domain: sde spi

text:
Sylvain Dupire
email: sylvain.dupire@irstea.fr

Franck Bourrier
email: franck.bourrier@irstea.fr

Frédéric Berger
email: frederic.berger@irstea.fr

Predicting load path and tensile forces during cable yarding operations on steep terrain

Keywords:

Cable yarding systems constitute an adapted solution for steep-slope harvesting in mountain forests. However, it requires many specific skills for both forest managers and operators. The objectives of this research were to 1) develop CableHelp model for the set-up of cable yarding systems where inputs are operational field data and outputs are load path and tensile forces and 2) to validate it with field experiments. The results show a high accuracy between the data predicted by the model and the field measurement. Furthermore, this work stresses out the importance of taking into account both the mainline effect and the friction between skyline and intermediate supports to properly calculate the skyline tension and load path. CableHelp model shows a great adaptability and ensures high accuracy predictions for any positions on the line profile and for different configurations: single span or multiple span profiles, uphill or downhill yarding and for different kinds of carriage. A direct application of this research is to optimize the set-up of cable lines in order to reduce the equipment wear as well as operating cost while respecting operator safety.

Introduction

Cable yarding systems are commonly used for steep-slope harvesting in mountain areas around the world. In France, until 1960, long cables were even the only harvesting system able to reach many valleys in the Alps and Pyrenees [START_REF] Bartoli | Lombardi in Arudy!". A snapshot of logging in the French Pyrenees from 1916 to 1975[END_REF]. Over the past fifty years, the know-how associated with this technique gradually disappeared with the heavy building of forest roads and the development of ground-based forest operation systems such as skidder [START_REF] Auban | Forest roads in mountainous regions -Assessment and technical proposals. An example in the central Pyrenees[END_REF]). In the others Alpine countries cable systems have persisted and have been optimized with the development of cable cranes. In Switzerland [START_REF] Brändli | Inventaire forestier national suisse. Résultats du troisième inventaire 2004-2006. Birmensdorf, Institut fédéral de recherches sur la forêt, la neige et le paysage WSL, Berne, Office fédéral de l'environnement Carson WW[END_REF], Austria and Trento Region in Italy [START_REF] Bartoli | Dossier débardage par câble[END_REF], timber extracted by cable yarding represent more than 20 % of the total harvested volume. Meanwhile, in the French Alps, this figure is really lower with only 3 % of the total harvested timber [START_REF] Grulois | Les systèmes d'exploitation forestière dans les Alpes françaises[END_REF]. On the other hand, half of the French mountain forests are currently considered as under-harvested, partly because skidder cannot access them for technical and economic reasons [START_REF] Vidal | La Forêt française -Les résultats issus des campagnes d'inventaire 2005 à 2009 -Rhône-Alpes[END_REF]. The reintroduction of cable yarding with its significant technical evolutions is an opportunity to access and manage those forests.

Set-up of the cable lines is a very technical step as well as an important part of total fixed costs of a cable yarding operation. With the growing availability of high resolution topographic datasets and the development of digital modeling, it is possible to implement decision-support tools to assess cable lines feasibility and facilitate the selection of relevant cable projects. Such a device can be composed of a Geographic Information System (GIS) based interface to locate different possible cable locations and a mechanical model to appreciate the optimal layout of intermediate supports and cable tensile forces to insure workers' safety with minimum costs.

Two different approaches are used concerning the mechanical analysis of cable yarding systems. European traditional method consists of linearized analyses of cable structures [START_REF] Pestal | Seilbahnen und Seilkrane für Holz-und Materialtransport[END_REF] while North American one lies on closer to reality non-linear analyses (Carson 1977;[START_REF] Chung | Optimization of cable logging layout using a heuristic algorithm for network programming[END_REF]. Although the load path during cable yarding is a dynamic problem, all the existing methods treat it as a static case due to the relatively low speed of the load along the skyline.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4

The predominant cable system in Europe is known as standing skyline. The skyline is fixed to anchors at both ends implying a constant unstretched skyline length for any load weight and location. The static response to a point load by such cable structures is characterized by three main points: 1) the skyline shape and tensile forces change with the load location; 2) the cable elasticity increases the total length of the skyline and 3) the loaded span length increases by gaining some of the available unloaded adjacent spans cable length [START_REF] Bont | Optimum geometric layout of a single cable road[END_REF]. As shown in [START_REF] Lyons | Considering Cable Stretch in Logging Applications[END_REF], the cable construction stretch can be neglected when the maximum working tension is less than one-third the minimum breaking strength of the cable. This is the case in practice in the European Union where the legal safety coefficient for cable yarding systems is fixed at 3. Temperature changes can also induce an additional stretch of the skyline which is most of the time marginal and can be neglected in the calculations [START_REF] Kato | A Note on the KATO-HORI's Tension Formulas for the Calculation of the Skyline Cables[END_REF].

In European countries, the common simplified method to assess the geometric layout of a cable road is established from linearized analyses of cable structures known as [START_REF] Pestal | Seilbahnen und Seilkrane für Holz-und Materialtransport[END_REF] equations where only the changes in skyline shape are considered. This method lead to shorter spans and more intermediate supports than necessary as shown in previous work [START_REF] Bont | Optimum geometric layout of a single cable road[END_REF].

In North America, non-linear analyses of cable structures for forestry purposes emerged with the development of computer technologies [START_REF] Carson | Running skyline design with a desk-top computer-plotter. Pacific North West Forest and Range Experiment Station[END_REF][START_REF] Chung | Development of a cable logging system analysis package for micro-computers[END_REF]. In this approach, cable elasticity and changes in shape and tensile forces according to load location are considered. These approaches, although more realistic, remain computer-time consuming and are concentrated on single-span cases which are not common in Europe. [START_REF] Bont | Optimum geometric layout of a single cable road[END_REF] developed a complete computer-aided program based on [START_REF] Zweifel | Seilbahnberechnung bei beidseitig verankerten Tragseilen[END_REF] "close-to-catenary" approach for multiple spans configuration which included all the cable responses cited previously. Their algorithm also enables optimizing the intermediate supports locations while respecting predefined safety conditions.

Although several researches in recent years related to cable systems, efforts are still needed in order to develop computerized methods that integrate accurate mathematical approaches for the structural analysis of cable systems (Cavalli 2012). This scientific lack meets the interests of forest operators and managers for an operational and accurate tool for optimizing the setup of cable yarding systems and operating this material in a safe and productive way.

Taking advantage of the previous research works, our objectives were thus 1) to develop an efficient model for the setup of cable yarding systems where inputs are operational field data such as geometric layout, initial configuration and skyline and carriage properties and outputs are the load path and tensile forces and 2) to validate this model with field experiments. The purpose of this paper is to propose an accurate forestry application of cable structure mechanics and to compare the theoretical equations used in CableHelp model we developed with realworld cables responses. We first focused on cable structure mechanical analysis and its adaptation to cable yarding systems. A first field experiment has then been used to validate the different model hypotheses before comparing model predictions to load path and tensile forces measured during a real cable yarding operation.

2.

Model development

2.1.

Available data for standing skyline The field parameters potentially available as inputs for the design of a cable yarding system using a model were identified in close relationship with cable yarding operators. Those parameters are listed in the Table 1. The geometric layout is generally given either with the site description or by positioning the cable line on a precise Digital Terrain Model (DTM) using GIS. If a DTM is used, a raster resolution taken from 1 to 5 meters and preferably derived from ALS LiDAR data is needed for an accurate result [START_REF] Akay | Using LiDAR technology in forestry activities[END_REF]. Cable and carriage properties can be given by the operators and the material manufacturers. The initial skyline tensile force has to be The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 known at one of the cable ends. In practice, modern tower yarder systems generally integrate a hydraulic pressure sensor on the skyline winch. If such system is not available one can also use portable digital cable tension meter. T o N

The elastic catenary: a mechanical cable structure analysis appropriated to suspended cable configuration

Figure 1 shows a cable suspended between two fixed points A and B with Cartesian coordinates (0,0) and (D,H), respectively. The span of the cable is D, and the vertical distance between the ends is H. The unstrained length of the cable L 0 corresponds to the cable length without any stress applied on it (cable self-weight is also excluded); it can also be named unstretched length. L 0 is the length that the portion of cable AB would have if it were laid on a totally flat terrain. A point on the cable has curvilinear abscissa s in the unstrained profile (the distance along the cable from the origin to that point is s when the cable is not stressed). When the cable self-weight force W is considered and a tensile force is applied at both side of the cable, the cable stretches to a new length L u corresponding to an unloaded configuration. If, in addition to the cable self-weight force W, a fixed concentrated vertical load F is hung at a point P with curvilinear abscissa s F , an additional stretch of the cable is observed and the new length of the cable is L l . Both L u and L l are strained (or stretched) length of the cable and we have L l > L u > L 0 .

