Background/Aim To set a safe giant slalom course, speed needs to be controlled in certain sections. Speed may be reduced by adjusting how the gates are set on a course. We studied the effect of elements of course-setting, entrance speed and terrain incline on the mechanics of turning (ie, turn speed, turn radius, and ground reaction force and impulse).
Methods During seven World Cup alpine giant slalom competitions, the course and terrain characteristics of the official racetracks and the mechanics of a professional-level athlete skiing the course immediately prior to competition were analysed with differential global navigation satellite system technology. Data were analysed using a linear mixed-effects model.
Results Course-setting geometry (vertical gate distance and horizontal gate offset), entrance speed and terrain incline modulated the injury-relevant factor turn speed. Depending on the terrain, the speed throughout a turn can be reduced by 0.5 m/s either by shortening the vertical gate distance by 4.9–6.9 m (from −20% to −29%) or by increasing the horizontal gate offset by 2.8–3.2 m (from +33% to +55%). However, increasing the horizontal gate offset causes the skier to turn with a smaller minimal turn radius, increase maximal ground reaction force and also increase impulse.
Discussion To reduce speed, we recommend decreasing the vertical gate distance rather than increasing the horizontal gate offset. Increasing horizontal gate offset would require the skiers to sharpen and prolong their turns (reducing turn radius), and this increases the acting ground reaction force and impulse and thus the athlete’s fatigue.
- injury prevention
- elite performance
- alpine skiing
- global positioning system
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The risk of injury is relatively high in World Cup (WC) competitive alpine skiing compared with other Olympic winter sports.1 2 More than 33% of athletes sustain an injury each season.3–5 The WC alpine skiing disciplines giant slalom (GS), super-G and downhill are equally dangerous per unit of time,6 and many injuries occur while the skier is turning, without falling or crashing.7 Injuries in downhill and super-G revealed to be associated with speed and the mechanical energy dissipated in crashing, whereas injuries in GS were primarily linked to the mechanics of turning (ie, high turn speeds, small turn radii, large ground reaction forces and high impulse).6
The course-setting rules of the International Ski Federation leave the coaches who set courses a lot of freedom to adapt the course to the terrain and establish safe courses (ie, location and number of gates). Hence, course-setting is a tool practitioners can use to directly influence safety of courses. A previous study on a large number of turns revealed that the steeper the terrain, the shorter the linear gate-to-gate distance (which is highly correlated with vertical gate distance8), and the larger the gate’s horizontal offset (in other studies also named horizontal gate distance8) the lower the skier’s speed.8 Thus, increasing the horizontal gate offset might be effective in reducing speed in GS.9 10 In a previous purely experimental study of one turn, a substantial increase in horizontal gate offset (ie, the amount of turning out of the direction of the fall line)11–13 was needed to substantially reduce skiers’ speed during one turn. The major drawbacks in reducing speed via an increased horizontal gate offset are twofold: (1) increased fatigue due to the turn forces acting over a longer time (ie, higher impulse); and (2) higher risk of getting closer to injury-inciting out-of-balance situations.11
At present, the effect of horizontal gate offset is unknown for different types of terrain, skier speeds and in real competition situations. Whether horizontal gate offset is the only course-setting characteristic that has an effect on speed is also unknown. There is a need to assess the effects of course-setting on factors such as turn speed, turn radius, and ground reaction force and impulse (proxy measure of fatigue),6 and to consider entrance speed and terrain incline as situational factors.8 14 15
The aims of our study were to (1) assess how course-setting characteristics, entrance speed and terrain incline influence the mechanics of turning (ie, turn speed, turn radius, and ground reaction force and impulse); and (2) determine whether manipulation of horizontal gate offset or vertical gate distance is a more reasonable way to reduce speed and risk of injury in real WC alpine GS races.
Within the time frame of two consecutive WC alpine skiing competition seasons, the following seven male GS races (ie, the first and second run for each) were biomechanically analysed: Sölden (Austria (AUT)) (two times), Beaver Creek (USA), Adelboden (Switzerland (SUI)) (two times), Hinterstoder (AUT) and Crans Montana (SUI). For each run of these WC races, one of the official forerunners was equipped with wearable measurement technology to collect mechanical data while skiing down the racetrack. In total, six different forerunners contributed to the data collection at the seven different WC races. Each forerunner was a former WC or current Europa Cup racer.
