Keywords: air traffic control, shift work organization, traffic load

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Effects of a modified shift work organization and traffic load on air traffic controllers' sleep and alertness during work and non-work activities

Claudine Mélan, Nadine Cascino

Introduction

Air traffic controllers' (ATCOs) sleep and fatigue are determined by work-related factors, i.e. shiftwork, night-shift, workload, type of work performed, break frequency and duration, work environment conditions (ambient lighting, noise...), and by work-independent factors (for a review, [START_REF] Nealley | The Effect of Fatigue on Air Traffic Controllers[END_REF][START_REF] Juda | Chronotype Modulates Sleep Duration, Sleep Quality, and Social Jet Lag in Shift-Workers[END_REF]. While it is acknowledged that shift-work and workload, the most widely researched factors [START_REF] Tucker | Working time, health, and safety: A research synthesis paper[END_REF], produce workrelated fatigue that may impact air traffic control (ATC) performance and safety, few field studies have examined the influence of these factors simultaneously [START_REF] Edwards | Factor interaction influences on human performance in air traffic control: The need for a multifactorial model[END_REF].

Traffic volume, traffic complexity, and working demanding positions several times during a shift cause fatigue (FAA, 2009). Fatigue is "a condition characterized by increased discomfort with lessened capacity of work, reduced efficiency of accomplishment, loss of power or capacity to respond to stimulation, and is usually accompanied by a feeling of weariness and tiredness" (Salazar, 2007, p. 1). Fatigue has been identified as a potential contributing factor in several operational errors [START_REF] Della Rocco | The role of shift work and fatigue in air traffic control operational errors and incidents[END_REF]FFA, 2009FFA, , 2013)), and in 21 percent of aviation accidents (Wang and Ké, 2013). According to ATCOs, mental workload, fatigue and alertness figure among the main human factors involved in ATC incidents, whereas an incident report indicated that these factors account for less than 24% of the incidents [START_REF] Edwards | Factor interaction influences on human performance in air traffic control: The need for a multifactorial model[END_REF]. These results may indicate a reporting bias in incident reports, with normally present factors such as workload and fatigue being underreported. Mental workload i.e. traffic peaks and periods of continuous activity are considered to be the main sources of stress in ATC, enhanced by the necessity to operate under time pressure and by safety and security concerns [START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF], and are associated with health complaints [START_REF] Cascino | An Exploration of Job Perceptions and Health Using an Integrative Approach: A Sample of Air Traffic Controllers Working in a Test Flight Center[END_REF][START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF].

Around the clock ATC may exacerbate fatigue generated by high task demands as it requires individuals to work at times when they would normally be sleeping. More especially counter-clockwise shift rotations, scheduled overtime and on-the-job training could create potential fatigue conditions. Countries and companies regulate working time arrangements, in particular the number of working hours and the minimum rest periods between shifts, but also the number of controllers assigned to a shift, and recuperative breaks. In the absence of accurate metrics and systematic controlled studies, the extent to which the new policies impact ATCOs' fatigue is difficult to determine (FAA, 2013).

Workload during air traffic control

Task demands or task load is the demand imposed by the ATC task and is mostly assessed in terms of workload, i.e. the controller's subjective experience of that demand.

Assessment of mental workload helps to understand the relationship between task demands and controller performance [START_REF] Bommer | A theoretical framework for evaluating mental workload resources in human systems design for manufacturing operations[END_REF], which is crucial in the context of rapidly increasing air traffic density. In aviation-related research, mental workload is mostly assessed by subjective rating tools [START_REF] Hart | Nasa-Task Load Index (NASA-TLX); 20 Years Later[END_REF][START_REF] Efthymiou | Workload perception of air traffic control officers and pilots during continuous descent operations approach procedures[END_REF][START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: Investigation in the field of aerospace activities[END_REF], due to the availability and usability of these tools [START_REF] Collet | Autonomic nervous system and subjective ratings of workload in air-traffic control[END_REF][START_REF] Endsley | Distribution of Attention, Situation Awareness, and Workload in a Passive Air Traffic Control Task: Implications for Operational Errors and Automation[END_REF][START_REF] Galster | Air Traffic Controller Performance and Workload Under Mature Free Flight: Conflict Detection and Resolution of Aircraft Self-Separation[END_REF], though traffic density or traffic load (i.e. aircraft count by sector volume) has also been shown to be associated with psychophysiological measures of workload [START_REF] Brookings | Psychophysiological responses to changes in workload during simulated air traffic control[END_REF][START_REF] Collet | Autonomic nervous system and subjective ratings of workload in air-traffic control[END_REF].

The present study focusses on ATCOs' sleep, fatigue and alertness in an en route ATC center (controlling commercial aircrafts flying in the airspace at high altitudes between airport approaches and departures). This working position is defined as a complex, safety-critical occupation involving a continuously changing workload [START_REF] Efthymiou | Workload perception of air traffic control officers and pilots during continuous descent operations approach procedures[END_REF]. In this working position, task load depends in particular on sector characteristics (sector volume), and traffic complexity in the sector i.e., number of aircraft, flight altitude transitions, direction variations, trajectory uncertainty, proximity of aircraft, proximity measures between aircraft and weather conditions [START_REF] Corver | Predicting Air Traffic Controller Workload: Trajectory Uncertainty as the Moderator of the Indirect Effect of Traffic Density on Controller Workload Through Traffic Conflict[END_REF][START_REF] Hilburn | Workload and air traffic control[END_REF][START_REF] Loft | Modeling and Predicting Mental Workload in En Route Air Traffic Control: Critical Review and Broader Implications[END_REF]. Traffic load has been described as one of the strongest predictors of controller workload [START_REF] Loft | Modeling and Predicting Mental Workload in En Route Air Traffic Control: Critical Review and Broader Implications[END_REF], more especially as it increases the likelihood that two or more aircraft will create traffic conflicts [START_REF] Corver | Predicting Air Traffic Controller Workload: Trajectory Uncertainty as the Moderator of the Indirect Effect of Traffic Density on Controller Workload Through Traffic Conflict[END_REF]. In addition to high task demands, variable workload and night work have been identified as risk factors for fatigue and disturbed sleep [START_REF] Åkerstedt | Sleep disturbances, work stress and work hours: A cross-sectional study[END_REF][START_REF] Bültmann | Psychosocial work characteristics as risk factors for the onset of fatigue and psychological distress: Prospective results from the Maastricht Cohort Study[END_REF][START_REF] Flo | Shift-related sleep problems vary according to work schedule[END_REF][START_REF] Takahashi | Psychosocial work characteristics predicting daytime sleepiness in day and shift workers[END_REF]. While the mental workload is perceived to be higher on day shifts (traffic peaks), a greater physical demand is perceived at night due to the need to remain alert and vigilant [START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF]. Workload variations also occur within shifts (day and night shifts) [START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: Investigation in the field of aerospace activities[END_REF], and the demands referring directly to the core ATC activities (psychological demands) are perceived as more demanding than those defining the context (physical demands, organizational demands, overcommitment and work-family interferences; [START_REF] Cascino | An Exploration of Job Perceptions and Health Using an Integrative Approach: A Sample of Air Traffic Controllers Working in a Test Flight Center[END_REF]. Operator internal factors, including fatigue, skills, experience [START_REF] Loura | Human Factors and Workload in Air traffic Control Operations -A Review of Literature[END_REF], and individual characteristics [START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF][START_REF] Nealley | The Effect of Fatigue on Air Traffic Controllers[END_REF] are considered to mediate the relationship between task demands and the controller workload.

Fatigue and shift work components

Fatigue is generally acknowledged to be influenced by sleep length, number of hours awake, and work hours [START_REF] Åkerstedt | Sleep Loss and Fatigue in Shift Work and Shift Work Disorder[END_REF][START_REF] Åkerstedt | Shift work and disturbed sleep/wakefulness[END_REF][START_REF] Mélan | Mnemonic Processing in Air Traffic Controllers (ATCs): Effects of Task Parameters and Work Organization[END_REF].

Short-term effects of shift work include reduced sleep, sleep quality and daytime alertness [START_REF] Åkerstedt | Sleep Loss and Fatigue in Shift Work and Shift Work Disorder[END_REF] for night and morning work [START_REF] Åkerstedt | Shift work and disturbed sleep/wakefulness[END_REF][START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF][START_REF] Flo | Shift-related sleep problems vary according to work schedule[END_REF][START_REF] Luna | A study of USAF air traffic controller shiftwork: sleep, fatigue, activity, and mood analyses[END_REF][START_REF] Sallinen | Shift work, sleep, and sleepiness -differences between shift schedules and systems[END_REF] as a result of a circadian misalignment, and a sleep debt with early starts of morning work [START_REF] Tucker | The impact of early and late shift changeovers on sleep, health, and well-being in 8-and 12-hour shift systems[END_REF][START_REF] Van De Ven | Associations between shift schedule characteristics with sleep, need for recovery, health and performance measures for regular (semi-)continuous 3-shift systems[END_REF]. Accumulated sleep loss is also associated with impaired cognitive performance [START_REF] Härmä | Workhours in relation to work stress, recovery and health[END_REF], safety outcomes [START_REF] Tucker | Working time, health, and safety: A research synthesis paper[END_REF][START_REF] Sluiter | Need for recovery from work related fatigue and its role in the development and prediction of subjective health complaints[END_REF], long-term health effects and even increased mortality (Åkerstedt et al., 2018).