A single cable suspended between two rigid supports can be modeled as an elastic catenary following the approach proposed in [START_REF] Irvine | Cable Structures[END_REF]. The tension within the cable T(s) and the Cartesian coordinates (x(s), z(s)) of a cable point situated at curvilinear abscissa s are derived following a Lagrangian formulation as functions of: the unstrained length L 0, the curvilinear abscissa s of this cable point and, if relevant, the curvilinear abscissa s F of the suspended load. Thereby, the shape of the cable (cable profile) is obtained by calculating all the couples of Cartesian coordinates (x(s), z(s)) for s taken from 0 to L 0 .

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 Fig. 1 Two different coordinates systems for the elastic catenary. The unstrained profile is represented in a Lagrangian frame. A point on the cable is located using the curvilinear abscissa s from the origin of the cable to this particular point. The strained profiles are represented in a two dimensional Cartesian frame (0, x, z). A point on the cable has the coordinates x(s), z(s) in the strained profiles. L0 is the unstrained cable length, Lu is the strained length of an unloaded cable and Ll is the strained length of a loaded cable.

In the case of a cable subjected only to its self-weight, the coordinates x(s), z(s) and the tension T(s) in the strained cable profile are derived from [START_REF] Irvine | Cable Structures[END_REF]: For a cable subjected to both its self-weight and a concentrated fixed load applied at s F , the expressions of x(s), z(s) and T(s) depend on the load position (s F ) and on the location of the cable point s. If the point is positioned

(1.1) ( ) [ ( ) ( ⁄ )] (2.1) ( ) ( ) [√ ( ) √ ( ⁄ ) ] (
The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 between the upper support and the load (0 ≤ s ≤ s F ) the expressions remain similar. For a cable point situated between the load and the lower support (s F ≤ s ≤ L 0 ) the expressions become [START_REF] Irvine | Cable Structures[END_REF]:

(1.2) ( ) [ ( ) ( ⁄ ) ( ⁄ ) ( ⁄ ) ] (2.2) ( ) ( ) [ √ ( ) √ ( ⁄ ) ( ) √ ( ⁄ ) √ ( ⁄ ) ] (3.2) ( ) √ ( )
Where: s F m Curvilinear abscissa of the load location on the unstrained cable profile F N Concentrated vertical load applied at the curvilinear abscissa s F .

F depends on the carriage Q c and load Q l weights and on the self-weights of the mainline q m and of the haulback line

q h : [ ( ( ) )]
These expressions contain as unknowns the horizontal (T h ) and vertical (T v ) reactions of the supports at the origin A. These quantities can be determined by solving the two dimensional system of equations { ( ) ( ) . The resolution of this system allows calculating the quantities required for the design of a cable yarding system. Amongst them, we are particularly interested in the load path (i.e. the sequence of load positions taken from 0 to L 0 ) and the evolution of the maximum tensile force T(s=0) according to the load position. In practice, knowing the position of the load allows ensuring that it does not touch the ground or that a minimum clearance between the load and the ground is respected. The accurate estimation of the maximum tensile force of the skyline for a given configuration enables checking the safety condition of the operators. This method also enables calculating the shape of the cable for each load position for the loaded profile.

Adaptation of the elastic catenary to a standing skyline configuration

General model structure

The approach proposed in [START_REF] Irvine | Cable Structures[END_REF] has been adapted to account for standing skyline specificities. The main assumption governing our model is that the unstrained (or unstretched) skyline length L 0 for the entire profile remains the same whatever the carriage position s F or load force F is. On the other hand, the strained (or stretched) skyline length L is evolving according to both the carriage configuration (loaded or unloaded) and its position s F along the cable profile. The second hypothesis is that the magnitude of the skyline tensile force evolves continuously along the cable profile except from three situations: 1) at intermediate supports level (only for multiple span configurations), 2) if the carriage is locked to the skyline or 3) if the carriage is self-motorized. In the first point, the friction between the skyline and the jack modifies the tensile force so that the tension measured at the loaded span

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 side is higher than the one at the unloaded span side. In the two last points the skyline tensile force at the upper side of the carriage is higher than the one at lower side as explained in [START_REF] Irvine | Cable Structures[END_REF].

Taking into consideration these assumptions, the general process of the model follows two main steps: 1) Using the two-dimensional equations system { ( ) ( ) and the appropriate initial settings, search of the initial unstrained length of the skyline for the entire profile L 0 which corresponds to the tension T 0 measured on the field for an unloaded carriage at position s c and 2) calculation of the load path and tensile forces within the skyline for different load positions s F along the cable taken from 0 to L 0 . According to the configuration tested and the type of carriage used for the operation, an additional step may be needed and consists in estimating the mainline or haulback influence and the friction between the skyline and the jack at intermediate supports.

The first step of the process is to calculate the unstrained skyline length L 0 from the initial settings of the system. An important point in our model is to use operational data as inputs. In order to meet the same initial conditions as observed on the field, the model calculate the unstrained cable length L 0 corresponding to the skyline tensile force T 0 measured at one of the cable ends during the tensioning step and with an unloaded carriage located at curvilinear abscissa s c . L 0 is initially fixed as the shortest distance between both supports (i.e. the diagonal distance) corrected with the cable elasticity:

(4) ( ) √ ( ) ⁄
An iterative method is then used to find L 0 . The skyline tension T(s) at the same support where T 0 was measured is calculated using the following boundary conditions in the two-dimensional system of equations { ( ) ( )

: s = L 0 , x(s) = D, z(s) = H, s F = s c . While T(s) is significantly different than T 0 (by default |T(s) -T 0 | ≤ 10 N), L 0 is incremented with
a small length  (by default  = 0.001 m). For each new iteration, a two-dimensional Newton-Raphson's method [START_REF] Ypma | Historical Development of the Newton-Raphson Method[END_REF]) is used to find the unique solution (T h , T v ) of the system of equations { ( ) ( ) that allows calculating

T(s).

The second step of the process is to calculate the load path and the maximum skyline tensile force on the loaded span. Once the unstrained cable length L 0 is known, the full load (i.e. loaded carriage) is applied and the model automatically moves the load each meter along the unstrained profile from the upper support (s F = 0) to the lower support (s F = L 0 ). For each load position s F , the couple (T h, T v ) solution of the system of equations { ( ) ( ) is determined and used to calculate the load position (x(s F ),z(s F )) and the theoretical maximum skyline tension T(s=0). This quantities are calculated with the equations (1.2) for x(s F ), (2.2) for z(s F ) and (3.1) for T(s=0). At the end of this process, all the load positions obtained represent the trajectory of the load. Moreover, the evolution of the maximum skyline tension T(s=0)(s F ) according to the load location is generated.

Calculation of the skyline tensile force with a configuration using a mainline

The method exposed in [START_REF] Irvine | Cable Structures[END_REF] deals with a fixed point loaded on the cable. This is true when considering either a self-motorized carriage or when the carriage is locked on the skyline (during loading and unloading phases).

As shown in Figure 2a, considering a fixed load implies that the magnitudes of skyline tension at each side of the carriage are not equal. The magnitude at upper side of the carriage T 1l is equal to T(s=s F ) in equation (3.1) while the magnitude at the lower side of the carriage T 2l is equal to T(s=s F ) in equation (3.2). As a consequence, in this configuration T 1l is always greater than T 2l [START_REF] Irvine | Cable Structures[END_REF].

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 However, during cable yarding operations, the load may move on the skyline with the help of one (uphill yarding) or two (downhill yarding) cable(s). Figure 2b shows the same case as Figure 2a but with the carriage hold by the mainline and not locked on skyline. With this configuration the skyline is free to move at the carriage level, the magnitudes of the tension at each side of the carriage are consequently equal (T 1f = T 2f ) and the mainline (or haulback) tensile force ⃗⃗⃗⃗⃗ required to hold the carriage contributes to support the concentrated load .

The assumption made to solve this situation is that the Cartesian coordinates of the carriage (x(s F ),z(s F )) when the carriage is hold with a mainline is not significantly different from the coordinates when the carriage is locked on the skyline. The mainline tension is estimated from the equilibrium equations of the carriage as shown in Figure 2b.

The angles  (between the left side of the skyline and the horizontal) and  (between the right side of the skyline and the horizontal) can be calculated as shown in equation ( 5) where ɛ is a small distance representing the vicinity of the carriage. λ is the angle between the horizontal and the mainline.

(5) | ( ) ( ) |, | ( ) ( ) |
The equilibrium equations of the carriage lead to the expression of the mainline tensile force T m (equation ( 6)) and of the skyline tensile force at both side of the carriage T 1f and T 2f (equation ( 7)). ( 6)

( ) ( ) ( ) ( ) (7) ( ) ( ) ( )
Where k = 1 if ⃗⃗⃗⃗⃗⃗ is oriented upwards and k = -1 if ⃗⃗⃗⃗⃗⃗ is oriented downwards This calculation process has to be repeated for each new load location s F . When using a horizontal symmetry, this method can also be applied to downhill yarding. At the end, the skyline tensile force taking into consideration the mainline influence is calculated for any point s F along the unstrained cable length.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4

Multiple span configurations and skyline friction at intermediate supports

Additional calculation steps have to be added to account for multiple span configurations, especially for the calculation of the initial layout and for modeling the displacement of the skyline according to the load position.