Data collection methodology
All kinematic data were collected using a differential global navigation satellite system (dGNSS).16 To capture the forerunner’s kinematics, a GPS (Global Positioning System)/GLONASS (Globalnaja nawigazionnaja sputnikowaja sistema) dual frequency (L1/L2) receiver (Alpha-G3T, Javad, San Jose, USA) recorded the position of an antenna (G5Ant-2AT1, Antcom, USA) positioned on the forerunner’s head at 50 Hz. To compute carrier phase double difference position solutions, two base stations were located at the start of the course and equipped with GNSS antennas (GrAnt-G3T, Javad) and Alpha-G3T receivers (Javad). At the start, all gate positions and the terrain geomorphology (snow surface) of each course were captured prior to the respective race using static dGNSS: Alpha-G3T receivers with GrAnt-G3T antenna (Javad) and Leica TPS 1230+ (Leica Geosystems, Switzerland). To reconstruct the snow surface in sufficient detail, 0.3 points per square metre were measured on average; however, more were measured in terrain transitions and fewer in uniform terrain.8
Computation of course characteristics and skier mechanics
Static dGNSS solutions of the snow surface and course-setting measurements were calculated in a postprocessing procedure using the geodetic GNSS software Justin (Javad). To represent the snow surface, the surveyed point cloud was triangulated using the Delaunay method and gridded on a rectangular grid to a digital terrain model. The incline of the local terrain was geometrically derived from the local terrain surface normal vectors, then averaged for the area of each turn and expressed as the angle to the horizontal plane, called TerrainINCLINE .8
Course-setting was described by the horizontal gate offset (GateOFFSET ), which in other studies is also called the horizontal gate distance,8 11 and the vertical gate distance (GateVERTICAL ) (figure 1). Gate OFFSET for gate (i) was computed as the normal projection of gate (i) on the vector connecting gate (i−1) and gate (i+1). In delay turns (ie, when two consecutive gates constitute one turn), the gate with the larger horizontal gate offset was chosen to represent the turn. GateVERTICAL was computed as the distance from gate (i−1) to the projection of gate (i) onto the vector between (i−1) and (i+1), as done previously.8 The direct linear gate distance was not included in the analysis since it is highly correlated with GateVERTICAL , but linearly independent from GateOFFSET .
Geodetic software (GrafNav NovAtel, Canada) was used to postcalculate double difference carrier phase solutions using L1/L2 frequency and GPS and GLONASS satellites.16 Turns for which the geodetic solution ambiguities failed to be solved were excluded from the study. Antenna position was filtered using cubic spline functions, and a mechanical pendulum model was applied to approximate the centre of mass position, as done in an earlier study.17 Ground reaction force, turn radius and speed were calculated from the pendulum model suggested by Gilgien and colleagues.10 18 Turn start and end were defined as the deflection points of the trajectory between two turns.8 Minimal turn radius (RadiusMIN ) was determined as the smallest radius in the turn, and maximal ground reaction force (GRFMAX ) was calculated as the highest ground reaction force in a turn. Entrance speed (SpeedIN ) into a turn was defined as the instantaneous speed at turn start. The change in speed (∆Speed) was computed as speed at the end of the turn (exit speed in figure 1) minus SpeedIN. Impulse was calculated from turn start to turn end as the integral of ground reaction force measured in body weight over turn time in seconds (BWs).6 10
For each parameter, mean and SD were calculated. Data were analysed using a linear mixed-effects model (MIXED procedure in SAS V.9.4 software). Because we had one of six different forerunners in each of the 14 runs, and the snow conditions in the different runs were not characterised, the model was set up with random variables, these being ‘Skier ID’ (six different skiers) and ‘Skier ID*Race ID’. The fixed predictor variables were GateOFFSET , GateVERTICAL , SpeedIN and TerrainINCLINE . The model was set up for each of the dependent variables (response variables), which were ∆Speed, RadiusMIN , GRFMAX and Impulse. All fixed effects were rescaled by dividing by 2 SD (see online supplementary appendix) before putting them into the model. This was done to have more standardised units when describing changes across the different response variables in a way that the results of the model can be read, for example ‘what change in GateOFFSET is needed to cause a 2SD change in ∆Speed’.
