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Aerodynamic Drag Modeling of Alpine Skiers
Performing Giant Slalom Turns
FRE
´DE
´RIC MEYER
1
, DAVID LE PELLEY
2
, and FABIO BORRANI
3
1
Sport Science Institute, University of Lausanne, Lausanne, SWITZERLAND;
2
Department of Mechanical Engineering,
Faculty of Engineering, The University of Auckland, Auckland, NEW ZEALAND; and
3
Department of Sport and
Exercise Science, Faculty of Science, The University of Auckland, Auckland, NEW ZEALAND
ABSTRACT
MEYER, F., D. LE PELLEY, and F. BORRANI. Aerodynamic Drag Modeling of Alpine Skiers Performing Giant Slalom Turns. Med.
Sci. Sports Exerc., Vol. 44, No. 6, pp. 1109–1115, 2012. Purpose: Aerodynamic drag plays an important role in performance for athletes
practicing sports that involve high-velocity motions. In giant slalom, the skier is continuously changing his/her body posture, and this
affects the energy dissipated in aerodynamic drag. It is therefore important to quantify this energy to understand the dynamic behavior
of the skier. The aims of this study were to model the aerodynamic drag of alpine skiers in giant slalom simulated conditions and to
apply these models in a field experiment to estimate energy dissipated through aerodynamic drag. Methods: The aerodynamic charac-
teristics of 15 recreational male and female skiers were measured in a wind tunnel while holding nine different skiing-specific postures.
The drag and the frontal area were recorded simultaneously for each posture. Four generalized and two individualized models of the
drag coefficient were built, using different sets of parameters. These models were subsequently applied in a field study designed to
compare the aerodynamic energy losses between a dynamic and a compact skiing technique. Results: The generalized models estimated
aerodynamic drag with an accuracy of between 11.00% and 14.28%, and the individualized models estimated aerodynamic drag with
an accuracy between 4.52% and 5.30%. The individualized model used for the field study showed that using a dynamic technique led
to 10% more aerodynamic drag energy loss than using a compact technique. Discussion: The individualized models were capable
of discriminating different techniques performed by advanced skiers and seemed more accurate than the generalized models. The
models presented here offer a simple yet accurate method to estimate the aerodynamic drag acting upon alpine skiers while rapidly
moving through the range of positions typical to turning technique. Key Words: WIND TUNNEL, ENERGY DISSIPATION,
PERFORMANCE, AIR FRICTION, ALPINE SKI
Athletes performing disciplines like running, speed
skating, cycling, or cross-country skiing have al-
ways been interested in optimizing their aerody-
namic drag to increase speed and achieve better performance
(8,14,15,18). In alpine skiing, the gravitational force is used
to increase the skier’s kinetic energy, whereas the aerody-
namic drag is one of the two nonconservative forces doing
negative work on the skier. Quantifying this parameter is
therefore important to understand skier performance.
Several studies have examined skier aerodynamic drag.
Watanabe and Ohtsuki (19,20) analyzed the aerodynamic
drag of a variety of skiing postures in a wind tunnel study
and skiing velocity in a field study. Later, Kaps et al. (7)
proposed a method to calculate snow friction and drag area
(C
D
A) during straight downhill skiing using photocells. The-
oretical drag analysis has been conducted by Savolainen (12)
to compare different skiers’ posture and determine factors
limiting speed. Performance coefficients taking into account
factors like mass (M), frontal area (A
F
), and drag coefficient
(C
D
) have been developed with wind tunnel tests by Luethi
and Denoth (9). Thompson and Friess (17) performed wind
tunnel tests to improve the aerodynamic efficiency of speed
skiers by optimizing their posture and equipment.
Although these studies have made valuable contributions
toward our understanding of the aerodynamic properties of
static skiing postures, they are limited in that alpine skiing
is primarily a dynamic sport where the skier continually
moves and changes positioning. To allow the drag analysis
of skiers performing turns, Barelle et al. (2) modeled the C
D
on the basis of athlete segment lengths and intersegmental
angles, thereby allowing the determination of aerodynamic
properties through a complete span of positions typically en-
countered in skiing. However, the segment lengths and in-
tersegmental angles required to use this model are often
difficult to obtain in field research settings.
