Supej (2014) Impact of the Steepness of the Slope on the Biomechanics of World

Full text

Supej, Hébert-Losier, and Holmberg Slope Steepness and Skiing Biomechanics
Page 1 of 9
http://dx.doi.org/10.1123/ijspp.2014-0200
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 i nvolving
sections of varying steepness.
Keywords: alpine skiing, athletic performance, kinematics, kinetics, winter sports
Alpine ski racing is a demanding sport performed in intricate
1
outdoor environments. Indeed, several biomechanical1 and environ-
mental2 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
\<<<<<<<<<<<<<<<FIGURE 1>>>>>>>>>>>>>>>>>>>>\
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
turn completion (Figure 1[B]).15 Hence, at similar velocities and gate
1
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
Matej.Supej@fsp.uni-lj.si.
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 energy-
dissipation 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,
University of Ljubljana, Slovenia), and World Cup race director and
event organizers all approved our observational research study and

Supej, Hébert-Losier, and Holmberg Slope Steepness and Skiing Biomechanics
Page 2 of 9
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.
\<<<<<<<<<<<<<<<FIGURE 2>>>>>>>>>>>>>>>>>>>>\
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-m-
long 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] = –]v2/2]/ z – 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 ,
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 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 Kolmogorov-
Smirnov 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 linear-
regression 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).
\<<<<<<<<<<<<<<<FIGURE 3>>>>>>>>>>>>>>>>>>>>\
\<<<<<<<<<<<<<<<FIGURE 4>>>>>>>>>>>>>>>>>>>>\
As observed in Figures 3 and 4, the relative duration of each
turn phase was similar between slopes (<2% difference). The RCG
during initiation and completion generally exceeded 30 m on both
slopes, except at the start of turn completion on the steeper slope
(Figure 3[A] and 3[B]). The RCG was significantly shorter (ie, sharper
turns) on the steeper than flatter slope during the second half of
steering 1 and the transition from steering 2 to completion. The
minimum RCG was achieved pregate on the steeper slope but postgate
on the flatter one. As would be expected, RSKIS was generally lower
than RCG on both slopes but showed similar turn characteristics
(Figure 3[A–D]).
Significantly lower v values were recorded on the steeper slope
in all phases of the ski turn except for steering 2 (Figure 3[E] and
3[F]). On the flatter slope, v increased during the first half of steering

Supej, Hébert-Losier, and Holmberg Slope Steepness and Skiing Biomechanics
Page 3 of 9
1 and thereafter decreased until the midpoint of steering 2, whereas v
slightly decreased throughout both steering phases on the steeper
slope. On the steeper compared with flatter slope, a was greater
during initiation but lower during steering 2 and completion (Figure
3[G] and 3[H]). Furthermore, a was predominantly positive during
initiation on the steeper slope but negative on the flatter one.
Significant between-slopes differences in GRFs were detected
throughout most of steering (Figure 4[A] and 4[B]). On the steeper
slope, GRFs were lower at the start of steering 1, greater in the
midpoint of steering, and lower again at the end of steering 2. On this
slope, the highest GRFs were relatively condensed over a brief time
period at the start of steering 2 but spread across steering 1 and 2 on
the flatter slope with a later peak. In terms of diff(emech), the steeper
slope showed higher values during initiation and the first half of
steering 1, lower values during steering phase 2 and completion, and
comparable values to the flatter slope during the second half of
steering 1 (Figure 4[C] and 4[D]).
The hip lateral angulation was significantly lower at the
beginning of the initiation and end of steering 2 on the steeper than
flatter slope and also generally more pronounced during steering 1 on
the steeper slope (Figure 4[E] and 4[F]). The knee angulations were
more pronounced during the second half of initiation and first half of
steering 1 on the steeper slope (Figure 4[G] and 4[H]), with a trend (P
.067) toward higher knee angulations detected during the middle of
steering 2.
