Download FRICTION DURING ALPINE SKI RACING

FRICTION DURING ALPINE SKI RACING
Michael Schiestl1, Peter Kaps1, Martin Mössner2, Werner Nachbauer2
1 Department
of Engineering Mathematics, Geometry and Computer Science, University of Innsbruck
2 Department
of Sport Science, University of Innsbruck, A-6020 Innsbruck, Austria
Purpose: The measurement of frictional forces generally require expensive laboratory and wind tunnel
tests. We have developed a method to analyse friction and drag during an actual ski race and at
relatively low costs.
Method:
1
The first 700m of the skiing slope Streif in Kitzbühel
were geodetically surveyed to obtain a mesh of terrain
points. The Clough-Tocher triangulation was used to
generate a smooth snow surface. Additionally, the
coordinates of numerous pass points were measured
along the track.
2
Several skiers were video taped during the World Cup
race. If a sufficient number of pass points is visible a
special modification of the direct linear transformation
(DLT) allows photogrammetric reconstruction of the skier’s
position on the snow surface from images of a single
camera.
Start
Mausefalle
Steilhang
U-Haken
3
This way a skier’s trajectory could be obtained on large
parts of the track. Smoothing the curve led to an
improvement of the data’s accuracy.
Stefan Eberharter in the Mausefalle
30
4 By setting up the equation of motion
r
r
r r
m&x& = Fgravity + Fconstrnt + Ffriction
one can retrace the measured trajectory. This way the
total frictional force (consisting of snow friction and drag)
as well as the reaction force (due to the path constraint)
acting on the skier could be calculated as a function of
time.
measured data
smoothed curve
20
Stefan Eberharter in the Mausefalle
250
velocity [m/s]
acceleration [m/s²]
total friction [daN=kg]
constraint force [daN=kg]
10
200
X [m]
0
150
−10
−20
100
−30
50
−40
−40
−20
0
20
Y [m]
40
60
80
0
−50
8.5
9
9.5
10
10.5
11
Time t [sec]
11.5
12
12.5
13
Conclusion: This method may help to analyse and compare the skills and equipment of different
skiers. It may also lead to a better understanding of the underlying physical laws describing snow
friction and drag forces involved in Alpine skiing.
This document is available under: http://Michael.Schiestl.name/publications
Contact: [email protected]