The first mixed model was calculated including all 571 turns across the entire range of terrain inclines.
Second, to test whether the mean values were equal between the three terrain incline groups, each of the predictor and outcome parameters was tested using one-way analysis of variance (ANOVA), with a Tukey post-hoc test when an overall difference between the groups was detected. The significance level was set to α=<0.05.
Third, mixed models were calculated for steep, moderately steep and flat terrains, respectively. For this purpose, the terrain incline range (3.4°–34.4°) was split into three equal groups, with the borders being 13.7° and 24.1°, resulting in 108 flat turns, 292 moderately steep turns and 173 steep turns. The results of these three mixed models are given in the online supplementary appendix.
Finally, the mixed models of the three terrain incline groups were used to calculate how large the change in each single predictor variable—GateOFFSET, GateVERTICAL, SpeedIN and TerrainINCLINE —would need to be in order to reduce speed by 0.5 m/s (∆Speed=−0.5 m/s) through a turn (results in table 1 and online supplementary appendix), and what effect that change in the predictors would have on the outcome variables RadiusMIN , GRFMAX and Impulse. The results for the predictors that course-setters can manipulate directly, GateOFFSET and GateVERTICAL , are given in table 2. The results for all predictors and the underlying mixed model are provided in the online supplementary appendix.
Effects of course-setting characteristics, entrance speed and terrain incline on the mechanics of turning
The statistical analysis across all 571 turns (table 3) shows that both an increase in GateOFFSET and a decrease in GateVERTICAL significantly reduced speed while turning. Speed (∆Speed) was reduced to a larger extent if SpeedIN was increased or if TerrainINCLINE was smaller. RadiusMIN was significantly decreased if GateOFFSET was increased, SpeedIN was decreased or TerrainINCLINE was smaller (flatter). GateVERTICAL had no significant effect on RadiusMIN. GRFMAX was significantly larger if GateOFFSET was increased, SpeedIN was higher or TerrainINCLINE was larger (steeper). GateVERTICAL had no significant effect on GRFMAX . Finally, Impulse was found to increase with increasing GateOFFSET .
Differences in the mechanics of turning between flat, moderate and steep terrains
The mean, SD, and minimal and maximal values for predictors and outcome variables of the mixed model for the three terrain categories are presented in table 4. ANOVA revealed that the mean values for flat, moderate and steep terrains were significantly different at the α≤0.01 level for all predictors and outcome variables, except for ∆Speed (m/s) in flat versus moderate terrain (α=0.11) and GRF MAX in moderate versus steep terrain (α=0.52). SpeedIN decreased the steeper the terrain became. The mean GateOFFSET increased with larger TerrainINCLINE (steeper), while GateVERTICAL decreased the steeper the terrain was. In moderate TerrainINCLINE , the mean turn speed was held approximately constant (∆Speed ~0), while in steep terrain ∆Speed became positive (speed increase) and in more flat terrain ∆Speed was negative (speed reduction). RadiusMIN became substantially smaller and Impulse increased with increasing steepness of the terrain. However, the mean GRF MAX was independent of TerrainINCLINE .
What are the terrain-specific effects of course-setting on the mechanics of turning?
To fully understand our data, the results of the mixed model for ∆Speed, RadiusMIN , GRFMAX and Impulse, the change needed for the predictors GateOFFSET , GateVERTICAL , SpeedIN and TerrainINCLINE to cause a reduction in speed (∆Speed) of −0.5 m/s, and the effect on ∆Speed, RadiusMIN , GRFMAX and Impulse for flat, moderate and steep terrains are given in the online supplementary appendix. The results for the two predictors that course-setters can influence directly (GateVERTICA L and GateOFFSET ) and the changes needed to reduce speed (∆Speed) by −0.5 m/s are given in table 1, and their effects on RadiusMIN , GRFMAX and Impulse for the three different terrains are given in table 2.
