International Journal of Sports Physiology and Performance, 2015, 10, 361-368 http://dx.doi.org/10.1123/ijspp.2014-0200 © 2015 Human Kinetics, Inc.
www.IJSPP-Journal.com ORIGINAL INVESTIGATION
Impact of the Steepness of the Slope on the Biomechanics of World Cup Slalom Skiers Matej Supej, Kim Hébert-Losier, and Hans-Christer Holmberg Purpose: Numerous environmental factors can affect alpine-ski-racing performance, including the steepness of the slope. However, little research has focused on this factor. Accordingly, the authors’ aim was to determine the impact of the steepness of the slope on the biomechanics of World Cup slalom ski racers. Methods: The authors collected 3-dimensional kinematic data during a World Cup race from 10 male slalom skiers throughout turns performed on a relatively flat (19.8°) and steep (25.2°) slope under otherwise similar course conditions. Results: Kinematic data revealed differences between the 2 slopes regarding the turn radii of the skis and center of gravity, velocity, acceleration, and differential specific mechanical energy (all P < .001). Ground-reaction forces (GRFs) also tended toward differences (P = .06). Examining the time-course behaviors of variables during turn cycles indicated that steeper slopes were associated with slower velocities but greater accelerations during turn initiation, narrower turns with peak GRFs concentrated at the midpoint of steering, more pronounced lateral angulations of the knees and hips at the start of steering that later became less pronounced, and overall slower turns that involved deceleration at completion. Consequently, distinct energy-dissipation-patterns were apparent on the 2 slope inclines, with greater pregate and lesser postgate dissipation on the steeper slope. The steepness of the slope also affected the relationships between mechanical skiing variables. Conclusions: The findings suggest that specific considerations during training and preparation would benefit the race performance of slalom skiers on courses involving sections of varying steepness. Keywords: alpine skiing, athletic performance, kinematics, kinetics, winter sports Alpine ski racing is a demanding sport performed in intricate outdoor environments. Indeed, several biomechanical1 and environmental2 factors influence alpine-ski-racing performance, and when the mechanical loads exceed a skier’s capacity, the injury risk increases.3 Although alpine-skiing research has focused on ski–snow friction,4 turning technique,5 and loading patterns,6,7 the impact of the steepness of the slope on skiing mechanics remains scarcely documented. In most carved turns, the skis remain in contact with the snow, and the skier’s center of gravity (CG) travels on a more direct path around the gate than the skis (Figure 1[A]).8,9 The distinct paths of the CG and skis result from the skier’s turn inclination, where centrifugal, gravitational, and ski–snow friction forces are balanced.10,11 Then again, the ski-turn radius relies in great part on the edging angles of the skis,10,12 with both affecting the inclination of the CG and lateral angulations of the knees and hips (Figure 1[B]).13 Considering the relationships between a skier’s path, turn radius, and body and ski positions, the slope steepness must presumably affect human skiing mechanics. Such findings would concur with the strong relationship reported to exist between the average activation of lower-limb muscles and the level of ski-slope inclination (r = .92).14 In theory, during turn initiation, more pronounced bodily inclinations of a skier or knee and hip lateral angulations are needed to attain similar edging angles on a steeper slope and, conversely, smaller bodily inclinations or knee and hip lateral angulations during Supej is with the Dept of Biomechanics, University of Ljubljana, Ljubljana, Slovenia. Hébert-Losier and Holmberg are with the Dept of Health Sciences, Mid Sweden University, Östersund, Sweden. Address author correspondence to Matej Supej at [email protected].