Combinations of specific shift work features may further enhance the conflict of work schedules with the operators' biological clock, and deteriorate sleep, performance and health [START_REF] Van De Ven | Associations between shift schedule characteristics with sleep, need for recovery, health and performance measures for regular (semi-)continuous 3-shift systems[END_REF]. This has been reported for instance for the combined influence of circadian and time-on-task factors [START_REF] Folkard | Shiftwork, safety and productivity[END_REF], low levels of workload and lack of alertness on night shifts [START_REF] Lee | Air Traffic Controllers' Situation Awareness and Workload under Dynamic Air Traffic Situations[END_REF], consecutive night shifts [START_REF] Folkard | Shiftwork, safety and productivity[END_REF][START_REF] Garde | The effects of the number of consecutive night shifts on sleep duration and quality[END_REF], backward-compared to forward-rotating shift systems [START_REF] Knauth | Preventive and compensatory measures for shift workers[END_REF][START_REF] Sallinen | Shift work, sleep, and sleepiness -differences between shift schedules and systems[END_REF], and slow versus fast shift rotations [START_REF] Juda | Chronotype Modulates Sleep Duration, Sleep Quality, and Social Jet Lag in Shift-Workers[END_REF]. Further, ATCOs under 8-h alternate shifts, rather than 6-h rotational shifts showed lower scores for quality of life, and less sleep time on working days, which characterizes inadequate shiftwork for this population [START_REF] Sonati | Quality of Life, Health, and Sleep of Air Traffic Controllers with Different Shift Systems[END_REF]. Conversely, organizational interventions redesigning shift-work schedules according to ergonomic criteria, i.e. a switch from slow to fast and from backward-to forward-rotating systems, and self-scheduling, improved health and work-life balance [START_REF] Bambra | Shifting Schedules. The Health Effects of Reorganizing Shift Work[END_REF]. Delaying time of the morning shift start to 7:00 or 8:00, and allowing a 2-hr break during the nightshift (taking turns to sleep) also led to higher job satisfaction in ATCOs [START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF][START_REF] Costa | Shift work and health: current problems and preventive actions[END_REF]. Some findings are however contradictory, in particular concerning densified work schedules (fewer work-days but longer shifts). Thus, working four days during 10h vs. five days during 8h did not affect ATCOs' performance [START_REF] Schroeder | Some effects of 8-vs. 10-hour work schedules on the test performance/alertness of air traffic control specialists[END_REF], nor when a forward-rotating 10h day/14h night system replaced a backward 8h rotating system, despite worsened sleepiness and mood across the extended work shifts [START_REF] Paley | The impact of a change in rotating shift schedules: A comparison of the effects of 8, 10 and 14 h work shifts[END_REF]. Likewise, total sleep duration did not differ between fast 12h rotations and weekly rotations of 8h, but night shift sleep decreased persistently while self-rated sleep need increased [START_REF] Di Milia | A longitudinal study of the compressed workweek: Comparing sleep on a weekly rotating 8 h system to a faster rotating 12 h system[END_REF]. Densified shift schedules are however quite popular due to social and domestic factors or advantages such as more free time available for personal needs [START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF].

Study aims

Due to additional flights over the summer holidays in an en route control centre the aircraft traffic in the centre was more intense during the summer period, with daily traffic peaks observed around 07:00, 13:00, 17:00 and 21:00. For these reasons, the local ATC centre authorities tested an experimental reorganization of work schedules between 22 July 2015 and Sunday 27 September 2015 in application of a decree (DEVA1517367A, published in the Official Journal of the French Republic, July 2015). The reorganization was designed to achieve a better match with the dense day-time traffic during the summer period (traffic peaks). This was achieved by assigning more ATCOs to the control room on day time (i.e. dividing the airspace into smaller air traffic sectors), by substituting a rest day by a work day, by delaying the beginning and end of shifts for part of the teams (overlapping shifts), and by reducing the duration of the breaks scheduled within each shift. In parallel, shift duration was limited to a maximum of 8h, except for the night shift. The decree was further accompanied by the requirement to test the efficiency of the shift schedule reorganization. Thus, once the modified shift-schedule had been introduced, the present authors were entrusted with the mission of assessing the impact of the new shift-schedule in terms of fatigue. To control for the effects of traffic density and of shift, we recommended adding these factors to the study design. Further, we proposed to assess the effects of these factors on other dimensions closely related to fatigue, in particular alertness and sleep.

Hence, the aim of the present study was to investigate the effects of both shift-schedule arrangements and traffic load on ATCOs' sleep, fatigue and alertness. A significant effect of traffic load was expected, with increased sleep length and alertness and reduced fatigue for lower aircraft traffic [START_REF] Åkerstedt | Sleep disturbances, work stress and work hours: A cross-sectional study[END_REF][START_REF] Corver | Predicting Air Traffic Controller Workload: Trajectory Uncertainty as the Moderator of the Indirect Effect of Traffic Density on Controller Workload Through Traffic Conflict[END_REF][START_REF] Nealley | The Effect of Fatigue on Air Traffic Controllers[END_REF][START_REF] Lee | Air Traffic Controllers' Situation Awareness and Workload under Dynamic Air Traffic Situations[END_REF]. We hypothesized that the beneficial effect would be most marked for morning shifts, as reduced traffic may counterbalance the well-known deleterious effects associated with early morning shift beginning [START_REF] Tucker | The impact of early and late shift changeovers on sleep, health, and well-being in 8-and 12-hour shift systems[END_REF]. Further, ATCOs' fatigue was expected to decrease and their sleep quality and duration to increase with the modified work schedule as a consequence of an increased number of controllers on position. The beneficial effects were expected to be reduced or even absent for the night shift as the length of this shift (10h) remained unchanged, in addition to shorter recuperative breaks, and a smaller number of ATCOs on position during the night shift [START_REF] Luna | A study of USAF air traffic controller shiftwork: sleep, fatigue, activity, and mood analyses[END_REF][START_REF] Mélan | Mnemonic Processing in Air Traffic Controllers (ATCs): Effects of Task Parameters and Work Organization[END_REF].

Materials and Methods

Procedure

The study project was initiated at the end of the first summer period that ATCOs worked according to the modified schedule. This excluded the possibility of performing real-time measures, including physiological recordings or actigraphy measures. A retrospective study design was therefore proposed, using a questionnaire. The first two sections of the questionnaire assessed the effects of the initial and of the experimental work-schedule respectively. A third section assessed the impact of traffic density. The three sections of the questionnaire were identical, but each referred to a different working period: (period 1) initial work-schedule with dense traffic (July to September 2014); (period 2) initial work-schedule with reduced traffic (October to December 2014); (period 3) experimental work-schedule with high traffic density (July to September 2015). The questionnaire was available on-line over a 5-week period (13 th January to 19 th February 2016) and all ATCOs of the center were informed that they should complete the three sections in a single session and that they could not switch back to previous pages or sections. The data collected for each period were compared in order to explore the impact of the modified work schedule (comparisons between periods 1 and 3) and the effects of traffic density (comparisons between periods 1 and 2).

Participants

All ATCOs working in the en route center situated in the North-East of France were invited to participate in the study. A total of 57 ATCOs volunteered to complete the questionnaire, representing 21% of the ATCOs working in the center. Their mean age was 38.9 (range 28 to 56) and they had been air traffic controllers for a mean of 11 years (range 1 to 36). 17 (29.8%) were female and 40 (70.2%) were male. The distributions according to gender and age were close to those of the entire ATCO population (respectively, 25.6% and 73.4% for gender and 35.8 for mean age).

Work schedules

ATCOs worked rapidly rotating shift systems of 12 days. Table 1 indicates the beginning and end of each shift (shift duration), and the duration of breaks for both the initial shift-schedule (white lines) and for the modified shift schedule (grey lines). This information is provided for the 12 two-member teams (the radar and the planner) working a shift. Each team was in charge of one air space sector.

During the initial work cycle, ATCOs alternated three shifts, three rest days (R), and again three shifts and three rest days. At the beginning of the cycle they worked successively a morning shift (M1, 06:00-13:00), a day shift (D, 08:00-18:30) and an evening-shift (E1, 15:00-23:00), and after the mid-cycle rest days, again a morning shift (M2, 07:00-13:00) and an evening-shift (E2, 15:15-23:45) followed by a night shift (N, 19:45-06:00). The work cycle can be summarized as follows, M1DE1RRRM2E2N2RRR.

