47
INFLUENCE OF THE SKI SIDE CUT 
ON VIBRATIONS IN ALPINE SKIING
VPLIV STRANSKEGA LOKA SMU^I 
NA VIBRACIJE PRI ALPSKEM SMU^ANJU
Otmar Kugovnik*
Bojan Nemec**
Matej Supej*
Milan ^oh*
Kugovnik, O., Nemec, B., Supej, M., & ^oh, M. (2000). Influence of the ski side cut on vibrations… KinSI, 6(1–2): 47–50
Abstract
In the paper we studied the influence of the ski side
cut on vibrations during the ski turn. Vibrations were
measured using ground reaction force measuring sys-
tem. In our tests we found out that the vibrations on
skis with emphasized side cut are generally lower
comparing to the skis with classical side cut. On the
other hand, carving skis can provoke excessive vibra-
tion in the case of side skidding. We have explained
this phenomena using a heuristic model of side skid-
ding for carving skis. The model was verified with the
measurements on the ski slope.
Keywords: measurement, skiing, mathematical mo-
del
Izvle~ek
V ~lanku smo preu~evali odvisnost vibracij med izved-
bo smu~arskega zavoja in geometrijo stranskega loka
smu~i. Z uporabo sistema za merjenje reakcijskih sil
podlage smo pokazali, da smu~i s poudarjenim stran-
skim lokom v splo{nem povzro~ajo manj vibracij med
izvedbo zavoja kot smu~i s klasi~nim stranskim lokom.
Med {tudijem pa smo identificirali situacije, kjer lahko
smu~i s poudarjenim stranskim lokom povzro~ijo do-
datne vibracije. Fenomen smo razlo`ili s heuristi~nim
modelom oddrsavanja pri smu~eh s poudarjenim
stranskim lokom, ki smo ga verificirali z meritvami na
terenu.
Klju~ne besede: merjenje, smu~anje, matemati~ni
model 
(Received: 04. 11. 1999 – Accepted: 13. 11. 2000)
*University of Ljubljana - Faculty of Sport, Gortanova 22, SI-1000
Ljubljana, Slovenia
**Jo`ef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
Contact address
Bojan NEMEC
Jo`ef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia
Tel: +386 1 477-36-56
Fax: +386 1 251-93-85
E-mail: Bojan.Nemec@ijs.si

48
INTRODUCTION
It is well known that vibrations in alpine skiing have
great influence on precise curve tracking as well as on
injuries. Vibrations are mostly due to the terrain ir-
regularities, but can be generated with the side skid-
ding during imprecise curve tracking (Kugovnik and
Nemec, 1998). Ski equipment manufacturers try to
reduce influence of vibrations using new designs and
new materials. One of the important aspects in vi-
bration damping is also side cut of the skis.
In our work we have analysed the influence of the
side cut of the skis on vibration caused by side skid-
ding. Two categories of skis were compared: skis with
classic and extreme side cut. Vibrations were esti-
mated with measuring ground reaction forces. Power
spectrum density of the measured force signals de-
termined the amplitude and frequency of the vibra-
tions.
During our analyses, we have noticed that the carv-
ing skis act differently if the skidding occurs. We tried
to explain the behaviour using mathematical model of
the skidding. In the past years several mathematical
models of a turning snow ski were presented. The
most critical point in this task is the modelling of the
snow impact force. Different snow conditions require
different models. Renshaw and Motte (Renshaw and
Motte, 1989) developed an empirical formula for icy
snow impact model, where the ground reaction force
depends on cutting depth and inclination angle.
Hirano and Tada (Hirano and Tada, 1996) proposed
another model, where they accomplished the mate-
rial cutting theory. This model is valid for well-packed
snow. Another model proposed by Hirano and Tada
(Hirano and Tada, 1994) is based on snow pushing,
calculated with water jet analogy. This model could be
used on soft, powder snow, but with many restric-
tions, since this model does not produce any ground
reaction forces without skidding. However, all pro-
posed models assume turning with skidding, which is
reasonable assumption for ski turn on classical skis.
With carving skis it is possible to turn the skis without
skidding, but experiments have shown that an effect
similar to the side skidding can be noticed on certain
circumstances on carving skis, too. In the paper we
present a model for side skidding on well packed
snow, which can be used also on carving skis. Our
model was based on some heuristic assumptions, but
was verified with the measurements on ski slope.
Similar study was presented in (Niessen, Muller,
Raschner and Schwameder, 1996), but focused on vi-
brations of the skis. On contrary, our study takes into
consideration vibrations measured on the ski boots,
i.e. vibrations that are transferred to the skier's body.
METHODS
Vibrations were measured using equipment for
ground reaction force measurement (Nemec, 1997).
Four force transducers per each leg inserted in the ski
boot sole were used to capture the reactive forces
with rate of 100 measurements per seconds. The
measurement was synchronised with the video im-
age. The block diagram of the ground reaction forces
measuring equipment is presented in Fig 1. The com-
puter program enables step by step analyses of the
ground reaction forces and simultaneously analyses
of the digitised video movie. Vibrations were obtained
applying the fast Fourier transform on the measured
force signals. We have used MATHALB and Signal
processing Toolbox to accomplish this task. Power
spectrum density analyses of the captured signals
shows frequency and magnitude of the vibrations.
With the applied sampling rate of the ground reac-
tion force measuring system (100 Hz), vibrations of
frequencies up to 50 Hz can be measured.
Vibrations were studied on turns of a typical giant
slalom run. The skier was experienced ski instructor.
He performed equal ski turns; first using skis with em-
phasised ski cut (carving skis) with radius of 12 m and
next using skis with classical ski cut with radius of
45 m. The snow was well packed, but not icy. The air
temperature was +2°C.
RESULTS
Typical response of ground reaction forces and pow-
er spectrum density for carving and classical skis is
shown in Fig 2,3,4 and 5 respectively. As it can be
seen from the force plot, vibrations are smaller on
carving skis. A better insight in vibration can be ob-
tained observing power spectrum density plot, which
shows the force vibration amplitude related to the fre-
quency (Kugovnik and Nemec, 1998). Vibration at
frequencies lower than 2 Hz are manly due to the
loading and unloading phase during the ski turn, while
vibrations of frequencies over 2 Hz represent unde-
sirable vibrations. From the results it can be conclud-
ed, that side skidding causes vibrations with frequen-
cies over 2 Hz.  Side skidding phase in the force plot
was identified observing the video image. Over 100
ski runs were analysed and from those we have cho-
sen the turns with the side skidding. In most cases
they were correlated with the increased vibrations.
Unfortunately, these ski runs were not performed at
the same time, same snow condition and with the
same skier, therefore statistical analysis was not feasi-
ble. Namely, the major part of the vibrations mea-
sured during the ski turn is due to the terrain irregu-
larities.
Kugovnik, O., Nemec, B., Supej, M., & ^oh, M. (2000). Influence of the ski side cut on vibrations… KinSI, 6(1–2): 47–50