turn completion (Figure 1[B]).15 Hence, at similar velocities and gate distances, skiers should adjust knee and hip lateral angulations on different slope inclinations as soon as further increasing the bodily inclination compromises balance. Once a skier’s adaptations are insufficient to adjust to different slope inclines, modifications in the turn radii or ground-reaction forces (GRFs) are likely. Conversely, because skiers typically travel more parallel to the fall line during steering and in proximity to gates, the slope steepness seemingly affects skiing mechanics to a lesser extent.15 Given that the potential energy available per turn is greater on steeper slopes,16 slope inclination per se might also affect energy dissipation and, consequently, accelerations and velocities. However, steeper slopes are not necessarily skied at faster velocities, with velocities shown to increase during the transition from a steeper to a flatter slope when gates are relatively far apart.13 Considering that velocity, turn radii, GRFs, and energydissipation behaviors are all related to alpine-skiing performance and technique,1,16–18 determining the impact of the steepness of the slope on these parameters might be useful to coaches, skiers, and organizers of racing events. Accordingly, our aim was to determine the influence of the steepness of the slope on kinematic and kinetic variables during a slalom ski race.
Methods Ten elite male World Cup slalom skiers (age, 26.9 ± 2.5 y; performance level, 2.7 ± 2.5 World Cup and/or World Championships podium places in the current season; International Ski Federation [FIS] points, 4.9 ± 5.7; current race standing, 5 skiers finished in the top 10) participated in this study after providing written informed consent. The FIS, institutional ethical committee (Faculty of Sport, 361
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362 Supej, Hébert-Losier, and Holmberg
Figure 1 — Frontal-plane illustration of (A) the movement of a skier’s center of gravity and skis during the various phases of a turn and (B) the lateral angulation of the knees and hips, as well as the inclination of the center of gravity, before and after a gate. Note that the lateral angulations are projections of joint angles onto a plane perpendicular to the velocity of the center of gravity.
University of Ljubljana, Slovenia), and World Cup race director and event organizers all approved our observational research study and protocol, which adhered to the latest amendments of the Declaration of Helsinki. Biomechanical measurements were performed during slalom World Cup races held in Kranjska Gora, Slovenia, using 3-dimensional (3D) kinematic analyses. Skiers were recorded on the first run over 2 different sections of a course with 64 gates. The steeper section analyzed herein was between gates 8 and 11 and had an average slope inclination of 25.2° (47%). The flatter section was between gates 18 and 21 and had an average slope inclination of 19.8° (36%). The 4 gates in each section were equidistant vertically (steeper, 11.6 ± 0.3 m; flatter, 11.7 ± 0.3 m) and horizontally (3.8 ± 0.5 and 3.9 ± 0.5 m, respectively). All gate distances and course settings complied with FIS rules. On race day, the environmental conditions were ideal (ie, hard groomed snow and subzero temperatures) and remained stable during data collection. For 3D kinematic measurements, 6 generator-locked 50 Hz Sony DV-CAM DSR 300 PK (Sony Corp, Tokyo, Japan) professional camcorders with fixed position and image settings were used on each of the 2 sections (Figure 2). In each section, camcorders were divided into 3 pairs, each covering 1 subspace and ensuring a capture volume that included all 4 gates and 3 full turns. In addition, 2 pan-tilt-zoom Sony mini-DV DCR-TVR 30 E camcorders (Sony Corp, Tokyo, Japan) were used to record the skiers laterally from both sides to assist in completing kinematic data sets. As previously reported,16,19 the measurement volumes were calibrated using an electronic tachymeter, Leica TCR1102 X-Range (Leica Geosystems AG, Heerbrugg, Switzerland), and eight 1.95-mlong aluminum calibration poles. APAS Ariel 3D kinematic software (Ariel Dynamics Inc, San Diego, CA) was used to transform the 2 × 2D into 3D data. To determine the error of measurement, we recorded the location of the inside poles of gates once using the tachymeter and once using the 3D kinematical measurements. The standard deviation of the differences in the location of the poles was less than 2 cm. Fifteen reference points were used to digitize a 12-segment standardized model of a skier, where each segment represented a