In the modified work-cycle, the shifts were organized in the same order and the cycle-duration did not change (12 days). The main modification concerned the substitution of the third midcycle rest day by a work shift for half of the teams, thereby reducing the number of rest days. This additional day shift (08:00 to 15:00 +/-1hr) is noted D* in the work cycle (M1DE1RRD*M2E2N2RRR). A second modification consisted in delaying the beginning and end of shifts for part of the 12 teams working a given shift. Both these modifications ensured that more ATCOs were in the control room at critical moments of the shift with respect to traffic peaks. This made it possible to control more air traffic sectors, and conversely to reduce the number of aircraft to be handled within each sector relative to the number typically handled when they worked according to the initial shift schedule.

Further, though the rest breaks were scheduled approximately after two hours of air traffic control in the initial and modified shift schedules, their duration decreased particularly during the shifts after mid-cycle, independently of reductions that resulted from a reduction in shift duration (in particular for the day shift D; see below). Thus, rest break duration on the morning and evening shifts following mid-cycle was reduced by 15 or 30 minutes in the modified shift schedule. More importantly, the duration of the breaks was shortened by 1 to 2h30 during the night shift in the modified compared to the initial work schedule.

To mitigate the densifying effects of the work schedules, the maximum shift duration (shift length) was limited to 8 and a half hours for shifts worked during the day. Consequently, the particularly long day shift, lasting initially between 10h30 and 11h30, was reduced by two to three hours depending on the teams. The duration of the morning and evening shifts, which lasted initially between 9 and 11 hours for two teams, was set to a maximum of 8h30 for all the teams in the modified shift system. The length of the night shift was not modified: It lasted 10h for 10/12 teams in the initial schedule, and also for 8/12 teams in the modified schedule. On the night shift all the twelve teams worked until 06:00 in the initial schedule, but only eight teams in the modified shift schedule. The four remaining teams ended the shift shortly after midnight. Table 1. Work cycles, shift beginning and shift end, shift duration, and break duration for the initial shiftwork schedule (white lines) and the modified shiftwork schedule (grey lines).

Shift

Materials

In order to investigate the effects of shift schedule and traffic load on several psychological and physiological dimensions according to the shift worked, we developed a specific selfadministered questionnaire. Existing tools mostly assess operators' perceptions of shift work conditions in general rather than on specific shifts. Further, existing tools mostly focus on one psychological dimension, i.e. either on sleep, or on alertness. In the present questionnaire three shift-types were considered by grouping comparable schedules into "morning-shift" (M1, M2), "evening-shift" (D, E1, E2) and "night-shift" (N) respectively. The questionnaire included three identical sections relating respectively to the three 3-month periods described above. Each section comprised the same 24 items and was introduced by adequate rating instructions in reference to the work schedule and traffic period. Participants were asked to rate most of the items separately for each shift type and for rest days, and some items as an overall measure concerning the entire period. The present report focuses on ATCOs' self-ratings of sleep, Satisfaction with sleep duration ("The duration of my sleep, the night before a morning/afternoon/night-shift/rest day was…") and sleep quality ("The quality of my sleep, the night before a morning/afternoon/night-shift/rest day was...") were rated on a 6-point Likert scale (from 1 "not satisfied" to 6 "very satisfied").

• Alertness and fatigue (5 items) were assessed for each shift and on rest days using 6point Likert-type scales (from 1 "not satisfied/strongly disagree" to 6 "very satisfied/strongly agree"). These items related to on-shift fatigue ("During the morning/afternoon/night-shift I sometimes felt tired") and alertness at the beginning of the shift ("I felt very fit at the beginning of the morning/afternoon/night-shift") and at the end ("I felt very fit at the end of the morning/afternoon/night-shift"). Alertness outside working hours was also explored, i.e. alertness upon awakening ("My energy level upon awakening on a morning/afternoon/night-shift/rest day was…") and during non-work activities ("My energy level during non-work activities on a morning/afternoon/night-shift/rest day was…").

• Satisfaction with the work organization (2 items) was evaluated for the entire period by indicating satisfaction with the work schedule ("I evaluate the work schedules for the period...") and with break duration ("In my opinion, the daily work breaks were…") on 6-point Likert-type scales (from 1 "not satisfied" to 6 "very satisfied").

Statistical analysis

The study data correspond to the responses collected with the on-line questionnaire. ATCOs' self-ratings on each of the 15 items (i.e. variables) were considered separately for each study period, and for each shift-type. Raw rating scores were considered for those items rated on 6point scales and sleep duration (for night sleep, day-time sleep, naps, total sleep) was expressed in minutes.

All variables had a normal distribution (except for sleep duration) and were analyzed with 2way repeated measure ANOVAs of study period and shift (morning/afternoon/night-shift/rest day), followed by planned pairwise comparisons. The effects of work organization were assessed by the comparison of the initial shift schedule (period 1) and of the modified schedule (period 3). The effects of traffic load were determined by comparing the high and reduced traffic periods (periods 1 and 2 respectively). Sleep duration data were analyzed with non-parametric statistics (Friedman's test followed by Wilcoxon's test). Pearson's correlation test was used to test for significant associations between two variables. For all statistics, the level of statistical significance corresponded to p < .05.

Results

Effects of traffic density on sleep duration and subjective variables

As expected, results indicated a marked effect of traffic density on most of the variables investigated. 2 and3), and thereafter the total sleep duration over the 24-h day was considered (Figure 1). The duration of the night rest and of the total sleep time were not significantly modified according to traffic density, whereas ATCOs' self-reported satisfaction with the duration of their sleep (Figure 2) varied consistently according to work period (F(2,159) = 6.05, p = .003), with significant higher satisfaction when the traffic load was low (M = 4.39) rather than high (M = 4.08; p < .001). Likewise, satisfaction with sleep quality (Figure 2) was significantly affected by work period (F(2,106) = 4.14, p < .019), and an interaction of work period x shift (F(6,318) = 3.49, p = .002). Satisfaction with sleep quality was lower when the traffic load was high (M = 4.33) rather than reduced (M = 4.54), but this difference fell short of significance (p < .065). The interaction between research period and shift indicated on each research period lower satisfaction prior morning shifts compared to all other shifts and rest days, and prior night and evening shifts compared to rest days, while their satisfaction with sleep quality was comparable for evening and night shifts. Analysis of ATCOs' alertness outside work (Figure 3) revealed a significant effect of research period (F(2,106) = 12.95, p < .001) on alertness upon awakening and an interaction between research period and shift on this variable (F(6,318) = 2.53, p = .02). Alertness was higher with reduced traffic load (M = 4.52) compared to high traffic load (initial shift schedule, M = 4.0, p < .001). The interaction with shift resulted in each research period from significant lower alertness for morning shifts compared to the other shifts and rest days, and on evening shifts and night shifts compared to rest days. ATCOs rated their alertness upon awaking however at comparable levels on evening and night shifts. Alertness during daily non-work activities also differed according to research period (F(2,106) = 7.17, p = .001). As for alertness upon ATCOs' alertness ratings at work (Figure 4) differed significantly between research periods for shift beginning (F(2,106) = 6.41, p < .002) and for shift end (F(2,106) = 6.98, p < .001).

Pairwise comparisons revealed no significant differences for alertness on shift beginning according to traffic load (initial work schedule, low traffic load, M = 4.09; high traffic load, M = 3.96), whereas on shift end ATCOs rated alertness at a significant higher level when traffic load was lower rather than high (respectively, M = 3.08 and 2.47; p < .001). Analyses of ATCOs' on-shift fatigue self-ratings (Figure 4, right panel) also revealed a significant effect of research period (F(2,106) = 6.70, p < .002), with more moments of fatigue when the traffic load was high (M = 4.30) than low (M = 3.65; p < .001).

In addition to sleep and alertness ratings, ATCOs also rated their overall satisfaction with the work schedule and with the breaks scheduled during the shifts. Analyses of the results indicated an effect of research period on both satisfaction measures (F(2,106) = 12.001, p < .001; F(2,106) = 18.37, p < .001 respectively). Satisfaction with the work schedule and break scheduling was increased when the traffic load was reduced (M = 4.50 and M = 4.83, respectively) rather than high (M = 3.61 and M = 3.85, respectively.

Effects of shift-schedule on sleep duration and subjective variables

No effect of shift schedule was observed on sleep duration and satisfaction, nor on alertness.

The duration of the night rest and of the total sleep time (Figure 1

Effects of shift on sleep duration

Table 2 summarizes the percentage of ATCOs taking a nap when they worked either shift-type and on rest days. The table shows that about half of the ATCOs had a nap when they worked a morning shift or a night shift (45% to 50%), but only 10% or less when they worked an evening shift. On rest days, about 25% of the ATCOs took a nap, of an intermediary duration. As the number of ATCOs napping varied considerably according to the shift worked, these data could not be analyzed with statistical tools. The table indicates, however, that no marked apparent differences occurred for the napping behavior according to shift schedule or traffic load.

Table 3. ATCOs' mean nap duration (mn) for the three research periods according to the shift worked and on rest days.