Fig. 3 Calculation of skyline friction at intermediate support

A friction force at intermediate supports between the skyline and the jack may additionally be taken into account when considering a multiple span configuration (see Figure 3). The direction of the support reaction force ⃗ is assumed to be along the bisectrix between both sides of the skyline. The angle  between ⃗ and the vertical can be taken conveniently as

( )
. The friction force is oriented in the opposite direction compared to ⃗ as the skyline moves from the unloaded span to the loaded span. A classical Coulomb friction model is used to relate f and R as shown in equation ( 8) where the friction angle φ depends on the materials on which the friction takes place.

(8)

Considering the equilibrium equation of the skyline portion lying on the jack, it is possible to obtain the skyline tensile force at the unloaded span side T 1 and the support reaction force R:

(9) ( ) ( ) ( ) ( ) and ( ) ( ) ( )
The process presented above for accounting for the friction force is used during the two main phases of the multiple span modeling. As for single span, the first phase consists in estimating the total unstrained cable length L 0 on the entire profile. A step by step process is used to find L 0 . We first process span 1 noted S1 where the initial skyline tension T 0 and the unloaded carriage position s c are known. The unstrained skyline length L 0_S1 is calculated following the same process as for single span. Once L 0_S1 is known, it is possible to calculate the skyline tensile force T 01 at the first intermediate support IS1. This tensile force is corrected taking into account the friction force at intermediate support IS1 to give T 01f the tensile force at the upper side of span 2. Second, the unstrained cable length L 0_S2 for the span 2 is handled similarly by replacing T 0 by T 01f and s C by 0. We obtain T 02 at the second intermediate support IS2 which is corrected taking into account the friction at intermediate support to give T 02f . The same process is used for the n spans Si of the multiple span configuration. Finally the total unstrained cable length L 0 is obtained by summing all the individual span lengths:

(10) ∑

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4

The second phase consists in calculating the load path and maximum skyline tensile force along the entire profile. For a standing skyline configuration the total unstrained cable length L 0 that corresponds to the initial settings has to remain constant no matter if the skyline is loaded or unloaded. The total unstrained skyline length L 0_l in loaded configuration is calculated following the equation ( 11): (11) For a load located on span i: ∑ ∑

In equation ( 11), L 0_lS corresponds to the unstrained length of the skyline on the loaded span i and L 0_lSj corresponds to the unstrained length of the skyline on the other spans j (with j ≠ i). An iterative method is used to find the correct L 0_lS that induces L 0_l = L 0 .

A step by step process is used where L 0_lS is initially taken as equal to L 0_Si . Knowing L 0 , the skyline tensile forces T i-1 and T i at both ends of the loaded span can be calculated. These forces are corrected with the friction force to give respectively T i-1f and T if . The unstrained skyline lengths L 0_lSi-1 and L 0_lSi+1 of the adjacent unloaded spans are then calculated by seeking the value that match the tensile force known at the end they have in common with the loaded span. The n spans of the profile are processed step by step in order to ensure that the magnitude of the tensile force is evolving continuously along the profile. Finally we obtain the total unstrained skyline length for a loaded configuration L 0_l .

For each load position s F , the model iterates on the unstrained skyline length L 0_lS of the loaded span. When the total unstrained skyline length for a loaded configuration L 0_l corresponds to the initial total unstrained skyline length L 0 (by default the tolerance is | L 0_l -L 0 | ≤ 0.001m), the process stops and the load position and maximum tensile force are calculated. This process allows respecting the two main assumptions of a constant unstrained length and of a magnitude of the skyline tensile force evolving continuously along the profile (including the exceptions raised before concerning that point). All the calculation process has been computed in the CableHelp model using the open source Python language with its associated libraries Numpy [START_REF] Oliphant | Python for Scientific Computing[END_REF] and Matplotlib [START_REF] Hunter | Matplotlib: A 2D Graphics Environment[END_REF].

Field experiments

Field experiments were set up with the aim of comparing field results with model predictions in terms of skyline tensile force and cable profiles for different load positions along the cable. Accurate comparison requires specific and precise measurements of the cable positions and tensile forces that cannot be carried out easily during real cable yarding operations without disturbing it. Moreover, it is practically complex to design small-scale experiments fulfilling similitudes rules. These reasons lead us to build a first standing skyline system with the objectives of validating our assumptions and getting first elements of the model relevance. This experiment has been completed with measurements done during a real cable yarding operation.

Single and double span experiments

A first set of configurations has been carried out in the park in front of the center Irstea -Grenoble (experimental set up see Annex 2). 7 single span and 3 double span configurations have been tested. Their characteristics are described in Table 2. First, the trees (DBH 40 to 45 cm) serving as supports have been anchored to ensure their stability. A load cell has been installed on the first tree and plugged to a data logger. One side of the skyline has

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 been fixed directly on the load cell and the other to a manual hoist used to stretch it. Reference points have been previously marked each meter along the unstrained skyline with origin at the cable end situated at the load cell level. The carriage movement was ensured by the mainline or the haulback according to its position. Those cables were moving with the help of manual hoists. The load was represented by a 265 kg steel ball lifted up with an electric hoist (75 kg) tied on the carriage (25 kg). For the 3 double span configurations, a load cell has also been added on the upper side of the carriage to measure the mainline tension. For each configuration tested, the load was positioned successively on each point of reference previously marked on the skyline (i.e. each meter in the curvilinear unstrained cable profile). For each load location we measured: the tensile force in the skyline and three pairs of coordinates (x, z) for the positions of the carriage and both cable ends. These coordinates were measured using a total station combining an electronic theodolite with an electronic distance meter.

Real cable yarding operation

The first experiment presented the advantage of being relatively easy to implement but it has three major disadvantages. First, the spans were short comparing to the skyline characteristics (d s , q s , E s ). This may produce a system that is insensitive to elasticity and self-weight of the cable. Second, the skyline slope in the single and double span experiments varies from 2 % to 14 % which correspond to relatively flat configurations. During real cable yarding operations the skyline slope is often larger than 40 %. Third, the trees used as anchor might represent more rigid supports than in real cable yarding operation as the skyline tension applied was small comparing to real configurations.

These three main disadvantages lead us to follow a real cable crane operation in the National forest of Gargas situated in a northern slope of the French Alps (UTM Long 5°55'17", Lat 44°52'37", see Annex 3). The cable yarding operation was ensured by a small cable crane (Larix Lamako) with an uphill extraction of the logs. The carriage (Sherpa U 3T) moved with the help of both a mainline and a haulback line (q m = q h = 0.529 kg•m -1 ). Only one intermediate support was present and placed at the upper part of the profile. The total horizontal length of the profile was about 260 meters and the vertical length of about 150 meters. The average chord slope of the spans is about 60%. The total suspended weight is of 1 430 kg (Q c = 410 kg and Q l = 1020 kg). The last configuration RCYO of the Table 2 gives details of this configuration.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4

The skyline tensile force was measured with a 20 kN load cell located at the anchor level to avoid damaging the skyline. The load path was measured with a total station associated to its specific target which was previously fixed on the carriage. The measurements concern 30 static positions only located on the second span (the longest one). The carriage was hold with the mainline and the load was fully suspended. For each position we waited for the equilibrium of the carriage before measuring the skyline tensile force and the position of the carriage.

4.

Results : Comparison between field experiments and model prediction 4.1.

Single and double span experiments

Load path

As described above, we considered that the load path is not affected by the eventual corrections induced by the mainline or the friction at intermediate support. 123 positions gathering all the single and double span configurations have been measured during the field experiments. All of them have been taken into account in the load path comparison. The load path is calculated respectively with equation (1.2) for the x axis and equation (2.2) for the z axis. Table 3 shows the root-mean-squared error (RMSE), the coefficient of variation of the root-mean-squared error CV(RMSE) and the bias between the measured and predicted load path along both x and z axis for the 10 different configurations tested. The model predicted the load path along x axis with a RMSE from 0.1 to 3.6 mm. The error along z axis is higher with a RMSE from 0.3 to 7.5 mm. For both x and z axis, the coefficient of variation of the RMSE is nearby 0 % and no systematic bias is observed.

Tensile forces

Figure 4 shows the effect of the correction of mainline tension on the skyline tensile force for the single span configuration U2-L. In this configuration, the cable profile was inclined and the load cell was placed at the upper support with curvilinear abscissa 0. Without correction, the skyline tension prediction is higher than the field The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 measurements when the load is close to the upper support; it comes closer to the field measurements when the load position is situated nearby the basal point of the cable profile. The correction proposed for the skyline tensile force prediction improves the accuracy.