body part linked to another via a point-like joint. The masses and CG of segments, as well as the CG of the body, were calculated using the linked-segment parameters of Dempster.20 The raw kinematic data from each measurement were extracted from the APAS software and joined using customized scripts in Matlab 2007a (The MathWorks, Inc, Natick, MA). To merge data sets, the scripts verified for consistency in the first differential of the CG trajectory within adjacent subspaces and overlapping areas. Before computing variables, data were smoothed using a third-order Butterworth zero-lag digital filter with a 7-Hz cutoff frequency, such as in previous investigations,21 and applied here to limit white noise. Customized scripts were used to calculate the specific mechanical energy (emech = v2/2 + gz) and differential specific mechanical energy (diff[emech] = –Δ[v2/2]/Δz – g) from the 3D kinematic data in Matlab, where v represents the absolute velocity of the skier’s CG calculated from the CG’s trajectory using linear approximation; z, the altitude; g, the gravitational acceleration; and Δ, the finite difference operator (ie, the discrete altitude differential).16 The diff(emech) estimates the skier’s energy dissipation in relation to the difference in altitude. Negative and positive diff(emech) values represent decreasing and increasing specific mechanical energy per altitude difference, respectively, where higher values indicate more efficient skiing. The turn radii of the CG (RCG) and skis (RSKIS) were calculated by fitting an arc segment on each set of 3 neighboring points for the CG and midpoint between the ankle joints, respectively. The skier’s acceleration, a, was calculated by differentiating v. Newton’s Second Law was used to estimate GRFs (normalized to body weight [BW]), calculated as the sum of the acceleration vector multiplied by the mass of the skier and the static component of the gravitational force. Finally, the knee and hip angles were projected onto a plane perpendicular to v to define knee and hip lateral angulations (Figure 1[B]).13 Previous research has demonstrated the reliability and validity of the kinematic variables derived herein using camcorders.13,19,22–24 In summary, our measurement errors were estimated to be less than 0.067 m/s for the unfiltered v, ~5 cm (ie, 1%) greater for RSKIS values computed from the midpoint of the ankles to a point on a ski, ± 0.25 BW for GRFs derived from double differentiation of
Downloaded by Australian Catholic University on 09/24/16, Volume 10, Article Number 3
Slope Steepness and Skiing Biomechanics 363
Figure 2 — Schematization of the motion-acquisition system’s placement.
kinematic data, and less than 2.5° for the unfiltered hip and knee lateral angulations. The magnitudes of measurement errors were deemed acceptable for the purpose of this study. Turn cycles were divided into the 4 following phases: initiation, steering 1, steering 2, and completion (Figure 1[A]). Only areas where RSKIS was above 15 m were considered in defining turn initiation and completion, since 15 m was the upper limit of the skis’ side-cut radius used in this study. These areas were divided into 2 consecutive phases (completion of the previous turn and initiation of the considered turn) based on the point in time where the CG’s trajectory crossed the skis’ trajectory, projected orthogonally onto the snow surface.25,26 Finally, the steering phase was divided in 2, using the position of the turn gate as deterministic reference. For all variables, means ± SDs were computed and diagrams representing turn-cycle characteristics were constructed. The means were compared between slopes using a 2-sample KolmogorovSmirnov test. For analyzing differences along the turn cycles, variables were time-normalized as a percentage of the total turn time. Mean and SD values were calculated for every 2% of turn cycles for all turns. Finally, scatter plots were generated to investigate the relationships between variables, and trends determined using linearregression lines and associated Pearson correlation coefficients (r), slope of the linearly regressed line (k), and y-intercept of the slope (n). Statistical analyses and calculations were performed in Matlab, with a significance level set at P < .05.