As indicated by the left panel on Figure 1, ATCOs indicated a night rest of about six hours prior to a morning shift and about eight and a half hours prior to an evening and a night shift, and on rest days. The difference between shifts was significant for the three research periods, i.e., when traffic load was high (initial work schedule, X²(3, 56) = 124, p < .001; modified work schedule, X²(3, 52) = 106.99, p < .001), and when traffic load was reduced, X²(3, 54) = 99.69, p < .001).

Post-hoc tests revealed a significantly reduced night rest prior to morning shifts compared to the other shifts and to rest days in each of the three research periods (in all cases, p <.001).

Further, the night rest was longer before a night shift compared to a rest day during the two periods with high traffic independently of the shift schedule (initial shift schedule, p = .003; modified shift schedule, p = .004) and compared to the evening shift worked according to the modified shift schedule (p = .004).

Analyses of the total sleep duration (night rest plus naps; Figure 1, right panel) confirmed the significant differences between shifts during high traffic periods worked with the initial shift schedule (X²(3,56) = 116.13, p < .001) and with the modified shift schedule (X²(3, 52) = 103.02, p <.001), and during the reduced traffic period (X²(3, 54) = 90.46, p < .001). As for the night rest, the total sleep duration in all research periods was significantly reduced prior to morning shifts compared to the evening and night shifts (in all cases, p < .001). While the total sleep duration was enhanced prior to night shifts compared to evening shifts and rest days, in this case systematically in all research periods (in all cases, p < .001), a difference between evening shifts and rest days occurred only when ATCOs worked the modified shift system (p = .032).

Effects of shift on sleep satisfaction, alertness and fatigue

ATCOs' self-reported satisfaction with the duration and the quality of their sleep is illustrated on 3.42; in both cases, p < .001), while no difference occurred between morning and night shifts.

Correlation analyses

Correlation analyses were performed between the different variables in order to test for

Summary of the results

As expected, results revealed beneficial effects when the aircraft traffic load was lower, as indicated by significant reduced moments of fatigue and higher alertness at work and outside worktime, in addition to enhanced sleep satisfaction. In contrast, working the modified work organization did not produce similar positive effects on neither of the subjective measures.

Further, neither work organization, nor traffic load yielded a significant effect on the more objective variable of sleep duration. However, the factor of shift induced a consistent main effect rather than an interaction on all the objective and subjective variables investigated.

Further, while ATCOs reported a shorter sleep duration prior the morning shift compared to the other shifts, they indicated decreased sleep satisfaction and alertness and increased on-job fatigue prior both morning and night shifts compared to evening shifts. Interactions between research period and shift, observed for satisfaction with sleep quality and for alertness upon awakening, confirmed the effects of shift.

Discussion

Assessment of the results with regards to the research questions

In the present study ATCOs were asked to make shift-specific judgments for sleep length and satisfaction, and for alertness and fatigue rather than average judgments or "best case scenarios". They rated separately their on-job alertness and their alertness while doing nonwork activities, given that both work related and non-work related factors have been shown to affect fatigue [START_REF] Nealley | The Effect of Fatigue on Air Traffic Controllers[END_REF] and work load [START_REF] Cascino | An Exploration of Job Perceptions and Health Using an Integrative Approach: A Sample of Air Traffic Controllers Working in a Test Flight Center[END_REF][START_REF] Edwards | Factor interaction influences on human performance in air traffic control: The need for a multifactorial model[END_REF]. Further, workload on each shift was assessed by rating alertness once for shift beginning and once for shift end and by rating on-shift fatigue. This methodology revealed significant differences in particular for sleep duration, sleep satisfaction, and alertness according to shifts (and rest days) and according to traffic load and work organization. A Traffic load induced marked effects on ATCOs' perceptions, in agreement with the literature [START_REF] Corver | Predicting Air Traffic Controller Workload: Trajectory Uncertainty as the Moderator of the Indirect Effect of Traffic Density on Controller Workload Through Traffic Conflict[END_REF][START_REF] Loft | Modeling and Predicting Mental Workload in En Route Air Traffic Control: Critical Review and Broader Implications[END_REF][START_REF] Takahashi | Psychosocial work characteristics predicting daytime sleepiness in day and shift workers[END_REF]Wang and Ké, 2013).

ATCOs reported increased on-shift fatigue and decreased alertness on shift end for the period with high traffic load. The significant increase in fatigue before and after work in ATCOs has been shown to be related to an increase in mental load [START_REF] Triyanti | Workload and Fatigue Assessment on Air Traffic[END_REF]. The results support the idea that controller internal factors including alertness and fatigue mediate the relationship between task demands and the workload experienced by ATCOs [START_REF] Edwards | Factor interaction influences on human performance in air traffic control: The need for a multifactorial model[END_REF][START_REF] Loura | Human Factors and Workload in Air traffic Control Operations -A Review of Literature[END_REF]. End of shift fatigue has thus been accurately predicted in nurses by including work demand variables from organizational data sources and from individual measures [START_REF] Brzozowski | redicting nurse fatigue from measures of work demands[END_REF]. Furthermore, alertness upon awakening and during daily non-work activities was also enhanced in the period with reduced traffic load. These results indicate, though indirectly, that work interfered with ATCOs' general state while they were engaged in non-work activities.

Such interferences have been reported in relation with health complaints [START_REF] Cascino | An Exploration of Job Perceptions and Health Using an Integrative Approach: A Sample of Air Traffic Controllers Working in a Test Flight Center[END_REF] and stress the interest of considering in future shiftwork studies measures that provide information about participants' fitness outside working hours. Moreover, the reported sleep duration did not change according to traffic load, in contrast to the results reported in other studies [START_REF] Åkerstedt | Sleep disturbances, work stress and work hours: A cross-sectional study[END_REF][START_REF] Corver | Predicting Air Traffic Controller Workload: Trajectory Uncertainty as the Moderator of the Indirect Effect of Traffic Density on Controller Workload Through Traffic Conflict[END_REF][START_REF] Nealley | The Effect of Fatigue on Air Traffic Controllers[END_REF][START_REF] Lee | Air Traffic Controllers' Situation Awareness and Workload under Dynamic Air Traffic Situations[END_REF].

However, ATCOs' satisfaction with the duration of sleep was increased during the period with decreased traffic. Further, the more ATCOs were satisfied with the duration and quality of their sleep, the more they declared being alert during the day and also on shift. Taken together, these findings indicate that satisfaction measures may usefully refine sleep duration measures. Lower satisfaction with sleep duration has also been suggested to reflect an anticipatory effect of high workload [START_REF] Mélan | A multidisciplinary approach of workload assessment in real-job situations: Investigation in the field of aerospace activities[END_REF]. This explanation may also account for decreased satisfaction with sleep prior to morning shifts associated with high traffic.

Tangible results were also obtained when ATCOs were asked to rate alertness and sleep according to the shift worked. More especially, the night rest was reduced by more than two hours for morning shifts compared to other shifts and rest days, confirming in this occupational situation the well-established curtailment of sleep by early start of morning shifts [START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF][START_REF] Tucker | The impact of early and late shift changeovers on sleep, health, and well-being in 8-and 12-hour shift systems[END_REF][START_REF] Van De Ven | Associations between shift schedule characteristics with sleep, need for recovery, health and performance measures for regular (semi-)continuous 3-shift systems[END_REF]. Naps increased the total sleep time per 24-h day by approximately one hour for the morning and night shifts, enabling partial recovery from the sleep debt on a day-to-day basis. Total sleep time remained significantly shorter for morning shifts while it was enhanced for night shifts compared to rest days. Garde and co-workers (2020) reported shorter sleep for night shifts compared to recovery days. However, recovery days included both day shifts and rest days, which may have resulted in a lower mean sleep duration than the one that might be expected when only rest days are considered. Further, in their study night shifts lasted 8h whereas they lasted 10h in the present study, suggesting that the longer sleep duration reported here for the night shift may be attributed to the combined effects of time-of-day effects (circadian nadir) and of time-on-task factors [START_REF] Folkard | Shiftwork, safety and productivity[END_REF][START_REF] Lee | Air Traffic Controllers' Situation Awareness and Workload under Dynamic Air Traffic Situations[END_REF][START_REF] Sonati | Quality of Life, Health, and Sleep of Air Traffic Controllers with Different Shift Systems[END_REF]. Clearly, night shifts are associated with a high need for recovery which needs to be satisfied in order to maintain efficient cognitive functioning over time [START_REF] Sluiter | Need for recovery from work related fatigue and its role in the development and prediction of subjective health complaints[END_REF][START_REF] Härmä | Workhours in relation to work stress, recovery and health[END_REF][START_REF] Sallinen | Shift work, sleep, and sleepiness -differences between shift schedules and systems[END_REF] and health [START_REF] Costa | Shift work and health: current problems and preventive actions[END_REF]Wang and Ké, 2013).

Further, naps on rest days also probably provided an opportunity to recover on a weekly basis by compensating short night sleep on workdays (Åkerstedt et al., 2018). Indeed, 25% of the ATCOs had a nap on rest days and about 50% when they worked morning or night shifts.

