee of the University Savoie Mont Blanc.

Athletes were equipped with a GNSS system and with specialized force platforms attached to race-boots and skis (see Figure 1), and then performed one warm-up of free skiing starting from the top of the mountain through the experimental course. Athletes then performed a competition-style personalized warm-up, followed by 2-3 familiarization runs. Once comfortable and familiar with the course and equipment, athletes proceeded to a small hut near the starting gate and performed a short calibration procedure for the equipment on solid ground (detailed in Section 3.3.1.).

-----Figure 1. Skier equipped with experimental technology. Pictured is a skier performing a trial, while equipped with boot-mounted force platforms, wired to an acquisition card carried in a small bag around the waist with a GNSS unit secured inside.

-----Athletes performed skiing trials on an 18-gate GS course, interspersed with approximately 15 minutes of passive rest (including non-fatiguing calibration procedures). The number of trials was decided based on whether the athlete reported submaximal effort or undue mistakes during their previous trial, corroborated by the experimenters, up to a maximum of 3 trials. During their trials, athletes took up place at the top of the course, the starting gate was set for timing, and athletes began their trial in their own time. The athletes were instructed to ski at maximum pace and were questioned on their efforts post-trial. Where more than one trial was performed, the trial with the fastest T was selected for final analysis.

Equipment and course characteristics

Course setting and monitoring environmental conditions

Throughout the duration of experimentation, snow quality (hardness, crystalline structure, and temperature) was monitored, as well as environmental conditions (temperature, wind, and visibility). The average temperature was ~1ºC, with the nights preceding testing having temperatures low enough to freeze snow on the course. The course setting was initially performed by a high-level ski federation coach, adhering to a GS setup: 18 gates, ~25º slope relief (see Figure 2). Netting poles were placed along the periphery of the slope which remained in place throughout the duration of the study, and to corroborate gate positions they were measured with respect to at least two external poles and the gates preceding them. Where necessary, measurements were made to additional immoveable points (pylons and skitrack mountings). As such, for each point we were able to triangulate the initial position, and corroborated using Force in giant-slalom skiing 5 both external and internal points, and accurately replicate the course setting throughout experimentation.

----Figure 2. Course representation. Depicted is a skier (not to scale, for clarity) traversing the course setup. ×, gates; grey line, athlete trajectory through analyzed gates (expanded for clarity); dashed lines represent the separation of the various analysis sections (speed, overspeed, and flat), with the approximate section characteristics (i.e., latitude and altitude) displayed in the corresponding axes (y-and z-axis, respectively). Note: since no course mapping was performed, section characteristics represent the average value between the turn-switches demarcating the beginning and end of each section, across all athletes and trials.

----

Ski equipment

For each trial, skiers were equipped with the same pair of race skis (model: LAB X-RACE GS, Salomon, Annecy, France; radius: 30 m; length: 1.93 m) and bindings (model: X19 LAB, Salomon, Annecy, France), the bases and edges of which were prepared by a ski technician before each experimental day. The skis were fitted with a binding plate fabricated to accommodate the elongated clip-in length resulting from the sensor attachment (+60 mm). Athletes were provided with a selection of race model ski boots (model: X LAB+ 140 WC, Salomon, Annecy, France), in 1 size (10 mm) increments between sizes 24.5 and 28.5. Where preferred, use of personal boot-liners (and/or tongues) was allowed. Athletes used their own race suits (or were supplied with the appropriately sized suit) and other International Ski Federation (FIS) approved race clothing and protective gear (e.g., helmet, goggles, and back protectors).

Positional measurement

Athletes were equipped with a portable (~20 g) sports GNSS system (model: Stadium tracker, Mac-Lloyd Sport, Paris, France), which was mounted in a small hip bag attached at approximately the height of COM (L5 vertebrae). The GNSS collected positional data from both Russian (GLONASS) and American (GPS) satellite constellation systems and featured a 9-axis accelerometer and IMU system (18 and 100 Hz, respectively; end data down sampled to 10 Hz). Data were collected using the manufacturer supplied software which featured a fusion algorithm designed to improve positioning accuracy by combining satellite derived data with that from the inertial sensors (26,27). Time between the start and end of the run was measured using an FIS approved wireless system (model: 'Basic wireless solution', Tag Heuer, La Chaux-de-Fonds, Switzerland), comprising of a starting-gate trigger and a dual-beam photo-voltaic cell set at approximately thigh height at the final gate in the course. For redundancy and data corroboration, two cameras (model: Hero 5, GoPro, San Mateo, USA) were used to record each skier: one operated by a researcher filming gates 6 through 9, and the second held by another researcher who followed the skier at approximately 5-10 m. Both cameras were affixed to handheld stabilizers (model: G5, FeiyuTech, Guilin, China). Cameras were manually time synchronized with each trial by filming part of the calibration process.

GNSS validity and reliability

GNSS units are widely used in the sporting literature (26), and while they can provide worthwhile data regarding a variety of relevant metrics for skiing performance in a practical and easy manner (28), accuracy is system dependent and highly variable (29). To test the accuracy of our system and methodological approach, we performed two separate analyses: i) a quasi-validity study, in which we compared key variables from the system against a criterion Real-Time Kinematic (RTK) system (see supplementary data), and ii) a test of intra-athlete reliability, where key kinematic variables were compared in athletes who completed two maximum effort trials of the current testing protocol (N=6). Lastly, as a strategy to reduce the potential error associated with our units, we selected an analysis approach that examined only turn-averaged data that was subsequently further averaged over a minimum of three turns (30).

Force measurement

A custom designed force collection ( 25) system was used in this study to provide 3-dimensional SRFs (see Figure 1, and Figure 3). The system (model: ISkiSet, Sensix, Poitiers, France) comprised of two cylindrical force sensors per boot each containing six full-bridge strain gauges. Each force sensor was affixed between two brackets to create a floating frame, where the sensors were the only point of connection between the skier and the ski. The units weighed 1.2 kg each boot and raised the clip-in height by 6 mm. The units connected by cable to a small hip-mounted acquisition card (model: Jam Ingénierie, Chambery, France), which was equipped with a synchronized inertial unit (model: LSM9DS1, STMicroelectronics, Geneva, Switzerland). Raw output, acceleration, and gyroscopic movement were amplified and recorded at a sampling frequency of 200 Hz. Each set of boots underwent a lab-based calibration procedure Force in giant-slalom skiing 6 (details explained in 31) to provide an accurate estimate of force and torque on each axis. The result was a selection of boot-specific calibration matrices that were applied (model: MATLAB 2019B, Mathworks, MA, USA) to the raw amplitude signal from the force. The raw voltage provided by the sensors was converted into force units using the appropriate calibration matrix per boot size.

-----Figure 3. Ski-specialized force plates. Pictured are the specialized force-plate devices used to collect the primary SRF data in this study, attached to a pair of standardized boots used during the experiment. The novelty of these devices in contrast to previous designs is that the circular strain gauges are situated at the front and rear of the boots, where they are affixed between two 'floating' metal brackets as the only point of connection between the skier and the ski. This shift in the placement of the strain gauges enabled clip-in height to be minimized, and the mass to be reoriented more distally compared to previous iterations. Each force plate could provide force and moments in three axes (medio-lateral=x, antero-posterior=y, normal=z), but only resultant forces were examined in this study.

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Data Analysis

Calibration, synchronization, filtering and turn selection processes

During the calibration procedures, athletes collected trials while balancing on each ski; the raised force plate was 'zeroed', with the other plate collecting athlete BM. These files were saved for later use in normalizing variables to BM, which corresponds to total system mass, including all clothing and technology equipped during the skiing trial (i.e., athlete tare BM, plus the normalized mass of the skis, force plates, boots, and personal equipment). Pre-and post-trial athletes performed a strong double limbed jump on their skis; this was to provide a clear spike on force and acceleration signals (from both the GNSS and the force-plate acquisition card) to synchronize data streams.

Force data were then combined to create a resultant value for each limb and zeroed. Data from the GNSS were resampled to match the force plates (i.e., from 10 to 200 Hz) using cubic spline interpolation, and then smoothed using a 2 nd order Savitzky-Golay filter with a window of 201 frames. Force-plate and GNSS data were synchronized using algorithmic cross-correlation applied around the impulses created from the athlete's jumping motion (100 frames either side of detected peaks from the on-board accelerometers of the GNSS and force-plate acquisition card). The filtering frequency for force and positional data was first approximated based on previous research (32,33), and then confirmed via Fast-Fourier transformation, and manual observation of the power spectral density, to remove higher frequency domain data not relevant to our analyses (e.g., vibration (34)). Subsequently, the force and positional data were filtered using 2 nd order low-pass Butterworth at 8 and 1.5 Hz, respectively. From this point, the synchronized and filtered data streams were separated into distinct turns using the point of inflexion in the trajectory (35). These turn-switch events were determined by searching for the point of sign change (+ to -, or vice versa) on the triple derived trajectory data. The final temporal markers were used to cut the synchronized force and positional data into distinct matrices corresponding to each turn. 14 turns (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) were selected for final analysis, representing athletes having attained reasonable speed (i.e., stopped pushing with poles and skating to accelerate) to the turn directly preceding the final gate.

Section selection

From the total analyzed turns, two main steps of analysis were chosen: i) 'course' averaged variables, where the average performance over the total analyzed turns was considered as a single coherent value for testing our hypotheses, and ii) 'sectional' averaged variables, where the course was separated into distinct typical sections known by ski practitioners, each characterized by the specific relief of the course and basic kinematic data (i.e., velocity and turn time): a section with the intent of gaining speed (Section 1: 'speed', turns 3-5 and 15-16), a steep section where athletes managed speed that potentially was at risk of exceeding their 'velocity barrier' (Section 2: 'overspeed', turns 6-10), and a flat section where athletes maintained speed (Section 3: 'flat', turns [11][12][13][14]. The distinction was made separately by different experimenters possessing experience in high-level ski coaching.

For each force platform, axis data were combined into resultant force:

𝐹 res i = √𝐹 x 2 + 𝐹 y 2 + 𝐹 z 2 [1]
with Fresi the magnitude of the resultant SRF for each force plate (outside [Fout] and inside [Fins] limb per turn), and Fx, Fy, and Fz the magnitude of the force components in x-, y-, and z-axis of each ski referential. The magnitude of the total force produced by both limbs onto the snow (F) was obtained by the sum of the magnitudes of Fout and Fins and considered as the same magnitude as the resultant SRF applied to the COM. While the true magnitude of resultant SRF is unknown due to the impossibility of detecting the orientation of each ski in space (i.e., the true vector orientation for Fout and Fins), the error induced by any potential differences in SRF orientation at each ski on F is assumed to be minimal. The absolute difference between the limbs was calculated at each instant and expressed as a percentage of F:

𝑑𝑖𝑓𝑓 = |(𝐹 out -𝐹 ins )| 𝐹 ⁄ [2]
From this point, the following variables were calculated for each turn: average F (Ftot), average diff (Fdiff), peak values for F (Fmax) and for the outside and inside limbs (Fmaxout and Fmaxins, respectively). For data provided from the GNSS unit the following turn variables were calculated: velocity at the entry (vin) and averaged (vavg), and the cumulated displacement per turn (L, as the trajectory based performance parameter (11), for use in the analysis model described in Section 2.5). Turn radii (r) was calculated by fitting three consecutive points of the trajectory (at its native frequency of 10 Hz, up sampled to 200 Hz [i.e., 60 consecutive points]) with an arc segment (36). Radial force (Fr) was computed by summing the centripetal force and the component of the bodyweight (i.e., BW in N) acting on the radial direction of the turn when angle of the slope ≠0 (37):

𝐹 r = 𝑣 2
𝑟 ± 𝑔 sin 𝛼 cos 𝛽 [3] with α equal to slope relief, and β as the angle between the COM trajectory and that horizontal to the fall line. Then, r and Fr were averaged over each turn. The ratio of forces (RF) was expressed as the ratio between turn-averaged Fr and Ftot. See Figure 4 for an example of the course averaged output of primary kinetic variables.

----Figure 4. Turn-averaged force-outputs for a single high-performing athlete. Data, in this case, has been normalized as a percentage of turn duration. The solid black line represents total force output (Ftot); the longdash-dot black line represents the force output of the outside limb (Fin); the long-dash-dot-dot black line represents the force output of the inside limb (Fout); the short dashed black line represents radial force output (Fr); all force data are displayed as a factor of BW.

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The primary macroscopic performance factor in this study was total course time (T). In contextualizing sectional performance, we used the change in specific mechanical energy for the turn, normalized to the velocity at entry to the turn (vin) as a velocity-based parameter (11) and as the index of performance for the turn (∆emech⁄vin (21)):

∆𝑒 mech 𝑣 in ⁄ = ∆(𝑣 2 2 ⁄ + 𝑔 • 𝑧) 𝑣 in ⁄ [4]
where z corresponds to the altitude, and ∆ the change between two turn-switches (i.e., the beginning and end of a turn). ∆emech⁄vin provides a valuable method of accounting for the influence of performance of previous turns (2,9,11), and has been used to describe the withinturn performance of a range of athletes: a higher ∆emech⁄vin (commonly, the 'less negative') is interpreted as less energy dissipated or more energy produced (if any), since the value is negative when energy is dissipated (2,9).

Statistical analysis

Statistical analyses were performed using JASP (version: 0.11.1, JASP Team, Amsterdam, Netherlands). T originally violated the assumption of distribution normality (Shapiro-Wilkes score, p=.04), which after further inspection was due to an outlier in the dataset.

While the data appeared congruent with the other scores and consistent with video observations, data from this athlete were removed due to the sensitivity of the subsequent models to outliers (final N=15).

Force in giant-slalom skiing 8

In the first instance, key variables (turn time [Tturn], vin, ∆emech/vin, L, Fr, RF, Ftot, Fout, Fins, Fdiff, Fmax, Fmaxout and Fmaxins) were compared between sections using repeated measures ANOVAs with Holm post-hoc tests, and Cohen's d for magnitude of difference. To characterize the determinant nature of force production, we developed a stepped analysis procedure (Figure 5) to be applied to all datasets: course, speed, overspeed, and flat. The model consisted of two primary statistical approaches: Bivariate correlation, using Pearson's correlation (r±95%CIs, p) and stepwise multiple regression (standardized β, F, R 2 change [per variable], and model R 2 [adjusted], p) analyses. In the first level, correlational analysis tested sectional performance parameters (∆emech/vin and L) against course performance (T). The following level tested the clear predictive nature of sectional Fr to sectional ∆emech/vin and to T. The next two levels of the model employed multiple regression analyses to test the relationship and contribution of force magnitude (Ftot) and application effectiveness (RF) to Fr. Subsequently, Ftot output was contextualized using the same multiple regression model to test the output and balance between the limbs (outside limb [Fout] and the difference between the limbs [Fdiff]).

----Figure 5. Modular outline of approach to data analysis, applied to all sectional datasets. 'Multiple regression' models (continuous lines) feature stepwise entry criteria, and 'Correlation' models (dashed lines) are Pearson's product moment correlation coefficient.

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The strength of Pearson's correlations was interpreted using threshold values of r<0.1, 0.3, 0.5, and 0.8 to represent trivial, small (minor), moderate, large (strong), and very large (very strong) effects, respectively (30). For Cohen's d threshold values for qualitative interpretation of effect magnitude were d<0.2, 0.2, 0.5, and 0.8 as trivial, small (minor), moderate, large (strong), and very large (very strong) effects, respectively. The alpha value for all tests was set at .05.

RESULTS

For the reliability in course level kinematic data, the systematic variability was <2.1%, and the random variability was CV<2.86% for all variables except for ∆emech/vin (CV=4.95%). For sectional data, systematic variability was 0.3-4.6%, and the intra-athlete variability was CV=1.3-5.7% for all variables except for ∆emech/vin, which ranged from CV=6.4-9.21%. For the validity comparison with the RTK system, bias between the systems for 'sectional' turn groupings was -1.0-1.4%, agreement r=0. for Tturn, vin, L, and Fr (for ∆emech/vin, bias=-1.3%, r=0.82, and CV=9.1%). For full methodological details and results of both 'sectional' and 'turn-by-turn' analyses see supplementary information. The repeated-measures ANOVAs showed sectional effects in all variables except for RF, Fout, and Fdiff (see Table 1).

Level 1 -Relationships between course and sectional performance parameters

∆emech/vin over the course, and in speed and overspeed sections, was negatively predictive of T (Table 2). L did not significantly improve the model in any case. In the flat section, no combination of variable models clearly predicted T.

Level 2 -Relationships between course and sectional performance parameters and radial force

Fr produced throughout the course and in speed and overspeed sections was negatively correlated with T, and positively correlated with section specific ∆emech/vin (see Table 3). In the case of the flat section, Fr was related to T, but not with ∆emech/vin.

Level 3 -Contribution of 'technical' and 'physical' capacities

In all sections both Ftot and RF were predictive of Fr (both variables clearly contributed to the predictive model) and explained the quasi-entire variance (R²>0.99) in Fr (see Table 4). Over the course and in the three sections, both RF and Ftot explained an important part of variance in Fr (R² change from 0.36 to 0.64) and presented high normalized effects (β>0.63), although the order of the two predictors in the explained variance and prediction strength changed with each section. Grey background denotes no clear prediction of independent variable; Course, data averaged over total analysis window (14 turns); CI, confidence interval; 1. Speed, turn averaged data from speed section; 2. Overspeed, turn averaged data from overspeed section; 3. Flat, turn averaged data from flat section; T, time in seconds between start and finish of course; Fr, radial force; ∆emech/vin, change in specific mechanical energy normalized to entry velocity of each turn; Note: all variables with the exception of T are averaged per the relevant section. (r=-0.002-0.13, p=.645-.996).

FORCE IN GIANT-SLALOM SKIING

DISCUSSION

This study showed that GS course performance in experienced to World Cup level skiers is better explained by an ability to minimize the dissipation of energy per section, rather than the distance traveled. This same finding was generally applicable within distinct sections of the course, except for a flat section in which neither normalized speed energy dissipation nor trajectory parameters could clearly distinguish athletes. Radial force output was strongly or very strongly related to course performance, and strongly related to less energy dissipation in most sections. Elevated production of radial force was explained firstly by a greater capacity to produce total force, and secondly to apply a greater proportion of this force in the radial direction. Greater force production capability was linked to an increased capability to generate force to the outside ski, and subsequently to apply force to the inside ski (i.e., a reduced difference between the limbs). In general, each of our hypotheses were confirmed, but were contextualized with stronger, weaker, or even absent relationships in specific sections; notably, the course performance was predicted by neither trajectory nor speed performance parameters in the flat section, and performance within this section (energy dissipation) was not clearly predicted by radial force production.

In general, our findings support other analyses (11) that preference methods of attaining and maintaining velocity while minimizing energy loss (e.g., carving (1)(2)(3)9)), rather than aiming to reduce path length (2,8). In our results course, speed, and overspeed sectional ∆emech/vin explained a substantial proportion of variance in T (R 2 =0.46-0.67, p<.003), whereas L did not. The overall lack of clear association between L and performance (course, speed, and overspeed sections) points to better athletes selecting strategies that enabled them to minimize dissipation of energy regardless of the trajectory. This could be a product of higher performing athletes possessing enhanced perceptual, technical, and physical capabilities, resulting in enhanced pattern flexibility to select the optimal trajectory per turn and entry characteristics. The lack of clear predictive value of speed and trajectory parameters in the flat section might highlight that these variables do not represent the best measure of performance in this section or that different strategies in this section can be associated to similar performances. Notably, the much lower relief of this flat section and potential energy production behaviors of the athletes could feasibly reduce the predictive ability of ∆emech/vin (38). Instead, performance might be more clearly predicted by 'determinant' parts of the course (9,16) that stress technical and physical athletic limits. The minorly weakened relationship between sectional ∆emech/vin and T in the overspeed section might be a result of athlete tactics; notably the purposeful dissipation of energy to benefit later turns (2). Such a tactic would create a negative result in the turn/section in which the dissipation occurred (in our analyses, weaken the negative correlation) but produce a net positive on overall performance. The first turn of the overspeed section follows a delayed gate, which might have necessitated some dissipation of energy ( 14) to avoid mistakes and elevate performance in later turns. Lastly, it is worth considering that ∆emech/vin is sensitive to computational and methodological errors, albeit at acceptable levels in our analyses (i.e., CV<10%).

Consequently, the error associated with this variable might have prevented the detection of otherwise significant interesting effects.

In general, there were strong to very strong associations between lower course times and greater Fr. Although there is little empirical data on Fr in skiing, our findings are congruent with evidence that performance is largely determined by attaining a high average velocity (5), and carving represents the optimal approach to skiing at speed while minimizing ski-snow friction (24). Logically it should follow that athletes exhibiting greater Fr would likewise minimize energy dissipation (i.e., a less negative ∆emech/vin), however this was not the case in all sections. While a clear and substantial relationship existed between elevated Fr and ∆emech/vin over the course and in speed and overspeed sections, this relationship was unclear in the flat section; which might suggest greater variability in the technique adopted to generate Fr (e.g., energy gain). Likewise, the moderate association observed between Fr and ∆emech/vin in the steep overspeed section, might suggest tactfully shedding some speed and circumspectly maintaining or even increasing Fr in later turns (observed in conserved strong relationship between Fr and T in overspeed section).

In any case, athletes who developed high sectional Fr were likely to attain faster course times, and thus logically would present a higher velocity barrier.

FORCE IN GIANT-SLALOM SKIING

In all sections, the combination of total SRF magnitude (Ftot) and the capability to apply a larger proportion of that output in the radial direction (RF) significantly predicted Fr. On average, 68% of Ftot was applied radially, with much greater values observed in overspeed and flat compared to the speed section. In this case, RF represents a ratio of 'mechanical effectiveness' in which better athletes theoretically apply a greater proportion of their total output in an efficient manner (i.e., higher proportion of Ftot radially). A similar model has been presented in sprint running and cycling, where it has been subsequently used to better understand the determinants of acceleration performance and orient training goals (39). Our results show that the weighted contribution of Ftot and RF to Fr changes in explanatory magnitude and hierarchical order depending on the section. On the one hand, in the speed section Ftot had much greater explanatory power than RF (R 2 =0.64 and 0.36, respectively). One possibility is that better athletes generated force in response to targeted dissipation, and transient and random vibrations ( 7) that might otherwise disrupt the motion of lesser capable skiers to maintain optimal skiing technique (and generate high levels of Fr). In the flat section Fr was much more strongly associated with RF than Ftot (R 2 =0.60 vs. 0.39, respectively), which might highlight the reduced necessity for targeted dissipation with athletes further from their velocity ceilings; the substantially lower ∆emech/vin in this section strengthens this theory, and it is possible that athletes performed positive muscular work and gained additional energy (38), which served to both partly compensate energy dissipation and to elevate Fr. Several studies have recorded positive values of energy loss in skiing, suggesting that some energy was regained (9,14,19) during rhythmic turns. However, in the overspeed section and over the total course, Ftot and RF were quite balanced in their contributions to elevated Fr (e.g., course, R 2 =0.50 and 0.49, respectively). These findings have interesting implications for practice, since in general better athletes both technically orient a larger proportion of force to perform at preferable trajectories and speeds (i.e., elevate carving, as a product of improved Fr) and display generally enhanced force output on the skis. However, since the absolute physical aptitude of the skiers were not measured in this study (rather, the ability to exhibit output within the constraints of skiing) it is unclear whether force output on the skis (radial, or otherwise) represents or is limited by i) maximum athletic capacity, ii) maximum athletic capacity mediated by various constraints (technique, tactic etc.), or iii) a combination of these and other factors. Evidence of near maximal muscular activation during skiing (40) and enhanced physical capacity for force in skiers ( 6) would support the theory of physical capability being a determinant factor, but further evidence is needed.

Athletes produced force at approximately a 2:1 ratio between the outside and inside limbs. While greater force applied to the outside limb was hierarchically the strongest predictor of global force output in all sections (p<.001), a strong inverse relationship with the difference between limbs was observed (p<.001) in all sections; specifically, a globally higher total force output was explained by a higher force output of the operative limb and an associated more equal application of force between the limbs (i.e., disproportionately greater contribution of the inside limb). These findings were further corroborated with individual correlations between force produced to both the inside and outside limbs (Fins and Fout, respectively) and sectional Ftot, without relationship between the limbs. There are several possible explanations for this finding, each of which assume a relationship between total force and carving (24) (tested in Level 3). There are two scenarios representing better performance (i.e., a higher Fr): tighter turns (i.e., lower radius and shorter trajectory) and turns performed at higher speeds. In the former example, a skier aiming to reduce their turn radius must first increase the edging angle of the ski (41).

In this aim, athletes incline their body laterally towards the center of the turn, where applying force at this increased edging angle acts to bend and carve the skis through the snow resulting in a tighter radius (24). The capability to turn with tighter radii depends on the capability to produce forces to the mechanically advantageous outside limb at a biomechanically unique position. Increasing edging angle requires inclination of the upper body towards the turn center where some application of force to the inside ski is needed to maintain control and active balance (42). However, evidence showing supramaximal (>maximum voluntary isometric contraction) levels of activation (43) indicates turns that require very high levels of Fr may supersede the single-limb force-production capabilities of an athlete; in such a circumstance, there is no other option than to apply a proportion of force using the other limb (or to disperse energy). In any case, this finding highlights the necessity of conditioned force output for the inside limb, which is notable given the disparate knee and hip angles at which these forces are produced between the two limbs (23,44). In physical conditioning, high-level athletes might focus on the development of force application at angles of the knee/hip complex relevant to the outside ski and the inside ski (~-20º for the inside limb, using a non-carving approach (43) and -34º in recent literature (23)). Such an approach should elevate the force production of the lower limbs in total (i.e., increase Ftot) and allow for more flexibility in performing turns that require both greater force application in general and an enhanced contribution of the inside limb (i.e., more balanced force profile).

FORCE IN GIANT-SLALOM SKIING

Limitations

Athletes were required to wear a variety of relatively unfamiliar equipment which may have affected their performance. While steps were taken to resolve this factor (e.g., athletes provided with their preference of boots, familiarized and confirmed the setup did not unreasonably compromise their capabilities) athletes may not have performed at their peak. The methodological approach of averaging multiple turns was chosen to reduce error (30), provide a more macroscopic view of performance, and to highlight the capability of detecting worthwhile differences in performance using more accessible GNSS technology. While our results support the conclusions of more detailed analyses (11), including those from other disciplines (2,9,14), turn-by-turn analyses afforded by higher accuracy positional devices (e.g., low-cost RTK) would aid in further contextualizing the relationship between force output and performance in skiing. While in this study carving is considered the 'optimal' technique, there are instances in which athlete deviate from this approach and preference other strategies. These instances might result in a more beneficial overall performance for the athlete (5,16), but are not directly considered in our model.

CONCLUSIONS

Our results support other analyses that better GS performances are predicted by lower energy dissipation at higher speeds. Higher radial forces are related to performance and are determined by both total force production and an enhanced ability to orient a greater proportion radially. The contribution between production and orientation of force varies depending on course characteristics. Athletes who apply more force (and potentially perform better) adopt techniques which elevate total force output via the outside limb, and subsequently a proportionally greater contribution of the inside limb. These results strengthen evidence for enhanced force-output capacities in ski racers and might provoke conditioning focus for the inside limb. While both 'technical' and 'physical' force qualities appear determinant in GS skiing, we cannot conclude whether the athletes were truly exhibiting their physical limits; further detailed analyses, including cross-examination of off-snow tests of physical output, should help clarify these points. Increased force-output capacity, in combination with adopting techniques to improve force application effectiveness (RF) on the skis, should raise radial force capacity and allow athletes greater physical and technical freedom in trajectory selection. Lastly, these results may be context, technology, or athlete specific, and should be tested in greater depth.

INTRODUCTION

n alpine skiing, measurements of trajectory are valuable for biomechanics research and for practitioners to provide worthwhile feedback to athletes. Unfortunately, the nature of alpine skiing challenges collecting such data. Several accurate capture methods exist (e.g. motion capture), but their complexity often results in brief capture windows (1-3 turns). Global Navigation Satellite Systems (GNSS) have been proposed as a feasible means of providing a variety of important metrics for performance, ranging from simple time and velocity data, to more sensitive parameters like change in mechanical energy (1). As such, the ongoing development of increasingly accessible GNSS technology is of interest (2). Regardless, since substantial variability exists among and between GNSS units (3), it is important to ensure systems provide accurate and reliable enough data to detect worthwhile differences in performance metrics.

The aim of this pilot-study was to test the validity of a sports GNSS device to measure various performance parameters in alpine skiing. To this end, we performed two experiments: 1) a validity and reliability study for our custom compiled 'low-cost' Real-Time Kinematic system (RTK) on a known and repeatable trajectory against ground plot information, and 2) a criterion validity comparison between the RTK system and a sports GNSS system for individual turns, and multiple turns collapsed into 'sectional' averages.

METHODS AND MATERIALS

Procedures

Mountain coaster experiment

An RTK unit was fixed on a mountain coaster rail system, that circulated throughout an overcast morning of experimentation. The rail system was at a French ski resort (Saint François Longchamp, France; altitude ~1700 m), and consisted of a ~996 m track that turned back and forth alongside a ski slope, along which a twoseated sledge circulated at a velocity controlled by the riders (via a braking system). The sledge path was practically immovable, comprising of a central metal rail and two adjoining parallel rails.

The RTK antenna was placed in the center of a padded seat at the rear of the sledge above the riders' heads, and the electronics in a small bag affixed to the bottom of the seat. A base station was attached to the roof of a vehicle positioned in an unobstructed location near the bottom of the course. We performed 4 separate trials in the morning over three hours in overcast metrological conditions. Each run had different velocity traces (and time) due to non-repeatable braking patterns. The mountain coaster was selected for this test for three interrelated reasons: 1) it provided a quasi-identical trajectory across multiple runs, which significantly improved the ease with which numerous trials can be compared for reliability, 2) it shares key similarities to skiing, including a mountainous environment, similar speeds, and quasi-similar alternating turning styles, and 3) while unable to access a higher quality reference system against which to validate the system, we were provided with a digital highresolution ground-track document that allowed digitization for overlay and comparison.

Skiing experiment

Athletes performed two trials of a marked giant-slalom course while equipped with a custom-built RTK and a sports GNSS system. The experimental collection was performed during the final stages of habitual training, and as such the athletes were already familiar with the course, warmed-up, and ready for maximum effort skiing. Athletes performed 1-2 race-paced runs, after which various performance metrics were derived from individual turns and sections (consecutive grouped turns) and then compared to test the validity of the sports-GNSS device. Athletes provided written informed consent, the operational procedures were approved by the ethics board of University Savoie Mont Blanc, and procedures were in congruence with the Declaration of Helsinki.

The athletes were female regional-level skiers (N=4; age, 19±1 yr). Testing occurred on hard groomed snow, and during stable environmental conditions (~1 hr, during the morning). Brush gates were set by a federation coach to model a giant slalom setup (20 gates) on a moderate grade consistent grade slope (~17º relief). Athletes wore their own boots and used their own ski gear and equipment (e.g. helmet, goggles, and back protectors). Athletes were equipped with two distinct systems that provided positional data: 1) a sports GNSS system (model: Stadium tracker, Mac-Lloyd Sport, Paris, France), and 2) a custom-built RTK (as the 'criterion' measure).

Two separate 'rover' RTKs were worn by athletes during the testing period in a small backpack, with the antenna attached to the helmet in the same manner as the sports GNSS. An identical unit was used as a base/reference station that was fixed to a tripod on a flat open area above the testing site and remained stationary and unobstructed throughout the testing procedures.

Equipment

For both experiments, position was provided by RTK (see Supplementary Figure 1) compatible GNSS unit/s built from the following componentry: a high-fidelity antenna (model: ANN-MB, uBlox, Thalwil, Switzerland; gain, 28±3.0 dB) and RTK compatible receiver (model: M8T,uBlox,Thalwil,Switzerland), wired to a small portable computer (model: RasberryPi zero, Kubii, Lyon, France) and small battery pack (~100 g). The units were capable of reading signals from a variety of satellite systems (American For the skiing experiment, an additional sports GNSS system provided positional data from the Russian (GLONASS) and American (GPS) satellite systems at a down-sampled rate of 10 Hz fused with data from an onboard inertial measurement unit (4). The units were lightweight (~20 g per unit) and were worn attached to the helmet of the user using commercial Velcro.

----Supporting information 2. Figure 1. Low-cost Real-Time Kinematic (RTK) device. Clockwise from top: battery pack, RTK compatible receiver, padded bag to house electronics around waist, portable computer system, and high-fidelity antenna.

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Data analysis

For each experiment, rather than providing 'real-time' feedback, the data from the RTK rovers and base-station were extracted and analyzed post-operatively using programs from the RTKLIB (version: 2.4.3 b33) directory (5). The distinct navigational data from the rover and base station were combined to provide kinematic positioning solutions, with an elevation mask of 20° to exclude low-strength satellites (per the manufacturer's instructions). Where used, the sports GNSS data were downloaded using the manufacturer supplied software. From this point, the results were imported and processed using MATLAB (model: R2019b, Mathworks Inc., Natick, Massachusetts, USA).

Mountain coaster

The downhill portion of the run was separated from the total course for analysis, just after the release of the carriage for the first run (i.e., just after the first low speed turn). The rationale for this decision was that the beginning, uphill and straight portions of the start of the course were covered with roofing which impaired signal acquisition, in addition to comprising mostly slow or stationary periods of motion. Just before the downhill portion the RTK system transitioned to a fixed solution. Data were synchronized at a distinct geographical point and zeroed in all axis. The raw, unfiltered data were used for comparisons.

A reference ground track was generated from the information obtained from a high-quality digital document. Specifically, distinct data regarding the measurement scale, and the center axis of the sledge track was extracted using image digitization in MATLAB. Due to the lack of exact geographic positioning, the resulting longitude-latitude data for the ground track was rotated to fit the overlaid trajectories of the RTK system using cross-correlation. Note: the plans from which the ground track was digitized were preliminary building plans which did not necessarily represent the exact dimensions of the finished structure, and represented the center of the rails upon which the sledge ran (i.e., the RTK antenna was ~1.5 m above the rails, and the rails ranged from <1 m from the ground to >3 m). As such, this comparison features several limitations which we will discuss in the interpretations of the results.

Skiing

Positional data (longitude, latitude, and altitude) were smoothed (11 frame Savitzky-Golay), and then low-pass filtered (1 Hz 2 nd order Butterworth). The files were initially cut at just before and after the trial using velocity-time data. From this stage, individual turns were extracted using the point of inflexion in the triple derived longitude positional data (6) as distinct turn-switch events (i.e. the end of one turn, and the beginning of the proceeding turn). Turns during which the RTK system did not provide the most accurate outcome solution (i.e., 'float' rather than 'fixed' = four turns in total) were excluded from the analysis for both units. The final data selected for analysis consisted of 16-17 turns per athlete (total of 93 turns), depending on the 'tactical' approach to the first and last turn cycles (e.g., early skidding on the last turn was excluded).

Parameter computation

Mountain coaster

For the RTK validity test, only longitude, latitude, and altitude were extracted for comparison across different runs. No other variables were extracted, mostly due to different operator speeds across runs voiding the possibility of assessing other interesting variable sets (e.g., energy behaviors). The difference in longitude and altitude data from the 'criterion' digitized ground track in m were computed along position in latitude for each of the four trials.

Skiing experiment

Per each distinct data stream, for each turn the following variables were computed: turn-entry and averaged velocity (vin and vavg, respectively), cumulated displacement (L, see ( 7)), average radial force (8), and the difference in specific mechanical energy normalized to the velocity at turn entry (∆emech⁄vin ( 9)).

Two distinct data analysis approaches were employed to test the validity of the devices: 1) Data from all possible turns were individually compared between the units (e.g. L turn 1 for each athlete, GNSS vs RTK), and 2) data from each athlete (16 turns, with first turn excluded where necessary) were grouped into 4 consecutive turns, averaged and then compared in the same manner (e.g. L averaged across turns 1-4 for each athlete, GNSS vs RTK).

Statistical analysis

For the mountain coaster, we adopted a simplified approach to detecting systematic and random error and variability to measure validity and reliability, respectively. Specifically, along each dimension of latitude, the mean and standard deviation of the four units for altitude and longitude were calculated. Subsequently the mean, and standard deviation of the mean represented the systematic error, and variability across the entire run, respectively. To represent the random error and variability of the RTK units, the mean and standard deviation of the standard deviation were similarly calculated across the entire run.