Fig. 4 Comparison of skyline tensile force measured on field with the data predicted using the model with and without mainline tension correction for the configuration U2 -L. Corrected model prediction better fits the field measurement Table 4 presents the RMSE, CV(RMSE) and bias observed for the 7 different single span configurations tested. As noticed in Figure 4, the correction of the skyline tension with the mainline tension induces a positive effect. The error and the coefficient of variation are divided by a factor 3.6. After correction, the error concerning the skyline tension is between 64 and 199 N and the average coefficient of variation is 2.7 %. The mainline tension has been measured only for the 3 double span configurations for a total of 42 positions. The comparison between field measurements and predicted values gives an average error of about 76 N, a coefficient of variation of about 12 % and a bias of -30 N. Figure 5 shows the linear regression between the measurements carried out during the field experiment and the model predictions. The model predictions concerning

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 the mainline tension are rather scattered around the regression line (R² = 0.984). The skyline tension is better predicted with less dispersion around the regression line (R² = 0.997). 5 shows the influence of the friction angle value on the skyline tension predicted by the model (with mainline correction). If no friction is considered (friction angle is 0 rad), a systematic positive bias is observed. On the contrary, when the friction angle is high (0.3 rad), the model predicts lower tension values than measured during the field experiment (about -470 N). With a friction angle equal to 0.15 rad the skyline tension predicted by the model is very close to the one measured during the field experiments as shown with Figure 6.

Table 5 Example of the influence of the friction angle value on the skyline tension predicted by CableHelp model for the configuration Do2

Table 6 shows the RMSE, CV(RMSE) and bias observed concerning the skyline tensile force after correction of the mainline tension and with a friction angle of 0.15 rad. The model predicts as accurately the skyline tensile forces The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4

for double span as for single span with a RMSE of about 205 N. The coefficient of variation is similar than for single span and no systematical bias is observed. Real cable yarding operation 30 observations have been measured during the follow up of the real cable yarding operation. These data are compared with the outputs of the model in Table 7. Four modeling options have been considered: 1) model integrating mainline and friction effect, 2) model considering only mainline effect, 3) model considering only friction effect and 4) strict application of the model without any correction concerning mainline or friction.

Table 7 shows the RMSE, CV(RMSE) and bias observed for the load path and skyline tensile force for each option. The load path is best predicted with the option integrating mainline effect and friction at intermediate support. The model integrating mainline alone or friction alone improve also the prediction observed with the basic option without any correction.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4

Discussion and conclusion

Our research was aimed at 1) developing a numerical application for the setup up of cable yarding systems that uses operational field data as inputs and returns load path and tensile forces as outputs and 2) validating the method and the results with field measurements.

This research produced the following major findings. First, the approach proposed is closely related to the practical use of operational field data, especially when modeling the initial settings of a particular configuration. In most of the previous approaches, the basic tensile force T 0 corresponds to the initial tension without a carriage mounted on the skyline which in practice is not the case. As far as we know, the method proposed in this paper is the first to consider the carriage during this tensioning step when modeling the initial settings. The weight of the carriage alone can represent between 10 % and 25 % of the total suspended weight during the yarding step. Therefore, neglect the carriage weight when modeling the initial settings leads systematically to predict higher skyline tensile force when a load is applied.

Second, our study shows that the elastic catenary solution proposed in [START_REF] Irvine | Cable Structures[END_REF] and the adaptation performed within this work is appropriate to predict with a high accuracy the load path and tensile forces during cable yarding operations. The comparison between the experiments and the outputs of the model showed a high accuracy in the load path prediction. For the real experiment the error varies from 17 cm (0.07 %) for a complete application of the model (with mainline and friction) to 52 cm (0.23 %) for a basic application of the model (no friction, no mainline). Accuracy concerning the position of the load allows ensuring that it does not touch the ground or that a minimum clearance between the load and the ground is respected. This method has the same range of error as average precision (2 points•m -²) DTM in mountainous regions built from airborne laser scanning [START_REF] Hollaus | Accuracy of large-scale canopy heights derived from LiDAR data under operational constraints in a complex alpine environment[END_REF]. The model can therefore be used together with this kind of DTM to optimize the mounting of the line and the position of intermediate supports.

Skyline tension is also predicted with good accuracy with a maximum error of 2 655 N (3.7 %) in real conditions. In practice, tensile force is usually only checked during the setting of the line, the maximum loaded skyline tension is estimated based on the experience of operators and supposed to reach the safety recommendations. Our model allows precisely assessing this parameter taking into account the initial layout and enables checking the safety of operators. The wear of the material in loaded configuration can also be minimized as the minimal initial tensions needed for a correct functioning of the system can be also calculated.

The method proposed to estimate mainline tension shows a larger error (from 6 to 12 % in the first experiment). However, our results in the experimental configurations as well as in the real configuration show the importance of taking into account the mainline to predict accurately the skyline tension. Our approach could be certainly improved taking into account the interval between the two opposite wheels of the carriage in order to better transcribe its inclination. Potential improvements of both field measurements and model assumptions can also be envisaged to reduce the observed error of the mainline tension.

Third, our work stresses the influence of the friction between the skyline and the intermediate support. Most of the previous works [START_REF] Charland | Cable Systems with Elastic Supporting Elements[END_REF][START_REF] Chung | A computerized method for determining cable logging feasibility using a DEM[END_REF][START_REF] Bont | Optimum geometric layout of a single cable road[END_REF] considers that the friction between the rope and the jack can be neglected. However, our study shows its effect on skyline tension and load path. The study carried out by [START_REF] Mccoll | Lubricated fretting wear of a high-strength eutectoid steel rope wire[END_REF] demonstrated that, for a contact between a lubricated steel rope (skyline) and a steel surface (support jack), the friction angle can conveniently be taken in a range from 0.1 to 0.2 rad. The best prediction of skyline tension is obtained using a friction angle of 0.15 rad which is the median value of this range.

Fourth, to our knowledge, the complete experimental follow up of load path and tensile forces (in both skyline and mainline) for cable yarding configurations done within this study constitutes an exhaustive data set for the complete assessment of cable yarding systems design and for the evolution of their modeling. Among the previous The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 researches, Sessions (1976) provided a method for estimating skyline tension and avoiding overload. [START_REF] Fabiano | Skyline tension analysis in yarding operation: case studies in Italy. In: Pushing the boundaries with research and innovation in forest engineering[END_REF] followed the skyline tension with load cells for 69 cable lines and provided an interesting sum up of these field measurements. However, none of these works linked precisely skyline tension with load path.

More generally, this approach takes into account the three main points describing the cable response to a point load: changes in skyline shape and tensile forces according to the load position, changes of cable length due to cable elastic stretch and the multiple span specificities. Moreover, the model proposed demonstrates a high adaptability to many terrain configurations. Load path and tensile forces can be accurately predicted for any load position and for different configurations: single span or multi-span profiles, uphill or downhill yarding, self-motorized or classical carriage. An additional step toward adaptability is to integrate both full and partial suspension of the logs. Currently this work only deals with full suspension which is true only for short logs extraction. However, full tree yarding with branches processing at the landing area becomes more and more frequent. This extraction method implies partial suspension of the log which can change consequently the tensile forces [START_REF] Tobey | Skyline analysis with log drag[END_REF]. This topic has already been investigated, especially in North America [START_REF] Falk | Predicting the payload capability of cable logging systems including the effect of partial suspension[END_REF][START_REF] Kendrick | A solution procedure for calculating the standing skyline load path for partial and full suspension[END_REF]. Integrating a module able to take into accounts both full and partial suspension suggests also to cross our model with a high definition DTM in order to consider the interaction between the logs and the ground. Currently the model only considers a maximum skyline tensile force in order to ensure safety of operator. It could also be interesting to consider a minimum skyline tensile force which could be required to allow the passage of the loaded carriage over intermediate supports.

The field experiments conducted within this study showed the applicability of our model to real cable yarding operations. The results from this field data acquisition could be a first step toward an international database on cable yarding operations. However such field acquisitions are expensive and require very specific material. Future field acquisitions have to be chosen carefully in order to cover a wide range of situations. In addition to load path and tensile forces, further experimental measurements could concern friction at the intermediate supports and tension variation caused by partial suspension of the logs. Our experience during the real experiment showed that the use of load cell restricts the location of the skyline tensile force measurement. In further field experiments, portable wire rope tensiometers could be advantageously used to be free to measure the tensile force anywhere along the skyline.

At last, the real cable yarding operation followed in this study represents a typical operation in the Alps (uphill yarding with a short line on steep slope). However, in order to complete the validation of the model, further follow ups of cable operation could be done to test the accuracy in other configurations. The final validation could lead to an automatic optimization of cable yarding operations able to propose a solution for initial tensioning and intermediate support positioning. The calculation time observed for modeling the real experiment varied from 0.8 ms (basic calculation) to 0.5 s (mainline and friction integrated to the model) which is efficient enough for this kind of adaptation.