The scatter plots illustrate the GRF–RSKIS (Figure 5[A] and
5[B]) and RSKIS–diff(emech) (Figure 5[C] and 5[D]) relationships for
the steeper and flatter slopes, respectively. Distinct relationships were
observed for RSKIS radii above and below ~15 m, with the distinction
being clearer on the steeper slope (ie, less-rounded GRF plot and
distinct patterns for diff[emech]). The strength of the correlation
between GRF–RSKIS for radii <15 m was weaker on the steeper than
flatter slope (r = –.55 vs –.78, both P < .001), with the intercept
indicating lower GRFs at very short RSKIS (3.7 vs 4.2 BW).
Furthermore, on the flatter slope (Figure 5[B]), low GRFs (<~1.5
BW) at RSKIS <9 m were absent, contrasting with observations from
the steeper slope (Figure 5[A]).
\<<<<<<<<<<<<<<<FIGURE 5>>>>>>>>>>>>>>>>>>>>\
As for the RSKIS–diff(emech), correlations for RSKIS <15 m were
stronger on the steeper than flatter slope (r = .60 vs .34, both P <
.001), with relatively steeper slope lines (k = 0.21 vs 0.14 kg · m–2 · J–
1) but comparable intercepts (n = 10.1 vs 10.4 m). No significant
correlations were observed for RSKIS above 15 m.
Discussion
We examined and compared the biomechanics of slalom skiers during
a World Cup race on 2 slopes with different inclinations. Differences
in all the mechanical variables investigated were detected, with the
steeper slope resulting in slower velocities, but faster accelerations,
during turn initiations; turns with smaller radii and concentrated peak
GRFs in the midpoint of steering; more pronounced lower-body
lateral angulations at the start of steering that later became less
pronounced; and slower turns involving deceleration at turn
completion. These differences were reflected in distinct mechanical-
energy-dissipation patterns, with greater pregate and lesser postgate
energy dissipation on the steeper slope. It appears likely that the
overall greater energy dissipation on steeper slopes was due to less
precise, rough running of skis, with perhaps greater angles of the skis
relative to the direction of skiing—that is, greater attack angles.25
Furthermore, the relationships between mechanical variables differed
between slopes, supporting the idea that specific considerations
during training and preparation would be beneficial for performance
on courses with slopes of varying steepness.
Both RSKIS and RCG were shorter on the steeper slope, notably
during steering 1 and completion. Based on the relationships between
edging angles, turn radii, and slope inclinations described by Howe,15
longer turn radii and higher knee and hip lateral angulations can be
expected on steeper slopes during the first part of steering.
Congruently, our skiers adopted more pronounced knee and hip
lateral angulations during steering 1 on the steeper slope. Well-
performed turns are achieved with greater ease when elite skiers
employ a carving rather than skidding or pivoting turn technique.16
Considering the levels of our skiers (ie, very low FIS points), it is
reasonable to assume that all turns were carved with minimal skid in
our study, with skiers using high enough edge angles on the steeper
slope to ski turns adequately and safely, despite shorter turn radii.
In addition, the temporal distributions of the GRF throughout
the turn cycles were different on the 2 slopes, suggesting distinct ski–
snow interactions on the steeper and flatter slopes. During steering 1,
lower GRFs were present on the steeper slope, which may reflect
specific biomechanical turn characteristics to slope inclination
wherein skiers travel more parallel to the line of gravity. The lower
GRFs at the beginning of steering 1 suggest that skiers actively
initiated turns later on the steeper slope than the flatter slope.
However, our results regarding ski-turn radii do not support this
speculation. It is more likely that skiers performed some body
movement that influenced GRF profiles during turns, in agreement
with the differences we detected in lateral angulations.
Moreover, shorter CG turn radii were used at the onset of
steering on the steeper slope without increasing GRFs, indirectly
supporting the higher accelerations observed in this part of the turn.
The between-slopes differences in the biomechanical performance of
turns during steering 1 became even more evident when considering
the GRF–RSKIS relationships, as the skis were constantly loaded with
relatively high GRFs on the flatter slope at high turn rates (RSKIS <9
m). In contrast, a mix of high and low GRFs at such small radii was
observed on the steeper slope. The commonly used quasi-static model
of skiing biomechanics cannot fully explain the specific turn features
that characterized performance on the different inclines.