Despite these previous studies looking at the aerodynamic
properties of alpine skiers, the importance of air drag toward
performance in this dynamic sport is poorly understood. Me-
chanical energy (i.e., the sum of kinetic and potential energy)
Address for correspondence: Fre
´de
´ric Meyer, Institut des Sciences du Sport
de l’Universite
´de Lausanne, Universite
´de Lausanne, Batiment Vidy, 1015
Lausanne, Switzerland; E-mail: fmeyer.mail@gmail.com.
Submitted for publication June 2011.
Accepted for publication November 2011.
0195-9131/12/4406-1109/0
MEDICINE & SCIENCE IN SPORTS & EXERCISE
Ò
Copyright Ó2012 by the American College of Sports Medicine
DOI: 10.1249/MSS.0b013e3182443315
1109
APPLIED SCIENCES
Copyright © 2012 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.
was used by Supej (16) to deduce dissipated energy during
turns. Reid et al. (11) used the same method in slalom, but
the intrinsic factors influencing this energy dissipation have
not yet been analyzed.
Therefore, the first aim of this study was to develop mod-
els of the aerodynamic C
D
of alpine skiers performing turns.
The models should be able to take into account the skier’s
postural changes, using parameters that can be measured
in the field. Furthermore, the second purpose of this study
was to use the developed models to analyze the energy dis-
sipated by the aerodynamic drag of a skier using either
a dynamic technique, where the skier exposes a relatively
large A
F
to the wind, or a compact technique, where the skier
maintains an aerodynamic position, while performing giant
slalom turns on a ski slope.
METHODS
Wind Tunnel Experiment
Participants. Fifteen recreational male and female ski-
ers (mean TSD: body M= 75.9 T9.7 kg, height (H) = 1.79 T
0.07 m, age = 32.3 T6.7 yr) volunteered for the study. All
participants were healthy, without any joint motion problems.
Written informed consent was obtained from each partici-
pant before participation in the study, which was approved
by the University of Auckland Human Participants Ethics
Committee.
Wind tunnel setup. Testing was carried out at the
University of Auckland in a wind tunnel with an open jet
configuration, the jet having dimensions of 2.5 m (width
(W)) by 3.5 m (H), and a maximum flow speed of 18 mIs
j1
.
Turbulence levels were approximately 0.5% in the flow di-
rection, and the velocity profile was uniform.
Participants were positioned on a force platform capable
of measuring drag in the longitudinal wind direction. The
drag force (D) was calculated through measurement of the
displacement of a distorting force block, by using a Linear
Variable Displacement Transducer (RDP, Ltd., Heath Town,
United Kingdom). A 16-bit analog/digital converter (NI-6034;
National Instruments, Austin, TX) was used to acquire the
signal on a PC at a frequency of 200 Hz. The Linear Variable
Displacement Transducer was previously calibrated over a
suitable range of loads. This transducer exhibits a high degree
of linearity and repeatability, with an accuracy of approxi-
mately 1% of the measured reading and a repeatability of
0.5% (5). In accordance with Sayers and Ball (13), no flow
corrections were required in the open-circuit tunnels because
the blockage model (in our case, the person) was less than 1
m
2
and the open area was 12.25 m
2
.
The dynamic wind pressure was recorded with a Setra pres-
sure transducer via a pitot-static probe (Airflow Develop-
ments, Ltd., High Wycombe, United Kingdom) positioned
in the wind tunnel, upstream of the contracted section. Be-
fore the experiment, a second probe was positioned in the
middle of the testing volume to determine the ratio of dy-
namic pressure between the two locations. The measured
pressure at run time was then adjusted accordingly. The
accuracy of the dynamic pressure is approximately 2% of
the measured value with a repeatability of approximately
0.2%. Dynamic pressure, air temperature, and atmospheric
pressure were recorded to enable the drag to be correctly
nondimensionalized.
