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The coefficient of friction of skis on snow appears to be influenced by several factors, for example, speed, contact area, snow type, and ski properties. The purpose of this study was to determine simultaneously the coefficient of kinetic friction and the drag area in straight running on a slope with varying inclination and in traversing on an inclined plane. Experimental measurements were taken using photo cells for straight running and by film analysis for traversing. The skier was modeled as a particle that moves on the surface of a slope. The equation of motion with the algebraic constraints of the track of the skier represents a differential-algebraic equation which was solved numerically. The coefficient of friction and the drag area were calculated by minimizing the sum of the square errors between computed and measured time data.
For straight running, the computed coefficient of friction and the drag area were in the same range as obtained by other methods. For traversing, the coefficient of friction could be determined but not the drag area. The skier traversed in an upright position at a speed from 0 to 17 m/s. In this range of velocity the drag area is not constant. It corresponds to critical Reynolds numbers where a sudden drop in the drag coefficient occurs if the body segments are approximated by cylinders.
The results indicate that in both cases the applied method is adequate for determining simultaneously the coefficient of kinetic friction and the drag area if these parameters are independent of the velocity.
Alpine skiing, kinetic friction, drag area, time measurements, cinematographic measurements
Associate professor, Institut für Mathematik und Geometrie, Technikerstr. 13, University of Innsbruck, Innsbruck,
Associate professor, Institut für Sportwissenschaften, Fürstenweg 185, University of Innsbruck, Innsbruck,
Research assistant, Institut für Sportwissenschaften, University of Innsbruck, Innsbruck,