Descriptive data are presented as means±standard deviation. The RTK and GNSS data were compared using linear regression, Pearson's correlations, and typical error. Overall bias between the methods was assessed using the mean difference between the practical (GNSS) and that determined from a calibration equation via regression analysis of the criterion (RTK) and reported in raw units ±95% confidence intervals. Strength of agreement between the two measures was assessed using Pearson's correlation coefficient (r) on the log transformed data, and threshold values of 0.3, 0.5, 0.7, and 0.9 to represent weak, moderate, strong, and very strong agreement, respectively. Typical error of estimate as the coefficient of variation (CV%) provided a measure of error magnitude. Analysis was repeated on all turns in the first instance, and then on the grouped turns from all athletes.

RESULTS

For the mountain coaster, the mean systematic error compared to the ground track in longitude data was 0.697 m, with the variability along the course in this error being 0.616 m. For altitude, the mean systematic error compared to the ground track was 0.431 m, with the variability along the course in this error being 0.366 m. For longitude data, the mean random error was 23.18 mm, with the variability along the course of this error being 7.47 mm. For altitude, the mean random error was 185.42 mm, with the variability along the course of this error being 66.05 mm. The longitude-and altitudelatitude data are presented in Figure 2 and3, respectively.

Full descriptive data and results for the skiing test are presented in Supplementary Table 1, with plots of the bias ±95% limits of agreement (associated to Bland Altman plots) for the two levels of analyses displayed in Supplementary Figure 5. Turn-by-turn data were typically low bias (<1.5% for all variables, except ∆emech/vin [4.5%]), with moderate to very strong agreement in all variables. In general, variability was low (CV<5%) except for Fr and ∆emech/vin which exhibited large and very large error (7.0 and 12.9%), respectively.

Sectional data understandably shared similar bias scores to turn-by-turn analyses (<1.4%), but agreement was substantially improved with all but Fr representing strong or very strong agreement (moderate agreement for Fr). Similarly, error was markedly reduced by adopting a sectional approach, with all variables CV<9.1%.

DISCUSSION AND CONCLUSION

Despite systematic error in our measurements, we can infer validity and excellent reliability in our RTK. The sports GNSS unit provided sufficient estimates of several key turn-averaged performance parameters in ski racing. While surprisingly the values provided from turn-by-turn analyses appear generally acceptable, adopting a sectional approach markedly reduced systematic error. As such, practitioners and researchers might benefit from adopting a sectional approach in their analyses and athlete feedback; particularly when examining variables such as ∆emech/vin and Fr that are valuable in contextualizing skiing performance but suffer from inflated computational errors. Such an approach could feasibly allow the use of common sports GNSS technology into alpine skiing practice and research; albeit requiring post-processing and considering remaining error rates.

The results from our mountain coaster experiment depict low levels of random error and variability in both z-and x-axis data (altitude, and longitude). In fact, we assume these error rates are inflated, as the rails of the coaster slightly flexed as a function of the force applied to the track. Moreover, while the z-axis error was understandably higher (3), the necessity of normalizing along y-axis (latitude) data for our comparison is a clear explanation for overly inflated variability. In any case, these results are encouraging for the integration of similar technologies into alpine skiing practice, given the similar characteristics under which this experiment was performed (e.g., alpine environment, similar speeds and trajectory characteristics). Supporting information 6. Figure 5. Bland-Altman plot of the differences in variables calculated from the RTK and GNSS. vertical pairs of plots correspond to each variable, with the horizontal corresponding to either turn-by-turn analysis (a), or 'sectional' analyses (b). y-axes display the difference between the two devices for the corresponding variable, with the grey lines representing limits of agreement (±1.96 SD). vavg, averaged velocity; vin, velocity at turn entry; L, cumulated distance travelled; Fr, radial force; ∆emech/vin, change in specific mechanical energy normalized to velocity at turn entry; s, seconds; m/s, meters per second; m, meters; N/kg, Newtons per kilogram; Js/kg/m, joule seconds per kilogram per meter. Note: turn-time is not displayed in this figure, since the data were not easily readable (majority of differences were identical, at either 0 or 0.1s). While at face value the mountain coaster validity data appear average, there are several explanations for these results. Namely, the position of the RTK antenna was above that inferred from the ground track of the coaster, and along the track the rails were set to pivot the coaster back and forth. As such, this pivoting created an offset in the longitude-latitude position between the top of the sledge (i.e., the antenna position) and the ground track. This pivoting typically occurred during turning (i.e., to offset Fr), and probably explains the characteristic tracking of the RTK trajectory inside each turn (see the clear and repeated offsets in Figure 2). Moreover, since the digitized plan was not final, presumably there are some minor differences between our plot and that finalized on the course. For these reasons, we believe we can infer validity from our results, however validation using a true criterion device is needed.

FORCE IN GIANT

Particularly, concerns still exist regarding the capability of such units to detect appropriate targeting solutions in various environments, since a known issue with such 'low-cost' units is their disposition to fail to find a fixed solution, or detect a 'false' fix (3,10). More research using similar updated technology-notably integrating higher quality antennae and higher sampling frequencies in congruence with the concerns of previous investigations ( 10)-are warranted.

Among the limitations of this pilot approach were both units being mounted to the head, which was chosen for practicality (i.e., difficulty attaching both units in a small space, without compromising athlete safety), and for the likelihood of clear satellite coverage for both units. Moreover, our RTK system has not been validated due to the lack of access to technology with higher resolution. While tests of RTK systems (high (11) and low-cost ( 12)) report excellent accuracy, future applied research is needed in alpine skiing.

Sufficiently accurate performance data can be measured from sports GNSS units, particularly when paired with a 'sectional' approach to analyzing and presenting data. While acceptable, error associated with force and energy behaviors was still present and should be considered when interpreting study results. Our results suggest that while moderate quality GNSS units have their limitations and should be interpreted in tandem to the inflated error compared to more accurate tools and measurements, they might still represent a means of providing valuable performance metrics in research and practice. In alpine ski racing, different line choices can drastically affect turn or sectional performance. The straight-line transition between two turns is the main phase where skiers can gain speed in a race, open their trajectory, or reduce their path length. Between two turns, a skier can foster speed increase by spending more time in a straight line, inducing sharper turning phases (Z strategy). Inversely, speed can be conserved during the entire turn cycle by performing long curved turns separated by a short straight line (S strategy). This research aimed to evaluate the kinetic and kinematic specificities associated with the line strategy and to explore interactions of selected strategy with skier performance and energy dissipation. A mixed-level population of male alpine skiers (n = 17) skied a timed giant-slalom course while equipped with specialized force plates and a positional device collecting synchronized normal ground reaction force and position-time data, respectively. Time of edge switch was computed from the force signal as the period with the lowest force application on the outside ski. From positional data, turn cycles were separated into turning and straight-line phases (radius bellow and above 30 m, respectively). Time length, path length in the straight line, speed amplitude, and change in specific mechanical energy were computed for each turn and averaged for each skier. The path length during straight line was used to continuously characterize the line strategy within the spectrum between the Z (long straight line) and S (short straight line) strategy. Path length in the straight line was correlated with the amplitude of speed over a straight line (r = 0.672, p = 0.003) and relative and absolute time spent in the straight line (r = 0.967, p < 0.001). However, path length in straight line was not correlated with decrease of speed in the following turn (r = -0.418, p = 0.390) or time without force application on the outside ski (r = 0.195, p = 0.453). While higher-performing athletes on the course performed turns during which they dissipated less energy when normalized to entry speed (r = -0.620, p = 0.008), it appears they did so with variable turn strategies approaches.

APPENDIX IV: FRONT SPORTS ACT LIVING, IN PRESS

INTRODUCTION

To achieve the lowest possible race time, alpine skiers must continuously adapt their strategy and technique. Skiers perform turns according to their position, speed, and balance (influenced by the previous turn), individual capacity evolving with fatigue (technical, physical, psychological), and environmental factors (e.g., snow characteristics and micro reliefs, steepness, visibility, course setting, ski gear) (Supej and Holmberg, 2019). Some parameters cannot be anticipated before the race, which means skiers must continuously adapt their turn line strategy throughout the race.

In this article, the alpine skiing turn is defined by a straight line (SL) followed by a turning phase (TP). The trajectory and overarching turn characteristics the skiers choose (i.e., "line strategy") can generate substantial differences in turn-time in giant slalom (GS) [START_REF] Brodie | Fusion motion capture: a prototype system using inertial measurement units and GPS for the biomechanical analysis of ski racing[END_REF] or on the following sections (Supej and Cernigoj, 2006). Skiers accelerate quasi-exclusively by converting potential energy into kinetic energy during the SL, while aerodynamic and ski/snow friction dissipate energy notably during TP. Energy dissipation characteristics are used to quantify performance [START_REF] Hébert-Losier | Biomechanical factors influencing the performance of elite alpine ski racers[END_REF] and are commonly defined by the differential of the sum of kinetic and potential energy normalized to skier mass (m) (Supej, 2008;[START_REF] Reid | Turn characteristics and energy dissipation in slalom[END_REF]. Since performance is partially dependent on the turns preceding it, normalizing energy dissipation to the velocity at the entry of the corresponding segment (v in ) provides a means of characterizing sectional performance ( e mech/ v in ) (Supej and Holmberg, 2019). From a mechanical perspective, better turns are described by dissipating less energy via friction while following the most direct trajectory, which maximizes the transfer between potential to kinetic energy (Supej, 2008).

At every turn, skiers must balance between two strategic line approaches (Supej, 2008;Federolf, 2012).

The first line strategy focuses on reducing mechanical energy dissipation throughout the TP by avoiding skidding. This line strategy is typified by "carving" the skis in long arcing turning phases initiated higher on the slope and greater turn radii during the TP (Müller and Schwameder, 2003). It induces longer TP time, typically longer path lengths, an "S"-shape trajectory, and less speed gained during the SL due to less time spent close to the fall line. Barring high-energy dissipation during the TP, the technique should induce a low variation of energy dissipation during the turn. Coaches advise adopting this technique during low-dynamic phases and in flat, high-speed, and straight sections and do not recommend it after periods of high-speed dissipation (for example after heavy braking due to mistakes or cornering) (Lind and Sanders, 2004). The second-turn line strategy is based on maximizing the transfer of potential to kinetic energy between gates by following a trajectory closer to the fall line. Following this line strategy, skiers will typically delay the beginning of a TP and create a long SL between short TP resulting in a "Z"-shape trajectory. Since more time is spent close to the fall line, skiers gain more speed, and dissipate little energy during the extended SL phase. However, the approach is also characterized by sharper turns (i.e., lower radii), which might change ski-snow interactions and induce skidding and associated energy dissipation during the TP. Consequently, this approach is recommended by coaches in steep, turning, and high dynamic sections. Skiers adopting these two approaches could feasibly gain the same turn or sectional performance, with drastically different energy behaviors (i.e., variability in energy dissipation within the turn) during each turn. Theoretically, these two strategies are called "S" and "Z" strategies in this article, respectively, and represent opposite ends of a continuum of performance separated and identified by length of the SL.

Few studies have assessed the interaction between line strategy and performance. Articles focusing on turn line strategy and e mech in giant slalom (Supej, 2008) or in slalom (Federolf, 2012) have not presented clear correlations. This result may be linked to the small and homogeneous observed samples or specific factors relating to the course setup (e.g., a small number of gates observed). Moreover, for skiers with higher v in (typical of high-level skiers), increased velocity or preserved energy is more challenging than for other skiers, and the normalization per entry velocity (i.e., e mech/ v in ) effectively quantifies skiing efficiency. Consequently, subsequent investigations presented a very strong correlation between e mech/ v in and race time in slalom (Supej et al., 2011) and in GS (Spörri et al., 2018). In the latter example, the authors presented a mechanical model of performance that quantified the weighted contribution of the capacity to gain or maintain speed relative to the previous section performance (i.e., e mech/ v in ) and the trajectory of the skier (as the cumulated distance per turn) (Spörri et al., 2018). Better-performing skiers typically minimized energy dissipation relative to e mech/ v in , without an association with path length. The authors concluded that potentially the turn may be separated into phases with distinct aims, with the former half of the turn characterized by minimizing dissipation of energy and a shortening of the path length being preferable in the latter. Spörri et al. (2012) reported that a higher altitude of turn initiations and turn ends were associated with a reduction of time on short sections around the analyzed turn-albeit based on only one skier trial. However, while the interaction between line strategy and performance is associated with minimizing sectional energy dissipation relative to entry velocity, SL, and TP specific energy behaviors have never been clearly assessed.

According to Newtonian physics, a skier must apply external force to deviate from rectilinear motion to turn. When a skier is turning with carving technique, a radial force (i.e., in the direction of the center of the turn) is applied and depends on the speed, the mass of the skier, and the turn radius (radial force [F r= m•velocity 2 /r]). The radial force can be considered as the component of the ground reaction force acting in the direction of the center of the turn. Therefore, to increase this force, a skier can theoretically increase the lateral angulation with the snow and increase the resultant normal reaction force (i.e., the normal reaction force applied to the ski in the ski reference, nSkiRF). The positive correlation between mean nSkiRF value and performance is shown by some studies on direct and indirect measurement (Cross et al., 2019). Moreover, the application of nSkiRF differs with turn trajectory, radius (Nakazato et al., 2011), and skier level (Supej et al., 2011). According to the radial force equation above, at equal entry speed, the "Z"-shape trajectory strategy (i.e., associated with smaller turn radii during TP) will require higher nSkiRF during the TP, necessitating greater muscular output, and technical management of the ski snow contact (Federolf, 2012). High-level skiers present intrinsically better technical (i.e., capacity to carve at shorter turn radii) and physical skills [START_REF] Vogt | Eccentric exercise: Mechanisms and effects when used as training regime or training adjunct[END_REF][START_REF] Franchi | Maximal eccentric hamstrings strength in competitive alpine skiers: cross-sectional observations from youth to elite level[END_REF], which could allow them freedom to select the Z line strategy while maintaining ski snow contact with low skidding. The low variation of energy dissipation (i.e., "S" trajectory) technique is associated with carving, more extended turning phases, and longer force application time [START_REF] Brodie | Fusion motion capture: a prototype system using inertial measurement units and GPS for the biomechanical analysis of ski racing[END_REF]; consequently, time to transfer force from one ski to the other could be shorter. This time without nSkiRF on the outside foot is considered as the edge switch moment and could be related to the line strategy used and the technical abilities of the skiers. In this case, technical abilities may allow skiers to perform complex tasks quicker, apply force more effectively to the snow, and continually adapt their trajectory. The assessed lag between force application and consequences on trajectory could be an interesting parameter of technical level. However, the interaction between force application and energy dissipation strategies has never been directly assessed.

The turn switch (TS) is the event used to separate two turns. Despite appearing to be a key event of strategic decisions for skiers, behavior during this period has attracted less attention in the research. At present, there are several ways to separate a course into individual turns via detection of the TS from kinematic and kinetic markers (Fasel and Gilgien, 2016) and subsequently separate a course into individual turns. In the first instance, the available methods are dictated by the sensors involved during the experimentation: stereoscopic 3D cameras (Supej and Nemec, 2003;Spörri et al., 2016), GNSS (global navigation satellite system) with IMU (inertial measurement unit) (Fasel et al., 2016), or force plate (Schaff et al., 1996;Nakazato et al., 2011). These various sensors detect one or multiple events between two turns. According to various definitions, several events can define the end of a turn, the beginning of the following turn, or the switch event between two turns. In chronological order, the turning radius passes above 30 m (1), the skier stops applying force on external foot (2, corresponding to the ski-edge release), the minimum summated nSkiRF over a given turn cycle (3), beginning of force application on subsequent external foot (4, ski-edge taking), and a turn radius below 30 m (5). The order of these events is stable regardless of the skiers and turns (Delhaye et al., 2019). The time when the turn radius is above 30 m is associated with the duration of the SL and period between Fbeg to Fend is considered as edge switch time. While not tested, the distance traveled by the skier with a radius above 30 m and time without force application will theoretically vary according to the line strategy used. Since the timing of these TS events is feasibly a result of different techniques, biomechanical mechanisms, and/or interaction between them, a better understanding of the timing and energy behaviors during this phase could provide insight into skier performance.

The first aim of the study was to (i) identify the kinetic and kinematic characteristics associated with the line strategy. We hypothesize that line Z strategy (characterize by longer path length in the straight line) is associated with (i.a) shorter path length in entire turn, (i.b) greater speed amplitude during the straight line and the turning phase, (i.c) more energy dissipated during the turning phase and entire turn, (i.d) longer time in the straight line normalized to the entire turn time, and (i.e) a longer time without force application between turns. The second aim of the study was to (ii) evaluate the interaction between selected strategy and performance level. We hypothesized (ii.a) that highlevel skiers would be more inclined to use Z line strategy and (ii.b) line strategy would be associated with final race time.

MATERIALS AND METHODS

Participants

Seventeen male alpine skiers participated in this study (mean ± SD: age 28.6 ± 9.3 years, height 179.7 ± 5.7 cm, weight 75.6 ± 9.3 kg). Skiers had mixed performance levels, consisting of recreational club level (not ranked by International Ski Federation [FIS]) to top-ranked current and previous elite world cup competitors (FIS points < 2). Each skier was informed of the content of the study and gave their written consent to participate. The experiment was conducted under the Declaration of Helsinki and was approved by the local ethics committee of the Université Savoie Mont-Blanc.

Experimental Protocol and Data Collection

Following 2-3 familiarization trials of the course while being equipped with the various experimental technology, skiers performed one or two timed runs on a 16-gate giant slalom course. Skiers were instructed to ski as fast as possible while avoiding the risk of falling. The athletes were provided with instructions to prioritize finishing the race and within these constraints reduce the race time as much as possible. The course setting was initially performed by a national ski coach, per a 16-gate GS setup with an average distance of 23 m and an offset of 8 m on a 25 • inclined groom slope. Setup was close to competition setup featuring irregularities while avoiding sideslope, jumps, and slope-break during turns. Landmark poles were placed close to the course outside of the grooming area, and gate positions were measured relative to them and to these poles in order to triangulate them at every course setting. Skiers used the same pair of race skis (SALOMON Lab X-Race-Annecy-France; radius: 30 m, length: 193 cm) and were equipped with the same model of ski boots (SALOMON XLAB 140+ WC-Annecy-France). Skiers used their own race suits and other FISapproved race clothing and protective gear (e.g., helmet, goggles, back protectors).

Throughout the duration of experimentation (30 days), snow quality (hardness, humidity, and temperature) and environmental conditions (temperature, wind, and visibility) were observed. Testing took place during the first 3 h after the resort opening, the slope was groomed every night, and snow cleaning was performed between every run to limit the formation of micro-reliefs. Testing was performed only if the temperature during the preceding night was cold enough to freeze the snow. If these factors were not acceptable, experimentation was delayed until the conditions stabilized. Skiers were equipped with onboard validated force plates (Falda-Buscaiot et al., 2016). These force sensors (Sensix-Poitiers-France) 1400 gr per foot and raised the skier by 6 mm. The reaction force normal to the ski on the outside foot (nSkiRF) was amplified and recorded at 200 Hz. The power supply and acquisition gear were placed in a hip bag for a total weight of ∼1 kg. Calibration to body weight was performed by lifting each foot successively while being fully equipped with the technology and equipment. The calibration procedure was performed on the same flat hard surface before the start of the race. Position and doppler speed were recorded by a synchronized GNSS/IMU unit (MacLloyd-Paris-France) with factory fusion computations recorded at ∼10 Hz mounted on the hip. Race time was measured with a FIS approved laser cell system (Tag-Heuer-La Chaux-de-Fonds-Switzerland), which was used as the top level performance variable in the subsequent analyses (i.e., better performance = lesser course time).

Data Processing

Only the best performance (fastest time) was used for analysis, with the first turns of the race containing skating steps excluded. All the data analyses were performed using Matlab version R2019a (MathWorks-Natick-USA). To synchronize GNSS/IMU with a force plate, skiers hit the snow with their skis before and after the race to create acceleration and nSkiRF peak. Using these acceleration and force peaks, all data from force plate and GNSS/IMU were interpolated to resample data at 200 Hz. The "makima" method was used to perform a smoothing interpolation (with less undulation than "spline").

Four TS events were computed (Figure 1): two events from nSkiRF data and two from GNSS positional data. End of force application of the outside foot (F end ) and beginning of force application on the outside foot (F beg ) were detected on a 12-Hz low pass-filtered nSkiRF signal. The typical nSkiRF pattern on the outside ski during a turn is composed by a clear increase, a plateau, and a decrease (Figure 2); two consecutive patterns are separated by a period of low force application. Events on the force data were determined using the Perceptually Important Point method (PIP) [START_REF] Fu | Stock time series pattern matching: template-based vs. rule-based approaches[END_REF]. PIP is based on geometrical detection of the furthest vertical distance between data and a line between the endpoints of the interval. This computation is repeated five times to obtain the 7 PIPs (Figure 2). PIP6 and PIP2, respectively, represented F end and F beg events. All points were checked manually to ensure they corresponded to the end of the main decrease of force and the beginning of the main increase of force. The lag time between F end and F beg represents the switch between ski edges. The two events computed from positional data are the moment the turn radius passes above 30 meters (Traj >30 ) and under 30 m (Traj <30 ), corresponding to the end of the previous and start of the next turning phase, respectively (Spörri et al., 2012). Longitude and latitude positional data were converted into the Ellipsoid plane using WGS84 standard transformation. All radius and speed relevant parameters were computed using 2D data (longitude and latitude), and path length was computed in the 3D plane (longitude and latitude and altitude). Positional data were smoothed using a Savitzky-Golay filter (order 2, 1-s window). The radius was computed by circle fitting using the Pratt method (Pratt, 1987) (0.3-s window). Automatic detection was performed when the radius crossed the 30-m threshold, and in the case of multiple crossing at the TS last event was retained. The path length was computed as the cumulated displacement in all axes. The lag between Traj >30 and Traj <30 represents absolute time in SL (T SL in ms). Percentage of the turn in SL (T%SL in %) was defined as T SL relative to the sum of T SL and time of the following TP. The path length is computed for the SL and the sum of the SL and the following TP (Path SL+TP in m). Path length during edge switch was computed using the same approach (Path edge switch in m).

Speed was computed by the GNSS/IMU unit by Doppler measurement related to satellite motion. This computation method is more accurate than derivation of position. To compliment SL and edge switch detection, the amplitude of speed during the SL was computed as the difference between the minimum and maximum speed in the SL ( Speed SL) and for the entire turn ( Speed SL+TP).

Based on positional data, mechanical energy was computed at each point of the race as the sum of potential and kinetic energy, relative to the body mass of the skier (i.e., specific mechanical energy Supej, 2008;Supej et al., 2011). The change in specific mechanical energy was calculated for the following sectional divisions and normalized to the velocity of the first point ( e mech/ v in ): SL ( e mech/ v in SL), TP ( e mech/ v in TP), and SL + TP ( e mech/ v in SL+TP). Finally, race time is considered as the macroscopic indicator of skier performance level and e mech/ v in SL+TP e mech/ v in SL+TP is considered as the instantaneous performance level indicator.

Statistical Analysis

Normality of each parameter was tested using the Shapiro-Wilk test except course time which approaches an expected flat distribution. To evaluate the first aim of the study (i.e., assess the kinetic and kinematic characteristics associated with the line strategy), the correlation between path length in SL and kinematic turn parameters (absolute time in SL, time ratio, speed amplitude in SL, speed amplitude in entire turn, path length in entire turn and e mech/ v in in TP and during entire turn, time without force application) was tested using Pearson coefficient (r), the mean of skier turn cycles (n = 17). The second aim of the study regarding the interaction between line strategy and performance was also tested via correlation of straight-line length and race time (n = 17).

A hierarchical linear regression analysis was performed to determine whether the line strategy (assessed via the path length in SL) parameter improved the performance prediction provided by e mech/ v in SL+TP. This parameter is already defined in previous literature as a predictor of performance and thus was first forced into the regression. The adding of path length in SL in the equation is tested in a second step to test its influence on race time prediction. Coefficient of determination (r²) and change in r² ( r²) between models were calculated. All descriptive data were expressed as means ± standard deviation (SD), and all statistical analyses were performed on JASP (Version 0.13.1-Amsterdam-Netherlands) with an alpha level set at p = 0.05.

RESULTS

Mean course time was 29.47 s (SD: 1.85,min: 26.37,max: 34.61), the difference between the minimum and maximum time (i.e., 8.24 s). Once skating steps were removed, 185 turn cycles remained for the final analyses. Correlations between path length in the straight line and kinetics or kinematic parameters of the turn are reported in Table 1. T%SL (mean: 32.9%, SD: 4.32%, min: 26.78% max 43.58%) is well-correlated with the path length in SL (r = 0.967, p < 0.001).

Secondly, mean path length SL is computed for each skier during the race. The mean path length in SL of the population was 8.96 m (SD: 1.16, min: 7.71, max: 11.67). Correlations between race time and path length in SL (n = 17) are presented in Figure 3A. Correlations between race time and specific mechanical energy dissipation (n = 17) are presented in Figures 3B,C. There was a moderate relationship of e mech/ v in during turning phase (r = -0.505, p = 0.041) and entire turn (r = -0.620, p = 0.008) with race time.

The results of the hierarchical linear regression are summarized in Table 2. To assess the predictive power of the model, F and F change values were computed; the root mean square error (RMSE) of the predictive model (i.e., square root of the differences between observed and predicted race time values using full equation) was calculated to evaluate the accuracy of predicted race time in comparison with e mech/ v in SL+TP alone; the p-value indicates the significance of the model Path length in straight line is the cumulative distance traveled by the skiers between two turning phases where the radius is above 30 m. Successive correlated parameters are the path length in entire turn (both straight line and turning phase); speed amplitude during the straight line and turning phase; e mech /vin during the turning phase and entire turn; absolute time in a straight line, and relative time to the entire turn time. Edge switch time corresponds to the lag between end of the force application on the outside foot and start of the force application in the new outside foot and edge switch path to the distance travel during this period. Indices of correlation test Pearson's r (r) and p-value (p) were reported.

prediction. e mech/ v in SL+TP was forced in Model 0, path length in SL was added in Model 1, and path length in SL was finally not included in the model as a significant improvement of race time prediction (p = 0.301, R² change = 0.047).

DISCUSSION

Our first result focuses on the links between line strategy and mechanical or kinematic parameters of the turn. Line strategy has to be considered as a continuum characterized by path length in SL. However, the extremes of this continuum are dependent on the course setting and observed population. Consequently, this method only allows characterization of skiers on the same course. The increase in path length in SL was positively linked with longer absolute time in SL (r = 0.966, p < 0.001), and Speed SL (r = 0.554, p < 0.001). There was a trend for a negative correlation between the total path length during the entire turn and path length in SL (r = -0.481, p = 0.051). These results follow previous works (Federolf, 2012) and corroborate the statement that Z strategy is used by skiers to increase their speed between turns and decrease their total path length. However, a decrease of speed in the following turn was not correlated with the path length in SL (r = -0.418, p = 0.095). Skiers using the Z line strategy do not necessarily lose their additional speed gained in the SL in the following TP. Absence of significant results could be explained by the capacity of some skiers to conserve their speed even when using a Z line strategy. This capacity could come from a better technical level and better manipulation of the ski angle to decrease friction (Reid et al., 2020). This interpretation is supported by the absence of a relationship between strategy adopted and energy dissipation during the TP (r = -0.223, p = 0.390). Another explanation could be that some skiers using the S line strategy possibly drift at the beginning of the TP [START_REF] Müller | Comparisons of the ski turn techniques of experienced and intermediate skiers[END_REF], which increases delta of specific mechanical energy even with a short path length in SL. This behavior is used when skiers exceed their "velocity barrier" (Supej et al., 2011), in other words when skier's speed is too high to perform the turn imposed by the gate setting.

Absolute and relative time in SL were strongly associated with the path length in SL. However, time of edge switch based on the nSkiRF measurements (i.e., the time between end and start of force application on the outside foot) was independent of the path length in SL. The time of edge switch was not influenced by temporal pressure variation induced by shorter or longer SL. Consequently, the time of edge switch should not be used to quantify the duration of the straight-line trajectory. Rather than turn line strategy, this parameter might be indicative of balance or technical abilities.

The main questions of this study concerned the link between the performance level and the line strategy. In the first instance, path length in SL is not correlated with e mech/ v in SL+TP during entire turn (r = -0.064, p = 0.808). Moreover, a lack of relationship between path length in SL and race time (Figures 3A,B) indicates that the use of one predominant strategy is not necessarily linked with overall course performance. Absence of precise results is mainly due to the high variability of the strategy used by medium-and high-level skiers. Among skiers of a similar level (i.e., ranked 5th to 13th with race time between 28 and 30 s), there was substantial variation in SL path length. For example, two skiers performed mean SL path length above 11 m, yet others presented values <8 m. The choice of the strategy used could be determined by various anthropometrical (Haymes and Dickinson, 1980), physiological (White and Johnson, 1991), and technical profiles [START_REF] Raschner | Zum Einfluss anthropometrischer Merkmale auf die Wettkampfleistung im Slalom bei jugendlichen Skirennläufern (The influence of anthropometric characteristics on the performance in slalom in adolescent ski racers)[END_REF][START_REF] Müller | Longterm athletic development in youth alpine ski racing: the effect of physical fitness, ski racing technique, anthropometrics and biological maturity status on injuries[END_REF]. However, these interactions have not been recently evaluated on adult skiers. Finally, according to linear regression results, e mech/ v in SL+TP is negatively correlated with the performance, without a clear contribution of path length in SL. In agreement with previous works (Spörri et al., 2018), line strategy is not a predictor of the performance and does not lead to a decrease in the residuals of e mech/ v in SL+TP correlation. As such, it would seem that independent of the line strategy used, reducing sectional energy dissipation is a key behavior to decreasing race time. These results highlight the presence of skier profiles able to decrease their dissipation of specific mechanical energy, in particular on a given strategy.

In conclusion, the strategy used is associated with differences in kinetic parameters. Increasing the path length in SL (related to Z strategy) induces a higher speed variation during SL, longer turn absolute and relative time spent in SL, and a tendency of shorter length path. However, the strategy used is not linked to time without force application on outside ski between two turns. Overall, the strategy adopted does not appear to be strictly associated with course-level performance of the skiers. The significant dispersion of strategies for the same performance level highlights that radically different approaches can result in similar energy dissipation characteristics. Consequently, it would seem that better skiers possess a profile that enables them to decrease energy dissipation across a variety of preferred and adopted turn strategies.

LIMITATIONS

The top-level performance variable in this study was course time, which represents a macroscopic index and lacks the descriptive information potentially provided by more detailed analyses. Indeed, this parameter is not representative of each turn performance; a high-level skier who made a mistake is considered as the same level as a lower-level skier who did not. Moreover, race time is influenced by snow condition, and even under "acceptable snow conditions, " the snow quality variation between subjects could create differences between them. At last, race time is influenced here by the capacity of the skiers to be accustomed to ski gear and experiment devices. Finally, only male skiers were tested, and while we assume our findings apply to female skiers, more research is needed on female skiers. ). Very robust associations existed between maximum isometric force and speed performance (r = -0.88, P < .001), but only a trend for higher absolute isometric force in technical athletes (r = -0.49, P = .052). Alpine skiers display a preponderance for dynamic force output at low velocities, and isometric force for speed athletes, which highlights the interest in specific assessment and conditioning practices for ski athletes.

APPENDIX V: SCAND J MED SCI SPORTS, IN PRESS

K E Y W O R D S

alpine skiing, force velocity, isometric force, maximum power, squat jump general, successful athletes across the disciplines aim to minimize energy loss (ie, transform potential into kinetic energy) and maximize course speed, 1,2 which depends on the timed and controlled application of force to turn the skis without dissipating energy unnecessarily. Both elevated force production and an ability to apply it effectively are key components of skiing. 1,3 Force expression differs for each event and discipline 4 as a result of distinct performative constraints. For example, where TECH events are characterized by more frequent and rhythmic turns (~1.8 and 2.9 s for SL and GS, respectively), SPEED features considerably slower movement cycling (~4.0 and 5.0 s for SG and DH, respectively). 5 Discipline comparisons are rare, but typically show average turn-by-turn forces are higher in TECH compared to SPEED. 4 Nevertheless, longer turn and course durations result in much greater physical loads (ie, impulse) in SPEED vs TECH (DH > SG > GS). Moreover, while the time-course and magnitude of force output are notable, in both disciplines, peak values far exceed turn-averages (eg, in TECH, 1.74 to 1.95 bodyweight [BW] vs 3.15 BW for peak force 6 ). Although acute instances of force production could represent mistakes or energy dissipation (necessary or otherwise), 7 a capacity for both average and peak force appears essential. However, while elevated force production on-snow is a product of both enhanced physical and technical capabilities, the interplay between that expressed during skiing and that possessed by the athlete off-snow is a priori unclear: to what extent is the force developed during skiing limited by specific capacities?

The terminus of long arcing turns is rhythmic extension-flexion (loading-unloading) patterns of the lower limbs and uniquely slow and long contraction cycles. Even the most frequent turn cycling event (SL) exhibits markedly slower angular velocities of the lower limbs compared to common sports (eg, <80°/s for the outside knee 8 vs 1,185°/s 9 for average maximum knee flexion velocity of the swing-leg in sprint running). While the general trend for low-velocity-high-force muscular actions is maintained across disciplines, research generally corroborates distinct "stepped" changes in average angular velocity across events (knee and hip, SPEED < TECH) in parallel with turn duration (SPEED > TECH). 5,10,11 The associated contractile modes is a fundamental topic, albeit rarely studied explicitly, with eccentric modalities historically attracting disproportionate attention in the literature (eg, seminal research by Berg and colleagues 10,12 ). However, recent evidence reports the highest force output is produced during a pronounced quasi-isometric phase of the extended outside limb (ie, knee, ~128 to 138°) 5,6,11 for substantial durations during turning (eg, % of turn for outside limb: knee, ~11% for SL and 34 to 42% for GS and SPEED; hip, ~27 to 55% in TECH and ~60 to 81% for SPEED). 5 As such, high-force at low velocities and in quasi-isometric conditions appears a dominant function of modern ski turns, 6 performed close to or even exceeding maximum voluntary contraction. 12 These factors should be considered in assessing the muscular capacity of skiers.

While challenging to synthesize, there is a variety of evidence to suggest positive relationships between various force qualities and ski performance metrics. 3,13-16 Notably, variants of maximum effort BW squat jumps (SJ) and countermovement jumps (CMJ) feature prominently in skiing research 13 and in various published testing batteries, 14,17-19 albeit utilizing varying methodological approaches and non-interchangeable technologies (eg, "vertec" vs force platforms). While BW jumps are a practical and reliable means of assessing neuromuscular function, force is expressed at markedly greater extension velocities compared to skiing (average velocity = ~ 300°/s with moderate amplitude, 0.36 m jump height [h], and with 0.3 s push-off). Moreover, since h and maximum power (P max ) are macroscopic indexes of dynamic force production in approximately the center of the force-velocity (Fv) relationship, they lack data discriminating force at high and low velocities. These factors might partially explain the mixed results in the literature using these types of assessments, 13 such as inverse relationships between skiing performance in high-level skiers (GS standing [lower = better] vs h, r = 0.64), 20 or non-different scores between young and elite athletes. 21 Consequently, more specific measurements might provide insight into capacities discriminating alpine ski racers.

While skiers are viewed as "force-dominant" (ie, highforce-low-velocity on the Fv spectrum), 14 the literature targeting the assessment of these capacities is limited and aging. Studies using isokinetic dynamometry have remarked on the impressive force capacities of skiers, at least in respect to other sporting codes and recreational individuals. 15 Some older works show torque produced at the knee at low and not high velocities (30 vs 180°/s, respectively) separated club and national athletes, 16 but more recently was unable to differentiate between speed and technical specialists, nor were they associated with performance. 8,22 While the high isometric output of skiers is typically lauded, the little research that has adapted such testing into practice has almost exclusively used isolated joint assessments. 3,15,16 Similarly, reports exist of impressive dynamic strength capacities of skiers (eg, 1-repetition maximum squat), with the minimum benchmark for B-level Norwegian skiers set at 2.5 or 3 × BW for men and 2.2 × BW for women in the late 90s. 18 More recently, 1-repetition maximum squat was associated with the performance level of youth skiers (Spearman's rho, r s = 0.59, P = .017), 23 albeit various other correlations (eg, muscle mass, r s = 0.70, P = .003) potentially indicating ongoing development of generalized neuromuscular capacity below a certain performance level or age group. Some authors have used variations of ballistic jumps performed with additional loading to orient the mechanical conditions toward skiing, 24-28 albeit with mixed | 3 CROSS ET AL.

results. For example, in national-level junior skiers average power produced during loaded SJs at 40% BW was only correlated with skiing performance during the last of four consecutive years of monitoring (attributed to accrued physical development finally "matching" technical efficiency). 25 A recent example compiled a range of loaded-jump performances to create a force-velocity (Fv) profile of elite youth skiers and was able to differentiate between other alpine sports (ie, greater relative maximum power than cross-country skiers, and a more force-dominant profile than ski-jumping). 26 Little other research has directly attempted to quantify ski-specific force production in recent research, and a more detailed analysis of force-output capacities of skiers might provide clarity surrounding the relevance of specific capacities and performance characteristics.