A limitation with many wind tunnel systems is the in-
ability to measure the A
F
of an irregular moving object. This
only allows the C
D
Ato be calculated, which is of limited
use in many subsequent calculations. To enable a true C
D
to be calculated, a real-time A
F
measurement system was
developed. This consisted of a miniature camera (USB
UI-1485LE; IDS Imaging, Obersulm, Germany) positioned
in the wind tunnel upstream of the participant. The back-
ground was colored white, and the area covered by each
pixel was calculated by measuring the size of a reference
object positioned at the average plane of the participant.
During the test, the participant was dressed in a black suit,
which served both to provide a contrast for the photography
and to provide clothing uniformity for the drag measure-
ments. A 50% threshold was carried out on the grayscale
image of the participant, generating a black-and-white pic-
ture. The total number of black pixels against the white
background was then counted and converted into a true area
in square meters, which was displayed to the subject every
0.5 s. The accuracy of this system was approximately
0.001 m
2
. The black-and-white images were also used to
determine the skiers’ Hand Wby counting the number of
black pixels across the maximal horizontal and vertical dis-
tance between two anatomical reference points on the frontal
plane.
Experimental procedure. Before the test, each partic-
ipant’s upright Hand Mwere measured in meters and
kilograms, respectively, and the corresponding body surface
area (BodyS), which represents the total area of the skin, was
calculated using the method of Boyd (4):
BodyS ¼0:007184ð100UpHÞ0:725M0:425 ½1
To account for any weight-induced readings, the force
transducer was zeroed with the participant on the balance
under windless conditions at the start of each trial. The
maximal A
F
(MaxA) of each participant (standing upright
with the arms outstretched) was measured at the same time
through the miniature camera. The wind tunnel was then run
up to a speed of about 16 mIs
j1
, corresponding to typical
gate entry speeds in giant slalom conditions, and, therefore,
the Reynolds number was approximately the same as it would
be experienced by the participants in the field.
After a settling period, the participants assumed nine pos-
tures, with varying leg flexion and arm spacing (Fig. 1). A
red/green light switch was set up in front of the participants
to let them know when they had to change posture. Each
posture was repeated three times and held for 15 s during
which Dand A
F
were measured and averaged.
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The C
D
was calculated in the standard manner as follows:
CD¼2D
QV2AF½2
where Qis the air density and Vis the wind speed. The dy-
namic pressure (QV
2
/2) was measured with the Setra pres-
sure transducer, A
F
was measured with the miniature
camera, and Dwas measured with the force balance.
Model construction. When conducting field tests, a
participant’s anthropometric data may not always be avail-
able (as in competition settings), whereas other information
may be difficult to obtain (such as A
F
, which can only be
obtained from full frontal pictures). Therefore, models based
on different combinations of parameters (two to seven) were
built to accommodate the information typically available in
alpine field test conditions.
On the basis of the possible sets of available data, six
models were built: four generalized models using all par-
ticipants’ data, as well as two individualized models for each
participant. Table 1 summarizes the parameters that were
used in each of the six models.
Anthropomorphic parameters are inherent to an individ-
ual and do not vary with the position of the skier. They are
therefore not relevant to build individualized models. How-
ever, the use of these parameters can improve the accuracy
of the generalized models.
Field Experiment
The field experiment was carried out on an indoor ski
slope. One of the 15 participants volunteered to perform two
giant slalom runs in a white suit dotted with black hemi-
spherical markers. He was asked to execute ample active
movements on the first run and to remain more compact on
the second run. A total of six gates were set up with a linear
gate distance of 24 m and a lateral offset of 9 m. The first
three gates were used to initiate the rhythm, and the last
three were recorded. The slope angle was approximately
8 to 10 degrees. To record the skier’s position during the
turn, six piA1000-48gm cameras with a 1004 1004-pixel
resolution and running at 48 Hz (Basler AG, Ahrensburg,
Germany) were placed around the slope, three on each side.