This result agrees with a survey reporting that 57% of ATCOs had a nap when they worked

Study limitations

night shifts [START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF]. However, in Costa's study ATCOs reported sleeping roughly one hour more prior to morning shifts and one hour less following night shifts than the ATCOs reported on equivalent shifts in the present study. Unlike the work organization in the present study, shifts were scheduled according to ergonomic criteria, including late morning shift start, napping opportunities during night shifts, and shorter night shifts. Though methodological differences may contribute to the discrepant results, the data highlight the finding that shiftwork scheduling according to ergonomic criteria improves quality of life in shift-workers [START_REF] Khaleque | Sleep deficiency and quality of life of shift workers[END_REF][START_REF] Knauth | Designing better shift systems[END_REF]. More especially, redesigning better sleeping arrangements may improve sleep quality and thus daytime alertness and performance [START_REF] Iridiastadi | Fatigue in the Indonesian rail industry: A study examining passenger train drivers[END_REF]. Rest breaks are also associated with reductions in on-job sleepiness [START_REF] Onninen | Sleep and sleepiness in shift-working tram drivers[END_REF]. According to When-Chin and co-workers (2020), sufficient rest breaks and roster schedule optimization represent first-line countermeasure strategies, while monitoring ATCOs' task loads (i.e. traffic volume) is a secondary strategy.

Subjective measures refined the interpretation of self-reported sleep duration. They indicated a systematically lower satisfaction with sleep quality and duration prior to morning shifts, associated with lower alertness during non-work activities. Whereas on-job alertness and fatigue were comparably low on both morning and night shifts, sleep duration was shorter for morning shifts than for night shifts. Accordingly, the effects of night shifts on work activities appear to be as disruptive as those of early morning shifts despite the longer sleep length associated with night shifts. This finding contrasts with studies reporting concurrent decreases in objective and subjective sleep indicators [START_REF] Åkerstedt | Sleep Loss and Fatigue in Shift Work and Shift Work Disorder[END_REF][START_REF] Åkerstedt | Shift work and disturbed sleep/wakefulness[END_REF][START_REF] Juda | Chronotype Modulates Sleep Duration, Sleep Quality, and Social Jet Lag in Shift-Workers[END_REF][START_REF] Van De Ven | Associations between shift schedule characteristics with sleep, need for recovery, health and performance measures for regular (semi-)continuous 3-shift systems[END_REF], raising the possibility that the subjective satisfaction ratings used in the present study were inadequate to assess shift-work effects on sleep. In this respect, Berasteguia and colleagues showed that sleep-deprived individuals or people functioning under adverse circadian phase tend to underestimate fatigue-related impairments [START_REF] Berastegui | Fatigue-related risk perception among emergency physicians working extended shifts[END_REF]. They found no significant association between subjective sleepiness and time since awakening. On the other hand, subjective sleep variables, but not objective sleep duration, were positively correlated with on-job alertness, alertness upon awakening and while performing extra-professional activities and negatively correlated with moments of fatigue on duty. Taken together, these findings raise the possibility that objective and subjective sleep measures may assess different aspects of sleep.

In the present study, there are several methodological issues that need to be mentioned.

Due to the closing date of the data collection fixed by the ATC authorities, it was unfortunately impossible to include in the study design a reduced traffic period worked according to the new work schedule. This would have made it possible to explore the effects of traffic load when ATCOs worked the modified shift schedule. In addition, the concurrent change of several aspects of the work organization did not enable a detailed analysis of the respective contribution of each shift work feature to the above reported effects. Interpretation of the effects of specific aspects of a shift schedule was also complicated by the fact that studies in the literature mostly assess issues of major modifications to the shift system, such as densification of shifts or forward-vs. backward rotations. Comparisons are made even more difficult by the erratic work schedules in the field of air traffic control, with variable start and stop times for day, evening, and night times. Such irregular controller work schedules are known to induce fatigue (FFA, 2013). Further, retrospective self-ratings may not adequately report participants' momentary state, even more so when non-validated tools are used. Self-rated fatigue and alertness do not assess all the aspects of workload, i.e. the processes involved by task demands (planning, decision making, monitoring), internal factors (skills, training, experience, fatigue, various stressors), and individual characteristics [START_REF] Costa | Working and health conditions of Italian air traffic controllers[END_REF][START_REF] Loura | Human Factors and Workload in Air traffic Control Operations -A Review of Literature[END_REF][START_REF] Nealley | The Effect of Fatigue on Air Traffic Controllers[END_REF][START_REF] Wilson | Understanding fatigue in a naval submarine: Applying biomathematical models and workload measurement in an intensive longitudinal design[END_REF].

Concluding remarks

The present findings support the idea that reorganization of shift schedules should consider the well-known effects of circadian disruption induced in particular by early morning

  alertness and fatigue (15 items) while the results concerning the nine remaining items are not detailed in the present report as they relate to other dimensions, i.e. quality of work life (team atmosphere, overall quality of work life), workload and stress (overall workload, perceived stress on shift beginning and end and across the shift) and quality of non-work life (atmosphere in personal and family lives, conciliation between work and non-work activities, overall quality of life). The three sections of the questionnaire were completed outside working time in about 15 to 20 minutes altogether. • The assessment of sleep concerned both the duration of sleep (6 items) and the quality of sleep (2 items), rated separately for each shift and on rest days. The overall duration of sleep across the 24 h day was assessed by including nocturnal sleep (bedtime and waking hour) and diurnal sleep after night-shifts and naps (onset time and duration).

Figure 1 .

 1 Figure 1. Night sleep duration (left panel) and total sleep duration (night rest and naps, right panel) expressed in minutes (M/S.D.) for the three research periods according to the shift worked and on rest days.

Figure 2 .

 2 Figure 2. Self-rating scores (M/S.D.) of satisfaction with the quality (left panel) and the duration (right panel) of their night rest according to the shift worked and on rest days, for the three research periods.

Figure 3 .

 3 Figure 3. Alertness upon awakening (M/S.D., left panel) and during daily non-work activities (right panel) for the three research periods according to the shift worked and on rest days.

  in non-work activities was significantly enhanced when the traffic load was low (M = 4.36) rather than high (M=3.93, p < .001).

Figure 4 .

 4 Figure 4. Alertness on shift beginning (M/S.D., left panel) and on shift end (middle panel) and fatigue during the shift (right panel) for the three research periods and the shift worked.

  schedule, dense traffic initial shift-schedule, reduced traffic modified shift-schedule, dense traffic Alertness on shift beginning and shift end and moments of fatigue during the shifts (M/S.

  ) were not significantly modified according to shift-schedule. Likewise, no effect of shift schedule occurred on satisfaction with sleep duration (initial schedule, M = 4.09; experimental schedule, M = 4.12) and on satisfaction with sleep quality (initial schedule, M = 4.33; experimental schedule, M = 4.26; Figure 2). As indicated on Figure 3, no significant change occurred for alertness upon awakening (initial schedule, M = 4.01; experimental schedule, M = 4.05) and during daily non-work activities (initial schedule, M = 3.93; experimental schedule, M = 4.04). ATCOs' alertness ratings at work (Figure 4) for the beginning (initial schedule, M = 3.97; experimental schedule, M = 3.59) and end of shift (initial schedule, M = 2.47; experimental schedule, M = 2.78), and for on-shift fatigue self-ratings (Figure 4, right panel; initial schedule, M = 4.30; experimental schedule, M = 4.14) also revealed no significant change with work organization. Further, neither their overall satisfaction with the work schedule (initial schedule, M = 3.61; experimental schedule, M = 3.76) nor their overall satisfaction with the breaks scheduled during the shifts (initial schedule, M = 3.85; experimental schedule, M = 4.30) differed according to work organization.

Figure 2 .

 2 Statistical analyses revealed a main effects of shift (F(3,159) = 133.41; p < .001) that resulted from a markedly lower satisfaction with sleep length prior to morning shifts (M = 2.60) than prior to evening shifts (M = 4.41), night shifts (M = 4.73), and on rest days (M = 5.06) (in each case, p <.001). ATCOs were also less satisfied with the duration of the sleep that preceded a night shift (p = .008) than the one preceding an evening shift, and when they worked an evening (p < .001) or a night shift (p = .001) compared to rest days. Satisfaction with sleep quality also differed according to shift (F(3,159) = 91.20), p < .001), indicating lower satisfaction with the quality of sleep on morning shifts (M = 3.05) compared to evening shifts (M = 4.62), night shifts (M = 4.72), and rest days (M = 5.11), and on evening and night shifts compared to rest days (in all cases, p < .001), as was observed for satisfaction with the duration of sleep. However, unlike for the latter, ATCOs rated the sleep quality at the same level for evening and night shifts. ATCOs' self-ratings of alertness upon awakening, illustrated by the left panel of Figure 3, differed according to the shift worked (F(3,159) = 89.35, p < .001), with lower alertness for morning shifts (2.93) than for evening shifts (4.36), night shifts (4.53), and rest days (4.95), and on evening shifts and night shifts compared to rest days (for all comparisons, p < .001). Alertness upon awaking did however not differ between evening and night shifts. The effects of shift on alertness during daily non-work activities (Figure 3, right panel) (F(3,159) = 64.77, p < .001) resulted again from significantly lower alertness when ATCOs worked morning shifts (M = 3.0) than any other shift (respectively, evening shift 4.27 and night shift 4.19) or on rest days (M = 4.98), and on evening and night shifts compared to rest days (in all cases, p < .001), except again for similar alertness levels on evening and night shifts. ATCOs' ratings of alertness for shift beginning (Figure 4, left panel) differed significantly between shifts (F(2,106) = 52.30, p < .001), indicating significant lower alertness (p <.001) on morning shifts (M = 2.97) compared to evening (M = 4.36), and night shifts (M = 4.32), and comparable alertness levels on evening and night shifts. Alertness on shift end also varied between shifts (F(2,106) = 24.12 p < .001; Figure 4, middle panel), and this time alertness was significantly decreased both on morning (M = 2.48) and night shifts (M = 2.42) compared to evening shifts (M = 3.44; in both cases, p < .001). The effect of shift on ATCOs' self-ratings of on-shift fatigue (F(02,106) = 24.02, p < .001; Figure 4, right panel) resulted from increased fatigue on morning (M = 4.53) and night shifts (M = 4.13) compared to evening shifts (M =