Results The turn-cycle characteristics on the steeper and flatter slopes are represented in Figures 3 and 4. The means of variables differed significantly between these slope conditions for RCG (13.2 vs 16.5 m), RSKIS (8.7 vs 10.6 m), v (11.8 vs 12.4 m/s), a (–0.06 vs 0.68 m/
s2), and diff(emech) (–8.5 vs –6.3 J · kg–1 · m–1, all P < .01), with a trend for differences in the GRFs (1.3 vs 1.4 BW, P = .06). As observed in Figures 3 and 4, the relative duration of each turn phase was similar between slopes (
www.IJSPP-Journal.com ORIGINAL INVESTIGATION
Impact of the Steepness of the Slope on the Biomechanics of World Cup Slalom Skiers Matej Supej, Kim Hébert-Losier, and Hans-Christer Holmberg Purpose: Numerous environmental factors can affect alpine-ski-racing performance, including the steepness of the slope. However, little research has focused on this factor. Accordingly, the authors’ aim was to determine the impact of the steepness of the slope on the biomechanics of World Cup slalom ski racers. Methods: The authors collected 3-dimensional kinematic data during a World Cup race from 10 male slalom skiers throughout turns performed on a relatively flat (19.8°) and steep (25.2°) slope under otherwise similar course conditions. Results: Kinematic data revealed differences between the 2 slopes regarding the turn radii of the skis and center of gravity, velocity, acceleration, and differential specific mechanical energy (all P < .001). Ground-reaction forces (GRFs) also tended toward differences (P = .06). Examining the time-course behaviors of variables during turn cycles indicated that steeper slopes were associated with slower velocities but greater accelerations during turn initiation, narrower turns with peak GRFs concentrated at the midpoint of steering, more pronounced lateral angulations of the knees and hips at the start of steering that later became less pronounced, and overall slower turns that involved deceleration at completion. Consequently, distinct energy-dissipation-patterns were apparent on the 2 slope inclines, with greater pregate and lesser postgate dissipation on the steeper slope. The steepness of the slope also affected the relationships between mechanical skiing variables. Conclusions: The findings suggest that specific considerations during training and preparation would benefit the race performance of slalom skiers on courses involving sections of varying steepness. Keywords: alpine skiing, athletic performance, kinematics, kinetics, winter sports Alpine ski racing is a demanding sport performed in intricate outdoor environments. Indeed, several biomechanical1 and environmental2 factors influence alpine-ski-racing performance, and when the mechanical loads exceed a skier’s capacity, the injury risk increases.3 Although alpine-skiing research has focused on ski–snow friction,4 turning technique,5 and loading patterns,6,7 the impact of the steepness of the slope on skiing mechanics remains scarcely documented. In most carved turns, the skis remain in contact with the snow, and the skier’s center of gravity (CG) travels on a more direct path around the gate than the skis (Figure 1[A]).8,9 The distinct paths of the CG and skis result from the skier’s turn inclination, where centrifugal, gravitational, and ski–snow friction forces are balanced.10,11 Then again, the ski-turn radius relies in great part on the edging angles of the skis,10,12 with both affecting the inclination of the CG and lateral angulations of the knees and hips (Figure 1[B]).13 Considering the relationships between a skier’s path, turn radius, and body and ski positions, the slope steepness must presumably affect human skiing mechanics. Such findings would concur with the strong relationship reported to exist between the average activation of lower-limb muscles and the level of ski-slope inclination (r = .92).14 In theory, during turn initiation, more pronounced bodily inclinations of a skier or knee and hip lateral angulations are needed to attain similar edging angles on a steeper slope and, conversely, smaller bodily inclinations or knee and hip lateral angulations during Supej is with the Dept of Biomechanics, University of Ljubljana, Ljubljana, Slovenia. Hébert-Losier and Holmberg are with the Dept of Health Sciences, Mid Sweden University, Östersund, Sweden. Address author correspondence to Matej Supej at [email protected].
turn completion (Figure 1[B]).15 Hence, at similar velocities and gate distances, skiers should adjust knee and hip lateral angulations on different slope inclinations as soon as further increasing the bodily inclination compromises balance. Once a skier’s adaptations are insufficient to adjust to different slope inclines, modifications in the turn radii or ground-reaction forces (GRFs) are likely. Conversely, because skiers typically travel more parallel to the fall line during steering and in proximity to gates, the slope steepness seemingly affects skiing mechanics to a lesser extent.15 Given that the potential energy available per turn is greater on steeper slopes,16 slope inclination per se might also affect energy dissipation and, consequently, accelerations and velocities. However, steeper slopes are not necessarily skied at faster velocities, with velocities shown to increase during the transition from a steeper to a flatter slope when gates are relatively far apart.13 Considering that velocity, turn radii, GRFs, and energydissipation behaviors are all related to alpine-skiing performance and technique,1,16–18 determining the impact of the steepness of the slope on these parameters might be useful to coaches, skiers, and organizers of racing events. Accordingly, our aim was to determine the influence of the steepness of the slope on kinematic and kinetic variables during a slalom ski race.