Alternatively, skiers could be perceived as behaving like inverted
pendulums on an inclined surface with moving ground contact (skis),
where the skis must “catch” the skier’s CG to achieve and maintain
balance.
Our skiers tended to use greater hip and knee lateral angulations
on flatter slopes during steering 2, still using similar turn radii and,
hence, presumably comparable edging angles. Given morphological
constraints limiting knee lateral angulations, skiers rely to a greater
extent on hip lateral angulations to incline the skis more than the CG.
However, hip lateral angulations are also limited,27 with concerns that
a compensatory increase in hip flexion combined with high GRFs can
substantially increase intravertebral disc pressure28 and risk of injury.
Therefore, since carving skis’ turn radii are directly related to edge
angles10,12 and skiers must lean into turns for coronal balance, our
results suggest a benefit to using skis with different side-cuts on
courses with different slope inclinations, even with comparable gate
setups.
Examining the velocity and acceleration turn profiles assists in
understanding the skiing strategies used under the 2 different slope
conditions. On the turns analyzed, our skiers apparently favored a
more controlled approach to skiing on the steeper incline, using lower
and steadier velocities. On the flatter slope, mean skiing velocities
were higher and instantaneous velocities more erratic, consistent with
the wider range of mean accelerations. Positive accelerations mainly

Supej, Hébert-Losier, and Holmberg Slope Steepness and Skiing Biomechanics
Page 4 of 9
occurred during steering 2 and completion on both slopes, with
diff(emech) being highest on the flat slope, suggesting better exiting
conditions. However, since the minimal diff(emech) and a values were
also lower on the flatter slope, entrance and exit velocities of turn
cycles were quasi-similar under both slope conditions.
Nonetheless, the highest energy dissipation (ie, lowest
diff[emech]) appeared in the middle or second half of steering 1, with a
high rate of energy dissipation also present around the gate under both
inclinations. The high energy-dissipation rate occurred at the same
time as the lowest RCG, highest GRF, and greatest decrease in v. In
light of our findings, we propose that skiers should reduce use of
small turn radii associated with high GRF since the available potential
energy per gate decreases as the course progresses, meaning that
when velocity (ie, kinetic energy) is lost, more time is required to
reincrease velocity (ie, regain kinetic energy).16 Employing larger turn
radii may benefit ski-racing performance despite increasing the length
of the skiing trajectory because these turns are associated with lower
energy dissipation,16 greater skiing velocities,29 and a more favorable
distribution of GRFs (ie, smaller peak forces),30 as supports our
correlations established between GRF and RSKIS. Although tighter
turns permit a more direct line of skiing, wider turns enable faster
velocities, wherein instantaneous velocity influences performance to a
greater extent than the line choice or distance traveled.31
In this study, distinct GRF–RSKIS relationships at RSKIS radii
above and below ~15 m were observed, supporting the idea that the
skier–ground interactions operate differently during steering (ie, RSKIS
<15 m) than turn initiation and completion (ie, RSKIS >15 m). The
distinct relationships observed above and below RSKIS ~15 m support
the rationale for choosing RSKIS = 15 m as a dividing value between
turn initiation, steering, and completion. Furthermore, based on the
pronounced spread in energy-dissipation values recorded during
initiation and completion, it may be concluded that these phases are
crucial to race outcomes, with either substantial gains or substantial
losses in energy. Such differences in energetic behaviors between
skiers were more pronounced on the flatter slope, where the available
potential energy is lower16 and, therefore, the possibility to affect race
outcome is greater.