  relationships in particular between sleep duration and sleep satisfaction. Results indicate that sleep duration (night sleep and total sleep) was not correlated with sleep satisfaction (duration and quality) or any alertness measure (results not shown). However, sleep satisfaction measures (Table 4) were positively correlated with the different alertness measures (upon awakening, during extra-professional activities, on shift-beginning, on shift end), independently of shift and research period, except for alertness at the end of the night shift (satisfaction with sleep duration). Conversely, the subjective sleep indicators were negatively correlated with fatigue during the shift when ATCOs worked either shift with the initial shift organization or night shifts of the modified shift system.

  The modified work organization did not produce the expected beneficial effects, as results did not indicate an improvement in ATCOs' perceptions consecutively to the intervention. Rather, ATCOs indicated sleeping more prior to night shifts than prior to evening shifts while working the experimental work organization compared to the initial work organization. On the one hand, this was unexpected as the duration per se of the night shift was similar in both work organizations. On the other hand, the number of teams working the night shift was reduced in the modified shiftwork schedule and work breaks were much shorter. From this point of view, the work conditions had worsened and may explain an increased need for sleep prior to the night shift. Alternatively, this and other results concerning the modified work organization (longer sleep on rest days, low sleep satisfaction for night shifts) might reflect ATCOs' disagreement with the schedule change. The work schedule modifications proposed by the flight center authority aimed to achieve a better fit with traffic load. Informal discussions with several ATCOs highlighted that their main expectation was different, i.e. to arrange the work conditions during the very difficult night shift, in order to lessen the risk of extreme fatigue. Hence, this expectation was not considered in the work reorganization process and work conditions actually worsened. Taken together these considerations suggest, in agreement with several intervention studies, that participants' expectations and attitudes towards a shift schedule change may affect the expected results (van de Ven et al., 2016).

  shifts and by night work. They demonstrate that a work reorganization that favors sleep loss across a shift cycle, for instance by replacing a rest day by a work shift or by reducing the duration of work breaks and thus of napping during the nightshift, has deleterious consequences on alertness and increases the need for recovery. Other work-related factors, and in particular the workload induced by the density of the air traffic to be controlled, also enhance fatigue and reduce alertness, increasing the need for recovery across a work-cycle. Subjective measures proved to be very useful in assessing ATCOs' perceptions of alertness beyond the more objective measure of sleep duration. The findings indicate that managers should define shift systems based on ergonomic criteria in order to minimize sleep loss and allow appropriate recovery (on rest days), and ultimately ensure safety and security, in particular in safety-related job situations.

Table 2 .

 2 Percentage of ATCOs having naps for the three research periods according to the shift worked and on rest days.

	% of ATCOs having a nap
		Morning	Evening	Night
		shift	shift	shift	Rest day
	Initial shift schedule, dense traffic	45.61	10.53	56.14	28.07
	Initial shift schedule, reduced traffic	45.61	7.02	50.88	21.05
	Modified shift schedule, dense traffic	50.88	7.02	56.14	26.32

Table 3

 3 indicates a longer mean duration of naps when ATCOs worked a morning or a night shift (one hour at least), compared to days they worked an evening shift (around 20 minutes).

Table 4

 4

			Initial shift schedule, dense traffic
			Alertness	Alertness	Fatigue	Alertness	Alertness
			shift start	shift end	on shift	awakening	activities
		M	0.465**	0.427**	-0.481**	.588**	.642**
	Satisfaction	E	0.627**	0.487**	-0.323*	.787**	.621**
	with sleep duration	N	0.446**	0.185	-0.430**	.624**	.471**
		R	/ /	/ /	/ /	.655**	.642**
		M	0.431**	0.339*	-0.334*	.656**	.513**
	Satisfaction with sleep quality	E N	0.631** 0.456**	0.442** 0.118	-0.238 -0.372**	.555** .566**	.621** .495**
		R	/ /	/ /	/ /	.576**	.632**
			Initial shift schedule, reduced traffic
			Alertness	Alertness	Fatigue	Alertness	Alertness
			shift start	shift end	on shift	awakening	activities
		M	.609***	548***	-0.471***	.803***	.680***
	Satisfaction with sleep duration	E N R	664*** .607*** / /	.523*** .301* / /	-0.461*** -0.447*** / /	.834*** .808*** .788***	.759*** .701*** .526***
		M	.526**	.401**	-.377***	.733***	.632***
	Satisfaction with sleep quality	E N R	.661** .583** / /	.532*** .244 / /	-.521*** -.409** / /	.719*** .727*** .784***	811*** .670*** .489***
			Modified shift schedule, dense traffic
			Alertness	Alertness	Fatigue	Alertness	Alertness
			shift start	shift end	on shift	awakening	activities

. Results of correlation analyses between subjective sleep indicators (satisfaction with sleep duration and sleep quality) and various indicators of alertness and of on-job fatigue on morning shifts (M), evening shifts € and night shifts (N). Statistical significance: * p < .05; ** p < .01; *** p < .001.

Acknowledgments

This project was supported by the French air navigation agency (Direction Générale de l'Aviation Civile, France). We thank the head of the Department of the air flight center for providing access to the flight center. We also thank the air traffic controllers for their participation.

Declaration of interests

The authors declare no competing interests.

Effects of a modified shift work organization and traffic load on air traffic controllers' sleep and alertness during work and non-work activities

Claudine Mélan, Nadine Cascino

Declaration of interests

The authors declare no competing interests.


Benjamin Reichert

Jean-Benoît Le Cam

Arnaud Saint-Jalmes

Giuseppe Pucci

Self-propulsion of a volatile drop on the surface of an immiscible liquid bath

We demonstrate the self-propulsion of a volatile drop on the surface of a bath of an immiscible liquid. Evaporative heat pumping is converted into directed motion through thermo-capillary stresses, which arise from the coupling between surface-tension-driven flows and temperature advection. A propulsive force arises from convection-sustained temperature gradients along the drop interface, resulting in a warmer pool of liquid being advected by the hydrodynamic flow in the underlying bath toward the back of the drop. The dependence of the drop speed on the activity source, i.e. the evaporation flux, is derived with scaling arguments and captures the experimental data.

Drop evaporation is a key phenomenon in industrial and healthcare applications such as inkjet printing, aerosol dynamics and disease transmission [1,2]. Evaporation is also involved in everyday life phenomena, as the levitation of droplets above a cup of hot tea [3,4], the Leidenfrost [START_REF] Leidenfrost | De aquae communis nonnullis qualitatibus tractatus[END_REF] and the coffee-stain effects [START_REF] Deegan | [END_REF]. When evaporation is forced by a hot substrate, drops may levitate [4,[START_REF] Leidenfrost | De aquae communis nonnullis qualitatibus tractatus[END_REF]7] and even self-propel on the asymmetric vapor layer separating them from the substrate [8]. Drop self-propulsion may also occur in liquid bulk due to surface-tension gradients located at the drop's interface and known as Marangoni gradients [9]. These gradients usually have solutal origin and are often derived from theoretical postulates since they are difficult to probe [10][11][12][13][14]. The free surface of a liquid bath is a suitable platform for the self-propulsion of artificial bodies [15][16][17][18][19], including drops [20][21][22], and enable direct probing of flows [15,23,24] and concentration gradients [18]. Furthermore, recent works demonstrated that when a liquid free surface hosts a volatile immiscible liquid, evaporation is spontaneously converted into Marangoni gradients [25,26].

