The deformation of skis and the contact pressure between skis and snow are crucial factors for carved turns in alpine skiing. The purpose of the current study was to develop and to evaluate an optimization method to determine the bending and torsional stiffness that lead to a given bending and torsional deflection of the ski. Euler-Bernoulli beam theory and classical torsion theory were applied to model the deformation of the ski. Bending and torsional stiffness were approximated as linear combinations of B-splines. To compute the unknown coefficients, a parameter optimization problem was formulated and successfully solved by multiple shooting and least squares data fitting. The proposed optimization method was evaluated based on ski stiffness data and ski deformation data taken from a recently published simulation study. The ski deformation data were used as input data to the optimization method. The optimization method was capable of successfully reproducing the shape of the original bending and torsional stiffness data of the ski with a root mean square error below 1 N m2. In conclusion, the proposed computational method offers the possibility to calculate ski stiffness properties with respect to a given ski deformation.
Dieter Heinrich, Martin Mössner, Peter Kaps and Werner Nachbauer
Werner Nachbauer, Peter Kaps, Benno Nigg, Fritz Brunner, Alexander Lutz, Günter Obkircher and Martin Mössner
A video technique to obtain 3-D data in an Alpine skiing competition was investigated. The flight and landing phases of a jump were recorded during the 1994 Olympic combined downhill race. A direct linear transformation (DLT) implementation was applied, which computes the DLT parameters for each video image of each camera separately. As a consequence, one is able to pan and tilt the cameras and zoom the lenses. The problem of distributing control points in the large object space could be solved satisfactorily. The method proved to be suitable for obtaining 3-D data with reasonable accuracy, which is even sufficient for inverse dynamics. The computed resultant knee joint forces and moments compare well with results reported by other authors.