Although our results provide insights on the influence of the
steepness of the slope on the mechanics of slalom ski racing, the
extent to which these can be generalized to other slope inclinations is
uncertain. For instance, contrasting 2 shallower slopes (eg, 10° and
15°) might result in, among other mechanical distinctions, higher
velocities on the steeper 15° than flatter 10° slope. Nonetheless, the
selected slopes and gate combinations in the current study are quite
common in competitive slalom and adequately reflect the reality of
elite alpine ski racing. Furthermore, although the aim was to
determine the influence of slope incline on the mechanics of slalom
ski racing, the testing environment did not permit for the control of all
potential confounding factors on our findings and associated
interpretations—for example, whether only pure carving turns were
used—since the spray of snow did not allow for precise quantification
of ski-turn techniques. However, our study environment (ie, a World
Cup race including the best skiers in the world) strengthens the
external validity of our findings to elite slalom skiers and, although it
cannot be generalized to the typical skiing population, should be
regarded as an asset rather than a limitation.
Practical Applications and Conclusions
Environmental factors can influence alpine-ski-racing performance,
including the steepness of the slope. Despite similar course
conditions, our findings demonstrate that the mechanics of elite alpine
slalom ski racers on 2 slopes with different inclinations differed
significantly. The most pronounced differences were observed during
steering 1 and completion of turns. Although the shortest turn radii
were associated with the greatest energy dissipation on both inclines,
the patterns of dissipation differed, as did the interrelationships
between ski-turn radii, energy dissipation, and GRFs.
Moreover, distinct strategies were employed on the 2 slopes,
with steadier and slower velocities on the steeper slope and more
erratic and faster velocities on the flatter slope. The overall impact of
the steepness of slope on biomechanical aspects of skiing determined
here support the proposal that specific considerations during training
and race preparation would benefit the performance of slalom ski
racers on courses involving slopes of varying steepness, such as
employing skis with distinct side-cuts, adjusting racing strategies (ie,
velocity and acceleration behaviors), and modifying hip and knee
lateral angulations. We recommend that skiers perform training
session on steeper and flatter slopes separately to master performance
and thereafter incorporate training on slopes with mixed inclinations.
Furthermore, during race preparation, skiers should focus training on
slopes with an inclination profile similar to that of the race course to
perfect technique on given inclinations. Future research may
investigate whether our study findings also apply on slopes with
different inclinations than those studied here.
Acknowledgments
This study was supported financially by the Foundation for Financing Sport
Organizations in Slovenia and the Slovenian Research Agency.
References
1. Hébert-Losier K, Supej M, Holmberg H-C. Biomechanical factors
influencing the performance of elite alpine ski racers. Sports Med.
2014;44(4):519–533. PubMed doi:10.1007/s40279-013-0132-z
2. Spörri J, Kröll J, Schwameder H, Schiefermüller C, Müller E.
Course setting and selected biomechanical variables related to
injury risk in alpine ski racing: an explorative case study. Br J
Sports Med. 2012;46(15):1072–1077. PubMed
doi:10.1136/bjsports-2012-091425
3. Bere T, Flørenes TW, Krosshaug T, Nordsletten L, Bahr R. Events
leading to anterior cruciate ligament injury in World Cup Alpine
Skiing: a systematic video analysis of 20 cases. Br J Sports Med.
2011;45(16):1294–1302. PubMed doi:10.1136/bjsports-2011-
090517
4. Colbeck SC. A review of the friction of snow skis. J Sports Sci.
1994;12(3):285–295. PubMed doi:10.1080/02640419408732174
5. Müller E, Schwameder H. Biomechanical aspects of new
techniques in alpine skiing and ski-jumping. J Sports Sci.
2003;21(9):679–692. PubMed doi:10.1080/0264041031000140284
6. Quinn TP, Mote CD, Jr. Prediction of the loading along the leg
during snow skiing. J Biomech. 1992;25(6):609–625. PubMed
doi:10.1016/0021-9290(92)90103-8
7. Gilgien M, Spörri J, Chardonnens J, Kröll J, Müller E.
Determination of external forces in alpine skiing using a
differential global navigation satellite system. Sensors (Basel).
2013;13(8):9821–9835. PubMed doi:10.3390/s130809821
8. Shiefermüller C, Lindinger S, Müller E. The skier’s centre of
gravity as a reference point in movement analysis for difference
designated systems. In: E. Müller DB, R. Klika, S. Lindinger, H.