Methods Ten elite male World Cup slalom skiers (age, 26.9 ± 2.5 y; performance level, 2.7 ± 2.5 World Cup and/or World Championships podium places in the current season; International Ski Federation [FIS] points, 4.9 ± 5.7; current race standing, 5 skiers finished in the top 10) participated in this study after providing written informed consent. The FIS, institutional ethical committee (Faculty of Sport, 361
Downloaded by Australian Catholic University on 09/24/16, Volume 10, Article Number 3
362 Supej, Hébert-Losier, and Holmberg
Figure 1 — Frontal-plane illustration of (A) the movement of a skier’s center of gravity and skis during the various phases of a turn and (B) the lateral angulation of the knees and hips, as well as the inclination of the center of gravity, before and after a gate. Note that the lateral angulations are projections of joint angles onto a plane perpendicular to the velocity of the center of gravity.
University of Ljubljana, Slovenia), and World Cup race director and event organizers all approved our observational research study and protocol, which adhered to the latest amendments of the Declaration of Helsinki. Biomechanical measurements were performed during slalom World Cup races held in Kranjska Gora, Slovenia, using 3-dimensional (3D) kinematic analyses. Skiers were recorded on the first run over 2 different sections of a course with 64 gates. The steeper section analyzed herein was between gates 8 and 11 and had an average slope inclination of 25.2° (47%). The flatter section was between gates 18 and 21 and had an average slope inclination of 19.8° (36%). The 4 gates in each section were equidistant vertically (steeper, 11.6 ± 0.3 m; flatter, 11.7 ± 0.3 m) and horizontally (3.8 ± 0.5 and 3.9 ± 0.5 m, respectively). All gate distances and course settings complied with FIS rules. On race day, the environmental conditions were ideal (ie, hard groomed snow and subzero temperatures) and remained stable during data collection. For 3D kinematic measurements, 6 generator-locked 50 Hz Sony DV-CAM DSR 300 PK (Sony Corp, Tokyo, Japan) professional camcorders with fixed position and image settings were used on each of the 2 sections (Figure 2). In each section, camcorders were divided into 3 pairs, each covering 1 subspace and ensuring a capture volume that included all 4 gates and 3 full turns. In addition, 2 pan-tilt-zoom Sony mini-DV DCR-TVR 30 E camcorders (Sony Corp, Tokyo, Japan) were used to record the skiers laterally from both sides to assist in completing kinematic data sets. As previously reported,16,19 the measurement volumes were calibrated using an electronic tachymeter, Leica TCR1102 X-Range (Leica Geosystems AG, Heerbrugg, Switzerland), and eight 1.95-mlong aluminum calibration poles. APAS Ariel 3D kinematic software (Ariel Dynamics Inc, San Diego, CA) was used to transform the 2 × 2D into 3D data. To determine the error of measurement, we recorded the location of the inside poles of gates once using the tachymeter and once using the 3D kinematical measurements. The standard deviation of the differences in the location of the poles was less than 2 cm. Fifteen reference points were used to digitize a 12-segment standardized model of a skier, where each segment represented a
body part linked to another via a point-like joint. The masses and CG of segments, as well as the CG of the body, were calculated using the linked-segment parameters of Dempster.20 The raw kinematic data from each measurement were extracted from the APAS software and joined using customized scripts in Matlab 2007a (The MathWorks, Inc, Natick, MA). To merge data sets, the scripts verified for consistency in the first differential of the CG trajectory within adjacent subspaces and overlapping areas. Before computing variables, data were smoothed using a third-order Butterworth zero-lag digital filter with a 7-Hz cutoff frequency, such as in previous investigations,21 and applied here to limit white noise. Customized scripts were used to calculate the specific