The orientations of the two top and two bottom cameras
were fixed. The two cameras in the middle were mounted
onto specially built tripod heads that allowed operators to
pan and tilt the cameras while maintaining camera sensor
positions. Before the test, four calibration poles with three
markers each were set up around the center of the capture
volume and recorded with the cameras. Each calibration
marker, reference point, and camera position was measured
with a reflectorless total station (Sokkia Set530R; Sokkia
Topcon, Kanagawa, Japan). Each camera was connected by
Gigabit Ethernet to its own laptop, a battery pack, and a
custom synchronization unit. The synchronization unit sent
signals with the desired frequency to each camera, triggering
the cameras to save images to the RAM memory of their
associated laptops using a dedicated software (SwisTrack;
Lausanne, Switzerland). When the synchronization unit was
switched off or when the RAM memory was full, all the
images were transferred to the hard drive.
Sequences provided by the multiple-camera system and
three-dimensional positions of the points given by the to-
tal station were processed using the SIMI motion software
(SIMI Reality Motion Systems GmbH, Unterschleissheim,
Germany). The calibration markers were first used to deter-
mine the 11 standard parameters of the direct linear trans-
formation calibration method (1). Reference points were
affixed to the side of the ski hall to allow for the cameras’
panning and tilting angles to be determined during the tests.
The tridimensional reconstruction accuracy was controlled
by comparing the gate position given by the total station
with the position calculated with the software for the three
visible gates on the two runs. The center of M(CoM) of the
skier was calculated using the Hanavan method (6). Position
trajectories of the head, feet, and arms were exported to
calculate the skier’s Hand W. Because the anthropomorphic
data were available but the A
F
was not, the GM3 and IM2
models were both used to determine the evolution of the
aerodynamic C
D
over the turn cycle for the purpose of com-
parison. The energy losses due to aerodynamic friction
($Eaero) were calculated at each step of the turn as follows:
$Eaero ¼D$dist ½3
where $dist was the distance traveled by the skier’s CoM
and Dwas determined by rearranging equation 2 to give
the following:
D¼1
2CDAQairðVSkier þVwind Þ2½4
where V
Skier
is the speed of the skier’s CoM and V
wind
is
the component of the wind speed in the direction of the
skier’s speed. GM3 and IM2 were used to give an estimate
of the C
D
A, and combining equations 3 and 4 gives the dis-
sipated aerodynamic energy during a $tinterval ($dist is
replaced by V
Skier
$t):
$Eaero ¼1
2CDAQairðVSkier þVwind Þ2VSkier $t½5
TABLE 1. An overview of the parameters included in the six tested models.
C
D
AModel UpH MMaxA BodyS A
F
HW
GM1 ( ( ( ( (((
GM2 (((
GM3 (( ( ( ((
GM4 ((
IM1 (((
IM2 ((
UpH, upright H.
FIGURE 1—The nine tested skier positions as viewed by the frontal
camera.
AERODYNAMIC DRAG MODEL OF ALPINE SKIERS Medicine & Science in Sports & Exercise
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Because tests were performed in a ski hall, wind speed
can be neglected in this study. However, it is an important
parameter and must be considered during outdoor experi-
ments. For a whole turn, the total aerodynamic drag energy
dissipated is obtained by summing the previous equation
between t
0
, the beginning of the turn, and t
end
, the end of
the turn:
$Eaero ¼~
tend
t0
1
2CDAQairVSkier
3$t½6
Statistical Analysis
A backward stepwise linear regression was used to find
the best predictive parameters of the models. The cutoff
value for parameter acceptance was stated at Pe0.1. The
coefficient of determination (R
2
) and the SD of the estimate
of the models were calculated.
The validation of the generalized models was performed
by removing one participant from the data set, recalculating
the model coefficients with the remaining 14 participants,
and then using the removed participant to compare the model
prediction with an independent measure. A rotation through
all 15 participants was performed, and the mean error was
used to describe the model accuracy. The individualized
models were validated in the same way, by removing the re-
sult of one posture from the data set, recalculating the model
with the remaining eight postures, and applying the models
to the removed posture.
Bland–Altman plots (3) were used to compare the agree-
ment between the generalized models and the experimental
data. For the generalized and the individualized models, the
95% limit of agreement (T1.96 SD) was calculated. All the
statistical analyses were performed with SPSS 16 software
(SPSS, Inc., New York, NY), and significance was accepted
at PG0.05.