Fig. 2

 2 Fig. 2 Forces acting in the equilibrium equation of the carriage. When the carriage is locked on the skyline or is self-motorized (a) the magnitude of the skyline tension at the upper side of the carriage T 1l is greater than magnitude at the lower side of the carriage T 2l . When the carriage is hold by the mainline (b) at curvilinear abscissa s F , the magnitudes of the skyline tension at both sides of the carriage are considered as equal (T 1f = T 2f ).

Fig. 5

 5 Fig. 5 Comparison between experimental field measurements (abscissa) and data predicted by the model (ordinate). The mainline tension and the corrected skyline tensile force are shown respectively in (a) and (b). 42 positions are considered for the mainline tension and 82 for the skyline tension

Fig. 6

 6 Fig. 6 Influence of the friction of the skyline with the intermediate support on the skyline tension predicted by the model for the configuration Do2. If no friction is taken into account, the predicted tension is systematically above the measured tension. With a friction angle of 0.15 rad, experimental curve fits the modeling curve. Finally, with a friction angle of 0.3 rad, model predictions are above the experimental values

Table 1

 1 List of input parameters for the modeling of a cable yarding configuration

	Description

c m Tensile force measured at one of the skyline ends after tensioning step (with carriage at position s c and no load suspended)

Table 2

 2 List and description of field experiments followed up

	Code	Configuration	Load cell location	D1 m	Span 1 H1 m	D2 m	Span 2 H2 m	Span 3 D3 H3 m m	T0 N	Initial settings F N	ds mm	Skyline properties Es qs kN•mm -2 kg•m -1
	L-U	Single span	Lower support	15.0	0.3					770	1015	16.2	100	1.02
	L-L	Single span	Lower support	14.9	0.3					770	3595	16.2	100	1.02
	U1_U	Single span	Upper support	14.9	1.9					780	925	16.2	100	1.02
	U1_L	Single span	Upper support	14.9	1.9					780	3505	16.2	100	1.02
	U2_L	Single span	Upper support	14.8	1.9					1200	3505	16.2	100	1.02
	U3-U	Single span	Upper support	14.9	2.0					900	925	16.2	100	1.02
	U3-L	Single span	Upper support	14.87 1.9					900	3505	16.2	100	1.02
	Do1	Double span	Upper support	15.3	2.3	20.3	1.2		380	3540	16.2	100	1.02
	Do2	Double span	Upper support	15.4	2.2	20.3	1.1		290	3540	16.2	100	1.02
	Do3	Double span	Upper support	15.3	2.4	20.3	1.4		290	3540	16.2	100	1.02
	RCYO	Real operation Anchorage	24.1	14.78 197.4 113.0 39.7 24.8 45000	14024	16.0	91	1.23

Table 3

 3 Comparison between load path experimental measurements and data predicted by CableHelp model for the 10 different configurations tested (single and double span included) during the single and double span field experiments

	Configuration	Number of observations	Load path on the x axis RMSE CV(RMSE) mm %	Bias mm	RMSE mm	Load path on the z axis CV(RMSE) Bias % mm
	1 span L -U	15	2.1	0.03	-0.3	3.7	0.07	3.1
	1 span L -L	14	0.2	0.00	0.0	0.3	0.01	0.2
	1 span U1 -U	7	2.0	0.03	0.4	4.0	0.09	3.3
	1 span U1 -L	14	0.2	0.00	0.1	0.4	0.01	-0.1
	1 span U2 -L	14	0.1	0.00	0.0	0.3	0.01	-0.2
	1 span U3 -U	4	0.7	0.01	0.0	2.5	0.05	2.1
	1 span U3 -L	14	0.1	0.00	0.0	0.4	0.01	-0.2
	2 spans Do1	24	0.1	0.00	0.0	0.7	0.02	-0.6
	2 spans Do2	5	3.6	0.07	0.2	7.5	0.15	-1.4
	2 spans Do3	13	0.1	0.00	-0.1	1.1	0.04	-1.0
	All observations	124	1.1	0.02	/	2.3	0.05	/

Table 4

 4 Comparison between experimental measurements of tensile forces and data predicted by CableHelp model for the 7 different single span configurations tested

	Configuration	Number of observations	Skyline Tension without correction RMSE CV(RMSE) Bias N % N	Skyline Tension corrected RMSE CV(RMSE) Bias N % N
	1 span L -U	15	74	3.31	15	64	2.94	-22
	1 span L -L	14	401	6.33	218	160	2.66	-120
	1 span U1 -U	7	180	7.97	158	70	3.34	4
	1 span U1 -L	14	816	11.96	702	140	2.28	33
	1 span U2 -L	14	654	7.75	570	199	2.55	-77
	1 span U3 -U	4	64	1.86	62	97	2.94	-55
	1 span U3 -L	14	663	7.71	530	193	2.44	-128
	All observations	82	541	9.74	/	150	2.70	/

Table 6

 6 Comparison between experimental measurements of tensile forces and data predicted by CableHelp model for the 3 different double span configurations tested. The correction takes into account the mainline tension and a friction angle of 0.15 rad

	Configuration	Number of observations	RMSE N	Skyline Tension corrected CV(RMSE) Bias % N
	2 spans Do1	24	211	2.85	75
	2 spans Do2	5	160	2.09	54
	2 spans Do3	13	208	2.15	-154
	All observations	42	205	2.52	/
	4.2.

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 Annex 3 Scheme of the real cable yarding operation followed. Measurements concern the situation when the load is located on SPAN 2 to ensure a full suspension of the log.

Acknowledgments

This study has been carried out within the framework of the Interreg -Alpine Space Programme during the project Newfor n° 2-3-2-FR: "New technologies for a better mountain forest timber mobilization". Website: www.newfor.net

The final publication is available at Springer via http://dx.doi.org/10.1007/s10310-015-0503-4 The skyline tension is best predicted with the models integrating the mainline effect. As shown in Figure 7, the shape of the two curves corresponding to the two options with mainline fit the field measurements curve. For these two options the RMSE is about 1.1 kN and the coefficient of variation is about 1.5%. The curves corresponding to the model without mainline correction are lower than the field experiment curve at the lower part of the profile. For these options the RMSE is about 2.5 kN and the coefficient of variation about 3.5%.

Fig. 7 Comparison between skyline tensions predicted by the model and the 30 field measurements according to different options for the modeling.

The mainline integration influences the bias observed as it is positive for all variables when mainline is considered and negative when it is not considered. Integrating the friction has a positive effect on the load path prediction and a slight negative effect on the skyline tension prediction.

Finally, to appreciate the importance of skyline elasticity in the model, a "rigid" cable has been modeled (Emodulus was changed from 91 to 310 kN•mm -2 ). With the rigid cable, the basic application of the model (no correction of mainline and friction effect) returns less accurate predictions. Thus, the errors on load path and skyline tensile force increase respectively by a factor 1.5 (about 0.7 m) and 3.3 (about 8000 N) comparing to the basic application of the model with the real skyline elasticity.


Jacques Moret-Bailly

Rational astrophysics

Keywords: Line:formation. Radiative transfer. Scattering. 98.62.Ra Intergalactic matter, quasar absorption and emission-line systems, Lyman forests, optical black holes. 290.5910 Scattering, stimulated Raman

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

1.1 Rationality of science.

Rational mechanics uses ideal models as close as possible to observed systems, sometimes successfully, as celestial mechanics, sometimes roughly if friction is present. Here, we use Strömgren's model of stars [START_REF] Strömgren | The physical state of interstellar hydrogen[END_REF] : around a very hot, almost black source of light, a stellar wind, plasma mainly made up of protons and electrons cools on a sphere by adiabatic expansion into excited hydrogen atoms, then mixes with interstellar and intergalactic very low pressure atomic hydrogen. At time-scale ( 1 nanosecond) of electromagnetic pulses of ordinary light, this gas is collisionless so that Einstein's theory of coherent light-matter interactions [START_REF] Einstein | Zur Quantentheorie der Strahlung[END_REF][START_REF] Lamb | Analytical description of ultra-short optical pulse propagation in a resonant medium[END_REF] applies.

1.2 Some problems set by fundamental physics.

amateurs to professionals at the end of this century led to a search for productivity neglecting sometimes basic principles, from where inconsistencies. For instance :

• Planck showed in 1911 [START_REF] Planck | Eine neue Strahlungshypothese[END_REF] the need for the introduction of the "zero point field" into the black body radiation law, but addition of the corresponding half-quantum of energy is often forgotten. Thus, calculations of electromagnetic energies are sometimes false. In particular an error by a factor 2, often appears in the interpretation of measurements of low luminous radiances by photons counting. Some deduce from that error that classical electromagnetism is erroneous ! Let us remind that, according to Planck, the spectral radiance of a polarized ray at frequency ν, in a black body at temperature T is:

I = hν 3 2c 2 [1 + 2 exp(hν/kT )-1
]. This relation between spectral radiance, frequency and temperature allows, for instance, to assign a temperature to a light ray with given ν frequency.