Schwameder, eds. Science and Skiing III. Oxford, UK: Meyer &
Meyer Sport; 2005:172–185.
9. Supej M, Kugovnik O, Nemec B. DGPS measurement system in
alpine skiing track and center of mass estimation. In: Jiang AB,
Zhang H, eds. Proceedings of First Joint International Pre -
Olympic Conference of Sport Science and Sports Engineering:

Supej, Hébert-Losier, and Holmberg Slope Steepness and Skiing Biomechanics
Page 5 of 9
Computer Science in Sports. Vol 1. Liverpool, UK: World
Academic Union; 2008:120–125.
10. Howe J. Skiing Mechanics. Laporte, CO: Poudre Press; 1983.
11. Lind D, Sanders SP. The Physics of Skiing: Skiing at the Triple
Point. New York: Springer-Verlag; 1996.
12. Niessen W, Müller E. Carving—biomechanische aspekte zur
verwendung stark taillierter skier und erhoehter standflachen im
alpinen skisport. Leistungssport. 1999;29(1):39–44.
13. Supej M. 3D measurements of alpine skiing with an inertial sensor
motion capture suit and GNSS RTK system. J Sports Sci.
2010;28(7):759–769. PubMed doi:10.1080/02640411003716934
14. Clarys JP, Alewaeters K, Zinzen E. The influence of geographic
variations on the muscular activity in selected sports movements. J
Electromyogr Kinesiol. 2001;11(6):451–457. PubMed
doi:10.1016/S1050-6411(01)00020-7
15. Howe J. The New Skiing Mechanics: Including the Technology of
Short Radius Carved Turn Skiing and the Claw Ski. 2nd ed.
Waterford, ME: Mclntire; 2001.
16. Supej M. Differential specific mechanical energy as a quality
parameter in racing alpine skiing. J Appl Biomech.
2008;24(2):121–129. PubMed
17. Federolf P, Scheiber P, Rauscher E, et al. Impact of skier actions
on the gliding times in alpine skiing. Scand J Med Sci Sports.
2008;18(6):790–797. PubMed doi:10.1111/j.1600-
0838.2007.00745.x
18. Supej M, Kugovnik O, Nemec B. New advances in racing slalom
technique. Kinesiol Sloven. 2002;8(1):25–29.
19. Supej M, Holmberg HC. How gate setup and turn radii influence
energy dissipation in slalom ski racing. J Appl Biomech.
2010;26(4):454–464. PubMed
20. Dempster WT. Space Requirements of the Seated Operator.
WADC Technical Report No. 87892. Dayton, OH: Wright
Patterson Air Force Base; 1955:55–159.
21. Müller E, Bartlett R, Raschner C, Schwameder H, Benko-
Bernwick U, Lindinger S. Comparisons of the ski turn techniques
of experienced and intermediate skiers. J Sports Sci.
1998;16(6):545–559. PubMed doi:10.1080/026404198366515
22. Ehara Y, Fujimoto H, Miyazaki S, Mochimaru M, Tanaka S,
Yamamoto S. Comparison of the performance of 3D camera
systems II. Gait Posture. 1997;5(3):251–255. doi:10.1016/S0966-
6362(96)01093-4
23. Klous M, Müller E, Schwameder H. Collecting kinematic data on a
ski/snowboard track with panning, tilting, and zooming cameras: is
there sufficient accuracy for a biomechanical analysis? J Sports
Sci. 2010;28(12):1345–1353. PubMed
doi:10.1080/02640414.2010.507253
24. Lüthi A, Federolf M, Fauve M, et al. Determination of forces in
carving using three independent methods. In: Müller E, Bacharach
D, Klika R, Lindinger S, Schwameder H, eds. Science and Skiing
III. Oxford, UK: Meyer & Meyer Sport; 2005:96–106.
25. Reid R, Gilgien M, Moger T, et al. Turn characteristics and energy
dissipation in slalom. In: Müller SL, Stöggl T, eds. Science and
Skiing IV. Tyrol, Austria: Maidenhead and Meyer & Meyer Sport
(UK); 2009:419–429.
