Snow friction and drag during the downhill race in Kitzbühel - Schiestl, M.; Kaps, P.; Mössner, M.; Nachbauer, W. (International Congress Mountain & Sport. Updating study and research from laboratory to field. 11th-12th November 2005. Rovereto (TN) - Italy. Programme and book of abstracts, 2005)
The running time of a skier depends - among others - on snow friction as well as on air resistance. The drag area cdA and the friction coefficient ƒÊ are usually determined in the wind tunnel and from laboratory tests respectively. In the present work drag area and snow friction were simultaneously determined during the famous World Cup downhill race in Kitzbuhel. Such an analysis may help to compare the technical equipment and the skills of different skiers. Method: In 2002 the first 700m of the skiing slope (the Streif) were geodetically surveyed. The obtained terrain points were triangulated. In [1] a modification of the direct linear transformation (DLT) was developed which allows the reconstruction of an object's position located on a given surface from a single picture. In order to solve the skier's equation of motion a smooth surface is required. Using Clough-Tocher subdivisions a continuously differentiable surface interpolating the terrain points was generated. Stefan Eberharter's race was video taped on the surveyed section of the slope. Then the position coordinates of the tips of the skis and the toe pieces of the ski bindings were reconstructed to receive the trajectory on parts of the track. By smoothing this curve an accuracy of a few centimetres can be achieved. The skier's equation of motion can be written in the form of a differential algebraic equation (DAE). This way we simulated the race with the obtained trajectory as a constraint. Snow friction and drag were expected to exert a force of the form: f = ƒÊN + . cdAƒÏv2 with ƒÊ being the snow friction coefficient and cdA being the drag area - both assumed to be piecewise constant along the trajectory. Then the values were determined by least squares minimising the error between the measured and computed positions. Results: Results for a single turn are given: From time t = 0[s] to 0.58[s] values of µ = 0.40 and cdA = 0.9[m2] were determined. For the second part of the turn from time t = 0.58[s] to 1.92[s] values of µ = 0.10 and cdA = 0.55[m2] were obtained. The mean error between the measured and computed positions was less than 4 [mm]. Due to skidding effects in the turn the values of the friction constant are considerably higher than in straight running. The upright position of the skier causes the drag area to be about twice as large a can be observed for elite athletes in wind tunnel experiments. This is in accordance with values published for example in other sources.