49
Since carving skis enable to perform ski turn without
skidding, vibrations with frequencies over 2 Hz are
lower on carving skis. On the other hand, we can no-
tice higher amplitudes on power spectrum plots for
frequencies lower than 2 Hz with carving skis. This is
due to the greater radial forces, which are generally
obtained during the ski turn using carving skis and
performing the turns without skidding.
Fig 1: Measuring equipment
Fig 2. Ground reaction forces and force application
point of two turns on carving skis
Fig. 3. Power spectrum density of the left turn per-
formed on carving skis
Fig 4:Ground reaction forces of left turn on normal
skis
Fig. 5:Power spectrum density of the left turn per-
formed on normal skis
The above results were obtained if the ski turn on
carving skis was performed without the skidding. On
the other hand, we have noticed that skidding on
carving skis can provoke even greater vibrations com-
paring to the vibrations on the classical skis under the
same conditions. This phenomenon was noticed on-
ly on well-packed and icy snow. Typical response of
ground reaction forces and power spectrum density
for skidding on carving skis is shown in Fig 6 and 7 re-
spectively. The side skidding on carving skis was ex-
plained using a model for side skidding on well
packed snow, which can be applied, also on carving
skis.  
Fig. 6: Ground reaction forces of one ski turn with
skidding on carving skis
Fig. 7:Power spectrum density of the ski turn with
skidding on carving skis
Kugovnik, O., Nemec, B., Supej, M., & ^oh, M. (2000). Influence of the ski side cut on vibrations… KinSI, 6(1–2): 47–50

50
Fig. 8: force balance during the ski turn on well-
packed snow.
According with the Fig 8, the force balance equation
for a carving ski during the turn are presented with
the following equation
,
where F
c
denotes radial forces in ski turn, F
g
is gravi-
ty force, α is ski inclination angle, K
fr
is friction con-
stant and F
d
is dynamic force that causes the ski to
jump from the groove in the snow made by the ski.
When the dynamic force is positive, i.e. when the ra-
dial forces are too large or inclination angle is too low,
the ski jumps from the groove. Here, we will use a
heuristic assumption, that the bent ski is straightened
when it jumps from the groove. Since the inclination
angle remains the same, the tail and the shoulder of
the ski comes first in contact with the snow. The ski
then bends until the point under the ski boot sole
touches the ground. This is illustrated in Fig. 9.
Fig. 9: Bending of the skis in dependence of the side
cut and length of the skis.
From Fig. 9 is evident that the parallel shift distance d
normal to the ski direction l
s
depends on side cut ra-
dius and length of the ski.
Bulge factor h depends on side cut radius r and ef-
fective ski length l
s
and can be expressed as
.
Therefore, longer skis with the same side cut r cause
greater sideslip d. Additionally, larger bulge factor h
causes lower vibration frequencies with larger ampli-
tude, which is less favourable. Although our model is
based on heuristic assumption, that the bent ski is
straightened when it jumps from the groove, it gives
similar results as they were obtained with the simula-
tion of the side skidding using an industrial robot
(Nemec and Leonardi, 1999).
CONCLUSIONS
In the paper we have compared vibrations during the
ski turn using carving and classical side cut. It was
demonstrated that carving skis generally cause fewer
vibrations. Namely, carving skis enable to perform the
ski turn without the skidding, which can cause unde-
sirable vibrations. On the other hand, it was shown
that carving skis could generate greater vibrations on
certain snow conditions, if the skidding occurs during
the ski turn. We identified the skidding phase of the
ski turn by observing the video image of the skiing.
Statistical validation of the results was not possible,
since we didn’t succeed to measure enough ski runs
under the same circumstances. 
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Kugovnik, O., Nemec, B., Supej, M., & ^oh, M. (2000). Influence of the ski side cut on vibrations… KinSI, 6(1–2): 47–50