In this Letter, we demonstrate that the evaporation of a volatile drop floating on a liquid bath is converted into drop propulsion. We benefit from the drop location at the interface to experimentally characterize the surface temperature field, and thus Marangoni gradients, hydrodynamic flows and evaporation flux, which is the activity source. This allows us to rationalize the coupling between thermal transfers and hydrodynamic flows that govern selfpropulsion. Evaporative cooling engenders thermocapillary stresses and propulsion is triggered by a thermocapillary convective instability. Asymmetric stresses emerge on the drop interface as a result of the nonlinear interplay between Marangoni flow and temperature advection, which spontaneously breaks the symmetry of the drop temperature field. Temperature gradients are convection-sustained and give rise to a propulsive force via the permanent advection of warmer liquid from the underlying bath toward the back of the drop. liquid (liquid 1) floating on a bath of immiscible liquid (liquid 2) (Fig. 1). We denote ρ 1 (ρ 2 ), γ 1 (γ 2 ) and η 1 (η 2 ) the density, surface tension and dynamic viscosity of liquid 1 (liquid 2), respectively. γ 12 is the interfacial tension between liquid 1 and 2. We tested different liquid pairs and drop sizes (Sec. I in [27]) and observed that all drops initially stay still for ∼ 1 minute, then spontaneously set into motion with speed v ∼ 0.01 -0.1 mm.s -1 . As a result, it may take several minutes to detect the drop displacement with the naked eye. We focused on pancake-like drops with R ∼ 1 cm and h ∼ 1 mm, where h is the drop thickness (Fig. 1), the shape of which is due to the dominant effect of gravity with respect to capillarity [START_REF] De Gennes | Capillarity and wetting phenomena[END_REF]. The bath depth was fixed to H = 10 cm. We identified two propulsion behaviors differing in the trajectory's features. In the first, the drop motion is erratic with persistence length l < ∼ R (Fig. 1(a)), where l defines the typical distance over which the active particle loses information about its initial orientation [START_REF] Zöttl | [END_REF]. In the second, the trajectory is straighter with l R and the drop achieves a stationary speed after a transient acceleration phase (Fig. 1(c)). The second behavior is observed when a film of liquid 2 coats the drop. This film substantially attenuates surface temperature fluctuations, which are responsible for the erratic motion in the first behavior (Sec.V and Supplemental Movies 1, 2 in [27]). The presence of the film thus makes the system more tractable both experimentally and theoretically.

The experimental system consists of a drop of volatile

We focus on the second type of behavior and choose the pair ethanol/silicone oil (liquid properties in Sec.I in [27]). Thermal imaging and particle tracking velocimetry (PTV) (Secs. III, IV in [27]) were used to characterize the system temperature and velocity fields during the static (Fig. 2(ac)) and steady propulsion (Fig. 2(d-f)) phases for η 2 = 0.097 Pa.s. Once the drop is deposited onto the bath, the siliconeoil film develops on its surface within ∼ 100 ms and ethanol pervaporates by diffusing through the film (Fig. 2(c)). The drop cools down and displays axisymmetric flow and temperature fields (Fig. 2(a,b)), with average radial temperature gradient (T ++ -T --)/R > 0, where T ++ -T --5 K (Fig. 2(b,c)). T ++ and T --denote the highest and lowest temperature in the system throughout its dynamics. Two inward flows develop close to the upper and lower interfaces and an outward flow develops in the drop's bulk (Fig. 2(a,c)). Flow reversal occurs at the drop's axis of symmetry (Oz). In the oil, the flow is inward near the drop's lower interface and deviates downward in the vicinity of the drop's axis of symmetry (Fig. 2(a,c)). These flows are driven by interfacial stresses arising from the variation of interfacial tension with temperature along the radial direction. These Marangoni stresses are denoted ∇ (0) (γ 12 + γ 2 ) and ∇ (0) γ 12 for the upper and lower interfaces, respectively, and are directed toward the drop's center (Fig. 2(c)). The index (0) refers to the flow generated by these stresses, which remains the base flow throughout the drop dynamics. About one minute after drop deposition, thermal images reveal a symmetry breaking of the temperature field. A crescent-like cold patch with average temperature T -- appears in the vicinity of the drop horizontal contour (Fig. 2(e)). The angular extension of the patch, α, increases with time up to a stationary value α max (Fig. 3(c)). PTV shows that the zone of flow reversal shifts accordingly (Fig. 2(d,f)). Correspondingly, the drop starts moving in the direction opposite to the displacement of the patch, along the average temperature gradient (x direction in Fig. 2(e,f)).

In order to rationalize the mechanics of self-propulsion, we note that the Reynolds number comparing advection to viscous transport of momentum in the bath is Re = ρ 2 vR/η 2 ∼ 10 -2 with η 2 =0.1 Pa.s. We thus use the Stokes equation and describe the global flow during the stationary propulsion (Fig. 2(d,f)) as the superposition of an order (0) symmetric flow and an order (1) perturbation flow. The order (1) flow is associated to the average temperature difference ∆T = T ++ -T + 1 K between the fore and the aft of the drop. ∆T induces Marangoni stresses at the upper and lower interfaces that drag liquid from the fore to the aft, and are responsible for the displacement of the region of flow reversal (Fig. 2(f)). We develop our model in the laboratory frame of reference. In order to derive a scaling law for the drop stationary speed, we consider the x-component of the forces experienced by a cylindrical control volume of radius R and thickness h containing the drop (Fig. 2(e,f)). These forces arise as a result of the perturbative flow outside the drop, which is the sum of two flows (Fig. 2(f)). The first flow is the Stokes flow associated with the motion of a viscous disc in a quiescent fluid without Marangoni effect [30,31]. This yields the Stokes viscous drag F St ∼ -η 2 Rv s < 0 [START_REF] Guyon | Physical hydrodynamics[END_REF], with constant prefactor as (h/R), (η 1 /η 2 ) 1 [30,31,[START_REF] Kim | Microhydrodynamics: principles and selected applications[END_REF]. We denote u St > 0 the characteristic velocity of the Stokes flow in the x direction close to the lower interface in liquid 2 (Fig. 2(f)).

The second flow is due to the Marangoni stresses at the interface of a drop that is at rest with respect to the bath. We denote ∇ (1) γ 2 and ∇ (1) γ 12 the gradients at the upper and lower interfaces, respectively, which generate two forces. A first force is the result of the inhomogeneous, radial and outwardly pulling tension γ 2 [T (θ)] due to azimuthal temperature variations. It applies to the closed contour C (Fig. 2(e)) and reads ). F cam is the thermal analog of the force that drives camphor boats towards zones with lower surfactant concentration [35], but here F cam < 0 opposes the drop motion. A second force results from the Marangoni stress ∇ (1) γ 12 at the drop's lower interface, which induces a viscous stress response in the underlying bath that is oriented in the drop's direction of motion. The drop gains traction from the bath in order to propel. We denote u

F cam = C γ 2 • x dl = S ∇ (1) γ 2 • x dS ∼ - |dγ/dT |∆T R πR 2 , ( 1
(1) M < 0 the characteristic velocity of the perturbed flow in the x direction close to the lower interface in liquid 2 (Fig. 2

(f)). This flow produces a strain rate ∼ |u

(1) M |/R [36] and the resulting force on the lower side of the control volume reads

F prop ∼ η 2 |u (1) M | R • πR 2 . ( 2
)
The problem is thus reduced to computing u

M . In our experiments, viscous stress inside the drop is negligible with respect to its counterpart in the outer liquid, η 1 /h η 2 /R. Therefore, the continuity of stresses at the lower interface yields u

(1) M ∼ -|dγ/dx|R/η 2 ∼ -|dγ/dT |∆T /η 2 (Sec.VI in [27]). Substituting this expression in (2) we obtain F prop ∼ |dγ/dT |∆T R > 0. F prop has the same scaling as F cam , but opposite direction. Since the drop is moving in the direction of F prop , we may write

F prop + F cam ∼ |dγ/dT |∆T R > 0.
A scaling for the stationary speed is derived by balancing this expression with F St , which yields

v s ∼ dγ dT ∆T η 2 . (3)
In order to derive a scaling for ∆T , we analyze how evaporation energy is converted into liquid motion. We simultaneously measured the drop speed v(t), the angular extension of the cold patch α(t) and the evaporation flux J(t) for drop volume V = 0.4 ml and η 2 = 0.097 Pa.s (Fig. 3). The drop is deposited on the bath at t = 0 s and starts moving at t = 74 s. After a transient regime of acceleration, the drop achieves a stationary speed v s . We measure J(t) = -dV (t)/dt/A(t), where A(t) = πR 2 (t) is the area and V (t) = hA(t) is the drop volume (Sec.II [27]). v(t), α(t) and J(t) exhibit similar time scales of evolution toward the stationary regime, which suggests that v(t) is correlated to α(t) and J(t). We focus on the stationary regime and calculate how v s scales with the thermal evaporation flux, ρ 1 L v J s , where L v is the latent heat of evaporation of ethanol. We perform a thermal flux balance to relate ∆T to the heat flux of evaporation. u

(1) b = u (1)
M + u St < 0 is the characteristic velocity of the perturbed flow in the x direction. Heat transport in the bath is governed by two processes, convection and diffusion, the relative importance of which is quantified by a thermal Péclet number for each component of the flow, P e (0) = Ru ≈ 0.05 mm.s -1 for η 2 = 0.097 Pa.s, we obtain P e (0) ≈ 9 and P e (1) ≈ 4, which suggest that convection is dominant. The temperature difference ∆T is sustained by the cooling of fluid particles that move backward in the vicinity of the drop's upper interface, driven by the thermal evaporative flux ρ 1 L v J s . This temperature difference induces thermal convection in the underlying bath, ρ 2 C p ∆T |u