• The theory of electromagnetic waves interactions with a large number of identical particles, that Einstein established through thermodynamics in 1917 [START_REF] Einstein | Zur Quantentheorie der Strahlung[END_REF] was, for a long time, ignored by almost all physicists : one made much fun of Townes when he was building the first maser. The development of lasers theory and applications interested only a small number of physicists. Many physicists and almost all astrophysicists (devotees of big bang is implied) still neglect the importance of coherent interactions of light with matter, appearing to be unaware that refraction is its most elementary and useful application. To explain redshifts of light and stability of spiral galaxies, these astrophysicists support a disputed theory (Big bang, ΛCDM), little fertile, because observations oblige them to supplement it by doubtful physical concepts (dark energy, variation of fine structure constant, MOND,. . . )

Rational Astrophysics.

Rational astrophysics is exclusively based on theories verified in laboratory experiments (with obviously adapted space and time variables), and from observations of many stars. It is fertile, having no need for complementary theories. It is opposed to usual astrophysics based on the construction of a house of cards: a set of debatable theories, often introduced to solve the problems raised by previous theories.

Scientific strictness requires the use of words whose meaning is well defined. But two spectroscopic concepts are not correctly used by astrophysicists:

• Firstly, for a physicist, a laser (or maser) consists of a light-amplifying medium located inside an optical resonator (formed, for example, by two mirrors, each one superimposing on the other mirror its own image); thus, by neglecting energy losses by mirrors absorption and diffraction, a light ray is indefinitely trapped.

• Secondly, in spite of the invention of lasers, it seems that astrophysicists are unaware of coherent spectroscopy, following Menzel's opinion written in 1931 [START_REF] Menzel | The Dilution of Radiation in a Nebula[END_REF]: It is easily proved that the so-called stimulated emissions are unimportant in the nebulae. The point of view of physicists is exactly opposed since, for them, light interactions with very low pressure gases are exclusively coherent, which allows gas lasers operation.

Sky becomes black in stratosphere, in spite of the presence of gas observed by refraction of solar light. Our blue sky results from incoherent scatterings by impurities consisting of molecules in a collisional state.

Section 2 points out optical coherence theory and its major applications, superradiance and coherent, impulsive Raman effect.

Section 3 shows that absorption bound to superradiance of shells surrounding Strömgren spheres can be or become intense enough to make disappear stars in an optical black hole encircled by a possibly dotted ring. This transforms SN 1987A into SNR 1987A.

Section 4 establishes that Karlsson's law introduces redshifts which bring H atom Lyman beta and gamma frequencies to Lyman alpha one. This shows that redshifts known as cosmological arise from a coherent Raman effect in excited H atoms. From where a calculation of spectrum due to H atom around quasars.

Section 5 introduces a model for a general view of spectra of quasars. Section 6 underlines other applications of optical coherence such as dispersion of multiplets spectra emitted by remote stars without variation of the fine structure constant, the so-called abnormal acceleration of Pioneer 10 and 11 probes, bubbles in galaxies maps, black matter and energy, etc . . .

Optical coherence: Huygens' construction.

A wave is represented by some continuous function versus space variables and sinusoidal versus time. It does not take into account energy exchanges between waves and matter. This representation can be generalized to more complex cases, in particular by Fourier decompositions of temporal variations.

Equiphase surfaces are called Huygens' wave surfaces. To deduce an unknown wave surface from two very close wave surfaces, space contained between the latters is divided into infinitesimal, equal volumes, emitting spherical wavelets (in green, fig 1, left) with the same frequency than the incident wave.

After the same short propagation time, the envelopes of these wavelets are two waves, one is the sought wave and the other, retrograde, is destroyed by addition of the retrograde wave emitted at a quarter of a wavelength of the initial surface, because the phase of the latter is opposite.

In the center of fig 1, identical molecules (in red) excited by the incident wave at its frequency (Rayleigh excitation) also generate wavelets. But it is possible that these are out of phase, which phaseshifts the final wave: it is refraction, an example of coherent scattering. It is also possible that the amplitude be modified without variation of frequency (See section 3), or that the frequency is modified (See section 4.5).

On the right of figure 1, two (red) molecules are in a collisional process, generating an unique (blue) system. Properties of this system depend on many parameters. For example geometric ones, so the emitted wavelets are all different, do not interfere to form a new wave surface: thus light is scattered into all directions (blue circle). This incoherent diffusion produces the blue of sky which disappears in stratosphere.

In this paper, we assume that interactions of light with rare colliding molecules of nebulae may be neglected.

3 Coherent quantified interactions between noncolliding molecules and electromagnetic waves.

Einstein's Theory

In 1917, Einstein [START_REF] Einstein | Zur Quantentheorie der Strahlung[END_REF] showed through thermodynamics that spectral radiance I of a monochromatic and polarized light ray, propagating along a path dx in a medium made of identical molecules varies according to the law of classic look dI = BIdx, where B is Einstein's coefficient depending on nature and state of medium, frequency, direction and polarization of ray. I cannot be null, in agreement with existence of zero Kelvin field introduced by Planck [START_REF] Planck | Eine neue Strahlungshypothese[END_REF] in 1911 to modify formula of black body radiation which he had proposed in 1900.

Space-coherent interactions of light with a medium are more complicated than space-incoherent ones:

-Assuming a constant B along a ray, variation of I is exponential.

-Assuming that B does not notably depend upon orientation of rays in a common volume of interaction, a high radiance ray is more amplified or absorbed than a weak one.

-In low energy systems, stochastic zero point field generates stochastic, unstable emissions of light, as in aurora borealis.

-Stabilization of light emission (for instance in a laser) requires a resonant cavity or a convenient geometry of gas.

As coherence requires an absence of collisions, all changes of molecular energy are radiative. Assuming that gas state is constant, a positive amplification of a ray must be compensated by a negative one.

Transfers of energy named competitions of modes obey thermodynamics, but needed temperature of beams is often not properly computed using Planck's law, thus spectral frequency and spectral radiance, while one is tempted to use irradiance instead of radiance.

Strömgren's sphere and shell.

Strömgren [START_REF] Strömgren | The physical state of interstellar hydrogen[END_REF] showed that stars are surrounded by a sphere of stellar wind made out of protons and electrons too fast (too hot) to combine into atoms. Decrease of temperature around sphere generates under-shells of H atoms, excitation of which decreases with the distance from star. For instance the Earth is in solar wind detected through aurorae borealis. This wind cools, mainly by adiabatic expansion, into excited hydrogen atoms at around 10 AU from the Sun, and de-excited atoms at around 15 AU. In figure 2, the comparison of paths of rays in each under-shell shows that the longest path in a layer forming the shell is maximum for a ray which is tangent with the sphere. By taking into account a radial reduction in gas excitation by absorption of stellar radiation, and competition of modes, the limb of sphere is particularly brilliant.

Multiphotonic interactions.

A ruby laser absorbs white light emitted by a flash tube and emits a sharp red spectral line whose large spectral radiance shows that there is an energy transfer from the white continuous spectrum to a red emission. In a dye laser pumped by a neodyme yag laser, an energy transfer from a frequency to another one occurs. Likewise, subjected to a flow of intense white light, atomic hydrogen can be simultaneously excited at several frequencies whose algebraic sum is an eigen-frequency of the atom. In bright Strömgren's shells, atoms transfer all energy from white to superradiant light. Even neglecting different spectra and temperatures, this increases entropy because etendue (geometric extent) of beam defined by star and superradiant medium is much smaller than etendue defined by this medium and solid angle of superradiant emission.

In a collisionless, stable gas, all energy exchanges are radiative, so that energy transfers from star-light to superradiant light is efficient both for absorption and emission. In particular, except close to superradiant rays, hot light is strongly absorbed: Strömgren's shell generates a spectroscopic black hole. In a weak system, only far stars rays close to superradiant rays, are visibly amplified: weak background stars make a bright circle [START_REF] Arp | The 2dF Redshift Survey II: UGC 8584 -Redshift Periodicity and Rings[END_REF].

Observation of SNR1987A

The usual study of SNR1987A supernova poses many problems:

-The formation of the outer rings [START_REF] Burrows | Hubble Space Telescope Observations of the SN 1987A Triple Ring Nebula[END_REF] is not understood.

-When its rings appeared, the star progressively disappeared. Persistence and brightness of rings are not explained.

It is clear that atomic hydrogen plays a large part in rings spectroscopy [START_REF] Pun | Modeling the Hubble Space Telescope Ultraviolet and Optical Spectrum of Spot 1 on the Circumstellar Ring of SN 1987A[END_REF], but the needed hydrogen distribution cannot be explained [START_REF] Sugerman | A New View of the Circumstellar Environment of SN 1987A[END_REF]. Before lighting the rings, incoherent light-scattering by clouds was observed, establishing the hourglass-like geometry.

Assuming that a Strömgren sphere has been distorted in an equatorial plane by absorption or scattering (by planets) of light which heats the stellar wind, then many problems are solved:

• Formation of the hourglass does not result from an unequal distribution of hydrogen, but mainly from an unequal excitation of atoms.

• Energy radiated by the rings simply results from a quasi instantaneous transformation of energy received from the star.