To reduce speed (∆Speed) by 0.5 m/s throughout a turn, GateOFFSET would need to be increased by 2.9 m (+55% of mean GateOFFSET ) in flat terrain, by 3.2 m (+45%) in moderate terrain, and by 2.8 m (+33%) in steep terrain. To reduce speed (∆Speed) by 0.5 m/s throughout a turn, Gate VERTICAL would need to be shortened by 6.9 m (−27%) in moderate terrain and 4.9 m (−20%) in steep terrain, while it had no effect on ∆Speed in flat terrain.
The increase in GateOFFSET needed to reduce speed by 0.5 m/s resulted in a decrease in RadiusMIN of −3.7 m (−17%) in flat terrain, −3.6 m (−21%) in moderately steep terrain, and −1.9 m (−14%) in steep terrain. A change in GateVERTICA L had no significant effect on RadiusMIN . The increase in GateOFFSET needed to cause a reduction in speed of 0.5 m/s caused an increase in GRFMAX of +0.14 body weight (+6%) in flat terrain and +0.21 body weight (+8%) in moderately steep terrain. In steep terrain, an increase in GateOFFSET had no additional effect on GRF MAX . A change in GateVERTICA L had no significant effect on GRFMAX . The increase in GateOFFSET required to cause a reduction in speed by 0.5 m/s induced an increase in Impulse by +0.45 BWs (+22%) in flat terrain, by +0.55 BWs (+24%) in moderately steep terrain, and by +0.32 BWs (+13%) in steep terrain. A change in GateVERTICA L had no significant effect on Impulse.
The main findings of this study were the following: (1) Course-setting characteristics (ie, GateOFFSET and GateVERTICAL ), entrance speed (SpeedIN ) and terrain incline (TerrainINCLINE ) were significant modulators of turn speed (∆Speed), minimal turn radius (RadiusMIN ) and maximal ground reaction forces (GRFMAX ), while Impulse was mainly dependent on GateOFFSET . (2) To reduce speed (∆Speed) by 0.5 m/s throughout a turn, GateOFFSET would need to be increased by 2.9 m (+55%) in flat terrain, by 3.2 m (+45%) in moderate terrain, and by 2.8 m (+33%) in steep terrain; GateVERTICAL needs to be shortened by 6.9 m (−27%) in moderate terrain and 4.9 m (−20%) in steep terrain. (3) On flat terrain, increasing GateOFFSET was found to be the only effective measure to control speed. (4) To decrease speed in moderate and steep terrains, decreasing GateVERTICAL is preferable to increasing GateOFFSET , since shortening GateVERTICAL decreased speed without increasing GRFMAX and Impulse and without reducing RadiusMIN .
Influence of course-setting characteristics, entrance speed and terrain incline on the mechanics of turning
From our data, entrance speed, terrain incline, and both GateOFFSET and GateVERTICAL were important modulators of the injury risk-related factors of speed, minimal turn radius and maximal ground reaction force; however, impulse seems to mainly depend on horizontal gate offset (table 3).
Skiers seem to control speed to avoid exceeding a ‘velocity barrier’ in certain sections along the course and thus avoid mistakes.19 20 The data from this study may provide deeper insight into the underlying mechanism of this phenomenon. Across the races and situations assessed in this study, the mean GRFMAX was the same in moderate and steep terrains and only slightly smaller in flat terrain, while the mean SpeedIN and mean RadiusMIN significantly changed with TerrainINCLINE (table 4). Hence, GRFMAX could be a regulator of the ‘velocity barrier’. Thus, athletes seem to adjust their speed to the turn radius in order to hit the GRFMAX level that can be tolerated by their physical capacity and technical skills and the ski–snow interaction.
Course-setting as an injury prevention measure in competitive alpine skiing
From our data, in moderate and steep terrains, both a greater GateOFFSET and a smaller GateVERTICAL slowed down skiers (table 1). However, increasing GateOFFSET not only reduced speed but also had the unintended consequence of increasing risk of injury by reducing RadiusMIN , increasing Impulse, and in flat and moderate terrains also increasing GRFMAX . However, the same effect on ∆Speed was achieved by reducing GateVERTICAL without producing negative consequences for RadiusMIN , GRFMAX and Impulse (table 2), and probably also course length. Based on these results, decreasing GateVERTICAL appears to be a better way to adjust course-setting so as to reduce speed than increasing GateOFFSET . Moreover, today we see more and more races with sparse snow conditions and restricted slope widths, which additionally challenge/limit the potential for increasing GateOFFSET . In flat terrain, however, a change in GateVERTICAL had no effect on ∆Speed, and increasing GateOFFSET is thus the only effective measure to control speed in flat terrain.