Underlying force-production capacity determinants of skiing in general, and discipline-specific determinants, remain unclear. As such, the aims of this study were to (a) test the effect of disciplines in lower limb force-production capacities, and (b) subsequently test whether the latter were related to performance during the successive season. To that end, we implemented a protocol including methods to assess dynamic force production at extremely low and high velocities and maximum isometric force, to provide novel information on the specific force capacities of skiers. 1 ± 59.3 [range = 1-194]). This indicator was selected as that closest to the profiling including a relatively balanced opportunity for athletes from all events to score updated FIS points, before substantial worldwide interruptions to the racing schedule due to the novel coronavirus pandemic, COVID-19.

| MATERIALS AND METHODS

Force-production capacities were tested through two assessments: Fv profiling in loaded jumping to assess dynamic muscle output, and isometric mid-thigh pull (IMTP) to obtain maximal isometric force and rate of force development (RFD). The testing occurred during the preparatory phase, directly preceding the 2019/20 season. Not all athletes participated in both testing procedures due to availability (N presented where appropriate). All operational procedures were performed as part of the athletes' routine training and testing practices and were approved by the University Savoie Mont Blanc ethics committee, followed the research codes of the French Ski Federation, and were performed according to the World Medical Association (Declaration of Helsinki).

| Equipment and protocol

Athletes performed a ~20 minutes dynamic warm-up, consisting of a cardiovascular priming, mobilization, and increasing intensity submaximal loaded jumps (various anthropometric measurements were taken during this period). The protocol consisted of increasing loading barbell SJ and CMJs (reported elsewhere), followed by IMTP. Athletes wore their habitual training attire and footwear (ie, trainers or CrossFit style shoes).

| Loaded squat jump and countermovement jump procedures

Athletes performed maximal SJs unloaded and against four to six external loads ranging from 7.5 to 90 kg, 29 with a competition-grade Olympic lifting bar and plates (model: Elite bar and plates, Raze, Warwickshire) providing the resistance. For the SJ depth, athletes were initially set at a 90° knee angle and then allowed to adjust from this position based on the objective of jumping as high as possible with and without external load. 30,31 Once selected, the safety supports of a squat rack (model: FT700 power cage, FitTech, Brisbane) were set to this height to standardize push-off distance (h po , via cueing squat depth), and where necessary, thin rubber wedges were stacked on the safety bars to adjust to the rack height at a higher resolution (~10 mm). Limb length was measured from the head of the greater trochanter to the most distal point of the fully extended limb and plantarflexed foot, and h po was computed as the difference between limb length and the vertical distance between greater trochanter and floor in their starting position in the squat rack. 32 For each SJ, the athletes slowly descended until the bar lightly contacted the rack supports, after which they raised the bar slightly (ie, to their measured position), paused for 3 seconds, and jumped upwards with maximum ballistic intent. All parts of this procedure were verbally cued by the researcher (ie, "SQUAT!" and "3, 2, 1, GO!"). Athletes performed two repetitions at each load, separated by approximately ~15 seconds. The final number of sets was determined by whether trials were deemed unfit for analysis via immediate observation (eg, poor jump technique) or unrealistic via preliminary assessment of the Fv relationship (ie, R 2 < 0.90 and outlier analysis), described below. h was measured using an optical gate system (model: OptoJump Next, Microgate, Bolzano-Bozen, Italy) placed inside the footprint of the squat rack (see Figure 1). This equipment uses basic physics principles to provide a valid and reliable measurement of h. 33 The data were collected using the manufacturer software and exported in raw format for analysis.

| Isometric mid-thigh pull

Athletes performed the IMTP using a portable dynamometer consisting of an Olympic lifting bar with its ends and bearings removed (7.5 kg), attached to a rigid platform via a heavy-duty chain (see Figure 1). The portable system is a more advanced alternative to those presented in the literature, 34-37 which have provided acceptable measurement of peak force capacities but limited and mixed results for RFD (discussed in the limitations). 35 For the test, the athletes were instructed to set themselves in a position where they felt comfortable to present maximum effort (ie, like that of the second pull of the "clean-pull" movement, commonly used by alpine skiers 14 and other athletes). Where necessary, athlete starting position was adjusted to be within the ranges specified in the literature (ie, 125 to 145° knee and 140 to 150° hip), 38 while allowing some variation for individual technique. Athletes were instructed on the objective of "pulling as hard and as fast as possible" for each trial, and provided with the following verbal cues: to take up a stable position and to apply pretension and remove slack from the system ("position!"), a verbal countdown from three, and then an immediate and aggressive pull until the researcher halted the trial ("PULL, PULL, PULL, PULL … STOP"). The athletes performed two submaximal trials of these procedures, which included viewing the force-time trace post-trial to improve internal cueing. Athletes rested for 3 minutes and then performed two maximum effort ~ 5-second trials separated by 5 minutes. In the case of two mistrials, 38 an additional was performed.

During each trial, force-time data was measured continuously at 1000 Hz using a portable strain gauge system consisting of a custom-designed acquisition unit, comprising of an S-beam load cell (Model: 1000 kN S-Beam Load cell, Meltrons Millennium Mechatronics, Auckland) between two heavy-duty stainless-steel rings. Pull height was adjusted using a carabiner linked through the appropriate chain length, and a turnbuckle mounted through the center of the platform. Athletes applied pretension to aid in correct pre-trial positioning 38 and to avoid problems caused by system slack (eg, chain "snapping" taught, causing a force peak). Preload was monitored to ensure values were not unreasonably high or low, and we subsequently tested the relationship between preload magnitude (29 trials, 436 ± 200 N), maximum force, and RFD to ensure the variability did not substantially affect our results.

| Data analysis

2.3.1 | Jumping force-velocity relationship Mechanical output of the lower limbs can be estimated using a selection of validated equations 32,39 applied to h and anthropometric measurements of an athlete. Average force (F), velocity (v), and power (P) during the push-off phase were calculated using the highest h per condition: with m tot as the system mass (sum of body mass and external load), and g gravity ( 9.81 m/s/s). For each subject, individual force-velocity (Fv) relationships were compiled from F and v data using linear least-squares regressions. The x-and y-axis intercepts of the linear relationship defined the maximum theoretical force and velocity capability of the athlete (F 0 and v 0 , respectively). S Fv was obtained as the slope of the Fv relationship, and P max was computed 40 as 2.3.2 | Maximum isometric force and rate of force development Data were collected and analyzed using custom MATLAB (version: MATLAB 2019B, Mathworks, MA) acquisition and analysis scripts, respectively. The weight of the bar and load cell unit were added to the raw force-time data to represent the net force produced by the athlete across the trial. Unfiltered force-time data were analyzed with the initiation of force production determined using manual selection (see Figure 2). While algorithmic pull-initiation detection is typically recommended, 38 the lack of BW signal (ie, preload only) rendered manual detection preferable. 41 Any data showing countermovement was removed. "Maximum" (RFD max ) and "average" (RFD avg ) values were assessed as the maximum of a 50 ms moving average window, and the average value between 0 and 200 ms, of the time-derivative of the force signal, respectively. The maximum isometric force was determined as the maximum of a 500 ms moving average window of the force signal (F max ). Averaged values were selected to both improve reliability and to increase specificity to critical periods of force application in skiing (eg, turn initiation 5,6 ). Operator reliability was tested by analyzing 60 randomized trials, three times, each separated by 2 to 3 days, with the repeatability for variables dependent on initiation detection deemed acceptable for subsequent analysis (raw typical-error value of 1.37 N/s/kg and a quasi-perfect intraclass correlation [ICC > 0.99]).

F = m tot ⋅ g ⋅ ( h h po + 1
) . v = √ g ⋅ h 2 P = m tot ⋅ g ⋅ ( h h po + 1 ) ⋅ √ g ⋅ h 2 F I G U R E

| Statistical analysis

Statistical procedures were performed using JASP (version: 0.11.1, JASP Team, Amsterdam). Discipline differences were assessed via a general linear model controlling for both the effect of performance (ie, athlete standing) on the dependent variable as a covariate while allowing for non-parallel regression lines per group (ie, an interaction between performance and discipline, "group × covariate"). 42 The main effects of discipline and performance on the dependent variables (BW, h, P max, S Fv , F 0 , v 0 , F max , RFD max , RFD avg ), and interaction effect, were reported using omega-squared (ω 2 ), with contrasts for the mean difference and confidence intervals. Athlete age voided the assumption of normality (Sharpiro-Wilk = 0.73-0.83, P < .005), and so was unable to be entered into the linear model. Instead, discipline effects were tested using a non-parametric Mann-Whitney U test (U, rank-biserial correlation [r rb ]). The threshold values for qualitative interpretation of effect magnitude were ω 2 < 0.01, 0.01, 0.06, and 0.14 as trivial, small, moderate, large, and very large, respectively.

To further explore performance interactions for each discipline, distinct Pearson's correlational analyses (two-tailed) were performed between discipline-specific standing and force-capacity variables (r [lower confidence interval; upper confidence interval], and p). A Spearman's rank correlation coefficient (r s ) was used to test associations between age and performance in the place of the parametric analyses.

The strength of agreement was interpreted using values of r, or r s < 0.1, 0.3, 0.5, and 0.8, as thresholds for trivial, small, moderate, large, and very large, respectively.

Where relevant, descriptive statistics presented as means ± standard deviations, or median (interquartile range),

P max = F 0 ⋅ v 0 4
F I G U R E 2 Portable isometric mid-thigh pull platform (top) and associated force-time trace from a maximal trial. Data show a single trial, with the threshold overlays for the movement onset detection (large black dashes), the "window" during which the average rate of force development is calculated (dotted line), instantaneous maximum force ("+"), and the approximate window of maximum force used in this study (highest 500 ms average). with the alpha value for all tests at a = 0.05, with a < 0.1 considered as a trend toward a clear inference.

| RESULTS

Normative data and linear model analysis results for group comparisons of dynamic and isometric force measurements, including model effects with performance are in Table 1 and Figure 3. Pairwise correlations between standing and dynamic and isometric force are presented in Figures 4 and5, respectively. Fv data were very well fitted with linear regressions R 2 = 0.978 (0.027). We found no clear association between preload and F max (r = 0.233, P = .224), RFD max (r = -0.046, P = .811), nor RFD avg (r = 0.111, P = .565).

SPEED athletes were heavier than TECH (+6.7 [-2.53; 10.83] kg, F (1,27) = 7.75, P = .010, ω 2 = 0.14), with a very large performance effect depicting better athletes were heavier (F (1,27) = 10.13, P = .004, ω 2 = 0.19), and no interaction effect (F (1,27) = 1.71, P = .202, ω 2 = 0.015). For age there was no difference between disciplines in the non-parametric model (U = 91.5, r rb = -0.231, P = .278), however, very large associations existed between age and performance for both TECH (r s = -0.805 [-0.529; -0.927], P < .001) and SPEED (r s = -0.825 [-0.523; -0.943], P < .001).

| Dynamic force

Raw unloaded jump height did not differentiate the disciplines (F (1,27) = 1.77, P = .195), nor vary with performance (F (1,27) = 1.44, P = .24). SPEED athletes exhibited largely greater absolute F 0 (F (1,27) = 13.8, P < .001), and a trend for lower (force-dominant) S Fv (F (1,27) = 3.72, P = .064). SPEED athletes also possessed greater absolute P max (F (1,27) = 4.42, P = .045). There were very large associations between performance and a more negative S Fv (F (1,27) = 16.29, P < .001), associated with higher F 0 (absolute, F (1,27) = 28.25, P < .001; and relative, F (1,27) = 10.34, P = .003), and lower v 0 (F (1,27) = 4.96, P = .034). There were no associations with performance in the linear model for P max (F (1,27) = 0.573 to 0.639, P = .431 to .456). For absolute F 0 there was a small interaction suggesting a stronger association with performance in SPEED (F (1,27) = 5.22, P = .03).

There were large correlations between performance and a more negative S Fv in both SPEED (r = 0.67 [0.22; 0.89], P = .008), and TECH (r = 0.60 [0.17; 0.84], P = .011). This force-dominant profile was corroborated by strong associations for absolute F 0 in both disciplines (SPEED, r = -0.79 [-0.93; -0.46], P = .001; TECH, r = -0.57 [-0.83; -0.13], P = .016), and relative F 0 in SPEED (r = -0.62 [-0.86; -0.13], P = .019; TECH, r = -0.40 [-0.74; 0.1], P = .110).

There was a positive relationship between v 0 and performance (ie, higher value is with associated poorer standing) in TECH (r = 0.51 [0.04; 0.8], P = .035; SPEED, P = .291). No associations existed for h (P = .192 to .981) nor power (P = .100 to .753).

3.2 | Isometric force and rate of force development SPEED displayed much greater absolute F max (F (1,25) = 20.70, P < .001) and moderately greater relative F max (F (1,25) = 11.19, P = .003). RFD metrics typically did not separate the disciplines (P = .356 to 0.708), although there was a trend for minorly greater RFD avg in SPEED (F (1,25) = 3.56, P = .071). Both relative and absolute F max were strongly related to performance (absolute, F (1,25) = 33.78, P < .001; relative, F (1,25) = 21.52, P < .001) with a moderate interaction effect suggesting a stronger relationship for both variables in SPEED athletes (absolute, F (1,25) = 10.28, P = .004; relative, F (1,25) = 6.69, P = .016). This interaction was supported in the pairwise correlation results, where SPEED athletes exhibited very large correlations with performance for absolute and relative F max (both, r = -0.88 [-0.96; -0.63], P < .001) while only a trend existed for a moderate association for absolute F max in TECH athletes (r = -0.49 [-0.8; 0], P = .052; relative, P = .121).

Within the linear model there were large associations between performance and both RFD max (absolute, F (1,25)

| DISCUSSION

Our results support the force-dominant nature of skiers. SPEED athletes displayed higher absolute maximum forceproduction capacities in both dynamic and isometric contraction modes than TECH athletes, which might be associated with the extended quasi-isometric contractile mode and greater masses in their discipline. Skiing level was associated with elevated isometric force production, dynamic force capacity at low velocities, and an ability to develop force quickly. As such, maximum force capacities and rate of force development, rather than maximum power production, seem to characterize high-level skiers.

One of the strengths of this research is a broad athlete sample, which included athletes from C group national representation to a world-ranking leader in their respective event. Surprisingly robust associations between athlete age and standings showed that higher ranked athletes were both heavier and older. These results can be explained by three factors: (a) older athletes have more experience (eg, SPEED courses are relatively consistent across seasons) and potentially enhanced technical aspects in their respective disciplines due to accumulated time in on-snow training and competition, (b) older athletes might possess enhanced specific force-production capacities due more time accrued in targeted training (either on-or off-snow; 1 and 2 presumably increase performance), and (c) past a certain age, lower-level athletes are more likely to drop out (from injury, supplanted by younger skillful counterparts, or otherwise) which biases the sample of older athletes toward higher rankings. While long-term skill development is challenging to quantify, the concurrent association between increased body mass and performance might indicate ongoing neuromuscular adaptations (notably, hypertrophy). At the same time, all athletes had an extensive strength-training history (> 5 years, > twice per week); long-term conditioning, and on-snow training have likely stimulated specific muscular adaptations. Nevertheless, while a nuanced interpretation is more likely than merely older and heavier athletes being dominant, it is possible that some proportion of our results are simply a product of a long-term structural conditioning approach toward attaining strength rather than depicting a direct link between force capacities and performance. In any case, both longitudinal athlete development data, and expanded analyses using a larger pool of elite-level athletes, would clarify these points.

The unloaded jump data presented in this study are roughly congruent with published normative values on alpine skiers. 13 In our cohort, there were no clear differences between disciplines nor any interaction with performance for BW jump measures, which is notable given their wide use for ski athletes. 20,23 Since h is an index of neuromuscular capacity normalized to BW, it is unsurprising that while absolute P max differentiated skiers, relative values did not. Similarly, there was a total lack of association between P max and performance, and even a slight trend for lower values in higher-performing TECH athletes, which tends to support the general lack of discriminatory ability of force production at moderate velocities. 20 Nevertheless, the measure might be useful in development athletes, 14,43 and implies a progression of physical capabilities (eg, general neuromuscular output and muscle mass) may benefit lower-level athletes until a point of diminishing returns where more specific training and monitoring might be beneficial. In any case, while measuring ballistic force production in moderate velocity conditions via BW jumps can be valuable (eg, for tracking athlete training adaptations 29 or return to sports practices 21 ), our results challenge their mechanical relevance to alpine skiing. 3,13 Ski athletes displayed a baseline preponderance for dynamic force production at low velocities. For example, compared to a cohort of track and field athletes 44 skiers produced considerably higher F 0 in both absolute and relative means, albeit with a lower P max presumably caused by diminishing force output at higher velocities. Interestingly, when converting F 0 to 1-repetition maximum 45 our data are slightly lower than older anecdotal reports of the minimal level expected of B-level athletes and above (TECH, 2.15 ± 0.29 × BW; SPEED, 2.26 ± 0.35 × BW, vs > 2.5 × BW), and perhaps even lower due to bias induced by different squat depths (ie, approximately "half-squat" in our data vs deep-squat depth in the report). 18 Moreover, mean relative F 0 values are comparable to young elite Austrian skiers, albeit our group presumably possessing much higher absolute force capabilities from higher BW (+4.5 and +10.9 kg for group means of TECH and SPEED, respectively). 26 When comparing disciplines, SPEED athletes exhibited much higher absolute F 0 , but no differences existed when scaled to BM. These results are interesting since field measurements regularly show turn-averaged and peak-force output are higher in TECH, 2,12 albeit regularly scaled to BW. 4,7 One explanation could be that F I G U R E 3 Discipline-specific dynamic and isometric force data. Data correspond to the mean (diamond) power-force-velocity (right graph, "DYNAMIC") and isometric data (left graph, "ISO."), with the error bars representing the standard deviation around the mean (displayed as either positive or negative for graphical clarity, but representing the total deviation [ie, ±SD]). Technical and speed disciplines are represented in TECH (black lines) and SPEED (gray lines). Variables are as follows: P max , maximal power; F 0 , maximal theoretical force; v 0 , maximal theoretical velocity, W, for watts; N, for newtons; m/s, meters per second. SPEED athletes spend superior time in high-load conditions (> 1.5 × BW), 4 which could further stimulate conditional adaptations. Moreover, a reliance on gaining and maintaining velocity against dissipating factors is potentially more crucial in SPEED and might prompt goals of longitudinal increases in muscle mass. 14 Finally, it is possible that TECH skiers simply ski at a higher relative intensity of their maximum capacity, perhaps as a result of shorter race durations. While an absolute force-dominant profile (ie, more negative S Fv ) was similarly associated with performance in both disciplines, this was a product of a better association with force output at low velocities in SPEED (ie, F 0 ), and both increased output at lower velocities and decreased output at high velocities in TECH (ie, v 0 ). As such, while SPEED athletes may benefit from simply orienting force output qualities toward low velocities, a more targeted approach to rebalancing the Fv profile might be warranted in TECH athletes.

ISO. DYNAMIC

TECH

Both the absolute and (notably) relative F max values are among the highest reported in the normative data (eg, similar to high-level track cyclists and collegiate weightlifters), albeit on fixed IMTP systems rather than open chain. 46 Unfortunately, there is little information on the maximum isometric force output of skiers outside of that using isokinetic dynamometry. 5,22 Early data presented by Haymes, Dickinson 12 using an isometric leg-extension dynamometer (2930 ± 369 N), and that by Berg, Eiken, and Tesch 12 using an isometric leg press in World Cup skiers (2897 ± 708 N), roughly match our mixed-level cohort. SPEED athletes produced much greater F max than TECH in both absolute and relative terms, in parallel to robust relationships with performance. These results could be indicative of discipline-specific adaptations due to the greatly elongated and high-load quasi-isometric turning, 5,6,47 and the notable time spent in isometric contraction at the hip 5 due to adopting a tucked position to minimize air drag (16 to 37% of turn duration) in straight phases. 4 On the other hand, only a trend (P = .052) for an association between absolute F max was observed in TECH, which is congruent with evidence of comparatively shorter quasi-isometric actions during turning in the discipline. 5 Consequently, while isometric force capacity is likely still fundamental to TECH athletes, the capability to produce force dynamically appears of greater importance (albeit at low velocities).

Similarly to F max , both RFD max and RFD avg are comparable to values reported in the literature. 46 In general, RFD did not differentiate SPEED and TECH athletes, but all measures except one (RFD max scaled to BW for SPEED) were moderate to very-strongly related to performance in both disciplines. Feasibly, the need to apply force abruptly but with finesse, either during turning events (eg, turn initiation and turnswitch), to dampen transient vibrations, or to produce large force in response to course irregularities, could explain the F I G U R E 4 Pairwise correlations between variables of dynamic output and performance. Data correspond to the mean Pearson's correlation (diamond), with the error bars the 95% confidence intervals (including qualitative thresholds for interpretation on the x-axis; "+," positive; "-," negative). TECH (black, hollow diamond) and SPEED (gray, solid diamond) skiers. Variable pairs are: h, unloaded squat jump height; P max , maximal power; S Fv , slope of the linear force-velocity relationship; F 0 , maximal theoretical force; v 0 , maximal theoretical velocity; variable units are provided only to differentiate absolute variables (eg, W, for watts) from their body mass scaled counterparts (eg, W/kg, for watts per kilogram). importance of both RFD max and RFD avg , and support the associations with performance in both disciplines. 1,3 For example, while much slower turn cycles may imply less need for developed RFD in SPEED, 5 athletes still require the capability to produce force quickly to maintain trajectory while traversing slopes at extreme velocities. However, RFD becomes increasingly dependent on F max following initiation (ie, > 75 ms 41 ), and might explain the strong association between RFD avg and SPEED performance-although, this rationale is weakened by substantial relationships between both RFD measures and TECH performance in the relative absence of the critical nature of F max . In any case, our results support the discriminative nature of RFD in ski athletes from both disciplines, with a slight bias of maximum "early-phase" output in TECH athletes, and "late-phase" output in SPEED athletes.

Although there is limited information on the longitudinal effects of ski training on physiological adaptations, we assume the differences observed here are partially explained by the chronic unique demands of alpine skiing-and more specifically, disciplines-on the athletes. Consequently, we believe our results are indicative that there are specific force capacities underlying the needs of skiing disciplines and performative levels. More broadly, our results might support more direct associations between specific physical qualities and performance in the SPEED disciplines, compared to the more technically variable TECH disciplines. Since the effective force application across skiing disciplines is related to both physical capacity and the technical ability to apply it, targeted enhancement of specific force-production capacities is one means of enhancing performance. For example, improving specific athletic capacity might feasibly allow athletes to work at a lower relative percentage of their maximum, becoming more metabolically efficient and suffering fewer consequences of sustained skiing activity. 3 Another possibility is that an athlete with enhanced capacity can produce additional output when needed, avoid mistakes (eg, skidding to dissipate energy), and subsequently gain valuable time. In any case, the relationship is likely more complicated, and further research should investigate and clarify the association between specific physical capacities and force production on the snow.

| Limitations

While FIS points and standings provide a valid measure of macroscopic athlete level, they encompass accrued performance across multiple seasons influenced by a variety of factors (eg, tactical decisions regarding race participation and the level of other competing athletes). Consequently, standings are not necessarily representative of current skiing performance. While efforts were made to reduce the impact of this shortcoming (ie, race data from the closest time-point to F I G U R E 5 Pairwise correlations between variables of isometric force output and performance. Data correspond to the mean Pearson's correlation (diamond), with the error bars the 95% confidence intervals (including qualitative thresholds for interpretation on the x-axis; "+," positive; "-," negative). TECH (black, hollow diamond) and SPEED (gray, solid diamond) skiers. Variable pairs are: F max , maximum isometric force; RFD max , maximum rate of force development; RFD avg , average rate of force development; variable units are provided only to differentiate absolute variables (eg, N, for newtons) from their body mass scaled counterparts (eg, N/kg, for newtons per kilogram).

| 11

CROSS ET AL.

the field tests), the lack of a more direct measurement of "onsnow" performance may be a limitation of this work even if associated with its own shortcomings (eg, characterization of performance based on a single day or course).

A common, but notable, limitation with this research is the possibility that the results we observed are related to the geographical approaches of the talent development and coaching practices of the athletes (ie, French national team). A multisite data collection involving athletes from multiple countries would aid in elucidating associations between various physical characteristics and performance. While outside of the purview of this research, such an investigation might help isolate confounding nation-specific approaches to conditioning that might otherwise result in interpretations of performance association. 48 In the same manner, provided with a large enough sample, separating athletes into their specific events or multievent specialists would provide a clearer view of specific performance characteristics underlying athletic profiles.

As ski athletes are known to display a disproportionately stronger lower body compared to other sporting codes, 14 upper-body strength may have limited force production in the IMTP. Consequently, the isometric squat might provide a valid alternative for future research. While there are concerns regarding setup complexity, and thus reduced feasibility for integration into a team environment, there might be interest in assessing the dynamic and isometric output of individual limbs (eg, using force-platforms) in future ski research.

Our portable IMTP system was selected to improve the accessibility of isometric assessments, given the cost and ungainly nature of force-plate systems. However, while similar systems provide accurate F max with some systematic bias, 34- 37 the one report of RFD validity that exists depicts poor agreement compared to fixed-bar force-plate systems. 35 Our system overcomes several critical limitations of previous designs that feasibly improve RFD accuracy (eg, rigid base-plate [wood vs reinforced steel], high sampling frequency [< 100 vs 1000 Hz], and rigid tether [material lashing strap vs hardened metal chain]), and might be considered a different assessment than the criterion solution since they are fixed vs open chain. Nevertheless, our RFD results should be interpreted with these factors in mind. Lastly, our results do not assess other vital capacities, such as the maintenance of force output over multiple repetitions. 3 As such, while complicated to measure, future research should attempt to further integrate these specific parameters into tests of strength-endurance capacity.

| PERSPECTIVES

The aims of this study were to clarify whether distinct force capacities exist in skiers from different disciplines and whether they are associated with athlete performance level. Our results indicate that skiing disciplines differ based on the importance of force-production capacities in both dynamic and isometric modalities, with SPEED athletes being relatively dominant in absolute dynamic force production at low speeds and in isometric contraction modes. Better SPEED discipline skiers possessed and overall increased capacity for maximum isometric force, dynamic force at low velocities, and late-phase rate of force development. Better TECH athletes displayed elevated dynamic absolute force at low velocities and a trend for greater absolute isometric force, with both maximum and late-phase rate of force development similarly important. Force production at moderate velocities did not clearly separate disciplines, nor was it associated with performance. Cumulatively, our results indicate discipline-specific force-profiles might exist, and since better skiers possess specific characteristics, individual force-production capacities of the neuromuscular system might be a limiting factor of skiing performance. This strengthens the evidence for integrating assessments of isometric force and dynamic strength at low velocities in place of more generalized tests of force output in testing batteries for ski athletes.

INTRODUCTION

ower-Lower-limb explosivity and power output is a central physical component in many sports and is commonly assessed via jumping. The two most commonly used variants are the squat jump (SJ) and countermovement jump (CMJ), which differ based on the presence or lack of a swift downward motion directly preceding the upward propulsive phase (the latter and former jumps, respectively). The capability to produce force with and without countermovement is useful in characterising contextual performance, notably in situations or sports that necessitate minimal or no countermovement (e.g., a sprint-block start or turning during skiing).

Lower-limb power output is higher with countermovement than without (Bobbert & Casius, 2005;Van Hooren & Zolotarjova, 2017), with an s -shortening-cycle being the common interpretation. Of the mechanisms assumed to contribute to increased performance, several rely on eccentric contraction during the force enhancement [START_REF] Herzog | Residual force enhancement in skeletal muscle[END_REF]). However, it is unclear that typical amplitude countermovements result in active muscle fibre lengthening (Van Hooren & Zolotarjova, 2017). Rather, the principal explanation for an augmented performance with countermovement appears to be the increased development of active state pre-propulsive phase (and associated musculature being aligned and stretched pre-movement [i.e., reduced slack]), and the muscle fibres operating on a more favorable portion of the force-length-velocity curve (Bobbert & Casius, 2005;Van Hooren & Zolotarjova, 2017;van Ingen Schenau, 1984). Consequently, athletes who can generate greater muscle stimulation, and increase the active state of contractile elements, can perform more work during the initial phase of concentric contraction (Bobbert & Casius, 2005;Bobbert & van Zandwijk, 1999a). The result of these capabilities applied to jumping is greater force production during the pushoff phase, and a higher jump height (h) attained.

The effect of countermovement on lower-limb force production is commonly assessed in jumping as a CR), between h or the power developed during the concentric propulsive phases of a CMJ and SJ (e.g., McGuigan et al., 2006). Several variations exist (McGuigan et al., 2006;Pruyn, Watsford, & Murphy, 2016;Tufano et al., 2013), which have been implemented in the interest of better understanding the contributors to explosive performance within and across various sports. For example, McGuigan et al. (2006) showed that CRs varied across sports (e.g., greater in soccer than softball for males and females), and early reports by Komi (1984) jumping) displayed larger CRs (as CMJ-SJ, in h and work) than runners or physical education students. These results are interesting, since given the rationale above, a larger CR is not necessarily beneficial and might reflect an inability to produce force without countermovement via an inability to build up stimulation, more compliant musculature (i.e., lower stiffness (Pruyn et al., 2016)), non-beneficial forcelength-velocity characteristics, or other factors. While complicated by varying ratios across sporting disciplines, this perspective is tangentially supported by the fact that better athletes do not universally exhibit higher countermovement effects (Van Hooren & Zolotarjova, 2017).

One potentially confounding factor is that CRs are almost exclusively measured in bodyweight (BW) conditions; while undoubtedly practical and arguably relevant to various sporting situations (e.g., volleyball), the approach only quantifies the countermovement effect in a single and variable force-velocity (Fv) condition (Morin, Jiménez-Reyes, Brughelli, & Samozino, 2019). Moreover, even if h at BW is associated with force production in approximately the middle of the Fv spectrum, and consequently a might not accurately represent maximal power capabilities (Morin, Jiménez-Reyes, et al., 2019). The methodological impact of this problem was partially illustrated in large inter-athlete variation in CRs observed by using h vs. peak power developed during the jumps as the underlying variable (McGuigan et al., 2006). However, perhaps the main limitation of a BWonly approach is that it might not be pertinent for sports or sporting situations that rely on performance in more disctinct mechanical conditions. Specifically, since the balance in Fv capacities is independent of maximum power (Samozino et al., 2014), and various sports and sporting circumstances display distinct mechanical characteristics (Giroux, Rabita, Chollet, & Guilhem, 2016), we might expect the expression of countermovement to vary similarly according to the mechanical condition (Samozino et al., 2014). Consequently, exploring the effect of countermovement at different movement velocities would seem pertinent to understand the expression of force in broader conditions, since assessment in a single velocity condition may mask underlying differences in CR at high or low speeds.

L

Unfortunately, there is limited data on the interaction between velocity and countermovement effect, and this is constrained to averaged data lacking individual variability. The Fv profile compiled from multiple loaded jumps in both SJ (Jiménez-Reyes et al., 2017) and CMJ (Samozino, Rejc, Di Prampero, Belli, & Morin, 2012) provides a valid (Samozino, Morin, Hintzy, & Belli, 2010) and relatively simple means of assessing force expression per movement velocity, and associatedly the effect of countermovement separate from the movement itself. Few studies have compiled Fv profiles from SJ and CMJ movements together (Cuk et al., 2014;Cuk et al., 2016;Jiménez-Reyes et al., 2014). Jiménez-Reyes et al. ( 2014) compared the intra-individual mechanical profiles of high-level track and field athletes and observed globally increased mechanical capacity with a countermovement. On average, the group elevated Pmax was a product of the Fv maximum theoretical force [F0] and velocity [v0] increased). However, disproportionately higher increases in F0 vs. v0 (i.e., force at low vs. high velocities, respectively) were reported with countermovement. The authors interpreted the results as being due to a higher active state per the effect of increased loading on the countermovement phase (i.e., more substantial augmentation of maximum force capabilities) and the decreasing influence of neural and mechanical mechanisms with increasing speeds. These interpretations are plausible but inverted from the current understanding of the interplay between the jumps: a more significant countermovement difference infers an underdeveloped capability to produce force during the SJ (Van Hooren & Zolotarjova, 2017). In any case, these factors strengthen the theory that CRs might vary based on the mechanical conditions, and thus illustrate the need to further test the hypothesis.

A detailed examination of the effect of countermovement at different velocities, its variation in mechanically distinct sporting codes and with performance level could unveil unique and novel information on the mechanisms underlying countermovement augmentation for sports specific training purposes. One potential means of approaching such a problem is the assessment of CR in mechanically distinct sporting codes, with known and variable performance levels. In this study, we aimed to 1) examine the influence of velocity on the effect of Fv profiling, 2) to explore inter-individual variability on these factors, notably within mechanically distinct athlete populations (alpine skiers and track and field athletes), and 3) to test whether the expression of explosive capacity and the effect of countermovement contribute to sport-specific performance.

METHODS

Participants and study design

In this study, we recruited a range of male alpine skiers (N=23) and a cohort of male track and field athletes (N=30, season-best 100 m=10.67±0.25 s) as a point of comparison. Our rationale for testing our aims in this population was that the two disciplines anecdotally represent opposite ends of the mechanical spectrum: while sprinting is largely determined by a capability to apply force at high-velocities of the lower limbs (e.g., 664°/s leg-swing in sprinting (Miyashiro, Nagahara, Yamamoto, & Nishijima, 2019)), alpine skiing is dominated by prolonged flexion-extension patterns of the lower limbs (e.g., 49 to 88°/s at the knee (Alhammoud, Hansen, Meyer, Hautier, & Morel, 2020)) (see Figure 1). Consequently, while yet untested, these mechanically distinct cohorts present a unique means through which to test the variance of CRs across sports and with performance.

Figure 1. Overlay of the force output of the lower limbs of a skier and a sprinter. For the skier (BW=90 kg; dashed line), data corresponds to the course averaged output per limb (inside=grey, outside=black; solid line) from one turn as measured by specialised force-platforms from a raw dataset (Cross et al., 2019), showing both feet independently. For the sprinter (BW=72 kg), footstrikes (i.e., impulse followed by flight time and subsequent impulse of opposite limb) 2-7 of a maximum sprint are displayed (limb 1=black, limb 2=grey), as measured by in-ground force-plates from a raw dataset (Morin, Samozino, Murata, Cross, & Nagahara, 2019). While not displayed on this graph, the speed at which these forces are produced is very different, with very slow and very fast angular velocities of the lower limbs for skiing and sprinting, respectively.

The skiers hailed from both speed (super giant and downhill, N=11) and technical (slalom and giant slalom, N=12) disciplines, with an average world ranking of 85±62 in their best event (better<worse, extracted from the 9 th list for the 2019/2020 season released by the International Ski Federation). All athletes were high-level (national-international representatives), accustomed to the testing procedure with a history of resistance training and testing protocols. Athletes were free of any musculoskeletal injuries at the time of testing that would unduly influence their capability to participate to their fullest extent.

Athletes performed a ~1 hr testing battery, consisting of SJ and CMJ movements across different external loads, to compile Fv profiles with and without countermovement effect. While the testing occurred in disparate locations, the methodological procedures surrounding the assessment were functionally identical except where explicitly specified. Athletes were accustomed to the procedures, which were performed as part of their regular testing and condition practices. The appropriate local ethics committee approved all operational procedures (note: information omitted from blinded manuscript). Written consent was obtained from the athletes, and the procedures followed the guidelines of the World Medical Association (Declaration of Helsinki).