26. Supej M, Kugovnik O, Nemec B. Kinematic determination of the
beginning of a ski turn/Kinematicna definicija zacetka
smucarskega zavoja. Kinesiol Sloven. 2003;9(1):5–11.
27. Schünke M, Schulte E, Ross LM, Schumacher U, Lamperti ED.
The movements and biomechanics of the hip joint. Telger T, trans.
Thieme Atlas of Anatomy: General Anatomy and musculoskeletal
System. Stuttgart, Germany: Georg Thieme Verlag; 2006:386–387.
28. Wilke HJ, Neef P, Caimi M, Hoogland T, Claes LE. New in vivo
measurements of pressures in the intervertebral disc in daily life.
Spine. 1999;24(8):755–762. PubMed doi:10.1097/00007632-
199904150-00005
29. Spörri J, Kröll J, Schwameder H, Müller E. Turn characteristics of
a top world class athlete in giant slalom: a case study assessing
current performance prediction concepts. Int J Sports Sci
Coaching. 2012;7(4):647–660. doi:10.1260/1747-9541.7.4.647
30. Supej M, Kipp R, Holmberg HC. Mechanical parameters as
predictors of performance in alpine World Cup slalom racing.
Scand J Med Sci Sports. 2011;21(6):e72–e81. PubMed
doi:10.1111/j.1600-0838.2010.01159.x
31. Federolf PA. Quantifying instantaneous performance in alpine ski
racing. J Sports Sci. 2012;30(10):1063–1068. PubMed
doi:10.1080/02640414.2012.690073
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.

Supej, Hébert-Losier, and Holmberg Slope Steepness and Skiing Biomechanics
Page 6 of 9
Figure 2 — Schematization of the motion-acquisition system’s placement.

Supej, Hébert-Losier, and Holmberg Slope Steepness and Skiing Biomechanics
Page 7 of 9
Figure 3 — The diagrams showing (A) the center of gravity’s turn radii (RCG) for the steeper and (B) the flatter slope, (C) the skis’ turn radii (RSKIS) for
the steeper and (D) the flatter slope, (E) the absolute velocity (v) for the steeper and (F) the flatter slope, and (G) the acceleration (a) for the steeper and
(H) the flatter slope. The intervals of significant differences (P < .05) between the steeper and flatter slope are marked by a horizontal bold line. Larger
and smaller values are marked by L and S, respectively.

Supej, Hébert-Losier, and Holmberg Slope Steepness and Skiing Biomechanics
Page 8 of 9
Figure 4 — The diagrams showing (A) the ground-reaction forces (GRFs) for the steeper and (B) the flatter slope, (C) the differential specific
mechanical energy (diff[emech]) for the steeper and (D) the flatter slope, (E) the knee angulation for the steeper and (F) the flatter slope, and (G) the hip
angulation for the steeper and (H) the flatter slope. The intervals of significant differences (P < .05) between the steeper and flatter slope are marked by
a horizontal bold line. Larger and smaller values are marked by L and S, respectively.

Supej, Hébert-Losier, and Holmberg Slope Steepness and Skiing Biomechanics
Page 9 of 9
Figure 5 — Scatter plots showing the relationship between the ground-reaction forces (GRF) and the arithmetic mean of skis’ turn radii (RSKIS) for (A)
the steeper slope and (B) the flatter one. Scatter plots representing the relations between the differential specific mechanical energy (diff[emech]) and the
arithmetic mean of skis’ turn radii (RSKIS) are provided for (C) the steeper slope and (D) the flatter one. The initiation and completion phases’ data
(RSKIS > 15 m) are plotted by circles and the steering phases 1 and 2 (RSKIS < 15 m) by crosses. The line in all diagrams represents the linear regression
for the steering phases 1 and 2. The slope (k), y-intercept (n), correlation coefficient (r), and P value are also shown.