These results are of high practical relevance since WC alpine skiing course-setters tend to adapt course-setting to the terrain and probably control speed primarily using GateOFFSET .8 A simple explanation might be that coaches use measuring tape to measure and control the linear gate distance (ie, linear distance from gate to gate, which is strongly related to GateVERTICAL ) and keep that distance almost constant when setting courses,8 probably to keep a certain rhythm in a course.
Our study shows that the shortening distance needed in GateVERTICAL is about double the increase in GateOFFSET that is needed to have the same effect on ∆Speed. This might feel like a large change. However, the percentage changes required to shorten GateVERTICAL are only half of the percentage changes needed in GateOFFSET to reduce speed to a certain level. These facts should help course-setters better understand relative changes in GateVERTICAL and GateOFFSET and their effects on skier mechanics that are related to risk of injury.
We underscore that adjusting how the GS course is set reduces speed more than changes in equipment (increasing ski–snow friction) or clothing (increasing air drag) in GS. The potential effects of moderate course-setting modifications (0.05 m/s per turn) are remarkably high compared with equipment modifications.20 21
Limitations and comments on methods
We note at least three limitations. First, the current analysis has not looked at the interaction of consecutive turns or entire course sequences. Second, by splitting turns into three terrain incline categories, statistical power was reduced and a larger data set might have shown additional significant results for certain predictors. Third, the applied dGNSS methodology did not provide direct data describing the influence of course-setting on the mode of ski–snow interaction. Thus, we are speculating as to why speed is reduced as a function of ski–snow interaction. Most likely, decreasing GateVERTICAL led to more skidding while turning compared with increasing GateOFFSET . Thus, future studies should investigate in more detail the effect of course-setting on skidding and the underlying ski–snow interaction.
To set a safe GS course and to reduce speed, shortening the vertical gate distance seems to be more appropriate than increasing the horizontal gate offset, since it will slow the skier without increasing the ground reaction force and the athlete’s fatigue. We outline how much course-setting manipulations can slow skiers in different terrains, and these are directly applicable to course-setting and coaching.
What are the findings?
Depending on the terrain incline, a reduction of speed by 0.5 m/s throughout a turn can be achieved either by increasing the horizontal gate offset by 2.8–3.2 m (from +33% to +55%) or shortening the vertical gate distance by 4.9–6.9 m (from −20% to −29%).
To reduce speed in moderate and steep terrains, shortening the vertical gate distance instead of increasing the horizontal gate offset is suggested, since this approach decreases speed without increasing risk of injury through increased ground reaction force and impulse (as a proxy measure of fatigue).
How might it impact on clinical practice in the future?
This knowledge is expected to have a significant impact on sports practice since evidence-based guidance for course-setters is provided.
Contributors MG, JS, JK and EM conceptualised the study design. MG, JS and JK organised and coordinated the biomechanical data collections at the FIS WC races. MG, PC and LSL conducted the data processing, statistical analysis and data interpretation. MG and JS drafted the first version of the manuscript. All authors contributed to the intellectual content of the study, manuscript writing and approved the final version of this article.
Funding This study was financially supported by the International Ski Federation (FIS) Injury Surveillance System (ISS). The funding source had no involvement in the study design; in the collection, analysis and interpretation of data; in the writing of the report; or in the decision to submit this paper for publication.
Competing interests None declared.
Patient and public involvement Patients and/or the public were not involved in the design, or conduct, or reporting, or dissemination plans of this research.
Patient consent for publication Not required.
Ethics approval This study was approved by the Ethics Committee of the Department of Sport Science and Kinesiology at the University of Salzburg. All subjects provided written informed consent prior to participating in the investigation.
Provenance and peer review Not commissioned; externally peer reviewed.
Data availability statement All data relevant to the study are included in the article or uploaded as supplementary information. Access to the data underlying the study is restricted due to intellectual property reasons.