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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]