TABLE 2. Coefficients for the generalized models’ parameters and accuracies of the models.
C
D
AModel Cste UpH (m) M(kg) MaxA (m
2
) BodyS (m
2
)A
F
(m
2
)H(m) W(m) R
2
SD (m
2
)P
GM1 0.046 j0.155 — — — 0.649 0.181 0.039 0.972 0.016 G0.001
GM2 j0.215 0.573 0.187 0.045 0.962 0.019 G0.001
GM3 0.121 j0.373 — — 0.156 0.337 0.090 0.953 0.021 G0.001
GM4 j0.248 0.337 0.091 0.933 0.025 G0.001
FIGURE 2—Comparison of measured and calculated C
D
Awith Bland–Altman plots for the four generalized models. Solid horizontal lines represent
the 95% limits of agreement.
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RESULTS
Wind Tunnel Experiment
Developed models. Table 2 shows the multiplication
coefficient of each parameter, as well as the R
2
, the SD of
the estimate, and the significance of each model (P) devel-
oped to estimate the C
D
A. The 0.1 cutoff of parameter ac-
ceptance discarded M, MaxA, and BodyS from GM1, as
well as Mand MaxA from GM3.
GM1 offered the best accuracy with R
2
=0.972,PG0.001,
and an SD of the estimate = 0.016 m
2
. For GM2 and GM3,
the R
2
was 0.962 (SD = 0.019 m
2
,PG0.001) and 0.953
(SD = 0.021 m
2
,PG0.001), respectively. Finally, GM4
represented the worst model with an R
2
equal to 0.933
(SD = 0.025 m
2
,PG0.001).
Bland–Altman plots between the generalized models and
the experimental data are shown in Figure 2 for all the gen-
eralized models. The 95% limit of agreement is also reported
for GM1 (T11.00), GM2 (T11.99), GM3 (T13.25), and GM4
(T14.18) in Figures 2A, B, C, and D, respectively.
For the individualized models, the backward linear regres-
sion did not remove any parameters. IM1 reached an average
R
2
= 0.995 and an SD of the estimate = 0.009 m
2
. Validation
between the models and the measures gave a 95% limit of
agreement of T4.52%. IM2 showed slightly worse results
with R
2
= 0.989, SD = 0.01 m
2
, and a 95% limit of agree-
ment of T5.30%.
Field Experiment
To estimate his C
D
A, the following IM2 was individually
developed for the skier who performed the field test:
CDA¼0:349Hþ0:068W0:272 ½7
Figure 3A compares the evolution of C
D
Aover a turn
cycle, using the IM2 defined in equation 7, for the active
and compact techniques. The limit of agreement of 5.30%
given for the IM2 is also plotted for each technique, show-
ing a possible differentiation between the dynamic and the
compact skiing technique for 56% of the turn. The darker
gray area indicates an overlapping of the two techniques’
limit of agreement.
Figure 3B shows the comparison of the same data set, but
using GM3. The limit of agreement of 13.25% is also plotted
for each technique, showing an overlapping of the two tech-
niques during the whole turn.
Equation 5 gives the total energy dissipated because of
the aerodynamic drag and is illustrated in Figure 4 using
either the IM2 (Fig. 4A) or the GM3 (Fig. 4B) for one turn
performed with the two different techniques. The 95% limit
of agreement is also reported, showing the disparity of en-
ergy dissipation. For the current giant slalom, an active tech-
nique gives around 3500 J of energy dissipated during one
FIGURE 3—C
D
Afor both the compact and dynamic techniques using
the second individualized model (A) and the third generalized model (B).
FIGURE 4—Evolution of the energy dissipated due to aerodynamic
drag for both the compact and dynamic techniques using the second
individualized model (A) and the third generalized model (B).
AERODYNAMIC DRAG MODEL OF ALPINE SKIERS Medicine & Science in Sports & Exercise
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gate. This represents around 350 J more energy dissipation
in one turn than a compact position, which means a loss of
10% more energy during the whole run.
