Modeling of the ski-snow contact for a carved turn - Mössner, M.; Heinrich, D.; Schindelwig, K.; Kaps, P.; Schmiedmayer, H. B.; Schretter, H.; 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)
Introduction: We investigate carved turns with alpine skis. During the movement of a ski, snow is loaded and unloaded. Compacted snow is not elastic, i.e. deformations remain. Such effects are modeled by a hypoplastic constitutive equation. During a turn the shovel digs into the snow and the rear part of the ski keeps nearly the same penetration depth as the part with maximum load. This results in a higher resistance against shearing for the afterbody of the ski. In the present work we investigate the benefits of the hypoplastic against the elastic force law. Simulation results for a sledge on two skis will be compared to experimental track data. Method: The sledge and the skis were modeled as a system of rigid bodies. Bending and torsional stiffness were translated to rotational springs with given spring and damping coefficients. The values for the constants were taken from experiments on real skis [1,2]. For the calculation of the contact forces we attached a smooth surface at the bottom of the rigid segments of each ski. This surface coincides with the midpoints and tangential directions of the bases of the ski segments. We call this surface the running surface of the ski. All force calculations were calculated with respect to the running surface. For penetration the contact forces were modeled using a hypoplastic constitutive equation [3]. Because of this, reaction forces are different during loading and unloading of the ski. Shearing forces were limited by supplying an ultimate pressure that snow can withstand. Three experiments were designed in order to determine the properties of snow: 1) the elastic force-penetration relationship for static loading was obtained, 2) the ultimate shear pressure of snow was determined, and 3) the dynamic behavior of snow, such as loading/unloading and cutting, was investigated. In order to assess the validity of the improved snow contact model the movement of the sledge was recorded on a slope. Simulation results for the hypoplastic and the elastic constitutive equation were compared to the measured track data. Results/Discussion. The implementation proofed to be suitable to simulate the movement of a self-running sledge on skis. The penetration depth is more realistic for the hypoplastic than for the elastic constitutive equation. For the hypoplastic force law the rear part of the ski penetrates deeper into the snow than for the elastic force law. The sledge on skis gets a better side guidance. Hence faster turn velocities are possible. The model can be used to study the influence of construction properties of the skis (bending/torsional stiffness, shape,...) as well as of the snow conditions. Results to such investigations will be published elsewhere.