• Light emitted by SN1987A is totally absorbed, while that received from other stars, usually absorbed (because it is hot), can be amplified if it coincides with a ring. An optical black hole is formed.

• The black hole is transparent for cold light: while no star is observed inside inner ring, a glow persists, due to a weak emission by external regions of the hourglass: under Strömgren's shell, protons and electrons collisions may induce a production of atoms stable enough to allow emission of their spectral lines. This low atomic density, thus emission, increases with radius. On its way towards the hourglass surface, the emitted light is redshifted. Thus, the more light is redshifted, the less its radiance is.

Above surface, these rays are too cold to be absorbed or scattered into superradiant rays. But they are strongly redshifted [START_REF] Moret-Bailly | Structure and light emission of a Strömgren system[END_REF]. Such line profiles are usually observed in nebulae.

SNR1987A shows the most beautiful black hole of our galaxy ! 4 Spectroscopy of Lyman α lines of quasars.

Periodicities of Karlsson and Burbidge.

Let us call redshift Z the ratio of a reduction in frequency with respect to initial frequency. Karlsson and Burbidge [START_REF] Karlsson | Quasar redshifts and nearby galaxies[END_REF][START_REF] Burbidge | The Distribution of Redshifts in Quasi-Stellar Objects, N-Systems and Some Radio and Compact Galaxies[END_REF] noticed that most quasars redshifts observed during twentieth century are close to remarkable values given by the empirical formula Z(m) = mK, where m is integer 3, 4, 6, 7, 8, . . . , and K = 0, 061 is Karlsson's constant. These researchers could not use this formula to study quasars spectra, and it does not apply to presently observed highly redshifted quasars. The lack of values 1, 2, 5 of m is surprising and brings to rewrite the formula:

Z(p, q) = p × (3K) + q × (4K), where p and q are nonnegative integers.

Compute the redshifts Z (β,α) and Z (γ,α) which transform Lyman beta (Ly β ) and Lyman gamma (Ly γ ) frequencies (ν β and ν γ ) of H atom into ν α frequency. As Rydberg's constant simplifies:

Z (β,α) = [ν β -ν α ]/ν α = [(1 -1/32) -(1 -1/22)]/(1 -1/22)] ≈ 5/27 ≈ 0.1852 ≈ 3 × 0.0617 ≈ 3K; Z (γ,α) = [ν γ -ν α ]/ν α =[(1-1/42) -(1-1/22)]/(1-1/22) ] = 1/4 = 0,25 = 4*0.0625 ≈ 4K.
Thus, in spectrum, fundamental 3K (or 4K) redshifts bring the absorbed Ly β (or Ly γ ) line onto the Ly α line. Noting that only one Ly β (not redshifted) and no (redshifted) Ly γ line is observed in quasars spectra, P. Petitjean [START_REF] Petitjean | Le contenu baryonique de l'univers révélé par les raies d'absorption dans le spectre des quasars[END_REF] shows perfect coincidences of missing lines with α lines, hence the validity of improved Karlsson's law for (p,q)= (0.1) or (1,0) , 3K or 4K being replaced by Z (β,α) or Z (γ,α) .

Is it also good for others values of p and q ?

Why do these coincidences which correspond to absence of Lyman α absorption stop redshift ?

Redshifted Ly α lines.

Assume that Lyman spectrum is absorbed, next that a redshift process starts. A stop of redshift when an absorbed line reaches Ly α frequency produces Karlsson's (corrected) redshift for the absorbed line.

How to apply this redshift to all frequencies in the spectrum ? By a Doppler effect, all light frequencies are multiplied by a constant, ratio of source and observer speeds. Are all frequencies multiplied by the same constant in quasar redshifts ? No, but though the error is not large, it shows that redshift does result from an interaction with matter (as dispersion in refraction). Remark that successive redshifts multiply the frequencies several times, but do not add redshifts as Karlsson's law does.

Building approximate absorption spectrum of Ly α lines.

Assume that when Ly β line is shifted to Ly α one, all absorbed frequencies are roughly multiplied by ν α /ν β , and also that 3P atoms resulting from Ly β absorption produces a very weak redshift.

A quasar spectrum shows generally sharp, saturated lines. Assuming this applies to all α lines, and neglecting dispersion the principle applied in fig. 4

is very simple :

Initially, the quasar emits a blackbody spectrum of an extremely hot source. It extends to UV-X region. Sharp, almost saturated lines will be absorbed, as seen in spectra. Then, it is assumed that light (thus its absorbed lines) is redshifted if Lyman α absorption is possible.

-A-At the beginning, Ly α , Ly β and Ly γ lines of H atom, eventually strong lines of other gas, are absorbed.

-B-Let ν x be the frequency of an absorbed line greater than and closest to ν α . The spectrum, that is all absorbed lines and emission profile, is redshifted so that ν x is shifted to ν α . This multiplies all frequencies by ν α /ν x .

-C-As redshift produced by Ly β absorption is very weak, redshift is nearly stopped. Ly β and Ly γ lines are absorbed, if it is possible, in the shifted emission spectrum. Other gas frequencies may be absorbed.

-D -If a new frequency ν x is found, and if enough energy remains at Ly β frequency to push absorbed line off Ly α frequency, go to A.

-E -Else, by successive shifts, it does not remain enough energy at Ly β frequency to shift absorbed line off alpha absorption line, the process stops, and laboratory frequency absorbed Ly β line is visible.

Remark: Increasing m, Karlsson's law adds redshifts, a wrong way to combine successive absorptions. Thus Karlsson could not obtain good results.

Dispersion of redshifts.

Previous results are obtained assuming that by a redshift, all absorbed frequencies are multiplied by a constant. This neglects that redshifts being ruled by H atom, as refraction, it depends on atomic resonances, thus on frequencies.

However, comparison of computed and observed spectra shows that, in first approximation, dispersion may be neglected. More accuracy would require the multiplication of frequencies by a dispersion function obtained either experimentally or through ab initio computations.

4.5 Physics of redshifts in quasars spectra. Stop of redshifts corresponds to that of Lyman α absorption, therefore to the non-creation of 2P excited hydrogen atoms from non-excited 1S ones. (We have already deduced that redshift of spectra occurs through light propagation in 2P hydrogen). Redshifts are subjected to the following conditions:

-So that spectral lines be very sharp, atomic hydrogen pressure must be low.

-So that gas excitation results only from Lyman alpha absorption, it is necessary to avoid a thermal excitation which implies a temperature lower than 50,000 K.

-Interactions must be coherent for images not to be destroyed.

-For the light frequency to change, energy must be exchanged with gas, that is the interaction must be a Raman's one.

But, as wavelengths of exciting and Raman scattered beams are different, the phases difference δ between a scattered ray at a fixed point A and one scattered at a variable point M is proportional to the length of arc AM, so that where δ reaches π, scattered rays cancel.

A solution is to use an optically anisotropic medium to have the same wavelength at two frequencies (with different polarization). For instance, using crystals allows to double frequency of an infrared laser ray to obtain a blue one.

A solution applicable to a gas, named Impulsive Stimulated Raman Scattering (ISRS) is studied by many equivalent models such as:

• In incident light, sharp lines linewidths are increased by pulsing the source, so that spectra of incident and scattered lines are expanded. Lines become broad enough for a common, intermediate spectral region corresponding to a shifted frequency.

• Figure 5 shows addition of two waves having same initial phases. Before apparition of beats, addition gives mainly an intermediate frequency selected by a stop of experiment. Use of pulsed light restarts experiment.

• More precisely, a Fourier computation extracts shifted frequency from the sum of incident and Raman scattered pulsed electromagnetic fields.

ISRS experiments are mainly used to study chemical reactions dynamics; the source of pulses is a femtosecond laser.

G. L. Lamb wrote the conditions for coherence, thus ISRS [START_REF] Burbidge | The Distribution of Redshifts in Quasi-Stellar Objects, N-Systems and Some Radio and Compact Galaxies[END_REF]: length of light pulses must be shorter than all implied time constants.

Variation of ISRS versus length of light pulses.

Michelson interferometers allow to split a light beam, then mix obtained beams after different paths, to observe interferences. Using light emitted by a thermal source, interferences may be observed only if difference of paths is lower than 0.3 meters. This shows that usual, thermal light may be represented by 1 nanosecond long coherent light pulses. Thus, pulses making usual light are k = 10 5 times longer, for example, than the 10 femtoseconds pulses of common laboratory lasers.

Compared to laboratory ISRS experiments, the use of natural light requires lower time constants, longer paths:

• Time separating (on the average) two molecular collisions must be increased, thus pressure must be reduced by factor k = 1ns/10f s = 10 5 . This reduces scattered Raman amplitude, thus frequency shift by k factor.

• A reduction of Raman resonance period has a direct effect in the calculation of frequency mix, and an indirect effect by reducing population difference between resonant levels at equilibrium by the factor k.

Thus, the effect is reduced by factor k 3 = 10 15 : observation of frequency shift requires an astronomical path.