DISCUSSION
The most important finding of this study is the accuracy
of the individualized models, which allow for very good
estimation of skier aerodynamic properties while perform-
ing giant slalom turns. Indeed, these models, which explain
98.9% and 99.5% of the experimental data, have an accu-
racy better than 5.30% to determine the skier’s aerodynamic
C
D
. The accuracy obtained is good enough for discrimina-
tion of different techniques performed by advanced skiers,
as seen in Figure 3A.
The generalized models developed are a little less accu-
rate, explaining between 93.3% and 97.2% of the experi-
mental data, corresponding to 11.00% and 14.18% error for
the 95% limit of agreement. Using anthropomorphic data
to build the generalized models led to an improvement of
only 2%. Therefore, the accuracy differences of about 8%
between generalized and individualized models should be
due to other factors not measured in this study such as dif-
ferences in individual body posture held in the wind tunnel.
Similar to the model of Barelle et al. (2), the general-
ized models developed in this investigation allow a global
intraindividual comparison of a skier performing different
techniques but not accurate differentiation between skiers.
However, the parameters used in this study are less specific
than the segment lengths and angles used by Barelle et al.
(2) and offer a wider and more generic use of the models.
This allows the backward linear regression method to choose
the relevant parameters and refuse parameters that are not
necessary for the model. More flexibility is therefore possi-
ble for further parameter integration. Barelle et al. (2) con-
sidered many more positions to allow the variation of the
different parameters, but finally, the C
D
found in both stud-
ies corresponds very well for the different positions a skier
can reach during a run.
The developed models help to understand intrinsic factors
of energy dissipation as calculated by Supej (16) and Reid
et al. (11). They both found high energy dissipation around
the gate crossing and low energy dissipation during gate
transition, which is inverted compared with the curves of
Eaero in Figure 4. The energy dissipation due to snow fric-
tion, estimated by Meyer and Borrani (10), indicates a higher
importance of the ski–snow friction in giant slalom and
curves corresponding to the results obtained by Supej (16)
and Reid et al. (11).
The study undertaken here is a first approximation of the
skier’s aerodynamic drag, which is correct in the field in
the case of little or no ambient wind speed. In this case, the
wind flow onto the skier will always be head-on, regardless
of his/her direction of travel (no yaw angle). If there is a
substantial wind speed, the aerodynamic drag experienced
by the skier will change depending on his/her direction of
travel (yaw angle different from zero). To model this sce-
nario, further tests would have to be conducted at a range of
a skier’s yaw angles in the wind tunnel. Then, a new dy-
namic model could calculate the skier’s aerodynamic drag
considering wind speed and relative direction and the ski-
er’s yaw angle at each point of the turn. In contrast, for small
yaw angles, the current model serves as a good estimation
of the aerodynamic drag.
One limitation of the current method is that the various
postures in the wind tunnel used to develop the models (Fig. 1)
are symmetric and differ from asymmetric skier positions
achieved when turning, a fact that may jeopardize the model
validity. Unfortunately, the repeatability of holding more
turn-specific postures in the wind tunnel was poor because
of the difficulty of holding unbalanced positions. A second
limitation is that the models reported here use the wind tun-
nel measurements of a series of static positions to model ski-
ers who change their position continuously while turning. It
may be that the dynamic behavior of the aerodynamic drag
of a skier in continuous movement may somehow differ
from that of a set of static positions. However, wind tunnel
measurements are currently limited to static positions as the
ground force platform would record each CoM acceleration,
making it difficult to isolate the aerodynamic D.
In conclusion, this article provides simple and functional
models to calculate the aerodynamic drag of alpine skiers
performing giant slalom turns. The developed models offer a
mean accuracy between 4.52% and 14.18%, depending on
the selected parameters. Using these models in skiing field
studies may help to improve our understanding of the role of
aerodynamic drag in skier performance. A functional model
of ski–snow friction while performing turns still needs to be
developed to have a full overview of where, how, and when
athletes lose energy during turns.
This work was supported by a grant from the Swiss Federal Office
for Sport.