ρ 2 C p ∆T |u (1) b | = c ρ 1 L v J s , (4)
where c represents the fraction of thermal evaporation flux that is converted into the convective heat flux of the perturbed flow. By substituting u

≈ 0.05 mm.s -1 , J s = 1.2 × 10 -6 m.s -1 and ∆T 1 K from experiments in (4), we found c = 0.08, which suggests that the evaporation flux is not modified by the drop propulsion at leading order. Furthermore, we note that u St ∼ v s for Stokes flow past a viscous body in the limit

η 1 /η 2 1 [32]. Since u (1)
M and v s have the same scaling (cf.( 3)) then u

(1) b ∼ -|dγ/dT |∆T /η 2 . We thus obtain ∆T ∼ [η 2 ρ 1 L v J s /ρ 2 C p |dγ/dT |]
1/2 , that combined with (3) yields the scaling of the drop stationary speed with the stationary evaporation flux

v s ∼ [ρ 1 |dγ/dT |L v J s /ρ 2 η 2 C p ] 1/2 .
We now focus on the transient regime, characterized by an increasing angular extension α(t) of the cold crescent over the typical time τ ∼ 100 s (Fig. 3(b,c)). Since τ is much larger than the time scale of viscous diffusion of momentum in the bath, τ v = ρ 2 R 2 /η 2 ∼ 1 s, we consider the velocity field in the bath as quasi-stationary. Consequently, the scaling of v s can be extended to the transient regime by considering a geometrical factor g[α(t)] that takes into account the time evolution of the cold crescent-like patch (Fig. 3(c)). During the transient regime, ∇ (1) γ 2 and ∇ (1) γ 12 apply to the area S tr (α) = 2g(α)R 2 at the upper and lower side, respectively, of a time-varying control volume with g(α) = α/2 + cos(α/2) sin(α/2). S tr is a fraction of the total drop surface πR 2 and its contour is represented in Fig. 3(c). A force balance on the time-varying control volume gives

v(t) = βg(α) ρ 1 |dγ/dT | L v J(t) ρ 2 η 2 C p 1/2 . ( 5
)
Using the experimental J(t) in Fig. 3(b) this expression yields a reasonable fit to the experimental speed with β = 0.087 (red line in Fig. 3(a)). For α = α max we recover the stationary regime.

We now elucidate the nature of the activity source, i.e. the evaporation flux J. Drop evaporation is limited by vapor transport in air. The measured evaporation flux exceeds the diffusive flux of evaporation of an ethanol disk with radius R, j diff air = 4D 1 ρ sat /πRρ 1 [START_REF] Crank | The mathematics of diffusion[END_REF], where ρ sat is the saturation vapor density and D 1 is the diffusion coefficient of ethanol in air (Fig. 3(b)). This suggests that both diffusion and convection are involved in the evaporation process (Fig. 4(b)). The magnitude of the evaporative flux is determined by the order (0) flows associated to the temperature difference T ++ -T -- 5 K, which differs by no more than 1 K across bath viscosities. Convection in the air is driven by the drop upper interfacial flow, the speed of which can be tuned by varying the bath viscosity η 2 . We measured the variation of J s and v s with η 2 for drops with radii R = 4.0 mm and R = 8.0 mm (Fig. 4). η 2 J s is an affine function of η 2 (inset Fig. 4(a)), thus J s = a + b/η 2 . We identify a as the diffusive term and b/η 2 as the convective term. Their decoupling is typical for mass or heat transfer from a body immersed in a flow with low Re and P e up to O(1) [START_REF] Acrivos | [END_REF]. The order of magnitude of the fitting parameter a (Fig. 4(a)) is captured by j air diff = {6.4 × 10 -7 ; 3.2 × 10 -7 } m.s -1 for R = {4.0 ; 8.0} mm. The term b/η 2 results from a nontrivial coupling between the inner and outer flow through Marangoni stresses at the drop interface (Sec.VII [27]). The dependence on 1/η 2 is a signature of the dominant effect of outer shear stress over inner drop recirculation on the interfacial velocity for η 2 η 1 . The combination of the fit J s = a + b/η 2 with (5) with fixed β = 0.087 and g(α max ) yields

v s = β g(α max ) ρ 1 |dγ/dT | L v (a + b/η 2 ) ρ 2 η 2 C p 1/2 , (6)
which captures the dependence of the stationary speed on bath viscosity (Fig. 4(a)). This result demonstrates that both diffusion and convection are involved in the drop activity. Furthermore, equation ( 6) captures the experimental data for both radii. The dependence of drop speed on ra-dius is contained in the evaporative flux J s , which decreases with R. This is discussed in detail in Supplemental Material along with the dependence of self-propulsion on bath depth (Secs. VIII, IX in [27]). We investigated the spontaneous motion of a volatile drop on a liquid bath. This system allows direct probing of the physical origin of surface-tension gradients, which is quite unique in the context of active drops [11][12][13] and has allowed us to rationalize the propulsion mechanism. A propulsive force results from Marangoni stresses that arise at the drop's lower interface from convection-sustained temperature gradients. The direction of motion is opposite to the interfacial tension gradients and thus to a Marangoni surfer [17,35,39]. Since the drop develops tangential stresses in order to propel, it can be considered a twodimensional squirmer [40][41][42]. A recent work has shown that the combination of evaporation-induced wetting transition and Marangoni stresses of solutal origin triggers the spontaneous emulsification of a volatile drop on the surface of a liquid bath [26]. Spontaneous emulsification and selfpropulsion are the two essential ingredients for the design of interfacial active emulsions [42]. B.R. and G.P. thank the program CNRS Momentum for its support. The authors thank Isabelle Cantat and Adrien Bussonnière for useful discussions.

Figure 1 .

 1 Figure 1. Self-propulsion behaviors of volatile drops on liquid baths. First behavior: (a) the trajectory is erratic with l < ∼ R (top view) when the drop is in contact with air; (b) schematic side view, not to scale. Second behavior: (c) the trajectory is straighter with l R (top view) when a film of liquid 2 covers the drop; (d) schematic side view. (a) Drop of 90%v/v ethanol in water. (c) Ethanol drop. (a,c) Silicone oil bath with η2 = 0.097 Pa.s.

Figure 2 .

 2 Figure 2. Static symmetric (a-c) and propulsive asymmetric (d-f) state of an ethanol drop on a bath of silicone oil. (a,d) Streamlines resulting from 15 seconds of PTV (side view). (b,e) Surface temperature field (top view), with T ++ > T + > T -> T --. (c,f) Side view schematics. White arrows indicate flows. Blue and red arrows indicate Marangoni stresses associated to base and perturbed flow, respectively. (e,f) Dashed lines delimit the control volume used for the force balance. (a,d) R = 4.0 mm. (b,e) R = 8.0 mm. η2 = 0.097 Pa.s.

  ) where S is the area of the upper side of the control volume (Fig. 2(e)). Here and in the following we assume |dγ/dT | ∼ |dγ 2 /dT | ∼ |dγ 12 /dT | [34] (Sec.I [27]

Figure 3 .

 3 Figure 3. Time evolution of drop speed, evaporation flux and field. (a) ( * ) Experimental drop speed v(t), with vs the stationary speed. The solid line (-) results from (5) combined with the evaporation flux J(t) in (b). (b) Experimental evaporation flux J(t) (-) and angular extension α(t) (+) of the cold patch. Js is the stationary evaporation flux and αmax is the maximum angle. j diff air is the diffusive evaporation flux of an ethanol disk with radius R. (c) Temporal evolution of the surface temperature field (Supplemental Movie 1 [27]). The dashed line delimits the upper side of the control volume in the transient regime. R = 8.0 mm, η2 = 0.097 Pa.s.

  th and P e(1) = Ru

( 1 )

 1 b /D th . D th = λ 2 /ρ 2 C p is the thermal diffusion coefficient, with C p and λ 2 the thermal capacity and conductivity of silicone oil. For R ≈ 8 mm and measured velocities u (0) b ≈ 0.13 mm.s -1 and u (1) b

( 1 )

 1 b |, from the fore towards the aft of the drop. The heat flux balance reads

Figure 4 .

 4 Figure 4. Relation between drop speed vs and evaporation flux Js in the stationary regime. (a) vs vs. bath viscosity η2. Lines represent the scaling in (6) combined with the fits in the inset. Inset: lines represent fits of aη2+b. R = 4.0 mm: ( ), continuous lines and (a, b) = (4.1 × 10 -7 m.s -1 , 9.2 × 10 -8 m.Pa). R = 8.0 mm: (o), dashed lines and (a, b) = (3.3 × 10 -7 m.s -1 , 7.1 × 10 -8 m.Pa). (b) Side view schematic. White arrows indicate flows.