Procedures

Pre-session BW and limb length measurements were taken, following by a ~20 min dynamic warm-up. The athletes then selected their preferred squat depth and performed loaded SJ and CMJs while aiming to produce the highest h to compile Fv relationships (Morin & Samozino, 2016). Athletes wore regular training attire and trainers or Olympic lifting shoes for the testing procedures.

Force-velocity profile in squat and countermovement jump

To compile Fv relationships, athletes performed maximal squat and countermovement jumps. The testing was performed in either an enclosed squat rack (model: FT700 power cage, FitTech, Brisbane, Australia) or in a free-standing squat rack (model: Olympic Rack, Technogym, Gambettola, Italy), with either the safety-bars and a selection of rubber wedges or an elastic band used to standardise the depth of the jumps. Squat depth was individualised by first setting athletes around ~90° (via manual goniometer) and then allowing them to adjust for a final position (Janicijevic et al., 2019). Once selected, push-off distance (hpo) was measured via flexible tape as the difference between the length of the limb in the bottom position of the jump (i.e., the distance between the greater trochanter and the floor) and just before take-off (i.e., the distance between the greater trochanter and the end of the pointed toe).

Athletes performed consecutive SJ and CMJ movements for a selection of four to six external loads ranging from 7.5 to 90 kg (calibrated Olympic plates and bars) were used to provide resistance in the loaded jumps in addition to jumping unloaded (i.e., BW only). Each jump was separated by 3-5 min rest, loading magnitude was selected to give a span of loading sufficient to compile an accurate load-velocity profile (Morin & Samozino, 2016). For SJ, athletes slowly descended with the bar to their individualised and pre-set depth (i.e., slightly above the rack supports or lightly touching the elastic bands), rested isometrically for 3 s (verbally cued), and then jumped upwards with explosive intent. For CMJ, the same process was followed except without strict cueing and allowing countermovement (i.e., no pause). For each loading condition, one to two trials were performed with small intra-repetition rest, and 3 to 5 min passive rest was allowed between movement type and subsequent loading increase. h data were measured using optical gates (model: OptoJump Next, Microgate, Bolzano-Bozen, Italy) and calculations based on fundamental physics. Jump height data were monitored throughout, and loading was adjusted where necessary. Data were entered in real-time to compile a preliminary Fv relationship to help identify irregular jumps via the linear regression line (in addition to other disqualifying points, such as stumbling, irregular hpo, or other irregular movements).

Overall performance index

For skiers, the performance metric was their the bestevent world standing for the following season. For the sprinters, we used the time of their season-best 100 m competitive performance (non-competitors in the 100 m were omitted from the corresponding analyses).

Analysis

Jump analysis and force-velocity profiling

Data from the jump with the highest h per loading parameter were used to calculate the average force (F), power (P), and velocity (v) over the push-off phase using a validated method (Giroux, Rabita, Chollet, & Guilhem, 2015;Samozino, Morin, Hintzy, & Belli, 2008). Briefly, the method uses fundamental Newtonian physics applied to the raw h data, in combination with total mass (BW + external load; mtot) and the measurements of hpo: Fv and Pv relationships were fit with least-squares regressions. The theoretical limits of force production capacities at extremely low and high velocities (F0 and v0, respectively) were extrapolated as intercept between the curve and each axis and were used to compute maximum power (Pmax=F0•v0/4). The slope of the Fv relationship represented the balance in mechanical capabilities (SFv) and was further characterised by (Samozino et al., 2014) per BW (Fvimb; >100% is force dominant, <100% is velocity dominant) (Samozino et al., 2012).

Countermovement ratio CR (CMJ/SJ) were computed on unloaded h per movement (CRh) and key Fv: CRP for Pmax, CRF for F0, and CRv for v0 (i.e., at moderate, extremely low, and high velocities, respectively; Figure 2). Figure 2. Force-and power-velocity relationships compiled from multiple jumps with and without countermovement. Black and grey lines correspond to the force-and power-velocity relationships with and without countermovement, respectively. CRP and CRh correspond to ratios between with and without countermovement in maximum power (Pmax, as the peak of the parabolic power velocity relationship) and jump height (i.e., both existing in moderate velocity conditions); CRF and CRv the ratios between with and without countermovement for maximum theoretical force and velocity (F0 and v0, as the x-and y-axis intercepts of the linear force-velocity relationship and corresponding to very low and very high velocity implementing ratios on unloaded jumping movements that the jumps correspond to the peak of the powervelocity relationship (i.e., perfectly tracks maximum power, and the athlete is perfectly balanced for lowerlimb explosivity (Samozino et al., 2014)). The oval corresponds to an approximate band of error when using jump height as an indicator of maximum power capacity since it is dependent both on the maximum power and balance between force and velocity capacities (Morin, Jiménez-Reyes, et al., 2019).

Statistical analysis

Statistical analyses were performed using JASP (version: 0.12, JASP Team, Amsterdam, Netherlands). Where relevant, descriptive statistics are presented as means±standard deviation or median(interquartile range [IQR]) where explicitly stated.

To test initial differences between outputs in CMJ and SJ, data (h, Pmax, SFv, F0, v0 for both movements) from skiers and sprinters were pooled and analyzed using Statistical analyses were performed using JASP (version: 0.12, JASP Team, Amsterdam, Netherlands). Where relevant, descriptive statistics are presented as means±standard deviation or median(interquartile range [IQR]) where explicitly stated.

To test initial differences in output (h, Pmax, SFv, F0, v0 for both movements) with and without countermovement (i.e., SJ vs CMJ), data from skiers and sprinters were pooled and analysed using -rank paired samples tests. Nonparametric analyses were used after data from 4/5 variables were found to be not normally distributed . Data were reported using the Hodges Lehmann estimate and the rank-biserial correlation (rrb) to provide the magnitude of the effect. To test for associations between CRs at low and high velocities (i.e., CRF vs CRv rs, p-value) nonparametric correlations were performed on the pooled CR data.

Differences between sport disciplines in BW, h, and Fv characteristics in SJ (Pmax,SFv,F0,v0,and Fvimb) were assessed using independent Tunequal variances Ttest p<. standard deviation were used to provide a measure of effect magnitude. For CR ratios, both the assumption of normality and equality of variances were violated (Shapiro-p<.05), and therefore the nonparametric Mann-Whitney U tests were used. Results were reported as the median difference between the two groups (Hodges Lehmann estimate) and associated effect magnitude (rrb).

Multiple regression analyses were used to assess the potential association between mechanical capacity and CRs to performance. Each sport was analysed separately, with sports-specific performance entered as the dependent variable, and three separate models containing each CR and the corresponding Fv variable in CMJ (e.g., CRF and F0). Data met the pre-requisite assumptions for regression analyses, except for Pmax, which was minorly skewed. Logtransforming improved normality (Shapiro-Wilks, W=0.921 p=.117) but did not substantially change the results. Therefore, the analysis was performed on the -For each model, the standardised effect (β), F, model R 2 [adjusted], and p-values were reported. The thresholds for qualitative interpretation of effect magnitudes were: d<0.2, 0.2, 0.5, 0.8 and 1.2; r, rs, and rrb<0. 1, 0.1, 0.3, 0.5, and 0.8;as trivial, small, moderate, large, and very large, respectively (Sawilowsky, 2009). The alpha value was set at 0.05, with 0.1 considered a trend.

RESULTS

h, Pmax, F0, v0 were all very strongly increased by countermovement, whereas SFv was unclear (see Table 1). A clear and strong negative association (rs=-0.735, p<.001) was observed between CRF (median=1.091 [0.333]) and CRv (median=1.058 [0.413]) (see Figure 3, and Table 2). *** INSERT TABLES 1 & 2 HERE *** Figure 3. Comparison between sports and pooled correlation results for countermovement ratios. The graphic displays the median and interquartile ranges for countermovement ratios between key forcevelocity capacities: intercepts of the force-velocity relationships (F0 and v0, respectively), maximum power output (Pmax), and jump height (h). Boxplots are median and quartiles, with white filled boxes the mean and circles data from individual athletes (except where values significantly overlap). The dashed line represents a balance/equality between SJ and CMJ output, with values above the line (i.e., >1) representing a higher value with a countermovement and vice-versa. Comparisons between sport codes in the respective mechanical quality are displayed as Mann-Whitney test (U) and rank biserial correlation (rrb). Pairwise differences between mechanical capacities (F0 vs v0) for the pooled athlete data are presented in rs). **p<.01, ***p<.001.

Skiers and sprinters differed in several key mechanical variables, with sprinters having lower h, Pmax, v0, and a more negative SFv (Table 3, Figure 4). Skiers were much heavier (large difference between groups in BW), had a higher relative value of SFvopt%, and there was a trend for skiers displaying moderately higher absolute F0. No clear differences were observed in relative F0. There were moderate to large differences between skiers and sprinters for CRv (median=1.17 In skiing, multiple regression models, including F0 and CRF and v0 and CRv were related to performance (see Table 4). In the former, both variables contributed to the model; however, the model prediction was weaker in the latter case and mostly due to a strong positive relationship with v0 (inverse, since lower ranking is better) and no clear predictive quality with CRv. In the sprinters, only the model with Pmax and CRP was clearly associated with performance without a clear contribution of CRP to the model.

*** INSERT TABLE 4 HERE ***

DISCUSSION

According to the mean data, dynamic lower-limb force-output characteristics were augmented by countermovement. Countermovement effect in conditions common to research (i.e., in moderate conditions, around maximum power) did not differentiate sporting codes. However, the expression of countermovement effect appeared to differ across movement velocities and sporting groups, which led to marked differences at high and low extension velocities. Specifically, at lower velocities, the countermovement effect was small for skiers, with much greater variability at high velocities, whereas sprinters exhibited the inverse characteristics (a larger effect of countermovement at low velocities vs. high velocities). Similarly, countermovement effect might vary with performance, with better skiers possessing greater force output and a smaller countermovement effect at low velocities, albeit lacking association at any velocity and 100 m performance in sprinters. These results highlight a necessity to examine countermovement effect in conditions relevant to the sport, and have interesting, albeit complex, implications for training.

In congruence with the surrounding literature in skiing (Jordan, Aagaard, & Herzog, 2018) and sprinting (Jiménez-Reyes et al., 2014), h and Pmax were augmented via countermovement (+0.068 m and +415 W [17.2 and 17.5%], respectively). Moreover, the magnitude of the difference between raw h values are in line with previously reported (e.g., CRh = 1.03-1.17 for various sports (McGuigan et al., 2006)). The general agreement between CRh and CRP is unremarkable, given the underlying mechanical association between the two measurements (at least for group comparisons) (Morin, Jiménez-Reyes, et al., 2019). Overall, countermovement evoked an upward and rightward Fv profile shift (Bosco & Komi, 1979;Jiménez-Reyes et al., 2014), where both force at low and high velocities increased (i.e., CR >1)). However, while the slope of the Fv relationship (i.e., SFv) remained unchanged on average, substantial variability infers individuality in the effect of countermovement on distinct mechanical capabilities (observed in CRF and CRv). There was an inverse relationship between CRF and CRv, indicating that the effect of countermovement was not consistent across velocities between athletes. Moreover, while strongly related, a large proportion of variance unexplained between the CRF and CRv (rs 2 =46%) suggests the countermovement effect provides different information regarding lowerlimb force production capabilities at the extremes of the Fv relationship. Consequently, assessing the countermovement effect at a single velocity condition provides only a partial view of the phenomenon.

Unsurprisingly, skiers and sprinters differed in key lower-limb mechanical characteristics in the SJ. In the first instance, sprinters exhibited a much higher h (+0.101 m) and relative Pmax than skiers. Skiers presented a more force-oriented profile (closer to vs 65%, where 100% maximises h (Samozino et al., 2012)), which was particularly notable in absolute conditions (i.e., non-scaled to body-mass). Subsequently, skiers displayed a trend for moderately greater output in absolute F0 and possessed much lower v0. While substantial differences in force application in the field between the cohorts (e.g., orthogonal vs horizontal in skiing vs sprinting) complicate interpretation, our results may be reminiscent of skiers regularly performing in high force (Gilgien, Kröll, Spörri, Crivelli, & Müller, 2018) lowvelocity conditions (Alhammoud et al., 2020), compared to the rapid and elevated force output of sprinters at very high contraction velocities. Moreover, skiers exhibit peak torque in greater flexion at key joints (Alhammoud et al., 2019) compared to athletes involved in regular sprint running (e.g., rugby players (Brown, Brughelli, Griffiths, & Cronin, 2014)), which might create force-length-velocity characteristics supporting elevated work during the initial push-off at low extension velocities.

The change in Pmax or h via countermovement did not differentiate sports. However, coupled with the independence of SFv and power output (see Table 2), the effect of countermovement across the Fv relationship was different for each sport. Skiers presented a lower CRF, and sprinters had a lower CRv. Since a smaller countermovement augmentation (i.e., a lower CR) is potentially beneficial (Van Hooren & Zolotarjova, 2017), these findings are intuitive and congruent with the general force and velocity dominant performative nature of skiers and sprinters, respectively. This strengthens the importance of measuring CRs at various velocities, since the results from only one condition (notably, CRh or CRP), one might conclude CRs lack relevance or that skiers and sprinters share similar underlying muscular qualities (Bobbert & Casius, 2005;Van Hooren & Zolotarjova, 2017).

Low extension velocities increase the relative time to build-up stimulation in the SJ, while elevated external load stiffens the tendon, resulting in slower shortening velocities and hence higher force potential of muscle fibres. Since the absolute extension time is much greater in high force-low velocity conditions, the effect of maximum-voluntary force and non-elastic characteristics of the muscle may play a more significant role in the work produced (Maffiuletti et al., 2016) than at higher speeds. Both factors might explain the reduced CRF levels observed in the skiers, who habitually perform elongated contraction cycles during comparatively slow turns (Alhammoud et al., 2020;Berg & Eiken, 1999) and consequently large impulse (Gilgien et al., 2018) in their sport. Moreover, since concentric actions in skiing are preceded by lowforce (around turn-switch (Kröll et al., 2015)) and relatively low activation (Berg & Eiken, 1999), conceivably, skiers might accrue long-term adaptations that benefit increased activation (or non-inhibition) in these conditions. Another explanation might be forcelength relationships of the contributing musculature being closer to optimal in flexed positions, which would benefit force-production in the early push-off phase (Van Hooren & Zolotarjova, 2017). On the other hand, larger CRF in sprinters could be caused by inhibition due to the isometric phase, reduced coordinative capabilities during the concentric phase due to the heavy isoinertial loads necessitated by the assessment, less-optimal length-tension characteristics, or kinematic differences (i.e., benefiting skiers).

The theoretical extension times at maximum velocity and zero force are incredibly brief (e.g., ~0.13 s for skiers). Consequently, at the velocity end of the Fv spectrum shorter propulsive phases likely increase the relative effect of factors related to the maximum rate of force-development on the difference between jumps (Maffiuletti et al., 2016). A lag to reach maximal active state is a clear contribution (Bobbert, Gerritsen, Litjens, & Van Soest, 1996), with even small changes in activation timing drastically changing force-production (Bobbert & van Zandwijk, 1999b); feasibly, the impact of these factors would be exaggerated at higher extension velocities. Factors underlying muscle slack (Van Hooren & Bosch, 2016), notably tendon stiffness (Kubo et al., 2007), might be another explanation since they might represent a more significant proportion of extension time than activation qualities (although, stimulation and muscle slack co-vary) (Van Hooren & Zolotarjova, 2017). Consequently, sprinters may exhibit stiffer tendons compared to skiers (McMahon, Comfort, & Pearson, 2012) and superior activation qualities at high velocities, allowing increased work production in the initial portion of the extension (Pruyn et al., 2016). Inversely, compliant musculature assumedly explains the greater CRv in skiers. While little information exists on the stiffness of skiers, it is lack of relevance for performance is indirectly supported by lower-limb stiffness failing to separate adolescent and elite athletes (Jordan et al., 2018). Moreover, while skiers may be proficient in building up stimulation at low extension velocities, plausibly, they might lack coordinative abilities to correctly time muscular activation at high speeds in the SJ (Bobbert & van Zandwijk, 1999b), leading to larger and more variable CRv values.

In addition to our results indicating that countermovement effect appears to be dependent on velocity, and might vary based on the sport (per their integral mechanical characteristics), the results from the sport-distinct multiple regression analyses show that they might also vary based on performance. Notably, better ranked skiers exhibited both greater force output at low velocities (i.e., F0), and a lower CRF (33% variance), highlighting that both the capability to develop maximum force and to minimize countermovement effect at low speeds are important. The association between higher F0 and lower CRF and performance is in line with our interpretations regarding the adaptations from the prevalent high force, low velocity, non-countermovement, but continuously activated states during skiing (Berg & Eiken, 1999). As CRF is an index of force production at slow velocities directly preceded by elevated external constraints, it might be a valuable measure for skiers in the future. For sprinters, while a model containing Pmax and CRP explained 30% of the variance in 100 m season-best time, CRP did not improve the model (p>.05). In the same manner, better skiers exhibited lower force production at high velocity (v0), albeit without the predictive contribution of CRv (20% variance). As such, in support of the surrounding literature {Van Hooren, 2017 #1360} we cannot confirm an overall trend for CRs and performance level, but rather that in distinct sporting schenarios (e.g., for specific sports, at specific extension velocities) they might provide discriminative information for monitoring and potentially training implementation.

Limitations

CR variants appear to have acceptable reliability (Tufano et al., 2013) and have successfully described the performance in various sports cohorts (McGuigan et al., 2006). While CRs should present similar reliability to the underlying Fv variables, their sensitivity to track athlete profiles and adaptations to training and long term performance monitoring remains to be tested.

Conclusions

The effect of countermovement on force-production appears to vary across the Fv spectrum within and between sports. However, no clear conclusions could be drawn regarding sport-specific countermovement characteristics in conditions common to the literature. These factors emphasise the interest in assessing a broader range of force output-countermovement, or at least ensuring specific bands of velocity are targeted, to ensure characterisation of sports with unique mechanical profiles. A larger increase from countermovement does not appear to be globally beneficial for athletes, with athletes from mechanically disparate codes tending to show smaller ratios at extension velocities characteristic of their sport (i.e., skiers displaying a tendency towards smaller differences at low velocities and sprinters smaller at high velocities). These factors were further emphasised by some associations with performance, albeit not globally. Future research might aim to integrate more complex measurements and modelling using multijoint movements (e.g., jumping) and Fv profiling to better understand the mechanisms underlying performance and the expression of countermovement effect across sports and movement velocities. In general, more work is needed on the subject, preferably combined with other tests of athlete capacity, stiffness, and perhaps even muscle structure or length-tension capacities to elucidate underlying mechanisms. Such research would enable a more holistic view of countermovement effect as it pertains to sporting performance, and provide a better view of possibilities for monitoring performance and targeted training implementation.

Summary

• Countermovement effect can be integrated with a force-velocity approach in jumping to provide insight into its effect at high, moderate, and low velocities, independently from the assessment conditions.

• Countermovement effect on force production differs with extension speed, and appears to differ across sports. Consequently, countermovement effect should be assessed in mechanically-specific conditions, since assessment in non-relevant conditions might miss relevant information.

• While sports specific, there is evidence to suggest a smaller countermovement effect might be beneficial to some sports and sporting scenarios (per the appropriate movement velocity -jump performance; CRh, ratio between jump-height in countermovement jump versus squat-jump; CRP, ratio between maximum power determined from the peak of the power-velocity relationship in countermovement jump versus squat-jump; CRF, ratio between maximum theoretical force determined force-velocity relationship in countermovement jump versus squat-jump; CRv, ratio between maximum theoretical velocity determined force-velocity relationship in countermovement jump versus squat-jump; U, Mann-Whitney U test; CI, confidence intervals (95%); IQR, interquartile range. for unequal variances applied to analyses; SJ and CMJ, squat jump and countermovement jump, respectively; h, height; m, meters; Pmax, maximal power; W, watt; W/kg, watt per kg; SFv, Slope of the linear force-velocity relationship; F0, maximal theoretical force; N, newtons; N/kg, newtons per second; v0, maximal theoretical velocity; Fvimb, the imbalance between the current profile and the optimal for maximizing jump height at body mass. .797 stand. β, beta-weight in standardized units; F, F test; df, degrees of freedom; CRh, ratio between jump-height in countermovement jump versus squat-jump; CRP, ratio between maximum power determined from the peak of the power-velocity relationship in countermovement jump versus squat-jump; CRF, ratio between maximum theoretical force determined force-velocity relationship in countermovement jump versus squat-jump; CRv, ratio between maximum theoretical velocity determined force-velocity relationship in countermovement jump versus squat-jump;

INTRODUCTION

Repetitive near-maximal-or maximal-intensity e orts, such as sprinting, rowing, jumping, or stair climbing, are frequent in daily life and sporting activity. The key to successful performance during repeated movements relies on the production of mechanical power and its maintenance over a series of repetitions until task completion.

Power production capabilities depend on movement velocity and are well-represented by the parabolic power-velocity (Pv) relationship during multi-joint movements (Bobbert, 2012;Samozino et al., 2012;Jaric, 2015). The apex of the P-v relationships corresponds to the maximal power attained at optimal velocity (P max ), which is commonly accepted as a macroscopic measure of dynamic strength capabilities (Jaric, 2015;Alcazar et al., 2017). The ability to maintain power over a series of movements (i.e., strength-endurance) depends primarily on the output magnitude and is well-illustrated by the power-time relationship. Two distinct power-time relationships have been reported to characterize strength-endurance: (i) the inverse hyperbolic relationship between the absolute or relative power output and the duration during which this given power can be maintained, which can be obtained from 3 to 5 tests to exhaustion (Monod and Scherrer, 1965;[START_REF] Burnley | Power-duration relationship: physiology, fatigue, and the limits of human performance[END_REF], and (ii) the decrease in instantaneous power output over time during a single all-out exercise, which is instead associated with fatigability indices, such as the rate of power output loss over 30-s all-out cycling (Bar-Or, 1987). However, the same absolute or relative-to-P max (%P max ) power output can be developed in high force-low velocity conditions or in low force-high velocity conditions, and these di erent force-velocity (F-v) conditions can be interpreted as distinct ratios between the force output and the movement velocity (R Fv ).

The e ect of R Fv on strength-endurance has been studied indirectly by investigating the e ect of movement velocity using cyclic (e.g., cycling) and acyclic movements (e.g., knee extension; [START_REF] Elert | The relationship between contraction and relaxation during fatiguing isokinetic shoulder flexions. An electromyographic study[END_REF][START_REF] Barker | Human critical power-oxygen uptake relationship at di erent pedalling frequencies[END_REF]. Due to the specificity of cyclic movements, velocity is indirectly controlled by adjusting movement frequency (e.g., the pedaling cadence) or using a specific set-ups [START_REF] Dorel | Influence of two pedalling rate conditions on mechanical output and physiological responses during all-out intermittent exercise[END_REF][START_REF] Tomas | Fatigue during maximal sprint cycling: unique role of cumulative contraction cycles[END_REF]. During allout exercises, higher fatigability has been systematically observed at higher compared to lower movement frequencies in cyclic movements (i.e., cycling; e.g., [START_REF] Sargeant | Maximum leg force and power output during short-term dynamic exercise[END_REF]Beelen and Sargeant, 1991a). However, there is little consensus in acyclic movements (i.e., knee extension and shoulder flexion) since some studies report higher fatigability at higher movement velocities (e.g., [START_REF] Mathiassen | Influence of angular velocity and movement frequency on development of fatigue in repeated isokinetic knee extensions[END_REF][START_REF] Morel | Contraction velocity influence the magnitude and etiology of neuromuscular fatigue during repeated maximal contractions[END_REF] while others report opposite results [START_REF] Elert | The relationship between contraction and relaxation during fatiguing isokinetic shoulder flexions. An electromyographic study[END_REF][START_REF] Dalton | The agerelated slowing of voluntary shortening velocity exacerbates power loss during repeated fast knee extensions[END_REF]. Moreover, R Fv and %P max conditions were not fixed at each repetition over the tests due to the decrease in power output throughout all-out exercises. Consequently, it is challenging to evaluate the e ects of R Fv and %P max on strength-endurance, as well as the interactions between both mechanical conditions by the mean of all-out exercises. During tests to exhaustion performed at constant power output, only cyclic movements (i.e., cycling and paddling) were used to study the e ect of R Fv on strength-endurance. Similarly, there is a lack of consensus since some studies reported lower strength-endurance at higher movement frequencies [START_REF] Carnevale | E ects of pedaling speed on the powerduration relationship for high-intensity exercise[END_REF][START_REF] Barker | Human critical power-oxygen uptake relationship at di erent pedalling frequencies[END_REF] and others, lower strength-endurance at lower movement frequencies [START_REF] Leveque | E ect of paddling cadence on time to exhaustion and kinetics at the intensity associated with in elite white-water kayakers[END_REF][START_REF] Bessot | The e ect of pedal rate and time of day on the time to exhaustion from high-intensity exercise[END_REF]. Moreover, the sole e ect of R Fv cannot be examined when using cyclic movements due to the concomitant influence of both movement frequency and velocity on strength-endurance. Indeed, movement frequency alone impacts strength-endurance by changing (i) rest between repetitions and (ii) contraction number during a test of fixed duration (Enoka and Stuart, 1992;Broxterman et al., 2014). A lower time-to-exhaustion observed at higher movement frequencies can thus be due to shorter rest time between contractions and/or more contractions and/or higher contraction velocities. Overall, investigating the e ect R Fv on strength-endurance requires (i) the use of an acyclic movement, allowing the dissociation with the e ect of movement frequency, and (ii) the use of time-to exhaustion at constant power to control force-velocity and power output conditions throughout the test.

In parallel to R Fv , strength-endurance can also be influenced by the power reserve. Indeed, due to the parabolic shape of the Pv relationship, a change in R Fv at a matched %P max is associated with a change in the power reserve. This reserve corresponds to the di erence between the maximal power capability at a specific velocity and the power output at the same specific velocity (Sargeant, 1994(Sargeant, , 2007;;Zoladz et al., 2000). This reserve can also be interpreted as a velocity-specific relative power (%P max v): the lower %P max v, the larger the power reserve. When considering the same %P max , low force-high velocity conditions (often close to the optimal velocity) are associated with larger power reserve and lower %P max v, and might improve strength-endurance (Sargeant, 1994(Sargeant, , 2007;;Zoladz et al., 2000). Nevertheless, due to the concomitant change of R Fv and %P max v at matched %P max , it remains unclear whether the influence of R Fv on strengthendurance is independent of %P max v. Also, as matched %P max v can lead to di erent %P max , the question of which of the two indices better represents exercise intensity remains unanswered.

Clarifying the e ect of %P max , %P max v, and R Fv on strengthendurance could be of great interest for scientific and training purposes since typical strength-endurance evaluations have been in performing (i) single maximal e ort squat jump (SJ) with and without load (range of loads detailed in Section "Force-and Power-Velocity Relationships Assessment") and (ii) unloaded RSJs test until exhaustion (see section "Measurements and Data Analysis" for the exact definition of exhaustion). In the second session, individual F-v and P-v relationships of the lower limbs were evaluated from SJ with and without additional loads, then RSJ test was performed in one specific F-v-P conditions (P 3 v 4 ) for inter-day reliability analysis. From the third to the sixth session, each participant performed 12 RSJ tests randomly organized into 3 per session and separated by 30 min of passive rest (e.g., [START_REF] Karsten | Comparison of inter-trial recovery times for the determination of critical power and W' in cycling[END_REF][START_REF] Triska | Iso-duration determination of d' and cs under laboratory and field conditions[END_REF], which corresponded to: 1 RSJ test in each of the 10 F-v-P conditions, 1 RSJ test repeated one more time to assess intra-day reliability in the specific F-v-P conditions (P 3 v 4 ) and 1 RSJ test was not included in the data analysis of the present study (black vertical RSJ bar, Figure 2), because this test is dedicated to answer another aim not addressed here.

The six sessions began with body mass measurements and a standardized warm-up consisting of 5 min of self-paced treadmill running followed by ⇠15 min of dynamic lowerlimb movements (including unloaded squats with maximal intention and sub-maximal and maximal SJs in unloaded and loaded conditions) and concluding with 5 min of non-fatiguing personally selected exercises.

Familiarization Sessions

During the first session, the familiarization occurred in two distinct sets. The first set aimed to familiarize participants with the F-v and P-v relationships evaluation procedures. This first set included the same procedures as during the session 2, which are described in the next section, "Force-and Power-Velocity Relationships Assessment." The second set aimed to familiarize participants with the RSJ test. This second set comprised (i) three trials of unloaded RSJ, targeting ⇠50% of maximal jump height, separated each by 5 min of rest and ended when 10 successive repetitions were successfully performed at the target and, after 30 min of passive rest, (ii) two unloaded RSJ tests, aiming for maintaining the e ort of maximal jump height until exhaustion, interspersed by 30 min of passive rest. During this familiarization session, individual starting position for RSJ tests and F-v and P-v relationships assessment was recorded and was standardized throughout the study. The preferential starting position was chosen by the participant, which has been shown as the method with which force, velocity, and power output are maximized and most reliable in squat jump (Janicijevic D. et al., 2019;[START_REF] Janicijevic | Magnitude and reliability of mechanical outputs obtained during loaded squat jumps performed from di erent knee angles[END_REF]. Using a barbell or a wooden dowel held across the shoulders, the starting position was matched with lateral adjustable supports (⇠1 cm resolution), preventing participants from going beyond the starting position during the downward movement of SJ (Figure 3). Individual push-o distance (h po ) was determined as the di erence between the length of the lower limbs extended with maximal foot plantarflexion (iliac crest-toe distance) and the vertical distance between iliac crest and ground in the starting position.

Force-and Power-Velocity Relationships Assessment

The determination of individual F-v and P-v relationships included 5 SJs with loading conditions ranging from 0 to 100% of body weight, with each condition performed twice. For each trial, participants stood stationary holding a barbell on their shoulders for additional-load conditions or a wooden dowel (⇠400 g) for the unloaded condition (i.e., 0% of body weight). They lowered the bar to reach their individual starting position and after maintaining this position for 2 to 3 s, they were asked to jump maximally without countermovement. They were also prompted to touch down in the same leg position as they took o : extended leg with foot plantar flexion. If these requirements were not met, the trial was discarded, and then repeated. The trial with the greatest jump height across all trials was used to determine individual F-v and P-v relationships (Samozino et al., 2008(Samozino et al., , 2014)). When the force exerted against a certain load led to the coe cient of determination of the F-v relationship to be lower than 0.96, a third repetition was performed with that specific load to infirm or confirm the trial.

Repeated Jump Test

For each RSJ test, the practical setting of a given F-v-P condition consisted of modulating the additional load and the jump height based on fundamental laws of dynamics and following the equations proposed and validated by Samozino et al. (2008). Briefly, during the push-o phase of SJs, the mean force (F, Eq. 1), velocity (v, Eq. 2), and power (P, Eq. 3) developed by the lower limbs can be expressed as: where m body is the body mass, m bar the mass of the bar (including the mass of the bar [10 kg] and the additional mass), g the gravitational acceleration (9.81 m.s 2 ), and h the jump height.

From Eqs 1 and 2, the jump height (Eq. 4) and the additional mass (Eq. 5) can be computed as a function of the targeted F-v-P conditions: h = 2v 2 g (Eq. 4)

m bar = P v g( h h po ) + 1
m body (Eq. 5)

Consequently, participants were instructed to reach a targeted jump height under a specific loading condition, which allowed them to perform an RSJ test in targeted F-v-P conditions. The jump height was self-controlled and aided by continuous visual feedback of the jump height that was displayed, repetition by repetition, to the screen in front of the participant (Figure 3). Where the required additional mass was lower than the mass of the bar, participants wore a weighted vest with the appropriated added load (0.5 kg resolution) and the wooden dowel. The jumping frequency was adjusted at each RSJ test, considering 2.5 s rest time between two successive SJs. The jumping frequency was monitored using two audible beeps to signal (i) the initiation of the downward movement to reach the starting position and (ii) the initiation of the jump. Participants were verbally encouraged to maintain the targeted jump height as long as possible (i.e., until exhaustion). Once jump height dropped below the target, participants were provided with strong encouragements to continue with maximal intent (i.e., aiming for maximal height). All procedures were monitored by the experimenters via their own screen, hidden from the participants during their trials.

Measurements and Data Analysis

For SJs performed during RSJ tests and F-v and P-v relationships assessment, force, velocity, and power developed during the push-o phase were computed using Eqs 1-3. The jump height was determined from fundamental laws of dynamics and aerial time (Asmussen and Bonde-Petersen, 1974), the latter being obtained using an infrared timing system (OptoJumpNext, Microgate, Bolzano, Italy). For each participant, the F-v and Pv relationships were determined from F, v, and P values obtained from the 5 loading SJ conditions and were used to extrapolate F 0 and v 0 , the y and ⇥ intercept of the F-v relationship, respectively. Then, P max was computed as (Samozino et al., 2012):

P max = F 0 v 0 4 (Eq. 6)
For each of the 10 RSJ conditions, R Fv was computed as the ratio between the force developed (expressed relative to F 0 ) and the velocity (expressed relative to v 0 ). Exhaustion was defined as the inability to perform three consecutive jumps above 95% of the targeted jump height. Strength-endurance was quantified by (i) the maximum repetitions (SJ Rep ) and (ii) the cumulated mechanical work output (W tot ) associated to SJ Rep . SJ Rep corresponded to all repetitions preceding exhaustion, excluding the three jumps below the limit of 95% of the targeted performance and W tot was computed as the sum of the mechanical work of all repetitions of SJ Rep .

Statistical Analysis

All data are presented as mean ± standard deviation (SD). Intra-set RSJ height variability around the targeted jump height value was assessed using a coe cient of variation. Also, absolute intra-and inter-day reliability of SJ Rep in P 3 v 4 condition were assessed with the standard error of measurement (SEM; [START_REF] Hopkins | Reliability of power in physical performance tests[END_REF] expressed in raw units and standardized to inter-individual SD. Relative intraand inter-day reliability of SJ Rep in P 3 v 4 condition were assessed with intra-class correlation coe cient (ICC), which was interpreted as almost perfect (0.81 to 1.00), substantial (0.61 to 0.80), moderate (0.41 to 0.60), fair (0.21 to 0.40), slight (0.01 to 0.20), or poor (<0.01; [START_REF] Landis | The measurement of observer agreement for categorical data[END_REF]. The di erence between the two trials was tested with the paired sample t-test.

The respective e ects of %P max , %P max v, and R Fv on both SJ rep and W tot were examined using two separate stepwise multiple linear regressions performed from averaged data of the 10 F-v-P conditions of RSJ tests (n = 10), with %P max , %P max v, and R Fv as independent variables and SJ rep or W tot (logtransformed to support linearity of relationships, Monod and Scherrer, 1965;[START_REF] Jones | The ' critical power ' concept? applications to sports performance with a focus on intermittent high-intensity exercise[END_REF] as the dependent variable. To test the main e ects of %P max , %P max v and R Fv on both SJ rep and W tot , as well as their interaction, 2 twoway ANOVAs with repeated measures were performed on SJ rep and W tot , separately: (i) e ects of R Fv (low, medium and high levels) and %P max (⇠73%P max and ⇠85%P max ) and (ii) e ects of R Fv (low, medium, and high levels) and %P max v (85%P max v and 100%P max v). Each ANOVA was performed after checking for distribution normality and equality of variance with Shapiro-Wilk's and Mauchly's test, respectively. In the case of non-normality and violation of the assumption of sphericity, the non-linear logarithm transformation and the Greenhouse-Geisser's correction were applied, respectively [START_REF] Sainani | Dealing with non-normal data[END_REF]). Holm's post hoc test was used to highlight significant di erences between conditions, as well as simple main e ects to test the e ect of the first main factor at each level of the second factor, and vice-versa. For all statistical analyses, an alpha value of 0.05 was accepted as the level of significance.

RESULTS

All individual F-v relationships fitted by linear regressions showed very high quality (R 2 = 0.98 to 1; p < 0.001), and were associated to F 0 of 2202 ± 317 N (30.1 ± 3.5 N.kg 1 ), v 0 of 2.79 ± 0.43 m.s 1 , P max of 1542 ± 329 W (21.0 ± 4.0 W.kg 1 ) and h po of 0.45 ± 0.06 m. The SEM, ICC, and t-test's p-values between the trials performed in the P 3 v 4 condition to assess intra-day and inter-day reliability are presented in Table 1. RSJ additional load, targeted jump height, intraset coe cient of variation of jump height, and jumping frequency associated with the 10 F-v-P conditions are presented in Table 2. SJ Rep , R Fv , W tot, as well as the targeted and achieved absolute and relative force, velocity, and power values associated with the 10 F-v-P conditions are presented in Table 3.