mechanical energy (emech = v2/2 + gz) and differential specific mechanical energy (diff[emech] = –Δ[v2/2]/Δz – g) from the 3D kinematic data in Matlab, where v represents the absolute velocity of the skier’s CG calculated from the CG’s trajectory using linear approximation; z, the altitude; g, the gravitational acceleration; and Δ, the finite difference operator (ie, the discrete altitude differential).16 The diff(emech) estimates the skier’s energy dissipation in relation to the difference in altitude. Negative and positive diff(emech) values represent decreasing and increasing specific mechanical energy per altitude difference, respectively, where higher values indicate more efficient skiing. The turn radii of the CG (RCG) and skis (RSKIS) were calculated by fitting an arc segment on each set of 3 neighboring points for the CG and midpoint between the ankle joints, respectively. The skier’s acceleration, a, was calculated by differentiating v. Newton’s Second Law was used to estimate GRFs (normalized to body weight [BW]), calculated as the sum of the acceleration vector multiplied by the mass of the skier and the static component of the gravitational force. Finally, the knee and hip angles were projected onto a plane perpendicular to v to define knee and hip lateral angulations (Figure 1[B]).13 Previous research has demonstrated the reliability and validity of the kinematic variables derived herein using camcorders.13,19,22–24 In summary, our measurement errors were estimated to be less than 0.067 m/s for the unfiltered v, ~5 cm (ie, 1%) greater for RSKIS values computed from the midpoint of the ankles to a point on a ski, ± 0.25 BW for GRFs derived from double differentiation of
Downloaded by Australian Catholic University on 09/24/16, Volume 10, Article Number 3
Slope Steepness and Skiing Biomechanics 363
Figure 2 — Schematization of the motion-acquisition system’s placement.
kinematic data, and less than 2.5° for the unfiltered hip and knee lateral angulations. The magnitudes of measurement errors were deemed acceptable for the purpose of this study. Turn cycles were divided into the 4 following phases: initiation, steering 1, steering 2, and completion (Figure 1[A]). Only areas where RSKIS was above 15 m were considered in defining turn initiation and completion, since 15 m was the upper limit of the skis’ side-cut radius used in this study. These areas were divided into 2 consecutive phases (completion of the previous turn and initiation of the considered turn) based on the point in time where the CG’s trajectory crossed the skis’ trajectory, projected orthogonally onto the snow surface.25,26 Finally, the steering phase was divided in 2, using the position of the turn gate as deterministic reference. For all variables, means ± SDs were computed and diagrams representing turn-cycle characteristics were constructed. The means were compared between slopes using a 2-sample KolmogorovSmirnov test. For analyzing differences along the turn cycles, variables were time-normalized as a percentage of the total turn time. Mean and SD values were calculated for every 2% of turn cycles for all turns. Finally, scatter plots were generated to investigate the relationships between variables, and trends determined using linearregression lines and associated Pearson correlation coefficients (r), slope of the linearly regressed line (k), and y-intercept of the slope (n). Statistical analyses and calculations were performed in Matlab, with a significance level set at P < .05.
Results The turn-cycle characteristics on the steeper and flatter slopes are represented in Figures 3 and 4. The means of variables differed significantly between these slope conditions for RCG (13.2 vs 16.5 m), RSKIS (8.7 vs 10.6 m), v (11.8 vs 12.4 m/s), a (–0.06 vs 0.68 m/
s2), and diff(emech) (–8.5 vs –6.3 J · kg–1 · m–1, all P < .01), with a trend for differences in the GRFs (1.3 vs 1.4 BW, P = .06). As observed in Figures 3 and 4, the relative duration of each turn phase was similar between slopes (