The authors thank Dr. F. Formenti for his writing assistance.
The authors have no financial disclosure or conflict of interest
to declare.
The results of the present study do not constitute endorsement
by the American College of Sports Medicine.
REFERENCES
1. Abdel-Aziz YI, Karara HM. Direct linear transformation from
comparator coordinates into object space coordinates in close-
range photogrammetry. In: Proceedings of the American Society
of Photogrammetry Symposium on Close-Range Photogrammetry.
1971. p. 1–8.
2. Barelle C, Ruby A, Tavernier M. Experimental model of the
http://www.acsm-msse.org1114 Official Journal of the American College of Sports Medicine
APPLIED SCIENCES
Copyright © 2012 by the American College of Sports Medicine. Unauthorized reproduction of this article is prohibited.
aerodynamic drag coefficient in alpine skiing. J Appl Biomech.
2004;20:167–76.
3. Bland JM, Altman DG. Statistical methods for assessing agreement
between two methods of clinical measurement. Lancet.1986;
1(8476):307–10.
4. Boyd E. The Growth of the Surface Area of the Human Body.
Minneapolis (MN): University of Minnesota Press; 1935. p. 52–112.
5. Flay J, Vuletich IJ. Development of a wind tunnel test facility for
yacht aerodynamic studies. J Wind Eng Ind Aerodyn. 1995;58(3):
231–58.
6. Hanavan EP Jr. A mathematical model of the human body.
AMRL-TR-64-102. AMRL TR. 1964:1–149.
7. Kaps P, Nachbauer W, Mo¨ssner M. Determination of kinetic fric-
tion and drag area in alpine skiing. In: Ski Trauma and Skiing
Safety. 10th ed. 1996. p. 165–77.
8. Lopez JG, Rodriguez-Marroyo JA, Juneau CE, Peleteiro J,
Martinez AC, Villa JG. Reference values and improvement of
aerodynamic drag in professional cyclists. J Sport Sci. 2008;26(3):
277–86.
9. Luethi S, Denoth J. The influence of aerodynamic and anthropo-
metric factors on speed in skiing. J Appl Biomech. 1987;3:345–52.
10. Meyer F, Borrani F. 3D model reconstruction and analysis of
athletes performing giant slalom. In: Abstract Book of the 5th In-
ternational Congress on Science and Skiing; St. Christoph am
Arlberg (Austria). 2010. p. 64.
11. Reid R, Gilgien M, Moger T, et al. Turn characteristics and energy
dissipation in slalom. In: Lindinger S, Mu
¨ller E, Sto¨ggl T, editors.
Science and Skiing IV. Maidenhead: Meyer & Meyer Sport (UK),
Ltd.; 2009. p. 419–29.
12. Savolainen S. Theoretical drag analysis of a skier in the downhill
speed race. J Appl Biomech. 1989;5:26–39.
13. Sayers AT, Ball DR. Blockage corrections for rectangular flat
plates mounted in an open jet wind tunnel. Proc Inst Mech Eng C J
Mech Eng Sci. 1983;197:259–63.
14. Shanebrook JR, Jaszczak RD. Aerodynamic drag analysis of run-
ners. Med Sci Sports. 1976;8(1):43–5.
15. Spring E, Savolainen S, Erkkila T, Hamalainen T, Pihkala P. Drag
area of a cross country skier. J Appl Biomech. 1988;4:103–13.
16. Supej M. Differential specific mechanical energy as a quality
parameter in racing alpine skiing. J Appl Biomech. 2008;24(2):
121–9.
17. Thompson BE, Friess WA, Knapp KN 2nd. Aerodynamics of
speed skiers. Sports Eng. 2001;4:103–12.
18. van Ingen Schenau GJ. The influence of air friction in speed
skating. J Biomech. 1982;15(6):449–58.
19. Watanabe K, Ohtsuki T. Postural changes and aerodynamic forces
in alpine skiing. Ergonomics. 1977;20(2):121–31.
20. Watanabe K, Ohtsuki T. The effect of posture on the running speed
of skiing. Ergonomics. 1978;21(12):987–98.
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