The stepwise multiple regression analysis with SJ rep as the dependent variable showed that %P max v (88.4% of the variance explained, beta-weight of 0.812) and R Fv (9.1% of the variance explained, standardized beta-weight of 0.327) accounted for a significant amount of SJ rep variability (p < 0.001; F = 134.187). The regression model obtained was ln(SJ Rep ) = 17.042 -0.144(%P max v) -0.649(R Fv ), which indicated a very high goodness of fit (R 2 = 0.975, p < 0.001), with low residuals (RSME = 0.243).

The stepwise multiple regression analysis with W tot as the dependent variable showed that %P max v (89.2% of the variance explained, beta-weight of 0.825) and R Fv (7.9% of the variance explained, standardized beta-weight of 0.305) accounted for a significant amount of W tot variability (p < 0.001; F = 116.866). The regression model obtained was ln(W tot ) = 22.140 -0.132(%P max v) -0.545(R Fv ), which indicated a very high goodness of fit (R 2 = 0.971, p < 0.001), with low residuals (RSME = 0.234).

E ect of R Fv and %P max on SJ rep and W tot

The two-way ANOVA with repeated measures testing the e ect of %P max and R Fv on SJ rep showed a main e ect of R Fv (p < 0.001) and R Fv ⇥ %P max interaction (p < 0.001), but no main e ect of %P max (p = 0.129; Figure 4A). Post hoc comparisons revealed significant di erences (p < 0.001) for all comparisons between the three R Fv levels, with an increase of SJ rep when R Fv decreases. A simple main e ect of %P max was observed at the highest level of R Fv (p < 0.001), but not at the two lower levels (p = 0.129 and p = 0.782, for the lowest and the middle level, respectively). A simple main e ect of R Fv was observed at the two levels of power (p < 0.001).

The two-way ANOVA with repeated measures testing the e ect of %P max and R Fv on W tot showed a main e ect of R Fv (p < 0.001) and %P max (p < 0.001), and R Fv ⇥ %P max interaction (p < 0.001; Figure 4C). Post hoc comparisons revealed significant di erences for all comparisons between the three R Fv levels (p < 0.001), with an increase of W tot when R Fv decreases. A simple main e ect of %P max was observed at the low level of R Fv (p < 0.001), but not at the moderate and high levels (p = 0.954 et p = 0.323, respectively). There was a simple main e ect of R Fv at the two levels of power (p < 0.001).

E ect of R Fv and %P max v on SJ rep and W tot

The two-way ANOVA with repeated measures testing the e ect of %P max v and R Fv on SJ rep showed a main e ect of R Fv (p < 0.001) and %P max v (p < 0.001), and R Fv ⇥ P max v interaction (p = 0.03; Figure 4B). Post hoc comparisons revealed significant di erences in all comparisons between the three R Fv levels (p < 0.05), with an increase of SJ rep when R Fv decreases. A simple main e ect of %P max v was observed at each level of R Fv (p < 0.001). There was a simple main e ect of R Fv at 85%P max v (p < 0.001) and a trend at 100%P max v (p = 0.078).

The two-way ANOVA with repeated measures testing the e ect of %P max v and R Fv on W tot showed a main e ect of R Fv (p < 0.001) and %P max v (p < 0.001) and R Fv ⇥ %P max v interaction (p < 0.001; Figure 4D). Post hoc comparisons revealed significant di erences at the three R Fv levels (p < 0.05), with an increase of W tot when R Fv decreases. A simple main e ect of %P max v was observed at the three levels of R Fv (p < 0.001). There was a simple main e ect of R Fv observed at 85%P max v (p < 0.001), but only a trend at 100%P max v (p = 0.134).

DISCUSSION

The main finding of this study was that strength-endurance in repeated jumping depends on force, velocity, and power conditions, expressed relative to force-and power-velocity relationships. The large intra-individual di erences in both the maximum repetitions and total work produced across the 10 Fv-P conditions studied (from ⇠3 to ⇠150 repetitions and from ⇠2000 to ⇠70000 Joules) were almost entirely explained (⇠98%) by both the velocity-specific relative power and the ratio between force and velocity to generate power. Strength-endurance was higher at lower velocity-specific relative power and in lower force-higher velocity conditions. Intra-and inter-day reliability of the RSJ test to exhaustion was acceptable and congruent with previously reported reliabilities for tests to exhaustion of approximately similar duration (e.g., [START_REF] Coggan | Biological and technological variability of three anaerobic ergometer tests[END_REF][START_REF] Hinckson | Reliability of time to exhaustion analyzed with critical-power and log-log modeling[END_REF].

In comparison to %P max and R Fv , %P max v was the mechanical condition that a ected the most strength-endurance (i.e., ⇠88-89% of the variance explained in SJ rep and W tot ).%P max was not a predictor of strength-endurance, notably since it does not consider the change in power capability with the forcevelocity condition. Indeed, at the same %P max , the power output relative to the velocity-specific P max (i.e., P max v) can be drastically di erent according to the force-velocity conditions and lead to substantial di erences in strength endurance performance. It is worth noting that among the 10 F-v-P conditions, a lower %P max was not systematically associated with a higher strength-endurance. For example, the 3 F-v-P conditions at ⇠85%P max , ⇠73%P max , and ⇠62%P max were associated with performances of ⇠58, ⇠21, and 12 repetitions, respectively. This further highlights the inability of %P max to represent exercise intensity, notably when the exercises are not performed in the same force-velocity condition. Since the force-velocity condition varies during field performance and physical testing due to changing loading/resistive conditions and levers/equipment used, the common implementation of %P max to represent exercise intensity could be challenged (e.g., [START_REF] Harman | Exercise endurance time as a function of percent maximal power production[END_REF][START_REF] Bundle | Highspeed running performance: a new approach to assessment and prediction[END_REF]. Instead, it appears that %P max v better represents exercise intensity, since it considers the change in the individual maximal power capabilities according to the force-velocity condition. Thus, strength endurance seems to depend primarily on power output, expressed relative to the velocity-specific maximal power, and not to the maximal power value developed at optimal velocity. This supports the importance of the power reserve (Sargeant, 1994(Sargeant, , 2007;;Zoladz et al., 2000), and in turn, the influence of maximal power capabilities (i.e., the P-v relationship) on the individual ability to maintain sub-maximal power over time, notably at high exercise intensities.

The second strongest mechanical predictor of strengthendurance was R Fv , which explained ⇠8-9% of the variance in SJ Rep and W tot . Note that the remaining variance (⇠2-3%) is likely due to measurement errors. Decreasing R Fv (i.e., increasing movement velocity and decreasing the force output at matched %P max or %P max v) resulted in increased strengthendurance. These results confirm that, when standardizing rest time between repetitions, a change in force-velocity condition influences strength-endurance independently from a change in %P max v (Figures 4B,D) or a change in %P max (Figures 4A,C). These findings contrast previous hypotheses suggesting that increasing movement velocity is unbeneficial [START_REF] Mathiassen | Influence of angular velocity and movement frequency on development of fatigue in repeated isokinetic knee extensions[END_REF][START_REF] Carnevale | E ects of pedaling speed on the powerduration relationship for high-intensity exercise[END_REF][START_REF] Morel | Contraction velocity influence the magnitude and etiology of neuromuscular fatigue during repeated maximal contractions[END_REF], notably due to potentially higher proportions of fatigable type II muscle fiber recruitment (Beelen and Sargeant, 1991b;[START_REF] Blake | Early deactivation of slower muscle fibres at high movement frequencies[END_REF]. However, as these studies did not use standardized rest time between contractions and fixed repetitions across velocity conditions, the negative e ect of low rest time in high-frequency conditions could have counteracted the positive e ect of movement velocity. Additionally, as mechanical work per repetition was di erent across all Fv-P conditions, the total mechanical work produced until exhaustion is likely a better index of strength endurance, even if less practically relevant. However, although R Fv explained a comparatively small part of the overall variance, its change led to substantial di erences in strength-endurance (e.g., ⇠13, ⇠20, and ⇠60 repetitions at 85%P max v, with associated R Fv mean values of ⇠2.9, ⇠2. 1, ⇠1.3, respectively). It is worth noting that, the influence of R Fv on strengthendurance can change according to %P max v, as shown by the significant R Fv ⇥ P max v interaction. Indeed, the e ect of R Fv is further magnified at lower %P max v (Figures 4B,D). Taken together, these results show that increases in velocity and decreases in force at the same %P max v or %P max during acyclic movements (e.g., repeated jumps or callisthenic exercises) are rather beneficial than detrimental and could lead to substantial change in maximum repetitions and cumulated work until exhaustion. Strength-endurance at the individual level seems to be almost fully dependent on F-v-P conditions, expressed relative to the individualized F-v and Pv relationships. More specifically, performance is determined by the position of the exercise mechanical conditions on or under the F-v and P-v relationships, this position being characterized by %P max v and R Fv (expressed relative to F 0 and v 0 ; Figure 5).

Limitations of the Study

One limitation of this study is the restricted range investigated relative to the entire P-v spectrum, and coincidentally the extrapolation of the results on the e ect of %P max v and R Fv on strength-endurance beyond the optimal velocity. However, the range of movement velocities explored was maximized considering conditions occurring in sports activities (i.e., inertial and resistive conditions close to bodyweight and higher). The range of power explored was also nearly maximized, from maximal jump height to jump height of ⇠10 cm with di erent loadings. The latter was proposed as a cut-o jump height for accurate assessment of force, velocity and power output with the practical field method used in this study [START_REF] García-Ramos | Optimisation of applied loads when using the two-point method for assessing the force-velocity relationship during vertical jumps[END_REF]. Also, although rest time between contractions was controlled in the present study, slight di erences were observed in jumping frequencies across F-v-P conditions. However, due to the specificity of the RSJ test, other main mechanisms associated to the negative e ect of movement frequency, that is, the lower e ectiveness of force application [START_REF] Dorel | Force-velocity relationship in cycling revisited: benefit of twodimensional pedal forces analysis[END_REF] and higher internal work (Zoladz et al., 2000) may have minorly a ected our results. Another limitation is the focus on the understanding of the di erence in strength-endurance between di erent F-v-P mechanical conditions, without considering inter-individual di erences. Qualifying the physical abilities underlying di erences in strength-endurance for two participants in the same %P max v and R Fv would be a beneficial avenue of investigation for future research.

Practical Applications and Perspectives for Future Studies

• Strength-endurance evaluation should be standardized according to the individual F-v and P-v relationships, notably via %P max v and R Fv , rather than to (i) a given percentage of maximal force [START_REF] Mayhew | Relative muscular endurance performance as a predictor of bench press strength in college men and women[END_REF], (ii) the same movement velocity across individuals [START_REF] Câmara | Isokinetic strength and endurance in proximal and distal muscles in patients with peripheral artery disease[END_REF], or (iii) the same resistive force per bodyweight during all-out cycling exercises [START_REF] Bar-Or | The wingate anaerobic test[END_REF]. Without such standardization, inter-individual di erences in strength-endurance could be mainly due to di erent %P max v and R Fv conditions among individuals and not only a marker of di erent physical abilities. Such "Force-velocity-Power based training" could ensure strength and conditioning to improve the strengthendurance of athletes in competition-specific %P max v and R Fv conditions. • Similarly, standardizing dynamic fatiguing protocols and the subsequent fatigue assessment only relative to %P max or maximal isometric force [START_REF] Millet | Electrical stimulation for testing neuromuscular function: from sport to pathology[END_REF] could be challenged since each individual may experience di erent %P max v and R Fv conditions during both phases of such experimentation. Thus, it is likely that the typical high inter-individual variability response in fatigue level [START_REF] Morel | Critical peripheral fatigue thresholds among di erent force-velocity conditions: an individualbased model approach[END_REF] could be explained by the non-consideration of F-v-P conditions under which the evaluation or the e ort was performed.

• RSJ is a reliable, practical, and modifiable method to evaluate lower limb strength-endurance in a broad range of exercise conditions specific to field situations. Indeed, the results of the present study showed that strength-endurance assessment in jumping exhibited acceptable absolute and almost perfect relative intra-and inter-day reliability. These values are in agreement with those reported in cycling for e orts of approximately similar duration (e.g., [START_REF] Coggan | Biological and technological variability of three anaerobic ergometer tests[END_REF][START_REF] Hinckson | Reliability of time to exhaustion analyzed with critical-power and log-log modeling[END_REF]. The only requirements of an RSJ test are the measurements of body mass, pusho distance and continuous jump height over successive repetitions, and the use of Samozino et al's validated simple method to estimate force, velocity, and power in jumping (Samozino et al., 2008;[START_REF] Giroux | What is the best method for assessing lower limb force-velocity relationship?[END_REF]Jiménez-Reyes et al., 2014;[START_REF] García-Ramos | Force-velocity relationship in the countermovement jump exercise assessed by di erent measurement methods[END_REF]. Notably, there are many convenient methods of detecting the necessary variables (e.g., phone applications or other common devices, such as optical systems). Since di erent sporting scenarios involving repeated lower limb extensions feature di erent underlying expressions of movement frequency, force, velocity, and power output (e.g., volley-ball vs. skiing disciplines), it is possible to adapt these mechanical conditions through manipulating rest time, loading, and jump height. While the RSJ test is relatively simplistic, non-familiar cohorts of participants should be well-familiarized to ensure reasonable accuracy and reliability of assessment [START_REF] Hopkins | Reliability of power in physical performance tests[END_REF].

CONCLUSION

Strength-endurance in jumping, either characterized as the maximum repetitions or cumulated mechanical work performed until exhaustion, depends on both the velocity-specific relative power (or the power reserve) and the underlying force-velocity condition. Strength-endurance was higher when velocity-specific relative power was lower (i.e., larger power reserve) and when the force-velocity condition to generate power was oriented toward low force-high velocity (at least until optimal velocity). The RSJ is a reliable and practical method to assess strength-endurance of the lower limbs, with the possibility to easily set these mechanical conditions, by manipulating jump height, loading and rest time between jumps. Strength-endurance in acyclic movements depends on the position of the exercise mechanical conditions, in terms of relative force, velocity and power, which can be situated on or under the force-velocity and power-velocity relationships. Since maximal capabilities (i.e., force-and power-velocity relationships) and the exercise mechanical conditions (i.e., forcevelocity condition and velocity-specific relative power) influence strength-endurance performances, both should be controlled and targeted to standardize testing and training between individuals and to explore underlying mechanisms of fatigue.

Figure 1 .

 1 Figure 1. Depiction of factors underlining alpine ski racing performance

Figure 2 Figure 1 .Figure 2 .Figure 3 . 4 Figure 4 . 5 Figure 5 . 8 Figure 6 . 13 Figure 7 . 15 Figure 8 . 19 Figure 9 . 21 Figure 10 . 24 Figure 11 . 27 Figure 12 . 29 Figure 13 . 38 Figure 14 . 42 Figure 15 . 43 Figure 16 . 44 Figure 17 . 45 Figure 18 .Figure 19 .Figure 20 .Figure 21 .Figure 22 .

 212344558613715819921102411271229133814421543164417451819202122 Figure 2. Thesis structure

Figure 23 .

 23 Figure 23. Measurement of push-off distance for calculation of average force ...............

Figure 24 .

 24 Figure 24. Depiction of accessible data points in the linear force-velocity relationship during jumping .........................................................................................................................

Figure 25 .

 25 Figure 25. A theoretical representation of force-output frequency in skiing ...................

Figure 26 .

 26 Figure 26. Skier on the measurement course, equipped with the various technology ...

Figure 27 .

 27 Figure 27. Course representation ............................................................................................

Figure 28 .

 28 Figure 28. Force plate device ...................................................................................................

Figure 29 .

 29 Figure 29. Depiction of the technical index of force application in skiing ......................

Figure 30 .

 30 Figure 30. Extraction of components to compute radial force ..........................................

Figure 31 .

 31 Figure 31. Turn-averaged force outputs for a single high-performing athlete ..............

Figure 32 .

 32 Figure 32. Modular outline of data-analysis applied to all sectional datasets ...............

Figure 33 .

 33 Figure 33. Sample size plot ....................................................................................................

Figure 34 .

 34 Figure 34. RTK in skiing .........................................................................................................

Figure 35 .

 35 Figure 35. Illustration of mountain coaster sled setup ......................................................

Figure 36 .

 36 Figure 36. Low-cost Real-Time Kinematic (RTK) device. ..................................................

Figure 37 .

 37 Figure 37. Systematic and random error between the RTK device and the digitized ground-track data in longitude data ....................................................................................

Figure 38 .

 38 Figure 38. Systematic and random error between the RTK device and the digitized ground-track data in altitude data ........................................................................................

Figure 39 .

 39 Figure 39. 'Exploded' view of RTK and ground-track data ..............................................

Figure 40 .

 40 Figure 40. Bland-Altman plot of variables calculated from the RTK and GNSS devices ...................................................................................................................................................

Figure 41 .

 41 Figure 41. Representation of athlete squat-jump setup .....................................................

Figure 42 .

 42 Figure 42. Representation of isometric mid-thigh pull platform .....................................

Figure 43 .

 43 Figure 43. Force-time trace from a maximal isometric mid-thigh pull trial ...................

Figure 44 .

 44 Figure 44. Sample size plots ..................................................................................................

Figure 45 .

 45 Figure 45. Discipline-specific dynamic and isometric force data .....................................

Figure 46 .Figure 47 .

 4647 Figure 46. Pairwise correlations between variables of dynamic output and performance ...................................................................................................................................................

Figure 48 .

 48 Figure 48. Association between dynamic and isometric maximum force. .....................

Figure 50 .

 50 Figure 50. Force-and power-velocity relationships compiled from multiple jumps with and without countermovement ............................................................................................

Figure 51 .

 51 Figure 51. Sample size plots ..................................................................................................

Figure 52 .

 52 Figure 52. Comparison between sports and pooled correlation results for countermovement ratios ........................................................................................................

Figure 53 .

 53 Figure 53. Sports comparison in force-capacities determined from the squat jump ....

Figure 54 .

 54 Figure 54. Variability in the change in force-velocity profile with countermovement.

Figure 55 .

 55 Figure 55. Power-velocity graphic illustrating mechanical reserve ................................

Figure 56 .

 56 Figure 56. Depiction of the 3-dimensional strength endurance profile ..........................

Figure 57 .

 57 Figure 57. View of the effect of velocity condition on strength endurance ....................

Figure 58 .

 58 Figure 58. A model of specific strength-endurance assessment ......................................

Figure 59 .

 59 Figure 59. Mechanical settings for the endurance test ......................................................

Figure 60 .

 60 Figure 60. Graphical representation of the protocol for the force-endurance test ........

Figure 61 .

 61 Figure 61. Sample size plots ..................................................................................................

Figure 62 .

 62 Figure 62. Variation in jump height against athlete standing ..........................................

Figure 63 .

 63 Figure 63. The Pareto principle applied to training efficiency .........................................

Figure 64 .

 64 Figure 64. The muscle and strength pyramid .....................................................................

Figure 4 .

 4 Figure 4. Depiction of a slalom ski racer

Figure 5 .

 5 Figure 5. A representation of the preparatory training schedule of a high-level French ski racer

Figure 6 .

 6 Figure 6. The overlaid trajectory of two ski racers An image depicting two World Cup ski racers presenting slightly different path approaches to consecutive turns. Interestingly, the two athletes finished within 0.1 s of each other. Initially presented by LeMaster (2010) and used here with permission.

Figure 11 .

 11 Figure 11. Force output from individual limbs during a turn in different disciplinesThe image depicts the force-time data from individual limbs during giant slalom (black lines) and slalom (grey lines) courses. Ground reaction force data presented are inferred from pressure insoles and expressed relative to the average turn-time for each discipline. Figure adapted (data extracted using digitization and upscaled for clarity) fromKröll, Spörri, Kandler, et al. (2015).

Figure 12 .

 12 Figure 12. Frequency of knee angle-velocity data for skiing disciplines Distribution plot displaying the frequency of angular position at the knee and the angular velocity (y-and x-axis, respectively), across the inside and outside limbs (IL and OL, top and bottom graphs, respectively) and for the four main skiing disciplines (SL, GS, SG, and DH). Color gradients depict the frequency of occurrence, from dark red as most frequent to deep blue as the least (zero) frequent.Figure adapted from Alhammoud (2019).

  muscle actions is a central and relatively underemphasized theme in alpine skiing conditioning works. In corroboration with the literature discussed in the following sections, these information directly influenced testing regime selection to qualify the specific forceproduction capacities of high-level skiers.

Figure 15 .

 15 Figure 15. A basic illustration of a sarcomere A depiction of the three-filament model.

Figure 17 .

 17 Figure 17. Depiction of muscle actionsIllustration of muscle actions overlaid with an approximation of the force production characteristics associated with movement velocity: positive shortening velocities ('+' in the circle, below the x-axis) for concentric, negative lengthening velocities ('-' in the circle to the left of the x-axis) for eccentric actions, with isometric represented as the dashed line at null velocities ('zero') with the intercepting point ('×') of the force-velocity curve. The muscle-tendon units characterize the lengthening (center, to the left) and greater tensions (i.e., represented in the 10 kg load) associated with eccentric actions, and the shortening (center, to the right) and comparatively lesser tensions (i.e., represented in the 5 kg load) associated with concentric actions.

Figure 18 .

 18 Figure 18. External force-velocity and power-velocity relationships compiled from multi-joint explosive movement

Figure 20 .

 20 Figure 20. Contributing factors to lower limb ballistic push-off performance

Figure 24 .

 24 Figure 24. Depiction of accessible data points in the linear force-velocity relationship during jumping

Figure 25 .

 25 Figure 25. A theoretical representation of force-output frequency in skiing

  a. Clarifying the association between skiing performance and optimizing trajectories and maximizing velocity; b. Test the association between radial force, the respective contributions of force magnitude and orientation of force, and the balance of output of the two limbs, and performance characteristics;2) Test whether skiing performance depends on the force-capacities of high-level skiers, through notably; a. Studying whether they are unique compared to athletes originating from other sports; b. Determining whether there are differentiating capabilities exhibited in athletes from different disciplines; c. Testing the association between various force-capacities and competitive performance level, and; d. Determining whether athletes from different disciplines and performance levels could be separated using a targeted approach to assess strength-endurance. Each aim will be addressed explicitly in the relevant experimental sections and expanded with specific sub-aims where necessary. Briefly, Theme 1 (Chapter 3, Sections 3.1 and 3.2) addresses Aim 1. Section 3.2, compliments the methodological basis for the chapter preceding it and, consequently, addresses the same aims (albeit indirectly, via validation of the involved technology and experimental approach). Theme 2 (Chapter 4,Sections 4.1, 4.2, and 4.3) addresses Aims 2, with the former concerning the comparison of dynamic and isometric force-capacities between skiing disciplines and the latter focusing on characterizing skiers compared to a cohort of high-level sprinters in dynamic force and whether the specific mechanism of countermovement provides further characterization. Both chapters attempt to associate various force capacities with performative level. Chapter 4.3 deals specifically with Aim 5.

(

  N=15, club to World Cup level) were equipped with ski-mounted force plates and a global navigation satellite system to compute the following variables over 14 turns: path length (L), velocity normalized energy dissipation (∆emech/vin), radial force (Fr), total force (both limbs[Ftot], the outside limb, and the difference between limbs) and a ratio of force application (RF=Fr/Ftot). Data were course-averaged or separated into sectional turn groupings, averaged, and entered into stepped correlation and regression models. Our results support ∆emech/vin as a discriminative performance factor (R 2 =0.50-0.74, p<.003) in place of more direct trajectories, except in flat sections. Lower course times and better ∆emech/vin were associated with greater Fr (R 2 =0.34-0.69 and 0.31-0.52, respectively, p<.032), which was related to both Ftot and RF (standardized β=0.92-1.00 and 0.63-0.81, respectively, p<.001) which varied in predictive order throughout the sections. High Ftot was associated with increased outside limb force and a more balanced contribution of each limb (standardized β=1.04-1.18 and -0.65--0.92, respectively, p<.001). Both increasing total force output and technical effectiveness (i.e., proportionally more force radially) can increase Fr, which should increase the trajectories available to the skier on the ski course.

Français

  Bien que la production de force sur les skis soit considérée comme la clé du ski de haut niveau, sa pertinence est encore floue. Les objectifs de cette étude étaient 1) de clarifier les liens entre la performance et l'optimisation de la trajectoire ou la maximisation de la vitesse, 2) de tester l'importance de la force radiale, 3) d'explorer l'importance de l'intensité et de l'orientation de la force à la performance en virage, et 4) caractériser la contribution des jambes intérieurs et extérieurs à la production de force. Les skieurs (N=15) étaient équipés de plateformes de force montées sur les skis et d'un système global de navigation par satellite pour calculer les variables suivantes sur 14 virages : longueur de trajectoire (L), dissipation d'énergie normalisée par la vitesse (∆emech/vin), force radiale (Fr), force totale (les deux membres [Ftot], le membre extérieur et la différence entre les membres) et un ratio d'application de la force (RF=Fr/Ftot). Les données ont été moyennées par descente ou par sections de virages, et entrées dans des modèles de corrélation et de régression pas-à-pas. Nos résultats soutiennent ∆emech/vin comme facteur de performance discriminant (R 2 =0,50-0.74, p<,003) à la place de trajectoires plus directes, sauf dans les sections plates. Des durées de descente plus faibles et une meilleure ∆emech/vin étaient associées à un Fr plus élevé (R 2 =0,34-0,69 et 0,31-0,52, respectivement, p<,032), qui était lié à la fois à Ftot et à RF (β=0,92-1,00 et 0,63-0,81, respectivement, p<,001) et dont l'ordre prédictif variait entre les sections. Une Ftot élevée était associée à une augmentation de la force produite par la jambe extérieure et à une contribution plus équilibrée de chaque jambe (β=1,04-1,18 et -0,65--0,92, respectivement, p<,001). L'augmentation de la production de force totale et l'efficacité technique (c'est-àdire proportionnellement plus de force appliquée radialement) peuvent augmenter Fr, ce qui à son tour devrait se traduire par une plus grande performance lors des virages et sur la course entière.

  Alpine skiers with diverse backgrounds (N=16), training histories, and performance levels (i.e., ski-monitors and club participants to current World Cup competitors) participated in this study (age 26±5 yr; stature 1.79±0.06 m; body-mass [BM] 84.0±8.1 kg; course time [T] 29.14±1.60 s) over five weeks in winter. Athletes were devoid of any injuries that would affect their ability to participate fully in the testing. Before testing commenced, athletes were instructed on the testing procedures, allowed the opportunity to answer questions, and then provided written consent regarding their participation in the study. All operational procedures were completed within the ethical requirements of the Fédération Française de Ski, and the Code of Ethics of the World Medical Association (Declaration of Helsinki), and approved by the ethics committee of the University Savoie Mont Blanc.Athletes were equipped with a GNSS and specialized force platforms attached to raceboots and skis (see Figure26), and then performed one warm-up of freeskiing starting from the top of the mountain through the experimental course. Athletes then performed a competition-style personalized warm-up, followed by 2-3 familiarization runs. Once comfortable and familiar with the course and equipment, athletes proceeded to a small hut near the starting gate and performed a short calibration procedure for the equipment on solid ground.Athletes performed 1 to 3 skiing trials on an 18-gate GS course, interspersed with approximately 15 minutes of passive rest (including non-fatiguing calibration procedures). During their trials, athletes stopped atop the course, the starting gate was set for timing, and athletes began their trial in their own time. The athletes were instructed to ski at maximum pace and were questioned on their efforts post-trial. Where more than one trial was performed, the trial with the fastest course time was used for the final analysis.

Figure 26 .

 26 Figure 26. Skier on the measurement course, equipped with the various technology Visible in the figure are the boot mounted force platforms, wiring secured via elastic straps to the lower-limbs, and a small bag around the waist of the athlete with the acquisition card (GNSS unit secured inside, not visible).

Figure 30 .

 30 Figure 30. Extraction of components to compute radial forceThe dashed line represents the trajectory of the skier; + represents the moment of turnswitch (inflection point in trajectory); β the angle between the instantaneous trajectory of the skier (black arrow, inside slope image) and that horizontal to the fall line; and α as the angle between fall line of the slope and the horizontal, or the gradient of the slope.

Figure 31 .

 31 Figure 31. Turn-averaged force outputs for a single high-performing athlete Data, in this case, has been normalized as a percentage of turn duration. The solid black line represents total force output (Ftot); the dash-dot black line represents the force output of the outside limb (Fout); the dashed black line represents the force output of the inside limb (Fin); the dotted black line represents radial force output (Fr); all force data are displayed as a factor of BW.

  correlation, using Pearson's Correlation (r±95%CIs, p), and stepwise multiple regression (standardized β, F, R 2 change [per variable], and model R 2 [adjusted], p) analyses. In the first level, correlational analysis tested sectional performance parameters (∆emech/vin and L) against course time (T). The following level tested the explicit predictive nature of sectional Fr to sectional ∆emech/vin and course-performance. The next two levels of the model employed multiple regression analyses to test the relationship and contribution of force magnitude (Ftot) and application effectiveness (RF) to Fr. Subsequently, Ftot output was contextualized using the same multiple regression model to test the output and balance between the limbs (Fout and Fdiff,).

Level 1 -

 1 Relationships between course and sectional performance parameters ∆emech/vin over the course, and in speed and overspeed sections, was negatively predictive of T (Table

Level 3 -

 3 Contribution of 'technical' and 'physical' capacities Over the course and in the three sections, both RF and Ftot explained an important part of the variance in Fr (R² change from 0.36 to 0.64) and presented high normalized effects (standardized β>0.63), although the order of the two predictors in the explained variance and prediction strength changed with each section (see

Level 4 -

 4 Contribution of force to the outside limb and the balance between limbs to total force output In all sections, Ftot was (by order) positively correlated to Fout, and negatively correlated to Fdiff (see

FrançaisL

  'avènement de systèmes de navigation par satellite (GNSS), qui sont de plus en plus accessibles, présente des implications passionnantes pour la recherche et la pratique du ski alpin. Les objectifs de l'étude étaient de tester la validité et la fiabilité d'un système de cinétique en temps réel (RTK) à faible coût qui sera ensuite utilisé comme critère de mesure pour valider un système GNSS sportif (tel que celui utilisé dans l'étude précédente) pour la détection de variables macroscopiques de performance moyennées sur des sections en ski. Deux expériences ont été réalisées, consistant à 1) attacher un système RTK à une luge d'été qui descendait une piste sur des rails quatre fois dans un environnement alpin, et 2) attacher le RTK (référence) et un système GNSS sportif aux skieurs sur un parcours de slalom géant. Pour la première expérience, la validité et la fiabilité du système ont été testées en calculant l'erreur systématique et aléatoire, respectivement, par rapport à une trace au sol numérisée. Pour la deuxième expérience, la validité du GNSS a été évaluée pour la vitesse, la longueur du trajet, la force radiale et la dissipation d'énergie, sur les valeurs des virages individuels et moyennés par sections (quatre virages), en utilisant la régression linéaire, la corrélation et le coefficient de variation (CV). L'expérience de la luge d'été a révélé une erreur aléatoire et une variabilité très faible en longitude (0,023±0,0075 m) et en altitude (0,19±0,066 m). L'erreur et la variabilité systématique étaient modérées (moyenne=0,431-0,697 m, écart type=0,616-0,366 m) en raison des limites du plan au sol numérisé et d'un décalage entre les rails et la fixation de l'antenne qui a été exacerbé lors du virage (en raison de l'inclinaison de la luge vers le centre du virage). Pour le test de ski, les données montraient un biais généralement faible (<1,5% pour toutes les variables, à l'exception de la dissipation d'énergie[4,5%]), avec une concordance modérée à très forte pour toutes les variables. En général, la variabilité était faible (CV<5%) à l'exception de la force radiale et de la dissipation d'énergie pour l'analyse virage par virage(7,0 et 12,9%, respectivement). L'adoption d'une approche par section a considérablement amélioré la concordance et l'erreur, toutes représentant une concordance forte ou très forte, à l'exception de la force radiale (modérée) avec tous les CV<9,1%. Ces résultats témoignent de l'exactitude d'un RTK à faible coût dans des conditions de similaires au ski et prend en charge une approche moyennée en virages pour détecter des différences intéressantes dans une variété de variables de performance en utilisant des unités de position sportives communes.

  Cross, M. R., Delhaye, C., Morin, J.-B., Bowen, M., Coulmy, N., Hintzy, F., & Samozino, P. (2020). Force output in giant-slalom skiing: A practical model of force application effectiveness [Supplemental material: Pilot-data of sports GNSS validity using a lowcost Real-Time Kinematic (RTK) system as a criterion]. PLoS ONE. In press.

Procedures 3 .

 3 2.4.1.1

  (model: ANN-MB, uBlox, Thalwil, Switzerland; gain, 28±3.0 dB) and RTK compatible receiver (model: M8T, uBlox, Thalwil, Switzerland), wired to a small portable computer (model: RasberryPi zero, Kubii, Lyon, France) and small battery pack (~100 g). The units were capable of reading signals from a variety of satellite systems (American [GPS], Russian [GLONASS], European [Galileo], and Chinese [BeiDou]) on the L1 frequency at 10 Hz. Each unit cost ~150 euros, which was 5-10× less than commercial alternatives.

Figure 36 .

 36 Figure 36. Low-cost Real-Time Kinematic (RTK) device.

  Figure 38, respectively.

  limits of agreement (associated with Bland Altman plots) for the two levels of analyses displayed in Figure40. Turn-by-turn data were typically low bias (<1.5% for all variables, except emech/vin [4.5%]), with moderate to very strong agreement in all variables. In general, variability was low (CV<5%) except for Fr and ∆emech/vin, which exhibited large and very large error (7.0 and 12.9%), respectively.

Figure 37 .

 37 Figure 37. Systematic and random error between the RTK device and the digitized ground-track data in longitude dataThe figure depicts data collected from four trials of the RTK device, relative to that from the digitized ground plan of the mountain coaster, displayed here as longitude normalized to latitude. The top figure displays the longitude of the four runs (black lines) and the ground track (dashed line) as a function of the displacement in latitude. The small black box indicates the approximate range of the 'exploded' data displayed in Figure39. The bottom graph displays the mean systematic variability between the RTK and ground track in m (black) and the variability (light grey SD lines) along the latitude. Note: the variability is extremely low, so the SD bars cross the mean error.

Figure 38 .

 38 Figure 38. Systematic and random error between the RTK device and the digitized ground-track data in altitude dataThe figure depicts data collected from four trials of the RTK device, relative to that from the digitized ground plan of the mountain coaster, displayed here as altitude normalized to latitude. The top figure displays the altitude of the four runs (black lines) and the ground track (dashed line) as a function of the displacement in latitude. The small black box indicates the approximate range of the 'exploded' data displayed in Figure39. The bottom graph displays the mean systematic variability between the RTK and ground track in m (black) and the variability (light grey SD lines) along the latitude.

Figure 39 .

 39 Figure 39. 'Exploded' view of RTK and ground-track dataData here corresponds to the 'exploded' section of RTK and ground-track data displayed in Figure37and Figure38(top and bottom, respectively), corresponding (approximately, the box is oversized for visibility) to the small black box on each figure. The purpose here is to show that the graphic displays four separate trajectories (black lines) alongside the digitized ground path of the coaster (dashed line).

Figure 40 .

 40 Figure 40. Bland-Altman plot of variables calculated from the RTK and GNSS devicesVertical pairs of plots correspond to each variable, with the horizontal corresponding to either turn-by-turn analysis (a), or 'sectional' analyses (b). yaxes display the difference between the two devices for the corresponding variable, with the grey lines representing limits of agreement (±1.96 SD). vavg, averaged velocity; vin, the velocity at turn entry; L, cumulated distance traveled; Fr, radial force; ∆emech/vin, change in specific mechanical energy normalized to velocity at turn entry; s, seconds; m/s, meters per second; m, meters; N/kg, Newtons per kilogram; Js/kg/m, joule seconds per kilogram per meter. Note: turn time is not displayed in this figure since the data were not easily readable (most differences were identical, at either 0 or 0.1 s).

  of high-level skiing athletes, to understand determinant physical properties better, and notably to what extent force output during skiing, and in turn skiing performance, is limited by skier's force capacities. While this topic has attracted interest over the years, our opinion is that the tests implemented often do not thoroughly consider the underlying force-output characteristics of skiing. As such, the overarching aim of this (and the following) experimental chapters was to build on the measurements used in recent research and provide an updated view of essential characteristics in high-level ski athletes relative to their competitive level.Co-authored works associated with this sectionCross, M. R., Rivière, J. R., Coulmy, N., Morin, J.-B., & Samozino, P. (2020). Lower-limb force-production capacities in alpine skiing disciplines. Scand J Med Sci Sports, In press.