According to Lamb's conditions, Raman period must be larger than 1 nanosecond (frequency less than 1 GHz).

The periods of hyperfine resonances in excited levels of H atom are larger than 1ns, so they are suitable, whereas in the ground state, the 1420 MHz resonance has a period of 0.704 nanosecond, too short for an ISRS . As resonant frequencies decrease with the principal quantum number of atom, they produce generally negligible frequency shifts.

As excited hyperfine levels of H atom cannot be de-excited by too rare collisions, de-excitation of atoms requires other ISRS involving generally thermal, low frequency electromagnetic radiation.

Such sets of ISRSs, called Coherent Raman Effects on Incoherent Lights (CREIL), form parametric interactions which exchange energies between light beams, increasing entropy of sets of rays, without significantly altering 2P atomic hydrogen which plays a catalyst role.

Balance of coherent Raman effect in nebulae.

The Coherent Raman Effect on Incoherent Light (CREIL) modifies the frequency of a light ray by exchanging energy with other electromagnetic waves via catalysis involving hyperfine levels of a population of excited hydrogen atoms. Energy stored by hyperfine excitation, or exchanged by collisions is negligible.

Excited hydrogen atoms exist in hot hydrogen of nebulae (temperature above 100,000K). At a lower temperature, it is created by absorption of Lyman alpha line by atomic hydrogen.

5 Spectrum of a quasar surrounded by pure hydrogen.

Theory of neutron stars introduces accreting neutron stars, objects which should be seen despite a size comparable to Earth one, and the mass of Sun, because gas accretion makes them extremely hot. We assume that the quasars are the missing accreting neutron stars.

Here, we construct the spectrum of a neutron star immersed in a nebula of pure hydrogen, following light emitted by the star to the Earth without worrying about the scale of distances; the following subsections correspond to steps characterized by different types of interaction of light-matter interactions.

Kernel of quasar.

The quasar nucleus consists of neutrons resulting from atoms compression during collapse of mother star. In the absence of charged particles, it does not emit electromagnetic radiation.

Layer of very hot atoms.

Close to the nucleus are heavy atoms that are very hot, but have resisted star collapse because pressure was insufficient. These atoms emit a spectrum of hard X-rays.

Dense layer

Closer to the surface, temperature decreases, thus lighter atoms emit radiation at longer wavelengths.

In the highly compressed matter, the atoms can practically not move on the scale of light pulses duration; as in a crystal, their spectrum is not widened by Doppler effect. Thus, a CREIL effect is possible, which transfers energy from hot rays emitted near the core, to rays emitted above, that is to say from hard X-rays to rays emitted at a lower frequency.

However, rays emitted near the surface do not have a large enough common path participate in such exchanges. Thus frequency variations are represented by the sinusoidal aspect curve recorded by a UV-X spectrometer carried by the SOHO probe (fig 6).

Gas.

We can define the surface of a star as the region where atoms acquire a freedom that forbids a CREIL effect. The atmosphere, mainly composed of hydrogen, cools more rapidly than in other stars, for quasar is small. The atmosphere then strongly absorbs broad atomic hydrogen lines, which was first noticed by Gunn and Petersson.

Ionosphere.

If atmospheric conditions are favorable to the presence of a layer strongly ionized by the radiation or by the accretion of the nebula in which the quasar is found, violent electromagnetic storms occur, and the quasar is said to be noisy.

The Lyman lines of the H atom, which are fine at this pressure, are absorbed by the gas.

Very high region.

The light reaches a region where the pressure remains too high for a CREIL effect. The temperature is low enough for the hydrogen to be slightly excited.

The pumping of 1S atoms to more excited levels is not veryS atoms effective, because the lines are fine, which saturates absorptions. Gas pressure and temperature decrease, so that redshifts by CREIL appear.

Propagation of white light in very low pressure, cold atomic hydrogen.

We suppose that white light emitted by a very hot star propagates through low pressure, collisionless, atomic hydrogen, the temperature of which, between 3 000 and 50 000 K, breaks the molecules but does not excite the atoms. Absorption at Ly α frequency excite atoms from 1S to 2P state. This has two consequences:

A-Population of excited atoms increases, so that Einstein's B coefficient for Ly α increases until a superradiant ray bursts in the gas. This flash produces a flare, observed around the star. The beam which was amplified to start the flash has stochastic parameters, depending upon the history of a large volume of gas.

Superradiant emission de-excites atoms and, by a competition of modes, absorbs energy from all modes, in particular from observed mode, so that a line is absorbed in observed light. Pumping of atoms restarts, an other flash bursts, and so on. This relaxation process absorbs a lot of sharp lines making a forest.

B-Excited atoms produce a CREIL which redshifts the observed ray, so that absorbed spectral element is permanently renewed. This absorption of a very broad line is weak, invisible, except when it is increased by competition of modes, during the short flares.

C-If a strongly absorbed line is redshifted to Lyman α frequency, the redshift stops, all lines of gas, in particular Lyman β and γ are absorbed. See section 4.5.

However, if it remains enough energy at Ly β frequency, atoms pumped to 3P state produce a weak redshift until it comes energy at alpha frequency. Then go to A. Else, that is if the spectral element of spectrum shifted to β frequency was out of emission spectrum of the star, there is no more frequency shift.

Structuring space.

There are regions (spherical shells) in which light pumps atoms to 2P state, and is redshifted, other regions in which the latter does not arise because there is no energy in spectrum of light at ν α frequency. Other stars may try to superimpose their own structure. Difficult problem !

To the Earth.

There is no longer any noticeable interaction between light and gases until the spectrum is observed.

6 Other applications of CREIL.

Dispersion of redshifts.

Observation of multiplets emitted by atmosphere of quasars and other much redshifted stars, shows the dispersion of CREIL. Thus, there is no need to imagin a variation of fine structure constant. This dispersion is a strong argument for a redshift resulting from an interaction of light with matter.

Anomalous accelerations of Pioneer 10 and 11

The Strömgren shell of the Sun is between 10 and 15 AU.

Distance and acceleration of the probes are deduced from frequencies of microwave exchanged between probes and Earth. Anderson [START_REF] Anderson | Study of the anomalous acceleration of Pioneer 10 and 11[END_REF] observed an anomalous increase of frequencies when the probes crossed this region. He thought its origin was a Doppler shift due to an acceleration. But it was difficult to find an agreement between various considered sources of acceleration. In Strömgren's shell, excited hydrogen allows a flux of energy from sunlight to microwaves, frequencies of which are increased. Thus, there is no anomalous acceleration to Sun.

Hubble's law.

Hubble's law does not measure distances, but approximately column densities of excited (2P) atomic hydrogen. We write "approximately" because many electromagnetic waves may perturb measurementss. However, this interpretation explains errors due to use of Hubble's law which assumes implicitely that density of excited H atoms is constant. This density is large close to hot stars.

Remarkable consequences of improper use of Hubble's law: Distance of spiral galaxies is exaggerated, so that, for mechanical stability, it is necessary to increase their mass by dark matter.

Hot objects generate a lot of excited atomic hydrogen. Thus bubbles appear in maps of galaxies, universe seems spongy.

Conclusion.

Contemporary astrophysics introduces, like theories of the past, fantasy notions.

While, thanks to the discovery of gas lasers, many physicists understood that interactions of light with ultra-low pressure gas are exclusively coherent, astrophysicists did not use two fundamental effects of coherent spectroscopy: superradiance and coherent, pulsed, stimulated Raman effect. Willing also to imagine an origin of the Universe, they have built a wonderful and complex model.

Construction of a quasar model explaining previous observations has proved the importance of a coherent impulsive Raman effect which solves difficulties arising from an erroneous interpretation of frequency shifts in stars spectra. Superradiance and multiphotonic interactions in atomic hydrogen shells explain the observation of rings around stars and generation of optical black holes.

Why make it simple when you can make it complicated ?

Figure 1 :

 1 Figure 1: Huygens' constructions

Figure 2 :

 2 Figure 2: Sphere and Strömgren's shell (coquille).

Figure 3 :

 3 Figure 3: Supernova 1987A (Hubble)

Figure 4 :

 4 Figure 4: Building Lyman α spectrum of a quasar.

4. 5 . 1

 51 Conditions for a physical redshift: Impulsive Stimulated Raman Scattering: ISRS.

Figure 5 :

 5 Figure 5: Addition of different frequency sinusoids (red and blue), before beats.

Scientific development during the nineteenth century was prepared by encyclopedic rationalism of eighteenth century. But evolution of scientists from

Figure 6: Variations of the Sun's X-emission frequencies after Peter and Judge. [START_REF] Peter | On the Doppler Shifts of Solar Ultraviolet Emission Lines[END_REF]. The authors changed the observed signs of shifts thinking that there was a systematic error while processing measures.

In this paper, hoping to no longer play the role of Cassandra, we avoided calculations, limiting ourselves to a qualitative representation of the universe. Now we must cultivate our garden.