  Competitive male alpine ski athletes (SL=8, GS=9, SG=5, DH=9; 2019 base performance level, International Ski Federation [FIS] points=21.1±9.8 (range=0-35), standing=91.8±58.5 (range=1-185) participated in this study. At the time of testing, athletes belonged to the French national alpine squad (A team [World cup], N=12; B team [Europa cup], N=13, or C team [FIS cup], N=6). For the study, athletes were classified as either SPEED (N=14, age=23±4 yr; body mass [BM], 86±8 kg) or TECH (N=17, age=25±5 yr; BM, 80±5 kg) based on the event in which they held the lowest standing (i.e., highest world ranking) according to the 9 th FIS list for the 2019/20 season (FIS points=21.8±10.7 [range=0-40],

  extent. The full assessment occurred during the preparatory phase, directly preceding the 2019-2020 competitive season. The testing battery occurred in the National Training Center for high-level alpine athletes in France. All athletes regularly attended the testing venue and were comfortable and familiar with the experimental surroundings. Not all athletes participated in both testing procedures due to availability, with the N for each test listed in the appropriate tables. All operational procedures were performed as part of the athletes' routine training and testing practices and followed the ethics codes of the French Ski Federation, the University Savoie Mont Blanc, and the World Medical Association (Declaration of Helsinki).ProtocolAthletes performed a ~20 min dynamic warm-up, consisting of a cardiovascular priming, mobilization, and increasing intensity submaximal loaded jumps (various anthropometric measurements were taken during this period). The protocol consisted of increasing loading barbell SJ and CMJs (CMJ data are not reported in these analyses, see Chapter 4.2), followed by maximal intensity isometric mid-thigh pulls. Athletes wore their habitual training attire and footwear (i.e., trainers or CrossFit style shoes) throughout the protocol.4.1.4.2.1. Loaded squat jump and countermovement jump proceduresAthletes performed maximal SJs unloaded and against five or six external loads ranging from 7.5 to 90 kg(Morin & Samozino, 2016). Athletes jumped within a squat rack (model: FT700 power cage, FitTech, Brisbane, Australia) with the safety-bars adjusted to standardize push-off distance (hpo, via cueing squat depth) throughout the testing, and a competition-grade Olympic lifting bar and plates (model: Elite bar and plates, Raze,

  .1.4.3.2. Maximum isometric force and rate of force development Data were collected and analyzed using custom MATLAB (version: MATLAB 2019B, Mathworks, MA, USA) acquisition and analysis scripts, respectively. The weight of the bar and load-cell unit were added to the raw force-time data to represent the net force produced by the athlete across the trial. Unfiltered force-time data were analyzed with

Figure 43 .

 43 Figure 43. Force-time trace from a maximal isometric mid-thigh pull trialData show a single trial, with the threshold overlays for the movement onset detection (large black dashes), the 'window' during which the average rate of force development is calculated (dotted line), instantaneous maximum force ('+'), and the approximate window of maximum force used in this study (highest 500 ms average).

Figure 44 .

 44 Figure 44. Sample size plotsThe four contour plots presented here depict the sensitivity of the utilized statistical models to detect effects, with a Type 1 error rate of α=.05 and 80% power. Plot A relates to the general linear model and illustrates that with N=29 to 31, we can reasonably detect small-moderate effects (ω 2 >0.046). Plot B relates to the Pearson's correlations for each discipline(SPEED, TECH,, and indicates large effects can be reasonably detected (r=0.60 to 0.65 and 0.59 to 0.63, respectively). The black and grey dashed arrows correspond to the smaller and larger sample sizes for each test, respectively.

Figure 45 .

 45 Figure 45. Discipline-specific dynamic and isometric force data Data correspond to the mean (diamond) power-force-velocity (right graph, 'DYNAMIC') and isometric data (left graph, 'ISO.'), with the error bars representing the standard deviation around the mean (displayed as either positive or negative for graphical clarity, but representing the total deviation [i.e., ±SD]). Technical and speed disciplines are represented in TECH (black lines) and SPEED (grey lines). Variables are:Pmax, maximal power; F0, maximal theoretical force; v0, maximal theoretical velocity. W, watts; N, Newtons; m/s, meters per second.

  age there was no difference between disciplines in the non-parametric model (U=91.5, rrb=-0.231, p=.278), however very large associations existed between age and performance for both TECH (rs=-0.805[-0.529;-0.927], p<.001) and SPEED (rs=-0.825[-0.523;-0.943], p<.001). Dynamic force Raw unloaded jump height did not differentiate the disciplines (F(1,27)=1.77, p=.195), nor vary with performance (F(1,27)=1.44, p=.24). SPEED athletes exhibited largely greater absolute F0 (F(1,27)=13.8, p<.001), and a trend for lower (force-dominant) SFv (F(1,27)=3.72, p=.064). SPEED athletes also possessed greater absolute Pmax (F(1,27)=4.42, p=.045). There were very large associations between performance and a more negative SFv (F(1,27)=16.29, p<.001), associated with higher F0 (absolute, F(1,27)=28.25, p<.001; and relative, F(1,27)=10.34, p=.003), and lower v0 (F(1,27)=4.96, p=.034). There were no associations with performance in the linear model for Pmax (F(1,27)=0.573 to 0.639, p=.431 to .456). For absolute F0 there was a small interaction suggesting a stronger association with performance in SPEED (F(1,27)=5.22, p=.03).

  , p=.016), and relative F0 in SPEED (r=-0.62[-0.86;-0.13], p=.019; TECH, r=-0.40[-0.74;0.1], p=.110). There was a positive relationship between v0 and performance (i.e. higher value is associated poorer standing) in TECH (r=0.51[0.04;0.8], p=.035; SPEED, p=.291). No associations existed for h (p=.192 to .981) nor power (p=.100 to .753).Isometric force and RFDSPEED displayed much greater absolute Fmax (F(1,25)=20.70, p<.001) and moderately greater relative Fmax (F(1,25)=11.19, p=.003). RFD metrics typically did not separate the disciplines (p=.356 to 0.708), although there was a trend for minorly greater RFDavg in SPEED (F(1,25)=3.56, p=.071). Both relative and absolute Fmax were strongly related to performance (absolute, F(1,25)=33.78, p<.001; relative, F(1,25)=21.52, p<.001) with a moderate interaction effect suggesting a stronger relationship for both variables in SPEED athletes (absolute, F(1,25)=10.28, p=.004; relative, F(1,25)=6.69, p=.016). This interaction was supported in the pairwise correlation results, where SPEED athletes exhibited very large correlations with performance for absolute and relative Fmax (both, r=-0.88[-0.96;-0.63], p<.001) while only a trend existed for a moderate association for absolute Fmax in TECH athletes (r=-0.49[-0.8;0], p=.052; relative, p=.121). Within the linear model there were large associations between performance and both RFDmax (absolute, F(1,25)=11.55, p=.002; relative, F(1,25)=6.49, p=.017) and RFDavg (absolute, F(1,25)=27.76, p<.001; relative, F(1,25)=19.43, p<.001). While relative RFDmax was not associated with SPEED performance (p=.129), moderate to very large correlations existed for the other RFD measures for both SPEED (RFDmax absolute, r=-0.60[-0.86;-0.07], p=.031; RFDavg absolute r=-0.82[-0.94;-0.48], p<.001, relative, r=-0.78[-0.93;-0.4], p=.002) and TECH (RFDmax absolute, r=-0.56[-0.83;-0.09], p=.024, relative, r=-0.50[-0.8;-0.01], p=.048; RFDavg absolute r=-0.61[-0.85;-0.16], p=.013, relative, r=-0.55[-0.82;-0.08], p=.026).

factors: 1 )

 1 older athletes have more experience (e.g., SPEED courses are relatively consistent across seasons) and potentially enhanced technical aspects in their respective disciplines due to accumulated time in on-snow training and competition; 2) older athletes might possess enhanced specific force-production capacities due more time accrued in targeted training (either on-or off-snow; 1 and 2 presumably increase performance), and; 3) past a certain age, lower-level athletes are more likely to drop out (from injury, supplanted by younger skillful counterparts, or otherwise) which biases the sample of older athletes towards higher rankings. While long term skill development is challenging to quantify, the concurrent association between increased body mass and performance might indicate ongoing neuromuscular adaptations (notably, hypertrophy). Simultaneously, all athletes had an extensive strength-training history (>5 yr, >twice per week); long-term conditioning and on-snow training likely stimulate specific muscular adaptations. Nevertheless, while a nuanced interpretation is more likely than merely older and larger athletes being dominant, some proportion of our

Figure 48 .

 48 Figure 48. Association between dynamic and isometric maximum force.

  Lors d'un saut vertical, le contre-mouvement augmente la force produite pendant la phase concentrique suivante et augmente par conséquent les performances. Il y a peu d'informations sur la question de savoir si cette augmentation de force associée au contre-mouvement est spécifique à la vitesse et à chaque athlète. Nous avons utilisé une approche de profilage force-vitesse (Fv) chez des skieurs de haut niveau (N=23) et des sprinteurs (N=30) pour détecter les différences entre les athlètes dans l'effet de contremouvement à différentes vitesses et pour approfondir l'étude des différences entre les groupes de sportifs et niveaux de performance. Les rapports de contre-mouvement ont été calculés entre les variables Fv obtenues à partir de squat jump et contre-mouvement jump : hauteur de saut (CRh), puissance maximale (CRP), force théorique maximale (CRF) et vitesse théorique maximale (CRv). Des analyses de corrélation ont été effectuées sur les données CR regroupées pour tester l'association entre le CR dans la production de force à différentes vitesses (c'est-à-dire CRF vs. CRv). Les variables Fv et CR ont été comparées entre les groupes d'athlètes (T-test ou test U-test de Mann-Whitney, Cohen's d). Les analyses de régression multiple distinctes par sport ont détecté des associations entre la performance saisonnière (classement mondial ou temps sur 100 m) et les variables CR et Fv correspondantes (par exemple, la force maximale et la CRF).L'expression de l'effet de contre-mouvement différait avec les vitesses de mouvement(CRF vs. CRv,74, p<,001), mais avec une variabilité interindividuelle élevée pour SFv(rrb=0,031, p=,846). Les skieurs ont présenté un CRF plus faible (rrb=-0,675, p<,001) et les sprinteurs un CRv plus faible (rrb =0,426, p=,008), mais des conditions de vitesse « modérée » n'ont pas différencié les groupes (CRP ou CRh, p>,05). L'effet de contre-mouvement semble être à la fois spécifique à la vitesse et au sport et peut être associé à la performance dans certains sports (par exemple, le classement des skieurs était expliqué à 33% par une force maximale plus élevée et un CRF plus faible). Notamment, alors que l'effet de contremouvement n'était pas associé à la performance à n'importe quelle vitesse pour les sprinters, les meilleurs skieurs pourraient bénéficier de l'entraînement des mécanismes sous-jacents à la production de force sans contre-mouvement à basse vitesse conjointement à une augmentation globale des capacités de production de force maximale.

  Rivière, J. R., Van Hooren, B., Coulmy, N., Jiménez-Reyes, P.,Morin, J.-B.,

  attributed to: 1) a more significant development of active state pre-propulsive phase; 2) associated musculature being aligned and stretched pre-movement (i.e., reduced slack (Van Hooren & Bosch, 2016)), and; 3) the muscle fibers operating on a more favorable portion of the force-length-velocity curve(Bobbert & Casius, 2005; van Ingen Schenau, 1984). Consequently, athletes who can generate greater muscle stimulation and an increased active state of the contractile elements can perform more work during the initial phase of concentric contraction(Bobbert & Casius, 2005; Bobbert & van Zandwijk, 1999a)the result in jumping being a greater height attained. These underlying mechanisms have important implications for how the interplay between SJ and CMJ modalities is interpreted and how the difference between the two may differ between individuals based on various factors, including training level and sporting code.

Figure 49 .

 49 Figure 49. Overlay of the force output of the lower limbs of a skier and a sprinter

(

  slalom and giant slalom, N=12) disciplines, with a world ranking of 85±62 in their best event (better<worse). The sprinters were part of a national-level Spanish training group (average best performances, 100 m=10.67±0.25 s) and regularly participated in similar research projects(Jiménez-Reyes et al., 2014). While the testing occurred in disparate locations, the methodological procedures surrounding the assessment were functionally identical except where explicitly specified.Athletes performed a full Fv profiling battery in both SJ and CMJ movements based on jumping with different external loads. Athletes were familiar with the procedures, which were performed as part of their regular testing and condition practices. The appropriate local ethics committee approved operational procedures (University Savoie Mont Blanc, France, and the University of Pablo de Olavide, Spain, for skiers and sprinters, respectively). Written consent was obtained from the athletes, and the procedures followed the World Medical Association (Declaration of Helsinki).

4. 2 . 4 . 2 . 1 .

 2421 Force-velocity profile in squat and countermovement jumpTo compile Fv relationships, athletes performed maximal squat and countermovement jumps. The testing was performed in either an enclosed squat rack (model: FT700 power cage, FitTech, Brisbane, Australia) with the safety-bars and a selection of rubber wedges used to standardize push-off distance (hpo), or in a free-standing squat rack (model: Olympic Rack, Technogym, Gambettola, Italy) with an elastic band used to provide a light proprioceptive cue for the depth of the jumps for the athletes. Squat depth was then set around ~90° for both jumps[START_REF] Garcia-Ramos | Force-velocity relationship in the countermovement jump exercise assessed by different measurement methods[END_REF] Janicijevic, Knezevic, Mirkov, Perez-Castilla, Petrovic, & Garcia-Ramos, 2019; Janicijevic, Knezevic, Mirkov, Perez- Castilla, Petrovic, Samozino, et al., 2019), measured (for computations of hpo; via a flexible measuring tape), and maintained throughout testing. Four to six external loads were used to provide resistance in the loaded jumps in addition to jumping unloaded (i.e., BM only). Resistance for the loading conditions was provided via calibrated

Analysis 4 . 2 . 4 . 3 . 1 .

 42431 Jump analysis and force-velocity profiling

  and have successfully described performance in various sports cohorts[START_REF] Mcmahon | Relationship between reactive strength index variants in rugby league players[END_REF][START_REF] Ramirez-Campillo | Optimal reactive strength index: Is it an accurate variable to optimize plyometric training effects on measures of physical fitness in young soccer players?[END_REF][START_REF] Raschner | The relationship between ACL injuries and physical fitness in young competitive ski racers: a 10-year longitudinal study[END_REF]. While assumedly CRs should follow similar reliability to the underlying Fv variables, future research should explore the sensitivity to track athlete profiles and adaptations to training and long-term performance monitoring. Most research used to interpret our results and theorize the underlying mechanisms of CRs at different velocities are based on single muscle studies of different movements. Future research might aim to integrate more complex measurements and modeling using multi-joint actions (e.g., jumping) integrated with an Fv approach to better understand the mechanisms underlying performance and the expression of CRs in distinct sporting cohorts and at different movement velocities.

  Rivière, J. R., Peyrot, N., Cross, M. R., Messonnier, L. A., & Samozino, P. (2020a). Interindividual variability of the effect of force-velocity condition on strength endurance: towards a force-velocity-endurance profile. J Biomech, In preparation. Rivière, J. R., Peyrot, N., Cross, M. R., Messonnier, L. A., & Samozino, P. (2020b). Strength-endurance: Interaction between force-velocity condition and power output. Front Physiol, 11. https://doi.org/10.3389/fphys.2020.576725 Cross, M. R., Rivière, J. R., Coulmy, N., Morin, J.-B., & Samozino, P. (2020). An exploration of force-velocity condition specific strength-endurance assessment in alpine skiers. J Strength Cond Res, In preparation.

  Figure modified from[START_REF] Rivière | Effet des conditions mécaniques d'exercice sur les capacités de production de force des membres inférieurs lors d'extensions acycliques uniques et répétées[END_REF], originally proposed bySargeant (1994).New perspectivesRepeated squat jumps (RSJ) and similar acyclic movements allow movement frequency to be fixed (i.e., timing of each jump) and isolated from movement speed (i.e., the extension velocity) in strength endurance assessments-the result being control of the underlying mechanical conditions of the test. In a recent experiment, our research group(Rivière et al., 2020b) used a selection of 10 RSJ protocols to test the relative effects of %Pmaxv and RFv on strength-endurance performance (the maximum repetitions [Nrep] and cumulated work [Wtot] performed in each testing condition). Each test was characterized by different force-velocity-power conditions set per each athlete's Pv profile (N=14;

Figure 56 .

 56 Figure 56. Depiction of the 3-dimensional strength endurance profile A depiction of the power-velocity-endurance relationship, showing the change in strength-endurance performance depending on the position of the conditions relative to their positioning within the power-velocity curve. Adapted from Rivière (2020).

Figure 57 .

 57 Figure 57. View of the effect of velocity condition on strength enduranceThe figure depicts the comparison conditions forRivière et al. (2020a). Presented are the maximum power-velocity capabilities (characterized by the absolute maximum power capacities; Pmax), and depicts three different velocity conditions at the same %Pmaxv (in this case, represented by high velocity ('+') [corresponding to bodyweight, depicted in the dashed light-grey line], moderate ('~') and low ('-') velocity). The dark grey and light grey (dashed edge) three-dimensional shapes dashed represent two different athletes with different power-velocity-endurance profiles. Specifically, one athlete is better in low and moderate velocity conditions, and the other is better in high-velocity conditions. Figure adapted from Rivière (2020).

Figure 58 .

 58 Figure 58. A model of specific strength-endurance assessmentIn order, the model depicts the specific strength-endurance capacities that are important to the sport and are exhibited (to some degree) in the individual. The subsequent design of the test (the following level) should mimic the performative construct while retaining reliability and practicality-this includes the mechanical test settings, comprising mechanical reserve (specifically, %Pmaxv) and the force-velocity conditions of the test; these factors should be set both in regards to the sporting construct and to the capacity of the individual to standardize the assessment. The result (represented in the arrow striking the target) should be a worthwhile assessment of relevant strength-endurance capacities.

  strength-endurance capability(Turnbull et al., 2009): as such, several researchers have suggested the design of specific length tests for each cohort of athletes. Using the RSJ,[START_REF] Bosco | Evaluation and planning of conditioning training for alpine skiers[END_REF] separated Olympic level athletes from their counterparts, and a variant of the test was able to discriminate between young skiers(Emeterio & Gonzalez-Badillo, 2010). However, standardization in these tests is difficult (see discussion below) and perhaps as a consequence the results are far from uniform in the wider research[START_REF] Moritz Von Duvillard | Relationship of anaerobic performance tests to competitive alpine skiing events[END_REF].

  Pre-testing athletes performed a ~20 min warm-up, consisting of various priming and mobilization work specific to the testing to follow. During this period, athlete limb length and squat depth were measured to estimate take-off distance (hpo) for later computations of force output. Athletes then performed a selection of loaded squat jumps (SJ) to compile individualized Fv profiles(Morin & Samozino, 2016), a three-step familiarization of the endurance test, and subsequently performed the endurance test.4.3.4.3.1. Force-velocity profiling proceduresAthletes performed sets of maximal loaded SJs unloaded and against a selection of 5-7 broad and evenly spaced external loads(Morin & Samozino, 2016). The loading parameters were approximately by body mass, although not strictly standardized (per the linearity of the load-velocity profile (Iglesias-Soler et al., 2019)) with the final loading parameter resulting in a ~0.1 m jump height. The depth of the SJ was individualized

Figure 59 .

 59 Figure 59. Mechanical settings for the endurance testPower-and force-velocity relationships from a single athlete (A and B, respectively), indicating the placement of the mechanical conditions of the test. In both figures, black circles with while fill represent individual loads (ranging from ~0 to approximately 100%bodyweight). The solid black line represents either the 2 nd order polynomial fit of the power-velocity relationship or the least-square regression line of the linear forcevelocity relationship (for A and B, respectively). The dashed line corresponds to the setting of mechanical reserve for selecting the testing conditions, in this case, set at 80% of the athlete's maximal power output, per the fixed velocity condition (i.e., '80%Pmaxv'). The solid black cross ('+') represents the exact mechanical conditions for the test, normalized to both the mechanical capacity of the athlete and corresponding to a jump height of 0.10 m (or 0.7 m/s average concentric velocities).

  lactate measurements were taken in six athletes by drawing blood from the fingertip (3 µl) directly preceding the test and 3 min post-test while standing to estimate the lactate load of the testing procedures.EquipmentTesting was performed at habitual training facilities of the involved athletes, and they wore their typical training attire and footwear. SJs were performed within a squat rack (model: FT700 power cage, FitTech, Brisbane, Australia), using an Olympic lifting bar and bumper plates (model: Elite barbell and plates, Raze, Warwickshire, England) to load athletes during the Fv profile and subsequent endurance test. An electronic metronome amplified through an external speaker provided audible cues throughout the endurance test to aid the athletes in managing the correct jumping tempo. Where necessary, a flexible tape was used for anthropometric measurements, and a selection of slim rubber wedges used to regulate squat-depth during both tests (i.e., standardize hpo).

Figure 60 .

 60 Figure 60. Graphical representation of the protocol for the force-endurance testFrom the bottom to the top of the figure: Graphic for jump height (h)repetition data of athlete trial, showing the targeted jump height (solid black line) and surrounding 5% threshold, used to cut off athlete trial. Dark grey bars correspond to jumps included in final analyses (i.e., moving average of 3 > 95% of target), and dashed repetitions are excluded. The middle and top of the figure present the scientific and subsequent practical view of the test design, as presented practically within two repetitions. The small speaker icons (surrounded by a black circle) initiate the beginning of the squat jump (the 'concentric phase,' corresponding to the push-off time, tpo), subsequently followed by a displacement of the center of mass in the air (flight time, tf) of ~10 mm. Upon landing, the athlete eccentrically lowers the load to a pre-set depth, where they stay in isometric control until the following audible cue (2.5 s).

  course, it is impossible to ski at a high level without technical competency, regardless of the physical acuity of the athlete. However, the stage at which the physical development of the athlete-and additionally, which physical capabilities-becomes a limiting or differentiating factor for success or injury avoidance is ambiguous. On the one hand, athletes with poorly developed physical acuity might see large gains in their on-snow performance by investing time in early-phase strength and muscle gains. On the other hand, anything above a certain threshold of underlying qualities might suffice until technical skills are developed extensively. For example, in their research examining anaerobic power in elite Austrian skiers,Patterson et al. (

  2.1.4). While factors regarding the transfer to performance need clarification, there is likely little downside to more intelligent programming and monitoring of athletes, and ultimately maximizing specific musculature development. The caveat is that these factors do not detract from the quality or volume of other important factors (e.g., on-snow training).

Figure 64 .

 64 Figure 64. The muscle and strength pyramid The figure depicts a hierarchical approach to periodizing training approaches when considering strength and muscle growth as the primary adaptations. The representation shares similarities with the Pareto principle, where the emphasis is placed on ensuring lower-tier causes are targeted and ensured, acknowledging that they explain a large proportion of the outcome effects. This concept, and the figure, are adapted from Helms et al. (2018) with permission.

Force

  output on the skis is, by definition, a technical derivative mediated by the ski-snow interaction; the result is force production under vibration, instability, and other environmental factors (e.g., hypoxia, and low temperatures). Consequently, it would seem logical to integrate these factors into conditioning to better prepare athletes for the field by improving the capability to produce force under more 'ski-specific' constraints.However, as discussed above (and expanded upon below), this relies on the effective transfer of this training to on-snow performance and said training not unduly detracting lower-tier principles factors (e.g., overall training volume).

  transfers of resistance training was maintained (high-speed plyometric training was more effective than low-speed strength training), the training mode (i.e., uni-or bilaterally, as split-squat vs. squat) had no apparent effect[START_REF] Moran | Effects of bilateral and unilateral resistance training on horizontally orientated movement performance: A systematic review and meta-analysis[END_REF]. On the one hand, the lack of increased transfer of unilateral training to 'unilateral' sprinting performance is surprising and challenges their implementation based on arguments related to specificity. On the other hand, these results might indicate that well controlled instability work has the potential to develop skiing relevant capacities (e.g., cocontraction, and core stability)[START_REF] Appleby | Specificity and transfer of lowerbody strength: Influence of bilateral or unilateral lower-body resistance training[END_REF], without compromising specific neuromuscular adaptations, despite lower loads carried. While the transfer of these results between sprinting and skiing is tenuous, these results are promising for the development of specific strength characteristics for athletes suffering from long-term back pain or other factors that otherwise might compromise their training quality.While specific vibration and instability exercises might have unique applications for the development of force production in sport-specific contexts[START_REF] Behm | The role of instability with resistance training[END_REF], the transferability of these methods to practice requires more research. As discussed in Section 5.2.1.1, the point of diminishing returns from compounding sports-specificity in training is unclear, and the fact that over-utilizing such training may compromise core components of physical conditioning (i.e., reducing training volume) must be considered when shaping periodization. Force production during instability may promote the development of technical aspects of force production, but the unclear transfer of these adaptations to skiing raises the question of whether such factors are

  method. Technological limitations have complicated data capture capabilities and resulted in somewhat invasive designs (e.g. increased clip-in height, weight and modifications to the rigidity of the ski) that inevitably degrade measurement validity. A recent system presented by Falda-Buscaiot et al. (2016) shows promise by addressing several of the confounding factors featured in traditional devices. Using such technology in high-level skiing practice could feasibly provide a deeper understanding of athlete force production during both biomechanical and strength and conditioning practice.Using validated force plates(Falda-Buscaiot et al., 2016) we aimed to (i) compute magnitudes and balance of force produced on a giant slalom course, (ii) test the relationship between force output parameters and kinematic parameters, and (iii) test the relationship between course performance and force measures.Methods13 alpine skiing athletes of varied capabilities (club to world cup level) performed racepaced trials of a 16-gate giant slalom course (gate-to-gate distance and offset = 24 and 8 m; ~25° groomed). Athletes were equipped with a force plate system, and a modern GNSS system, to provide turn-by-turn GRFs and positional data during racepaced trials of the course.A validated force collection(Falda-Buscaiot et al., 2016) system, comprising of custom-routed aluminum frames housing two force sensors(Sensix, Poitiers, France)

Figure 1 )

 1 Figure1), and the large peaks and troughs observed might point to the necessity of high rate and magnitude force production absent in in-direct measurements of force output. Microover the snow in their edging, all could potentially explain our results, and further

Figure 1

 1 Figure 1 Turn-normalised resultant force output from a high level athlete. Black line, mean of all turns; grey area, standard deviation; and grey line, range of maximum and minimum values.

  13 mixed-level skiers (club to world cup competitors) performed a timed 16-gate giant slalom course. Gates were set by an International team coach with an average distance of 24 m and an offset of 8 m, on a ~25 ° inclined groom slope. All skiers were equipped with same model of ski and boots and were instructed to perform at comfortable race-pace. Boots were equipped with validated 3D force platforms (Falda-Buscaiot et al., 2016) recording at 200 Hz which provided force and torque data between ski boots and bindings. A synchronized cervical mounted GNSS/IMU unit (MacLloyd, Paris, FRA) with factory fusion computations recorded 3D position, Doppler speed at approximately 10 Hz. Athletes performed 1-2 runs of the course, for a total of 220 turns analyzed (excluding skating steps). All the kinematic and kinetic events are reported for one example turn on Figure 2.a and 2.b. A repeated measures ANOVA (1 factor, 6 modes) and Bonferroni Post-Hoc comparisons were performed, to test the effect of detection methods on the time of the different events, (P<0.05).

Figure 2

 2 Figure 2 Illustration signals of skiers COM trajectory (2.a) and normal Ground Reaction Force (2.b) with right and left foot in dotted lines (low-pass 8 Hz cut-off filter) and sum of both feet in solid line (lowpass 2 Hz cut-off filter). Respective TS event are noted on both panels.

  [GPS], Russian [GLONASS], European [Galileo], and Chinese [BeiDou]), on the L1 I FORCE IN GIANT-SLALOM SKIING: SUPP. MAT. 1 frequency at 10 Hz. Each unit cost ~150 euros, which was 5-10× less costly than comparable commercial alternatives.

FORCE

  IN GIANT-SLALOM SKIING: SUPP. MAT. 1

FORCE 2 .

 2 Figure depicts data collected from four trials of the RTK, relative to that from the digitized ground plan of the mountain coaster, displayed here as longitude normalized to latitude. The top figure displays the longitude of the four runs (black lines) and the ground track (dashed line) as a function of the displacement in latitude. The bottom graph displays the mean systematic variability between the RTK and ground track in m (black), and the variability (light grey SD lines) along the latitude. Note: the variability is extremely low, so the SD bars cross the mean error.

FIGURE 1 |

 1 FIGURE 1 | (A) Typical trajectory of skiers using Z line strategy (in gray) and S line strategy (in red). Triangles and diamonds correspond, respectively, to the turn radius passing above 30 m (Traj >30 ) and under 30 m (Traj <30 ), corresponding to the start and end of the straight line. (B) Typical evolution of the turn radius (in gray) and normal force applied to the ski (in blue) during a turn. Filled and dashed lines correspond, respectively, to the right and left foot; stars and crosses correspond to the end and beginning of force application.

FIGURE 2 |

 2 FIGURE 2 | Typical detection of beginning (Fbeg) and end (Fend) of force application on outside foot nSkiRF signal (in body weight BW) during a turn expressed in percentage of turn cycle.

FIGURE 3 |

 3 FIGURE 3 | Correlation between race time (in seconds) and (A) path length in straight line (radius pass above 30 m), and (B) specific mechanical energy relative to entry velocity, respectively: during the turning phase (radius below 30 m), and (C) during the entire turn (from the beginning of force application on the outside ski to next one).

2. 1 |

 1 Participants and experimental design Competitive male alpine ski athletes (SL = 8, GS = 9, SG = 5, DH = 9; 2019 base performance level, International Ski Federation [FIS] points = 21.1 ± 9.8 (range = 0-35), standing = 91.8 ± 58.5 (range = 1-185) participated in this study. At the time of testing, athletes belonged to the French national alpine squad (A team [World Cup], N = 12; B team [Europa Cup], N = 13; C team [FIS Cup], N = 6). For the study, athletes were classified as either SPEED (N = 14, age = 23 ± 4 years; body mass [BM], 86 ± 8 kg) or TECH (N = 17, age = 25 ± 5 years; BM, 80 ± 5 kg) based on the event in which they held the lowest standing (ie, highest world ranking) according to the 9th FIS list for the 2019/20 season (FIS points = 21.8 ± 10.7 [range = 0-40], standing = 93.

1

 1 Skier with testing equipment. Left panel: The image depicts an athlete in the approximate starting position for the onset of a maximal isometric pull. Visible is the bar (competition Olympic bar core), wireless strain gauge, and lashing system comprising a chain, carabiners, and a turnbuckle mounted to the base. The base platform comprised two parallel steel beams connected by a reinforced metal plate (in the shape of a widened "H"). Two pieces of grip-taped particleboard were bolted to the top of the platform. Not pictured: grip straps, which athletes could use when grip was a limiting factor in the test. Right panel: The bottom position of the squat before push-off, and after touching the bar against the rack supports and raising the bar (to their pre-set measured position). The optical gates are visible within the rack footprint (operated externally via laptop).

  = 11.55, P = .002; relative, F(1,25) = 6.49, P = .017) and RFD avg (absolute, F(1,25) = 27.76, P < .001; relative, F(1,25) = 19.43, P < .001). While relative RFD max was not associated with SPEED performance (P = .129), moderate to very large correlations existed for the other RFD measures for both SPEED (RFD max absolute, r = -0.60 [-0.86; -0.07], P = .031; RFD avg absolute r = -0.82 [-0.94; -0.48], P < .001, relative, r = -0.78[-0.93; -0.4], P = .002) and TECH (RFD max absolute, r = -0.56 [-0.83; -0.09], P = .024, relative, r = -0.50 [-0.8; -0.01], P = .048; RFD avg absolute r = -0.61 [-0.85; -0.16], P = .013, relative, r = -0.55 [-0.82; -0.08], P = .026).

1

 1 Comparison between disciplines in dynamic and isometric force variables using a general linear model including performance, and interaction.

  estimate=-0.092, p<.001) but not for CRh (median=1.20[0.213] vs median=1.17[0.205], Hodges Lehmann estimate=0.005; p=.663) and CRP (median=1.17[0.316] vs median=1.18[0.158], Hodges Lehmann estimate=-0.015, p=.471; Figure 3). *** INSERT TABLE 3 HERE ***

Figure 4 .

 4 Figure 4. Comparison between sports in forcecapacities determined from the squat jump. The data are the median (solid black line) and interquartile ranges (black dotted lines) of each cohort (skiers, top; sprinters bottom). Note x-axes are normalised to the same units.

FIGURE 2 |

 2 FIGURE 2 | Schematic overview of the experimental design realized by each participant.

FIGURE 3 |

 3 FIGURE 3 | Schematic setup for all squat jumps performed to determine individual F-v and P-v relationships and during RSJ tests to exhaustion.

F

  = (m body + m bar )g(

FIGURE 4 |

 4 FIGURE 4 | The maximum repetitions (A,B) and cumulated mechanical work (C,D), presented on a natural logarithmic scale at different velocities, at ⇠73%P max (black) and 85%P max (gray) on the (A,C), and at 85%P max v (black) and 100%P max v (gray) on the (B,D). The force-velocity ratio values associated to each condition are presented in black text. Power and force-velocity ratio main effects of the two-way ANOVAs for repeated measures are presented as black vertical and horizontal bars, respectively, with the associated p-values.

FIGURE 5 |

 5 FIGURE 5 | Schematic three-dimensional power-velocity-endurance relationships representing mean maximum repetitions across individuals in the 10 F-v-P conditions (colored horizontal cylinders). The dashed gray curve represents the different power-velocity conditions for jumps without load, from sub-maximal to maximal jump height. The crosshatched area under the gray and the black curve represents all power-velocity conditions that require assistance (i.e., total load lower than body mass), and thus were not measured.

Table 1 .

 1 Course and sectional descriptive data ..................................................................

Table 2 .

 2 Course performance (T) explained by turn modifiable factors averaged for each section (analysis 'Level 1') .....................................................................................................

Table 3

 3

	1.4. CONTENTS

. Correlations between radial force (Fr) and sectional (∆emech/vin) and course performance (T) (analysis 'Level 2') ..................................................................................... Table 4. Multiple regression analysis results assessing the importance of Ftot and RF to predict Fr, specific to the course and each section (analysis 'Level 3') ............................

Table 5 .

 5 Multiple regression analysis results assessing the importance of Fout and diff to explain Ftot and RF specific to the course and each section (analysis 'Level 4') ............. 111

Table 6 .

 6 Comparison of variables calculated from positional data collected from RTK and GNSS units ............................................................................................................................... 134

Table 7 .

 7 Comparison between disciplines in dynamic and isometric force variables using a general linear model, including performance and interaction ...................................... 159

Table 8 .

 8 Association between age, maximum force capacity, and athlete performance ................................................................................................................................................... 171

Table 9 .

 9 Pooled differences between squat jump and countermovement jump performance metrics using Wilcoxon's paired samples tests ........................................... 191

Table 10 .

 10 Differences between skiers and sprinters in countermovement ratios using the Mann-Whitney U test ............................................................................................................. 191

Table 11 .

 11 Differences between skiers and sprinters in anthropometric and mechanical variables in the squat jump using independent samples T-tests ..................................... 193

Table 12 .

 12 Multiple regression analysis results testing the importance of paired mechanical and countermovement variables and code specific performance ............... 195

Table 13

 13

	CHAPTER 1. OVERVIEW

. Comparison between disciplines in explosive-and isometric-force variables using a general linear model controlling for performance and allowing for an interaction effect .......................................................................................................................................... 230 Table 14. Importance of strength endurance and maximum capacity to athlete standing in the pooled athlete group and disciplines ........................................................................ 230

Very recently, Rivière (2020) directly addressed this topic in work that aimed to elucidate the effect of different mechanical conditions on strength-endurance performance. Briefly, the studies found that both inter-and intra-individual performance varies as a function of both the relative intensity of the testing conditions and the mechanical settings of the test relative to maximum capacities. The implications of these collaborative works are expounded in Section 2.3.4.6 and in the experimental work of this thesis (see Section 4.3).

	RFv can change the underlying characteristics of the movement, such as at high speeds
	and low force or low speeds and high force (corresponding to a right or left shift within
	the Pv relationship). Until recently, there was virtually no information regarding the
	effect of variation in Fv conditions on strength-endurance. Consequently, it is mostly
	unknown whether athletes who display superior strength endurance in one Fv condition
	will share these characteristics if the underlying expression of mechanical conditions
	changes (e.g., would changing the Fv condition in Figure 22 affect the performance of each
	athlete relative to one another?). This has important implications in understanding
	strength-endurance qualities in sporting codes dependent on performance in different
	Fv conditions (e.g., sprint cycling at fast velocities vs. skiing at very slow velocities), and
	on the subsequent assessment of relevant capacities.
	. However, various
	combinations of force and velocity conditions (i.e., RFv, as the ratio of force and velocity
	parameters to maximum capacities) can result in the same %Pmax. Subsequently, shifting

Table 1 . Course and sectional descriptive data Variable Sectional results (mean ± SD) Within- subject effects Post-hoc comparisons (Cohen's d)

 1

		Course	1. Speed	2. Overspeed	3. Flat			1 vs. 2	1 vs. 3	2 vs. 3
		mean ±SD	mean ±SD	mean ±SD	mean ±SD	F	p	d p	d p	d p
	Tturn (s)	1.60 ±0.10	1.70 ±0.13	1.64 ±0.094	1.44 ±0.094	112	<.001	0.887 .004	3.196 <.001	3.719 <.001
	vin (m/s)	15.60 ±0.89	15.23 ±1.07	15.88 ±0.98	16.31 ±0.96	15	<.001 -1.009 .003	-1.429 <.001 -0.465 .093
	L (m)	26.56 ±0.34	27.53 ±0.43	27.14 ±0.78	24.63 ±0.69	79	<.001	0.473 .089	2.979 <.001	2.279 <.001
	∆emech/vin (Js/kg/m)	-5.59 ±0.52	-5.45 ±0.73	-6.49 ±0.63	-4.65 ±0.50	64	<.001	1.797 <.001 -1.092 <.001 -3.262 <.001
	∆alt (m)	9.33 ±0.44	9.54 ±0.53	10.25 ±0.68	7.91 ±0.75	62	<.001 -0.824 .007	1.690 <.001	3.596 <.001
	Ftot (BW)	1.60 ±0.16	1.55 ±0.18	1.62 ±0.16	1.65 ±0.16	22	<.001 -1.095 .002	-1.687 <.001 -0.500 .073
	Fout (BW)	1.06 ±0.12	1.04 ±0.14	1.07 ±0.12	1.08 ±0.12	2	.169	-0.366 .357	-0.454 .302	-0.171 .518
	Fins (BW)	0.54 ±0.10	0.50 ±0.10	0.56 ±0.11	0.58 ±0.11	9	<.001 -0.993 .004	-1.053 .003	-0.223 .402
	Fdiff	0.32 ±0.084	0.35 ±0.10	0.31 ±0.09	0.30 ±0.09	2	.113	0.559 .145	0.511 .145	0.094 .721
	Fmax (BW)	3.48 ±0.38	3.21 ±0.37	3.80 ±0.42	3.44 ±0.43	37	<.001 -2.300 <.001 -0.589 .039	1.243 <.001
	Fmaxout (BW)	2.49 ±0.30	2.33 ±0.29	2.648 ±0.32	2.505 ±0.34	23	<.001 -1.740 <.001 -0.979 .004	0.766 .010
	Fmaxins (BW)	1.42 ±0.30	1.289 ±0.24	1.545 ±0.39	1.438 ±0.36	8	.002	-0.939 .008	-0.629 .057	0.449 .104
	Fr (BW)	1.06 ±0.11	1.00 ±0.11	1.07 ±0.11	1.10 ±0.16	6	.008	-1.091 .003	-0.804 .015	-0.216 .216
	RF	0.68 ±0.056	0.66 ±0.051	0.67 ±0.063	0.68 ±0.093	<1	.531	-0.261 .990	-0.258 .990	-0.128 .990

Descriptive data are displayed as mean ± standard deviation; within-subject effects are described by the F test and p-value; posthoc comparisons are represented in Cohen's d with Holm correction; Course, data averaged over total analysis window (14 turns); 1. Speed, turn averaged data from speed section; 2. Overspeed, turn averaged data from overspeed section; 3. Flat, turn averaged data from flat section; Tturn, average turn time per section; vin, velocity measured at entry to turn; L, cumulated displacement of path length, ∆emech/vin, change in specific mechanical energy, relative to entry velocity; Fr, radial force; Ftot, averaged total force output; Fout, averaged force output for outside limb; Fins, averaged force output for inside limb; Fdiff, difference in force between outside and inside limb; Fmax, averaged maximum total force output; Fmaxout, averaged maximum force output for outside limb; Fmaxins, averaged maximum force output for inside limb; RF, ratio of radial force to averaged force; s, seconds; m/s, meters per second; m, meters; Js/kg/m, joule seconds per kilogram per meter; BW, bodyweight.

Table 2 . Course performance (T) explained by turn modifiable factors averaged for each section (analysis 'Level 1')

 2

	Predictor	stand. β	p	R 2 change	F	df	model R 2
	Course				32	1, 13	0.686
	∆emech/vin	-0.842 <.001	0.708
	L		--	-
	1. Speed				37	1,13	0.717
	∆emech/vin	-0.859 <.001	0.737
	L		--
	2. Overspeed				13	1,13	0.460
	∆emech/vin	-0.706 .003	0.498
	L		--
	3. Flat				-	-	-
	∆emech/vin		--

L

stand. β, beta-weight in standardized units; p, p-value; F, F test; df, degrees of freedom; Grey background denotes no clear prediction (p>.05) of model to course performance; Course, data averaged over total analysis window (14 turns); 1. Speed, turn averaged data from speed section; 2. Overspeed, turn averaged data from overspeed section; 3. Flat, turn averaged data from flat section; ∆emech/vin, average change in specific mechanical energy, per entry velocity of each turn; L, averaged cumulated displacement per turn; bold denotes first variable to enter into predictive model.

Table 3 . Correlations between radial force (Fr) and sectional (∆emech/vin) and course performance (T) (analysis 'Level 2')

 3

	Sectional models	Pearson's r	p	Lower	95% CI	Upper
	Relationship between T and sectional Fr
	Course	-0.826	very strong	<.001	-0.940		-0.543
	1. Speed	-0.831	very strong	<.001	-0.942		-0.554
	2. Overspeed	-0.772	strong	<.001	-0.920		-0.430
	3. Flat	-0.582	strong	.023	-0.843		-0.100
	Relationship between sectional ∆emech/vin and sectional Fr
	Course	0.720	strong	.002	0.329		0.900
	1. Speed	0.647	strong	.009	0.202		0.871
	2. Overspeed	0.554	strong	.032	0.058		0.831
	3. Flat	0.261		.348	-0.290		0.682

Table 4 ).

 4

Table 5

 5

). Additional Pearson's correlations unveiled positive correlations between the force output for both limbs individually and Ftot in sections (r=0.

).

Table 4 . Multiple regression analysis results assessing the importance of Ftot and RF to predict Fr, specific to the course and each section (analysis 'Level 3')

 4

	Sectional model	stand. β	R 2 change	F	df	model R 2
	Course			449	1, 12	0.986
	Ftot	0.939	0.497
	RF	0.739	0.491
	1. Speed			649	1,12	0.989
	Ftot	1.003	0.635
	RF	0.631	0.356
	2. Overspeed			736	1,12	0.991
	Ftot	0.921	0.412
	RF	0.811	0.580
	3. Flat			382	1,12	0.982
	RF	0.918	0.600
	Ftot	0.637	0.385

stand. β, beta-weight in standardized units; p, p-value; F, F test; df, degrees of freedom; Course, data averaged over total analysis window (14 turns); 1. Speed, turn averaged data from speed section; 2. Overspeed, turn averaged data from overspeed section; 3. Flat, turn averaged data from flat section; Fr, radial force; Ftot, averaged resultant ground reaction force; RF, ratio of radial force to averaged force (from force plate); bold denotes first variable to enter into predictive model; all p<.001.

Table 5 . Multiple regression analysis results assessing the importance of Fout and diff to explain Ftot and RF specific to the course and each section (analysis 'Level 4') Sectional Model stand. β R 2 change F df model R 2

 5

	Course

stand. β, beta-weight in standardized units; p, p-value; F, F test; df, degrees of freedom; Course, data averaged over total analysis window (14 turns); 1. Speed, turns with moderate relief with the target of gaining speed; 2. Overspeed, turns with high relief with the target of managing built up speed; 3. Flat, turns with low relief and perceived low difficulty; Fout, averaged resultant ground reaction forces applied to outside limb in the turns; Fdiff, turn averaged ratio of the absolute difference between the force applied to inside and outside limb and the total force; bold denotes the first variable to enter into a predictive model; all p<.001.

Table 6 . Comparison of variables calculated from positional data collected from RTK and GNSS units

 6

	Turn variables	RTK Mean ±SD	GNSS Mean ±SD	Overall raw bias (95% CI)	RTK vs. GNSS Pearson's ( r )	Typical error ( % )

RTK, global navigation satellite system with real-time kinematic post-processing capabilities; GNSS, global navigation satellite system; SD, standard deviation; CI, confidence intervals; vavg, averaged velocity; vin, the velocity at turn entry; L, cumulated distance traveled; Fr, radial force; ∆emech/vin, change in specific mechanical energy normalized to velocity at turn entry; s, seconds; m/s, meters per second; m, meters; N/kg, Newtons per kilogram; Js/kg/m, joule seconds per kilogram per meter.

  Les deux disciplines de ski alpin affichent une prépondérance pour la production de force dynamique à basse vitesse et les athlètes de vitesse ont montré des niveaux élevés et significatifs de force isométrique. Il y avait un manque total de qualité prédictive pour des conditions de vitesse modérée (puissance maximale et hauteur de saut) dans l'une ou l'autre des disciplines. La production de force élevée observée dans ces cohortes et l'association généralisée entre la capacité de force élevée et la performance renforcent l'intérêt du développement et de l'évaluation de la force isométrique et de la force dynamique à basse vitesse chez les athlètes de ski.

	orienté en force (ω 2 =0,34, r=0,60 à 0,67, p<,001). Dans le même temps, il y avait une variété
	d'associations entre le taux maximal et moyen de développement de la force et la
	performance par discipline (r=-0,50 à -0,82, p<,048) et des associations robustes pour la

Nous visions à tester l'effet des disciplines (vitesse et technique) et du niveau de performance sur la saison sur les capacités production de force des membres inférieurs.

Nous avons évalué la production de force dynamique à des vitesses extrêmement faibles et élevées (via la relation force-vitesse), la force isométrique maximale et le taux de développement de la force (via le « mid-thigh pull »), pour fournir de nouvelles informations sur la capacité de production de force à différentes vitesses et modalités de contraction. Les différences de disciplines ont été évaluées via un modèle linéaire général contrôlant le niveau de performance des athlètes et un effet d'interaction entre le classement et la discipline. L'effet de la performance par discipline a été évalué à l'aide des corrélations de Pearson. La hauteur de saut sans charge ne différencie pas les disciplines, et seule la puissance absolue est plus élevée chez les athlètes de vitesse (ω 2 =0,10, p=,045); ni l'une ni l'autre n'étaient liées à la performance. Les athlètes de vitesse ont présenté une plus grande force dynamique à basse vitesse (F0; ω 2 =0,17, p<,001) et une force isométrique maximale relative et absolue plus grande (ω 2 =0,16 à 0,22, p<,003). Dans l'ensemble, il y avait de très fortes relations entre la performance et un profil Fv plus force isométrique maximale chez les athlètes de vitesse (r=-0,88, p<,001), il n'y avait qu'une tendance à une force isométrique absolue modérément plus élevée chez les athlètes techniques

(r=-0,49, p=,052)

.

  Holmberg, 2019), which depends on the timed and controlled application of force to turn the skis without dissipating energy unnecessarily.

	Both elevated force production and an ability to apply it effectively are key components
	of skiing (see Chapter 3.1) (Hebert-Losier et al., 2014; Supej & Holmberg, 2019; Turnbull

4.1.3. INTRODUCTION

Alpine skiing athletes must negotiate a challenging marked course while aiming for the shortest time from start to finish. In competition, there are four main events (slalom [SL], giant slalom [GS], super giant slalom [SG], and downhill [DH]), which collapse into technical ('TECH'=SL and GS) and speed ('SPEED'=SG and DH) 'disciplines.' In general, successful athletes across the disciplines minimize energy loss (i.e., transform potential into kinetic energy) and maximize course speed (Hebert-Losier et al., 2014; Supej &

Table 7 . Comparison between disciplines in dynamic and isometric force variables using a general linear model, including performance and interaction Variables

 7

	Descriptive data

  kg, F(1,27)=7.75, p=.010, ω 2 =0.14), with a very large performance effect depicting better athletes were heavier (F(1,27)=10.13, p=.004, ω 2 =0.19), and no interaction effect (F(1,27)=1.71, p=.202, ω 2 =0.015). For

Table 8 ;

 8 note, these analyses should be viewed with scrutiny since age was non-normal). The total model explained a large variance in performance (~63%), with both age and F0 explaining unique proportions of the model. Consequently, both age and force capacity appear to provide distinct proportions of performancepotentially representing experience and technical skill, and specific neuromuscular capacity, respectivelywhich is congruent with the reasoning expounded earlier in this work. Anecdotally, the highest-ranked athlete in our cohort (world number 1 in SL) was slightly younger than the mean but possessed force capacities in accordance with their performance level (i.e., among the best in the squad).

Table 8 . Association between age, maximum force capacity, and athlete performance

 8

	Model	stand. β	F	Skiers (N=31) p-value	df	model R 2
	Standing		26.399	<.001	2,28	0.629
	Age	-0.595		<.001
	F0	-0.394		.002

stand. β, beta-weight in standardized units; F, F test; df, degrees of freedom; model R 2 , adjusted variance explained by full model; Age, athlete age at the time of testing; F0, maximal theoretical force.

  Correlation analyses were performed on the pooled CR data to test the association between the CR in force production at different velocities (i.e., CRF vs. CRv). Fv and CR variables were compared between athlete groups (T-test or Mann-Whitney U test, Cohen's d). Sport-distinct multiple regression analyses detected associations between seasonal performance (world standing, or 100 m time) and matched CR and Fv variables (e.g., maximum force, and CRF). The expression of countermovement effect differed with movement velocities, as indicated by an inverse relationship between CRF and CRv (rs=-

0.74, p<.001), but with elevated inter-individual variability in the shift of Fv profile (rrb=0.031, p=.846). Skiers exhibited lower CRF (rrb=-0.675, p<.001) and sprinters lower CRv (rrb=0.426, p=.008), but 'moderate' velocity conditions did not differentiate groups (CRP

Table 9 . Pooled differences between squat jump and countermovement jump performance metrics using Wilcoxon's paired samples tests

 9 , squat jump and countermovement jump, respectively; h, jump height; m, meters; Pmax, maximal power; W, watt; v0, maximal theoretical velocity; m/s, meters per second; F0, maximal theoretical force; N, newton; SFv, Slope of the linear force-velocity relationship; IQR, interquartile range; W, Wilcoxon's signed-rank test; CI, confidence interval.

	Variable	SJ median(IQR)	CMJ median(IQR)	Hodges-Lehmann Estimate (95% CI)	W	p-value	Rank-Biserial Correlation (95% CI)
	h (m)	0.401(0.244)	0.471(0.297)	-0.068(-0.073; -0.063)	0	<.001	-1(-1; -1)
	Pmax (W)	2365(1913)	2720(2530)	-415(-451; -371)	2	<.001	-0.997(-0.998; -0.995)
	SFv (Ns/m)	-811(1061)	-844(806)	7.93(-55.45; 42.40)	738	.846	0.031(-0.271; 0.328)
	F0 (N)	2741(1669)	3002(1457)	-227(-282; -159)	143	<.001	-0.800(-0.887; -0.658)
	v0 (m/s)	3.37(2.67)	3.64(2.37)	-0.247(-0.343; -0.190)	112	<.001	-0.843(-0.913; -0.728)
	SJ and CMJ

vs. median=1.05

[0.151]

,

 p=.008)

and CRF (median=1.03

[0.282] vs. median=1.11[0.207]

, Hodges-Lehmann estimate=-0.092, p<.001) but not for CRh (median=1.20

[0.213]

vs. median=1.17

[0.205]

, Hodges-Lehmann estimate=0.005; p=.663) and CRP (median=1.17

[0.316] vs. median=1.18[0.158]

, Hodges-Lehmann estimate=-0.015, p=.471; Figure

52

).

Table 10 . Differences between skiers and sprinters in countermovement ratios using the Mann-Whitney U test

 10

	Variable	Skiers (N=23) median(IQR)	Sprinters (N=30) median(IQR)	Hodges-Lehmann Estimate (95% CI)	U	p-value	Rank-Biserial Correlation (95% CI)
	CRh	1.20(0.213)	1.17(0.205)	0.005(-0.025; 0.031)	370	.663	0.072(-0.239; 0.371)
	CRP	1.17(0.316)	1.18(0.158)	-0.015(-0.053; 0.025)	304	.471	-0.119(-0.41; 0.195)
	CRF	1.03(0.282)	1.11(0.207)	-0.092(-0.129; -0.051)	112	<.001	-0.675(-0.813; -0.465)
	CRv	1.17(0.413)	1.05(0.151)	0.118(0.03; 0.158)	492	.008	0.426(0.138; 0.648)

Table 11 . Differences between skiers and sprinters in anthropometric and mechanical variables in the squat jump using independent samples T- tests

 11 Welches correction for unequal variances applied to variable analyses; SJ and CMJ, squat jump and countermovement jump, respectively; h, height;

	Variable	Skiers (N=23) mean±SD	Sprinters (N=30) mean±SD	T-stat	df	p-value	Mean difference (95% CI)	Cohen's d (95% CI)
	Body mass (kg)	82.99±7.73	74.96±7.20	3.898	51	<.001	8.03(3.89; 12.16)	1.08(0.494; 1.658)
	h (m)	0.339±0.038	0.439±0.038	-9.536	51	<.001	-0.101(-0.122; -0.079)	-2.643(-3.382; -1.89)
	Pmax (W)	2101±359	2580±400	-4.534	51	<.001	-479(-690; -267)	-1.26(-1.85; -0.656)
	Pmax (W/kg)	25.28±3.21	34.38±3.76	-9.306	51	<.001	-9.10(-11.07; -7.14)	-2.58(-3.31; -1.83)
	SFv (Ns/m) *	-1036±260	-726±137	-5.209	31	<.001	-311(-432; -189)	-1.50(-2.15; -0.832)
	SFv (Ns/m/kg)	-12.47±2.84	-9.78±2.11	-3.958	51	<.001	-2.69(-4.05; -1.33)	-1.10(-1.68; -0.509)
	F0 (N) *	2915±430	2711±268	1.989	35	.055	203(-4.25; 411)	0.567(0.004; 1.123)
	F0 (N/kg)	35.06±3.29	36.33±3.51	-1.347	51	.184	-1.28(-3.18; 0.626)	-0.373(-0.92; 0.176)
	v0 (m/s)	2.915±0.519	3.816±0.528	-6.199	51	<.001	-0.901(-1.193; -0.609)	-1.72(-2.35; -1.075)
	Fvimb *	0.87±0.225	0.65±0.145	4.07	36	<.001	0.22(0.11; 0.329)	1.158(0.546; 1.758)
	*,

Table 12 . Multiple regression analysis results testing the importance of paired mechanical and countermovement variables and code specific performance

 12

	Model	Skiers (N=23)

  to fully stretch the musculotendinous unit, apply force to the bone, and increase the work performed in the initial portion of the extension. In fact, since the theoretical extension times around v0 are very brief (e.g., ~0.13 s for the mean v0 and hpo in the ski group), we can theorize a disproportionately large effect of stiffness on CRv,

	since by comparison the contraction dynamics (i.e., lag in force applied to the bone due
	to non-aligned or compliant musculature, summating electromechanical delays and
	compliance effects (Van Hooren & Bosch, 2016)) represents a much greater proportion
	of extension time than activation qualities (Van Hooren & Zolotarjova, 2017

at increasingly high velocities. In other words, since sprinters may exhibit stiffer tendons compared to skiers

(McMahon, Comfort, & Pearson, 2012)

, they may benefit from a reduction in time

  =8.64, p=.009, ω 2 =0.157), but there were no differences between disciplines in absolute accumulated work (p=.184), due primarily to better athletes displaying a greater capacity for force at lower velocities. The overall multiple regression

	cible), individualisée selon leurs caractéristiques mécaniques des membres inférieurs. La
	performance a été quantifiée à partir des répétitions maximales et du travail mécanique
	cumulé jusqu'à l'épuisement. Les différences entre les disciplines ont été testées à l'aide
	d'un modèle linéaire général, contrôlant les performances et la variation des conditions
	model was associated with performance (F(3,19)=6.37, p=.007) and showed that better de test, et les associations avec les performances ont été évaluées à l'aide d'une régression
	athletes had a greater capacity for maximum force without a clear contribution of multiple, avec la capacité de force maximale et l'endurance de force (travail total
	strength endurance. When performing the same analyses within each discipline accumulé) comme variables indépendantes. Les athlètes techniques ont effectué plus de
	separately, the model was only associated with performance in the speed discipline répétitions lors du test d'endurance de force (F(1,18)=8.64, p=.009, ω 2 =0.157), mais il n'y
	(F(3,7)=14.79, p=.002). Consequently, these results might indicate maximum force-avait pas de différences entre les disciplines dans le travail cumulé (p=.184), en grande
	production capacity, rather than strength endurance (i.e., capacity to maintain a relative partie liée au fait que les meilleurs athlètes affichent une plus grande capacité de force à
	et ii) pour individualiser les conditions de test aux capacités de chaque athlète. À cette
	fin, les qualités force-vitesse des membres inférieurs de 23 skieurs de niveau national des
	deux disciplines de ski (N=12 technique et N=11 vitesse) ont été testées, après quoi ils ont
	effectué un test d'endurance de force en squats sautés répétés récemment mis au point.
	Le test était basé sur des recherches très récentes de notre groupe et conçu pour être aussi

power), is vital to high-level skiers. However, several limitations in the methodological design render the results inconclusive. As such, while the methodological basis and justification for this study design were strong, its results evidence the critical need for further research to understand the appropriate strength-endurance capacities for skiing disciplines.

Français

En ski alpin, les athlètes doivent effectuer des efforts musculaires répétés lors de virages alternés sur un parcours raide et le plus rapidement possible. Logiquement, l'endurance de la force attire l'attention dans le profilage physique, mais la position actuelle de son importance est compliquée par les limites de la conception méthodologique et de l'ancienneté des résultats. Le but de cette étude était d'explorer l'importance de l'endurance de force chez les skieurs alpins de haut niveau en utilisant un protocole conçu à la fois i) pour contrôler et cibler les exigences mécaniques spécifiques du sport, spécifique que possible au ski -caractérisé par des athlètes effectuant des sauts répétées à une intensité définie relative (80%) aux capacités maximales et dans une condition de vitesse faible et de force élevée (imposée via une charge externe et une hauteur de saut des vitesses faibles. Le modèle global de régression multiple était associé à la performance (F

(3,19)

=6.37, p=.007), et a montré que les meilleurs skieurs avaient une plus grande capacité de force maximale sans une contribution claire de l'endurance de force (i.e., capacité de maintenir un niveau relatif de puissance). Lors de la réalisation des mêmes analyses dans chaque discipline séparément, le modèle était uniquement associé à la performance dans la discipline de vitesse (F(3,7)=14.79, p=.002). Par conséquent, ces résultats pourraient être interprétés comme la plus grande importance pour les skieurs de haut niveau de la capacité maximale de production de force comparé à l'endurance de force. Cependant, plusieurs limitations dans la conception méthodologique rendent les résultats peu concluants. En tant que tel, alors que la base méthodologique et la justification de cette conception de l'étude étaient solides, ces résultats démontrent le besoin critique de recherches supplémentaires pour comprendre les capacités d'endurance de force appropriées pour les disciplines de ski.

Table 13 . Comparison between disciplines in explosive-and isometric-force variables using a general linear model controlling for performance and allowing for an interaction effect Variables

 13

	Descriptive data

# , p<.1; * , p<.05; ** , p<.01; ***

Table 14 . Importance of strength endurance and maximum capacity to athlete standing in the pooled athlete group and disciplines Model Combined (N=23) SPEED (N=11) TECH (N=12)

 14

		β	F	p	model R 2	β	F	p	model R 2	β	F	p	model R 2
	Maximum capacity + strength endurance
			6.37	.007	0.328		14.79	.002	0.734		2.41	.146	.204
	F0	-0.619		.002		-0.810		.001		-0.596		.057
	Wtot	0.028		.875		0.201		.261		0.047		.867
	N, number of athletes in analysis; β, beta-weight in standardized units; F, F-test; p, p-value; model R 2 , adjusted variance explained by model; F0,
	maximum theoretical force; Wtot, absolute total cumulated work performed during the protocol.

  Is the effect of countermovement with speed trainable within athletes, and to what degree?

	5.1. PERSPECTIVES
	• Can we match force output characteristics on the snow-technical, tactical, or physical-to
	specific force-output profiles measured within the lab or gym (i.e., off-snow)? For example,
	does an athlete with a greater explosive maximum force display an 'aggressive' strategic
	approach, with higher peak force output and variation on the course? The rise of affordable
	and highly accurate positional technology should help provide data to answer this (and the
	above point).
	• What are the long-term adaptations in muscular profile from ski-specific training modalities,
	and what is the specific variation in output kinetics across ski-specific training and
	competitive seasons?
	•

  upwards of 14 sessions per week on various physical training; however, during the ski-camps, physical training frequency is reduced, and the focus is overwhelmingly on recovery and mobility. While athletes and coaches continue conditioning work during ski-camps (the quality of which varies, according to the

	facilities present), the preference is on maintaining conditioning and minimizing fatigue
	to maximize engagement in on-snow training. Because the preparatory period involves
	recovery (e.g., athlete vacations) and is interspersed with on-snow training, it is
	challenging to manage physical conditioning periodization. For example, in the French
	system, targeted training blocks rarely exceed ~6 weeks of continuous focus on

compiled data from interviews with trainers from various countries to provide a generalized profile of the activities of elite skiers. In general, the main 'off-snow' training period for athletes occurs between May and July, which continues until October or November with increasing emphasis placed on 'on-snow' training. During the former period, athletes will spend conditioning. Consequently, the number of dedicated training blocks that allow for structured periodization and associated adaptations is limited

(Helms et al., 2018)

. This further strengthens the need for appropriate conditioning practice to ensure ongoing efficient athlete development.

Table 1

 1 Correlations between course time and kinetic and kinematic variables.

		T	Favg	Fdiff	Fmax	Traj
	Favg	-0.74**
	Fdiff	0.36	-0.17
	Fmax	-0.60*	0.74	0.18
	Traj	-0.10	0.22	-0.016	0.12
	vavg	-0.97***	0.75**	-0.34	0.56*	0.30
	p<0.05; ** p<0.01; and *** p<0.001

T, total course time; Favg, averaged force output; bal, portion of total force between limbs; Fmax, peak force output; Traj, cumulated distance; vavg, averaged velocity output (all variables turn averaged).

Table 1

 1 Lag between methods.

	Method	Lag (ms) Std Dev (ms)
	Traj>30 *	-190 ± 173
	Fend *	-108 ± 48
	Fmin *	0 ± 0
	Fbeg	157 ± 91
	Trajinfl	160 ± 92
	Traj<30 *	458 ± 108
	*: Statistical differences with all other
		methods (p<0.001)

Table 1 : Course and sectional descriptive data. Variable Sectional results (mean ± SD) Within subject effects Post-hoc comparisons (Cohen's d)

 1 Descriptive data are displayed as mean ± standard deviation; within subject effects are described by the F test (F) and p-value (p); posthoc comparisons are represented in Cohen's d with Holm correction; Course, data averaged over total analysis window (14 turns); 1. Speed, turn averaged data from speed section; 2. Overspeed, turn averaged data from overspeed section; 3. Flat, turn averaged data from flat section; Tturn, average turn time per section; vin, velocity measured at entry to turn; L, cumulated path length; ∆emech/vin, change in specific mechanical energy, relative to entry velocity; Fr, radial force; Ftot, averaged total force output; Fout, averaged force output for outside limb; Fins, averaged force output for inside limb; Fdiff, difference in force between outside and inside limb; Fmax, averaged maximum total force output; Fmaxout, averaged maximum force output for outside limb; Fmaxins, averaged maximum force output for in limb; RF, ratio of radial force to averaged force; s, seconds; m/s, meters per second; m, meters; Js/kg/m, joule seconds per kilogram per meter; BW, bodyweight.

		Course	1. Speed	2. Overspeed	3. Flat			1 vs. 2	1 vs. 3	2 vs. 3
		mean ±SD	mean ±SD	mean ±SD	mean ±SD	F	p	d p	d p	d p
	Tturn (s)	1.60 ±0.10	1.70 ±0.13	1.64 ±0.094	1.44 ±0.094	112	<.001	0.887 .004	3.196 <.001	3.719 <.001
	vin (m/s)	15.60 ±0.89	15.23 ±1.07	15.88 ±0.98	16.31 ±0.96	15	<.001	-1.009 .003	-1.429 <.001 -0.465 .093
	L (m)	26.56 ±0.34	27.53 ±0.43	27.14 ±0.78	24.63 ±0.69	79	<.001	0.473 .089	2.979 <.001	2.279 <.001
	∆emech/vin (Js/kg/m)	-5.59 ±0.52	-5.45 ±0.73	-6.49 ±0.63	-4.65 ±0.50	64	<.001	1.797 <.001 -1.092 <.001 -3.262 <.001
	∆alt (m)	9.33 ±0.44	9.54 ±0.53	10.25 ±0.68	7.91 ±0.75	62	<.001	-0.824 .007	1.690 <.001	3.596 <.001
	Ftot (BW)	1.60 ±0.16	1.55 ±0.18	1.62 ±0.16	1.65 ±0.16	22	<.001	-1.095 .002	-1.687 <.001 -0.500 .073
	Fout (BW)	1.06 ±0.12	1.04 ±0.14	1.07 ±0.12	1.08 ±0.12	2	.169	-0.366 .357	-0.454 .302	-0.171 .518
	Fins (BW)	0.54 ±0.10	0.50 ±0.10	0.56 ±0.11	0.58 ±0.11	9	<.001	-0.993 .004	-1.053 .003	-0.223 .402
	Fdiff	0.32 ±0.084	0.35 ±0.10	0.31 ±0.09	0.30 ±0.09	2	.113	0.559 .145	0.511 .145	0.094 .721
	Fmax (BW)	3.48 ±0.38	3.21 ±0.37	3.80 ±0.42	3.44 ±0.43	37	<.001	-2.300 <.001 -0.589 .039	1.243 <.001
	Fmaxout (BW)	2.49 ±0.30	2.33 ±0.29	2.648 ±0.32	2.505 ±0.34	23	<.001	-1.740 <.001 -0.979 .004	0.766 .010
	Fmaxins (BW)	1.42 ±0.30	1.289 ±0.24	1.545 ±0.39	1.438 ±0.36	8	.002	-0.939 .008	-0.629 .057	0.449 .104
	Fr (BW)	1.06 ±0.11	1.00 ±0.11	1.07 ±0.11	1.10 ±0.16	6	.008	-1.091 .003	-0.804 .015	-0.216 .216
	RF	0.68 ±0.056	0.66 ±0.051	0.67 ±0.063	0.68 ±0.093	<1	.531	-0.261 .990	-0.258 .990	-0.128 .990

Table 2 .

 2 Course performance (T) explained by turn modifiable factors averaged for each section (analysis 'Level 1') beta-weight in standardized units; p, p-value; F, F test; df, degrees of freedom; Grey background denotes no clear model prediction (p>.05) of model to course performance; Course, data averaged over total analysis window (14 turns); 1. Speed, turn averaged data from speed section; 2. Overspeed, turn averaged data from overspeed section; 3. Flat, turn averaged data from flat section; ∆emech/vin, average change in specific mechanical energy, per entry velocity of each turn; L, averaged cumulated displacement per turn; bold denotes first variable to enter into predictive model.

	Predictor	stand. β p	R 2 change	F	df	model R 2
	Course			32	1, 13	0.686
	∆emech/vin	-0.842 <.001	0.708
	L	--	-
	1. Speed			37	1,13	0.717
	∆emech/vin	-0.859 <.001	0.737
	L	--
	2. Overspeed			13	1,13	0.460
	∆emech/vin	-0.706 .003	0.498
	L	--
	3. Flat			-	-	-
	∆emech/vin	--
	L
	stand. β,

Table 3 :

 3 Pearson's Product Moment Correlation Coefficients between radial force (Fr) and sectional (∆emech/vin) and course performance (T) (analysis 'Level 2')

	Sectional models	Pearson's r	P	95% CI Lower Upper
	Relationship between T and sectional Fr
	Course	-0.826	very strong	<.001	-0.940	-0.543
	1. Speed	-0.831	very strong	<.001	-0.942	-0.554
	2. Overspeed	-0.772	strong	<.001	-0.920	-0.430
	3. Flat	-0.582	strong	.023	-0.843	-0.100
	Relationship between sectional ∆emech/vin and sectional Fr
	Course	0.720	strong	.002	0.329	0.900
	1. Speed	0.647	strong	.009	0.202	0.871
	2. Overspeed	0.554	strong	.032	0.058	0.831
	3. Flat	0.261		.348	-0.290	0.682

Table 4 :

 4 Multiple regression analysis results assessing the importance of Ftot and RF to predict Fr, specific to the course and each section (analysis 'Level 3') beta-weight in standardized units; p, p-value; F, F test; df, degrees of freedom; Course, data averaged over total analysis window (14 turns); 1. Speed, turn averaged data from speed section; 2. Overspeed, turn averaged data from overspeed section; 3. Flat, turn averaged data from flat section; Fr, radial force; Ftot, averaged resultant ground reaction force; RF, ratio of radial force to averaged force (from force plate); bold denotes first variable to enter into predictive model; all p<.001.

	Sectional model	stand. β	R 2 change	F	df	model R 2
	Course			449	1, 12	0.986
	Ftot	0.939	0.497
	RF	0.739	0.491
	1. Speed			649	1,12	0.989
	Ftot	1.003	0.635
	RF	0.631	0.356
	2. Overspeed			736	1,12	0.991
	Ftot	0.921	0.412
	RF	0.811	0.580
	3. Flat			382	1,12	0.982
	RF	0.918	0.600
	Ftot	0.637	0.385
	stand. β,

Table 5 :

 5 Multiple regression analysis results assessing the importance of Fout and diff to explain Ftot specific to the course and each section (analysis 'Level 4') beta-weight in standardized units; F, F test; df, degrees of freedom; Course, data averaged over total analysis window (14 turns); 1. Speed, turns with moderate relief with the target of gaining speed; 2. Overspeed, turns with high relief with the target of managing built up speed; 3. Flat, turns with low relief and perceived low difficulty; Fout, averaged resultant ground reaction forces applied to outside limb in the turns; Fdiff, turnaveraged ratio of absolute difference between force applied to inside and outside limb and the total force; bold denotes first variable to enter into predictive model; all p<.001.

	Sectional Model	stand. β	R 2 change	F	df	model R 2
	Course			1013	1,12	0.995
	Fout	1.079	0.642
	Fdiff	-0.657	0.354
	1. Speed			1607	1,12	0.996
	Fout	1.179	0.697
	Fdiff	-0.647	0.299
	2. Overspeed			563	1,12	0.988
	Fout	1.044	0.551
	Fdiff	-0.728	0.438
	3. Flat			1824	1,12	0.996
	Fout	1.179	0.517
	Fdiff	-0.924	0.479
	stand. β,

FORCE IN GIANT-SLALOM SKIING Level 4 -Contribution of force to the outside limb and the balance between limbs to total force output

  In all sections Ftot was predicted by a model which (by order) positively correlated to Fout, and negatively correlated to Fdiff (see Table5). In contextualizing these results, additional Pearson's correlations unveiled positive correlations between the force output for both limbs individually and Ftot in sections (r=0.613-0.835, p<.001-.015), and no clear relationship in any section between Fins and Fout

-SLALOM SKIING: SUPP. MAT. 1 SupplementaryTable I .

 I Comparison of variables calculated from positional data collected from RTK and GNSS units Global Navigation Satellite System with Real-Time Kinematic post-processing capabilities; GNSS, Global Navigation Satellite System; SD, standard deviation; CI, confidence intervals; vavg, averaged velocity; vin, velocity at turn entry; L, cumulated distance travelled; Fr, radial force; ∆emech/vin, change in specific mechanical energy normalized to velocity at turn entry; s, seconds; m/s, meters per second; m, meters; N/kg, Newtons per kilogram; Js/kg/m, joule seconds per kilogram per meter.

		RTK	GNSS		RTK vs GNSS
	Turn variables	Mean ±SD	Mean ±SD	Overall raw bias (95% CI)	Pearson's ( r )	Typical error estimate ( % )
	Turn-by-turn (N=93)
	T (s)	1.58 ±0.13	1.58 ±0.15	0.0022 (-0.012; 0.017)	0.86	4.2
	vavg (m/s)	17.93 ±1.24	17.96 ±1.40	0.036 (-0.069; 0.14)	0.91	3.1
	vin (m/s)	18.06 ±1.54	17.89 ±1.63	-0.17 (-0.31; -0.034)	0.93	3.6
	L (m)	29.92 ±1.69	29.86 ±2.13	-0.054 (-0.24; 0.17)	0.62	4.5
	Fr (N/kg)	8.19 ±0.73	8.34 ±1.03	0.15 (0.0081; 0.30)	0.69	7.0
	∆emech/vin (Js/kg/m)	-3.72 ±0.52	-3.66 ±1.02	0.051 (-0.23; 0.13)	0.51	12.9
	Grouped turns (N=23)
	T (s)	1.58 ±0.08	1.58 ±0.08	0.0022 (-0.0058; 0.010)	0.97	1.2
	vavg (m/s)	18.17 ±0.43	18.19 ±0.65	0.018 (-0.16; 0.20)	0.78	1.5
	vin (m/s)	18.35 ±0.51	18.17 ±0.73	-0.18 (-0.35; -0.000029)	0.84	1.5
	L (m)	30.45 ±1.77	30.39 ±1.99	-0.066 (-0.34; 0.21)	0.95	1.8
	Fr (N/kg)	8.23 ±0.36	8.35 ±0.60	0.13 (-0.064; 0.32)	0.69	3.3
	∆emech/vin (Js/kg/m)	-3.83 ±0.65	-3.81 ±0.80	0.022 (-0.19; 0.15)	0.82	9.1
	RTK,

FORCE IN GIANT-SLALOM SKIING: SUPP. MAT. 1

  Influence of Line Strategy Between Two Turns on Performance in Giant SlalomClément Delhaye 1 *, Matthew R. Cross1,2 , Maximilien Bowen 1 , Pierre Samozino 1 and Frédérique Hintzy 1

	Delhaye, C., Cross, M. R., Bowen, M., Samozino, P., & Hintzy, F. (2020). Influence of line-
	strategy between two turns on performance in giant slalom. Frontiers in Sport and Active
	Living. In press.

TABLE 1 |

 1 Correlation tests between path length in straight line (Path SL), and kinetic and kinematic parameters of the turn.

		r Pearson	p
	Path SL+TP (m)	-0.481	0.051
	Speed SL (m/s)	0.672	0.003
	Speed TP (m/s)	-0.418	0.095
	e mech/ v in TP (J/kg/m/s)	-0.223	0.390
	e mech/ v in SL+TP (J/kg/m/s)	-0.064	0.808
	T%SL (%)	0.967	<0.001
	T SL (ms)	0.876	<0.001
	T Edge switch (ms)	0.195	0.453

TABLE 2 |

 2 Hierarchical linear regression model result, specific mechanical energy relative to entry velocity in entire turn ( e mech/ v in SL+TP) was forced in the Model 0; in Model 1, path length in SL was added to Model 0.

	Model	R	R 2	Adjusted R 2	RMSE	R² change	F change	F	p
	Model summary of regression analyses to determine prediction of race time
	0	0 . 6 2 1	0 . 3 8 5	0 . 3 4 4	1 . 5 6 6	0 . 3 8 5	9 . 3 9 6	9 . 3 9 6	0 . 0 0 8
	1	0 . 6 5 7	0 . 4 3 2	0 . 3 5 1	1 . 5 5 8	0 . 0 4 7	1 . 1 5 2	5 . 3 2 1	0 . 3 0 1

  Specific force capacities might be a limiting factor for alpine skiing performance, yet there is little consensus on the capabilities in question, and whether they differ between disciplines. We aimed to test discipline (speed and technical) and performance (event-specific world standing) effects on lower limb force-production qualities.

	Cross, M. R., Rivière, J. R., Coulmy, N., Morin, J.-B., & Samozino, P. (2020). Lower-limb
	force-production capacities in alpine skiing disciplines. Scand J Med Sci Sports, In press.

Scand J Med Sci Sports. 2020;00:1-13.

| 1 wileyonlinelibrary.com/journal/sms

1

| INTRODUCTION

Alpine skiing athletes must negotiate a challenging marked course while aiming for the shortest time from start to finish.

In competition, there are four main event-groupings (Slalom [SL], Giant Slalom [GS], Super Giant Slalom [SG], and Downhill [DH]), which collapse into technical ("TECH," SL and GS) and speed ("SPEED," SG and DH) "disciplines." In National-level skiers (N = 31) performed loaded squat jumps and isometric midthigh pulls to detect dynamic force output at extremely low and high velocities and maximum isometric force and rate of force development, respectively. Discipline differences were assessed via a general linear model including performance and allowing for interaction effects, with performance associations further characterized via distinct Pearson's correlations. Jump height did not differentiate disciplines, with absolute power slightly higher in speed athletes (F (1,27) = 4.42, P = .045, ω 2 = 0.10), and neither variables were related to performance. Speed athletes possessed greater dynamic force at low velocities (F 0 ; F (1,27) = 13.8, P < .001, ω 2 = 0.17), and greater relative and absolute maximum isometric force (F

(1,25)

= 11.19-20.70

, ω 2 = 0.16-0.22, P < .003). Overall, higher ranked athletes possessed more force-dominant profiles (F

(1,27)

= 16.28, ω 2 = 0.34; r = 0.60 to 0.67, P < .001) and increased rate of force development characteristics (average and maximum, r = -0.50 to -0.82, P < .048

Table 2 .

 2 SJ and CMJ, squat jump and countermovement jump, respectively; h, jump height; m, meters; Pmax, maximal power; W, watt; v0, maximal theoretical velocity; m/s, meters per second; F0, maximal theoretical force; N, newton; SFv, Slope of the linear force-velocity relationship; IQR, interquartile range; W, -rank test; CI, confidence interval. Differences between skiers and sprinters in countermovement ratios using Mann -Whitney U test

		). As such, there might be interest
	in developing the mechanisms underlying a reduced
	countermovement	effect	(e.g.,	rate-of-force
	development in squat-jump) depending on the sport.

Table 3 .

 3 Differences between skiers and sprinters in anthropometric and mechanical variables in the squat jump using independent samples T-tests

	Variable	Skiers (N=23) mean±SD	Sprinters (N=30) mean±SD	T-stat	df	p-value	Mean difference (95% CI)	d (95% CI)
	Bodymass (kg)	82.99±7.73	74.96±7.20	3.898	51	<.001	8.03(3.89; 12.16)	1.08(0.494; 1.658)
	h (m)	0.339±0.038	0.439±0.038	-9.536	51	<.001	-0.101(-0.122; -0.079)	-2.643(-3.382; -1.89)
	Pmax (W)	2101±359	2580±400	-4.534	51	<.001	-479(-690; -267)	-1.26(-1.85; -0.656)
	Pmax (W/kg)	25.28±3.21	34.38±3.76	-9.306	51	<.001	-9.10(-11.07; -7.14)	-2.58(-3.31; -1.83)
	SFv (Ns/m) *	-1036±260	-726±137	-5.209	31	<.001	-311(-432; -189)	-1.50(-2.15; -0.832)
	SFv (Ns/m/kg)	-12.47±2.84	-9.78±2.11	-3.958	51	<.001	-2.69(-4.05; -1.33)	-1.10(-1.68; -0.509)
	F0 (N) *	2915±430	2711±268	1.989	35	.055	203(-4.25; 411)	0.567(0.004; 1.123)
	F0 (N/kg)	35.06±3.29	36.33±3.51	-1.347	51	.184	-1.28(-3.18; 0.626)	-0.373(-0.92; 0.176)
	v0 (m/s)	2.915±0.519	3.816±0.528	-6.199	51	<.001	-0.901(-1.193; -0.609)	-1.72(-2.35; -1.075)
	Fvimb *	0.87±0.225	0.65±0.145	4.07	36	<.001	0.22(0.11; 0.329)	1.158(0.546; 1.758)
	*, Welches correction

Table 4 .

 4 Multiple regression analysis results testing the importance of paired mechanical and countermovement variables and code specific performance

	Model	Skiers (N=23)

TABLE 1 |

 1 Mean ± SD of the maximum repetitions in P 3 v 4 condition obtained from the two trials to assess intra-day and inter-day reliability analysis.

		Maximum repetitions			Reliability
		Trial 1	Trial 2	p-Value	SEM	Standardized SEM (inference)	ICC [95%CI]
	Intra-day reliability Inter-day reliability	17.8 ± 7.6 17.8 ± 8.8	16.9 ± 9.4 16.9 ± 9.4	0.363 0.480	2.36 2.79	0.28 (small) 0.31 (small)	0.94 [0.83;0.98] 0.92 [0.8;0.97]

TABLE 2 |

 2 Mean ± SD of additional load, intra-set RSJ jump height coefficient of variation and jumping frequency for the 10 F-v-P conditions.

			Additional load (kg)	Targeted jump height (cm)	Coefficient of variation (%)	Jumping frequency (Hz)
	P 5 P 4 P 3 P 2 P 1	v 6 v 6 v 6 v 4 v 3 v 5 v 3 v 2 v 3 v 1	11.2 ± 1.7 5.9 ± 1.2 0.2 ± 0.5 19.9 ± 4.3 46.9 ± 12.6 0.1 ± 0.5 31.3 ± 9.7 68.8 ± 17.1 15.6 ± 6.7 52.7 ± 14.3	25.8 ± 5.4 25.8 ± 5.4 25.8 ± 5.4 19.5 ± 4.4 14.2 ± 3.7 21.9 ± 4.8 14.2 ± 3.7 9.2 ± 2.6 14.2 ± 3.7 8.7 ± 2.6	1.98 ± 1.28 2.34 ± 0.75 3.24 ± 0.78 3.35 ± 1.33 3.39 ± 1.65 4.58 ± 3.15 5.22 ± 1.86 6.04 ± 4.38 5.89 ± 0.88 8.43 ± 3.98	0.36 ± 0.04 0.35 ± 0.02 0.35 ± 0.01 0.34 ± 0.01 0.31 ± 0.05 0.34 ± 0.01 0.33 ± 0.02 0.28 ± 0.05 0.33 ± 0.02 0.32 ± 0.01
	P

i : power output expressed relative to the power-velocity relationship; v i : velocity expressed relative to the power-velocity relationship.

Frontiers in

Physiology | www.frontiersin.org 6 October 2020 | Volume 11 | Article 576725

TABLE 3 |

 3 Mean± SD of the maximum repetitions, force-velocity ratio, absolute and relative achieved and targeted force, velocity and power output for each of the 10 F-v-P conditions.

	Cumulated Power (W) Power (%Pmax) Power (%Pmaxv) Force (N) Velocity (m.s 1 ) Force-velocity ratio Mechanical work (J)	mechanical (R Fv )	work (J)	Targeted Achieved Targeted Achieved Targeted Achieved Targeted Achieved Targeted Achieved Targeted Achieved Targeted Achieved	4079 ± 2925 9288 1466 ± 5381 29702 1372 ± 19616 1278 12016 ± 5391 2892 1278 ± 2099 70858 1278 ± 41274 1115 ± 2046 ± 1777 62586 ± 44091 8455 ± 5203 1115 951 951 ± 318 1422 ± 298 1363 ± 279 1248 ± 279 1270 ± 279 1240 ± 245 1115 ± ± 245 1057 ± 211 964 ± 211 969 ± 316 95.6 ± 2.4 92.5 ± 294 89.4 ± 1.9 88.8 ± 262 85.0 ± 0.0 83.3 ± 275 85.0 ± 0.0 84.9 ± 247 85.0 ± 0.0 86.5 ± 254 72.6 ± 0.8 72.4 ± 72.6 ± 0.8 72.4 ± 252 72.6 ± 0.8 68.9 ± 218 61.9 ± 0.7 62.5 ± 222 61.9 ± 0.7 62.9 ± 4.4 100.0 ± 2.6 93.6 ± 2.0 85.0 ± 2.4 92.0 ± 3.7 100.0 ± 1.8 78.3 ± 2.4 85.0 ± 7.1 100.0 ± 1.6 74.3 ± 2.9 85.0 ± 0.0 96.8 ± 0.4 92.9 ± 0.0 83.2 ± 1.0 91.4 ± 0.0 97.3 ± 1.8 78.2 ± 0.0 84.9 ± 0.0 94.9 ± 1.6 75.1 ± 0.0 86.5 ± 3.3 1297 ± 1.0 1213 ± 2.0 1130 ± 2.0 1295 ± 4.2 1518 ± 2.3 1069 ± 2.4 ± 9.4 1642 ± 2.4 1129 ± 3.6 1444 ± 169 1282 ± 158 1213 ± 148 1119 ± 167 1296 ± 201 1506 ± 137 1073 ± ± 222 1616 ± 145 1136 ± 193 1453 ± 164 1.12 ± 157 1.12 ± 139 1.12 ± 162 0.97 ± 188 0.83 ± 139 1.03 ± 0.83 ± 219 0.67 ± 144 0.83 ± 190 0.65 ± 0.12 1.10 ± 0.12 1.11 ± 0.12 1.10 ± 0.11 0.97 ± 0.11 0.82 ± 0.12 1.03 ± 0.11 0.83 ± 0.10 0.65 ± 0.11 0.84 ± 0.10 0.66 ± 0.13 1.49 ± 0.12 1.40 ± 0.12 1.30 ± 0.12 1.71 ± 0.10 2.37 ± 0.12 1.34 ± 0.11 2.07 ± 0.10 3.19 ± 0.11 1.76 ± 0.10 2.89 ± 0.21 1.50 ± 0.21 1.40 ± 0.21 1.30 ± 0.18 1.77 ± 0.10 2.41 ± 0.20 1.34 ± 0.10 2.06 ± 0.07 3.26 ± 0.11 1.76 ± 0.07 2.85 ± 0.22 587 ± 0.21 555 ± 0.19 512 ± 0.18 590 ± 0.12 693 ± 0.20 490 ± 0.12 ± 0.20 746 ± 0.11 523 ± 0.13 674 ± 97 582 ± 76 550 ± 97 508 ± 56 589 ± 117 686 ± 95 486 ± ± 60 739 ± 101 518 ± 104 668 ± 103 ± 99 ± 89 ± 102 ± 117 ± 87 ± ± 123 ± 90 ± 118
	Maximum	repetitions			± 4.56 ± 9.43 ± 37.39 ± 7.47 ± 2.97 ± 88.56 ± 10.97 ± 2.53 ± 86.76 ± 6.85 P5 v 6 6.21 P4 v 6 17.00 P 3 v 6 58.79 v4 19.86 v 3 4.21 P 20.64 2.93 124.07 12.64 2 v5 148.21 v v 2 3 v1 P1 v	P

i : power output expressed relative to the power-velocity relationship; v i : velocity expressed relative to the power-velocity relationship. Frontiers in Physiology | www.frontiersin.org 7 October 2020 | Volume 11 | Article 576725

with Fresi the magnitude of the resultant SRF for each force plate (outside [Fout] and inside[Fins] limb per turn), and Fx, Fy, and Fz the magnitude of the force components in x, y, and

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4.1. FORCE-PRODUCTION CAPACITIES IN SKI DISCIPLINES

& Samozino, P. (2020). The effect of countermovement on force production depends on average extension velocity: A study of alpine skiers and sprinters. J Sports Sci, In review.

[START_REF] Mcbride | Influence of preactivity and eccentric muscle activity on concentric performance during vertical jumping[END_REF]. These factors do not necessarily negate the contribution of the stretch reflex cycle or residual force. However, a modeling study byBobbert and

Univ Savoie Mont Blanc, Laboratoire Interuniversitaire de Biologie de la Motricité, EA 7424, F-73000 Chambéry, France

Département Scientifique et Sportif, Fédération Française de Ski, Annecy, France

Université Côte d'Azur, LAMHESS, Nice, France. *Corresponding author

Univ. Savoie Mont Blanc, Inter-University Laboratory of Human Movement Biology, Chambéry, France,

DépartementScientifique et Sportif, Fédération Française de Ski, Annecy, France

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ACKNOWLEDGEMENTS

This work could never have been realized without the support and guidance of many.

While contributions to specific projects are mentioned throughout this thesis, this section stands as the only informal part of an otherwise formal document where I can sincerely express my gratitude to those who played an essential role in my journey.

ACKNOWLEDGMENTS

We want to sincerely thank the staff associated with the École du Ski Français Avoriaz, and the 'société d'exploitation des remontés mécaniques d'avoriaz' (SERMA) for providing us with slope access, equipment, and for generally being accommodating throughout the experiments. Thanks to Thibaut Gregoire for his assistance in piloting and data analysis, and Pierre-Florent Busseneau for his assistance with data collection. Thank you to Loïc Le Quellec and Amy Nguyen for their assistance in setting the course, and consulting on the analysis and results of this study. Lastly, sincere thanks to all athletes who gave their time and best effort in the experimentation.

ACKNOWLEDGMENTS

The authors thank the staff associated with Avoriaz skiing resort and Ecole du ski français d'Avoriaz for their help during the experiments. Thanks to Nicolas Horvais, Loïc Le Quellec, and Amy Nguyen for their assistance in setting the course and their help in the experiment project. Thank you to Salomon's engineers and specifically Valéry Boget for their help and support with the ski equipment. Thank you to all the various students for their assistance during the experimentation, and notably Thibaut Gregoire for his assistance in the data treatment of the positional data. Lastly, sincere thanks are given to all skiers who gave their time and best effort in furthering science.

ACKNOWLEDGMENTS

The authors wish to sincerely thank the coaches and athletes who gave their time and maximal effort to contribute to the project. Thanks to Maximilien Bowen for his assistance in building the isometric testing platform, and to Amy Nguyen for her assistance during data collection. Thanks to Eric Helms and Riki Lindsay for their insight into the interpretation of the results.

ACKNOWLEDGMENTS

We sincerely thank the coaches and athletes associated with this testing for giving their time, and maximal efforts during the testing.

ACKNOWLEDGMENTS

We would like to show our gratitude to Pr. J.-B. Morin, Dr. S. Dorel, Dr. C. Nicol and Pr. G. Dalleau for their valuable discussions about the results of this study.

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(2016). IMU-and GNSS-based turn switch detection in alpine ski racing. In E. Muller, J. Kroll, S. Lindinger, J. Pfusterschmied, J. Sporri, & T. Stoggl (Eds.), 7th International Congress on Science and Skiing: St. Christoph a. Arlberg, Austria, December 10 -15, 2016, Proceedings. Berkshire, England: Meyer & Meyer Sport. Fasel, B., Spörri, J., Kröll, J., & Aminian, K. (2016). Alpine ski gate crossing detection using magnetometers. In E. Müller, J. Kröll, S. J. Lindinger, J. Pfusterschmied, J. Sporri, & T. Stöggl (Eds.), 7th International Congress on Science and Skiing: St. Christoph a. Arlberg, Austria, December 10 -15, 2016, Proceedings. (Vol. 7th). Berkshire, England: Meyer & Meyer Sport. Fasel, B., Spörri, J., Schutz, P., Lorenzetti, S., & Aminian, K. (2017a). An inertial sensorbased method for estimating the athlete's relative joint center positions and center of mass kinematics in alpine ski racing. Front Physiol, 8, 850. https://doi.org/10.3389/fphys.2017.00850 edition: Human kinetics. Harden, M., Wolf, A., Evans, M., Hicks, K. M., Thomas, K., & Howatson, G. (2020). Four weeks of augmented eccentric loading using a novel leg press device improved leg strength in well-trained athletes and professional sprint track cyclists. PLoS ONE, 15(7), e0236663. https://doi.org/10.1371/journal.pone.0236663 Harden, M., Wolf, A., Russell, M., Hicks, K. M., French, D., & Howatson, G. (2018). An evaluation of supramaximally loaded eccentric leg press exercise. J Strength Cond Res, 32(10), 2708-2714. https://doi.org/10.1519/JSC.0000000000002497 Hart, N. H., Nimphius, S., Cochrane, J. L., & Newton, R. U. (2012). Reliability and validity of unilateral and bilateral isometric strength measures using a customised, portable apparatus. J Aust Strength Cond, 20, 61-67. Haugen, T., Breitschadel, F., & Seiler, S. (2019). Sprint mechanical variables in elite athletes: Are force-velocity profiles sport specific or individual? PLoS One, 14(7), e0215551. https://doi.org/10.1371/journal.pone.0215551 Haugen, T., Breitschädel, F., Wiig, H., & Seiler, S. (2020). Countermovement jump height in national team athletes of various sports: A framework for practitioners and scientists. Int J Sports Physiol Perform, Epub, 1-6. https://doi.org/10.1123/ijspp.2019-0964 Haymes, E. M., & Dickinson, A. L. (1980). Characteristics of elite male and female ski racers. Med Sci Sports Exerc, 12(3), 153-158. https://doi.org/10.1249/00005768-198023000-00005 Hebert-Losier, K., Supej, M., & Holmberg, H. C. (2014). Biomechanical factors influencing the performance of elite Alpine ski racers. Sports Med, 44(4), 519-533. https://doi.org/10.1007/s40279-013-0132-z Heikkinen, D. (2003). Physical testing characteristics and technical event performance of junior alpine ski racers. The University of Maine. Helms, E. R., Morgan, A., & Valdez, A. (2018). The Muscle and Strength Training Pyramid: Training (Vol. 2) Helms, E. R., Storey, A., Cross, M. R., Brown, S. R., Lenetsky, S., Ramsay, H., . . . Zourdos, M. C. (2017). RPE and velocity relationships for the back squat, bench press, and deadlift in powerlifters. J Strength Cond Res, 31(2), 292-297. https://doi.org/10.1519/JSC.0000000000001517 Herbert, R. D., Clarke, J., Kwah, L. K., Diong, J., Martin, J., Clarke, E. C., . . . Gandevia, S. C. (2011). In vivo passive mechanical behaviour of muscle fascicles and tendons in human gastrocnemius muscle-tendon units. J Physiol, 589(Pt 21), 5257-5267. https://doi.org/10.1113/jphysiol.2011.212175 Herbert, R. D., Heroux, M. E., Diong, J., Bilston, L. E., Gandevia, S. C., & Lichtwark, G. A. (2015). Changes in the length and three-dimensional orientation of muscle fascicles and aponeuroses with passive length changes in human gastrocnemius muscles. J Physiol, 593(2), 441-455. https://doi.org/10.1113/jphysiol.2014.279166 Herzog, W. (2014). The role of titin in eccentric muscle contraction. J Exp Biol, 217(Pt 16), 2825-2833. https://doi.org/10.1242/jeb.099127 Herzog, W., Lee, E. J., & Rassier, D. E. (2006). Residual force enhancement in skeletal muscle. J Physiol, 574(Pt 3), 635-642. https://doi.org/10.1113/jphysiol.2006.107748

FUNDING

No relevant funding was received for this research.

DATA AVAILABILITY STATEMENT

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

DATA AVAILABILITY STATEMENT

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

When controlling for RFv, and standing, TECH athletes performed greater Nrep (F (1,18)=8.64, p=.009, ω 2 =0.157) and accumulated greater relative Wtot (F (1,18)=4.41, p=.050, ω 2 =0.103), but there was no clear difference between the disciplines in absolute Wtot performed (p=.184; see Table 13).

The overall multiple regression model showed force capacity, endurance, and performance were associated (F (3,19)=6. 37, p=.007), and showed that better athletes produced higher F0, without a clear contribution from Wtot (see Table 14). When performing the same analyses within each discipline separately, the model was only associated with SPEED discipline performance (F(3,7)=14. 79,p=.002;TECH,p=.146).

Standing in TECH athletes was associated with lower CVh (rs(21)=0.62, p=.032) but not SPEED (p=.968; see Figure 62).

Figure 62. Variation in jump height against athlete standing

The figure shows the variation in jump height from the targeted 0.1 m, as a function of performance in SPEED (grey circles and line) and TECH (black diamonds and line) disciplines. *p<.05. profile (observed in the strong relationship between isometric force, maximum explosive force, and performance in Chapter 4.1) might be more predictive when paired with a baseline capacity for aerobic and anaerobic capacities.

Ecological validity of the test

The lactate values collected post-test are congruent, if not slightly lower to that reported in the literature for skiing field studies of technical disciplines [START_REF] Bottollier | Energy demands in welltrained alpine ski racers during different duration of slalom and giant slalom runs[END_REF][START_REF] Polat | An examination of respiratory and metabolic demands of alpine skiing[END_REF]; to our knowledge, no field data exists on blood lactate values from SPEED disciplines. While only a small sample of TECH skiers (N=7) were tested, a strong association between peak lactate values and Wtot (rs=0.94, p=.017) at least partially supports an association between Wtot and acidosis tolerance or anaerobic energy supply capacity. Although maximal values of alpine skiers performing lab-based protocols and training far exceed these values (e.g., anecdotal reports of >20 mmol/L), the similarity between our values and that during a ski run tangentially support the specificity of our testing protocol and the underlying mechanical settings (at least, for TECH athletes).

The test was possibly set in dissimilar conditions of mechanical reserve for SPEED athletes, which can be evidenced in the duration of the test relative to field performance, and potentially the greater cumulated relative Wtot in TECH (and non-dissimilar absolute Wtot between the cohorts). Similar to observations in cycling tests with a 'cross over' point for performance between the disciplines (assumedly a cause of the transition between anaerobic and aerobic metabolism (Turnbull et al., 2009)), a longer duration test at a lower %Pmaxv might unveil the superior longer duration muscular endurance of SPEED athletes (Rivière et al., 2020a). This is further emphasized in the fact that SPEED athletes performed the test in conditions of greater force/power output when on-snow measurement suggests it is the inverse (Gilgien, Kröll, et al., 2018). This factor, paired with turn cycles and associated limb velocities being slower in SPEED vs. TECH (Alhammoud et al., 2020) and the test being much shorter than the typical SPEED event, might suggest revisiting the settings of the test for future experiments. For example, a reduction of 10%Pmaxv in moderate velocity conditions (85 to 75% at 0.83 m/s) results in a 6-fold increase in maximum repetitions. Consequently, perhaps unique setting for speeds, fixed at a lower %Pmaxv, might better represent performance in longer duration

SKI-SPECIFIC STRENGTH-ENDURANCE ASSESSMENT

Science and Skiing VIII the comparison (course time, rather than external measures of performance level [e.g.

FIS points]).

The objectives of this study were to determine the difference between events from

F Traj

The minimum sum of nGRF (2 nd order low-pass filtered at 2 Hz) of two skis (Fmin) was considered as the reference method. All the other events were expressed in time difference to Fmin. Turn beginning and end were manually determined on the low-pass filtered signal (2 nd order, 25 Hz) as the instant when force was applied or removed to the outside ski around the moment of Fmin (± 250 ms; Fbeg and Fend, respectively). The inflexion point was computed via triple derivation of the cervical trajectory (from GNSS data) as the sign change (Trajinfl). Finally in order to compute the beginning and the end of the straight line phase between two turns, the radius of the turn was calculated by fitting circles along the trajectory using Pratt method (Pratt, 1987) Data here corresponds to the 'exploded' section of RTK and ground-track data displayed in Figure 4 and Figure 5 (top and bottom, respectively). The purpose here is to show that the graphic does indeed display four separate trajectories (black lines) alongside the digitized ground path of the coaster (dashed line).

ETHICS STATEMENT

Each skier was informed of the content of the study and gave their written consent to participate. The experiment was conducted under the Declaration of Helsinki and was approved by the local ethics committee of the Université Savoie Mont-Blanc.

AUTHOR CONTRIBUTIONS

CD, FH, and MC conducted the data collection. CD, FH, MC, and PS conceptualized the study design and interpretation of the data. CD, MB, and MC contributed to the data analysis. CD drafted the manuscript. All authors revised it critically, approved the final version, and agreed to be accountable for all aspects of this work.

Conflict of Interest:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

CONFLICT OF INTEREST

The authors declare that the research was conducted in the absence of any factors that could be construed as a potential conflict of interest.

AUTHOR CONTRIBUTIONS

MRC and JRR collected the data. MRC analyzed the data and drafted the manuscript. All authors were involved in the research design, data interpretation, and subsequent revising of the manuscript.

CONFLICT OF INTEREST

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Context: Strength-endurance mainly depends on the power output, which is often expressed relative to the individual's maximal power capability (P max ). However, an individual can develop the same power, but in different combinations of force and velocity (force-velocity condition). Also, at matched power output, changing the forcevelocity condition results in a change of the velocity-specific relative power (P max v), associated with a change in the power reserve. So far, the effect of these changing conditions on strength-endurance remains unclear.

Strength

Purpose: We aimed to test the effects of force-velocity condition and power output on strength-endurance.

Methods: Fourteen sportsmen performed (i) force-and power-velocity relationships evaluation in squat jumps and (ii) strength-endurance evaluations during repeated squat jump tests in 10 different force-velocity-power conditions, individualized based on the force-and power-velocity relationships. Each condition was characterized by different (i) relative power (%P max ), (ii) velocity-specific relative power (%P max v), and (iii) ratio between force and velocity (R Fv ). Strength-endurance was assessed by the maximum repetitions (SJ Rep ), and the cumulated mechanical work (W tot ) performed until exhaustion during repeated squat jump tests. Intra and inter-day reliability of SJ Rep were tested in one of the 10 conditions. The effects of %P max , %P max v, and R Fv on SJ Rep and W tot were tested via stepwise multiple linear regressions and two-way ANOVAs.

Results: SJ Rep exhibited almost perfect intra-and inter-day reliability (ICC=0.94 and 0.92, respectively). SJ Rep and W tot were influenced by %P max v and R Fv (R 2 =0.975 and 0.971; RSME=0.243 and 0.234, respectively; both p < 0.001), with the effect of R Fv increasing with decreasing %P max v (interaction effect, p = 0.03). %P max was not considered as a significant predictor of strength-endurance by the multiple regressions analysis. SJ Rep and W tot were higher at lower %P max v and in low force-high velocity conditions (i.e., lower R Fv ).

Conclusion:

Strength-endurance was almost fully dependent on the position of the exercise conditions relative to the individual force-velocity and power-velocity standardized across individuals based on (i) the same relative load (e.g., percentage of the one-repetition maximum; [START_REF] Mayhew | Relative muscular endurance performance as a predictor of bench press strength in college men and women[END_REF], (ii) the same movement velocity across individuals [START_REF] Câmara | Isokinetic strength and endurance in proximal and distal muscles in patients with peripheral artery disease[END_REF] or (iii) the same resistive force per bodyweight during all-out cycling exercises [START_REF] Bar-Or | The wingate anaerobic test[END_REF]. Thus, provided R Fv a ects performance, inter-individual di erences in strength-endurance observed with these commonly used methods could be mainly due to di erent mechanical conditions relative to individual capabilities (i.e., %P max, % P max v, and/or R Fv ) rather than di erent physical abilities. These methods could represent both an inaccurate and non-specific means of assessing strength-endurance, and lead to practically ine ective testing and training regimes.

The aim of the present study was to test the e ects of forcevelocity condition (i.e., R Fv ) and power output (i.e., %P max and %P max v) on strength-endurance using an acyclic movement. We hypothesized that decreasing velocity-specific relative power (%P max v) increases strength-endurance via increasing power reserve, even if it led to no change or an increase in %P max . We theorized that R Fv influences strength-endurance independently from %P max v, due to the likely di erent etiology of fatigue between high force-low velocity and low force-high velocity conditions (Enoka and Stuart, 1992;[START_REF] Morel | Contraction velocity influence the magnitude and etiology of neuromuscular fatigue during repeated maximal contractions[END_REF][START_REF] Morel | Critical peripheral fatigue thresholds among di erent force-velocity conditions: an individualbased model approach[END_REF].

MATERIALS AND METHODS

Participants

Fourteen healthy participants (12 males and 2 females, age = 20 ± 2 years, mass = 73 ± 7 kg and height = 1.79 ± 0.09 m) gave their written informed consent to participate in this study, with all procedures in agreement with the declaration of Helsinki and the ethical standards of a local committee. All were involved in regular physical activity (14 ± 7 h of training per week) and were accustomed to strength-based resistance training (i.e., habitual use of submaximal to maximal loads). All participants were free of musculoskeletal pain or injury during the study.

Design

The main limitations of previous works were addressed in this study by using jumping exercises due to (i) the possibility to dissociate rest between repetitions from movement velocity, (ii) the acute and reliable quantification of the mean force, velocity, and power output by lower limbs, and (iii) its similarity to typical iso-inertial movements observed in sport and testing batteries.

To test the e ects of %P max v, %P max , and R Fv on strengthendurance, repeated squat jumps (RSJ) tests to exhaustion were performed in various force-velocity-power (F-v-P) conditions. Overall, 10 F-v-P conditions were determined relative to individual P-v relationship (detailed in the following sections), which meant conditions were graphically positioned on or under the P-v curve (gray points, Figure 1). This positioning of the F-v-P conditions implies each condition has similar coordinates relative to individual maximal capabilities (i.e., the P-v relationship), but various individual absolute force, velocity and power values. Thus, each F-v-P conditions was characterized by di erent power output (P 1 to P 5 ) and velocity (v 1 to v 6 ), FIGURE 1 | Typical individual power-velocity relationship representing 100 (black curve) and 85%P max v (gray curve), associated with single maximal squat jumps in different loading conditions (white points) and the 10 F-v-P conditions (gray points). Each F-v-P conditions is defined by specific power and velocity coordinates. The dashed gray curve represents the different power-velocity conditions for jumps without load, from sub-maximal to maximal jump height. The crosshatched area under the gray and the black curve represents all power-velocity conditions that require assistance (i.e., total load lower than body mass), and thus were not measured.

expressed relative to the individual P-v relationship (Figure 1). In addition, the positioning of F-v-P conditions follows the constraint imposed by dynamics principles during a vertical jump with and without additional load (represented by the white area under the P-v curve and the dashed gray line, respectively, Figure 1). The remaining crosshatched area represents F-v-P conditions requiring a simulated reduction in body weight with assistance.

The 10 F-v-P conditions were selected to represent: (i) 3 velocity conditions at two %P max (corresponding to P 3 v 3 , P 3 v 4 , and P 3 v 6 at 85%P max and to P 2 v 2 , P 2 v 3 , and P 2 v 5 at ⇠73%P max ), (ii) 3 velocity conditions at two %P max v (corresponding to P 1 v 1 , P 2 v 3 , and P 3 v 6 at 85%P max v and P 2 v 2 , P 3 v 3 , and P 4 v 6 at 100%P max v) and (iii) 3 power conditions at two velocities (corresponding to P 5 v 6 , P 4 v 6 , and P 3 v 6 at v 6 and to P 3 v 3 , P 2 v 3 , and P 1 v 3 at v 3 ). Note that all F-v-P conditions were determined only using power and velocity values to graphically position them relative to power capability as a common reference (i.e., P-v relationship), but changes in velocity across all di erent power conditions correspond also to changes in R Fv .

Protocol

This study comprised six sessions, separated by more than 48h of rest (Figure 2). The first session familiarized participants

ETHICS STATEMENT

The studies involving human participants were reviewed and approved by Comité d'Ethique de la Recherche à l'Université Savoie Mont Blanc. The patients/participants provided their written informed consent to participate in this study.

AUTHOR CONTRIBUTIONS

JR, PS, NP, and LM conceived and designed the experimentation. JR conducted the experiments and wrote the manuscript. JR, MC, and PS analyzed the data. All authors read and approved the manuscript.

Conflict of Interest:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2020 Rivière, Peyrot, Cross, Messonnier and Samozino. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.