Influence of ski bending stiffness on the turning radius of alpine skis at different edging angles and velocities - A computer simulation - Heinrich, D.; Mössner, M.; Kaps, P.; 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)
Aside from the side geometry, the bending and torsional stiffness along the ski are the main properties that affect the performance of carved turns. Given a specific load distribution the bending stiffness of the ski determines the local bending of the ski, consequently influencing carving and skidding, respectively. The aim of this paper was to present the results of the investigations of the bending stiffness on the turn radius and the pressure distribution along the running surface at different edging angles and initial velocities. For the simulations the skier was replaced by a sledge on two skis. Methods: The sledge and the skis were modelled in the multi-body system software LMS Virtual.Lab Motion. Bodies were assumed to be rigid. Bending and torsion of the ski segments were implemented by revolute joints with given stiffness and damping constants. In order to describe the loading-unloading behaviour of snow the ski-snow contact was modelled using a hypoplastic constitutive equation. Varied input data to the simulations were the bending stiffness of the skis, the edging angle of the skis, as well as the initial velocity of the sledge. Bending stiffness constants were determined in a bending experiment using a given real ski. Three different situations were investigated: 1) real, the measured bending stiffness, 2) soft, 50% of the measured bending stiffness, and 3) stiff, 200% of the measured bending stiffness. Simulations of a single turn for the real, soft and stiff skis were computed with two different initial velocities of 1 m/s and 5 m/s and three constant edging angles of 15°, 35°, and 55°. Other parameters such as torsional stiffness, side geometry or snow properties were kept constant. First the turn radius of the sledge was analysed. Secondly effects on the pressure distribution along the running surface of the skis and normal to the snow surface were studied. Results: The simulations with the soft, real and stiff skis showed that a larger edging angle of the skis resulted in a smaller turn radius and a higher initial velocity resulted in a larger turn radius. The smallest turn radius was encountered with the soft skis at an initial velocity of 1 m/s and an edging angle of 55°. The largest turn radius was obtained with the stiff skis at an initial velocity of 5 m/s and an edging angle of 15°. At a constant initial velocity the influence of the bending stiffness on the turn radius depended on the edging angle. At an initial velocity of 1 m/s for instance and an edging angle of 15° the turn radius of the real ski was smallest followed by the soft skis and the stiff skis. At the second edging angle of 35° the turn radius of the real skis was smallest, however followed by the stiff skis and the soft skis. At the third edging angle of 55° the turn radius of the soft skis was smallest followed by the real and the stiff skis. If the edging angle of soft, real or stiff skis was increased the pressure distribution along the running surface was shifted from the centre of the skis to the shovel and to the tail of the skis. In contrast, at a higher initial velocity the pressure distribution was shifted from the shovel and the tail of the skis to the centre of the skis. Discussion: In competitive skiing it is often important to make turns with small turn radii. Depending on speed and edging angle a softer or stiffer ski contributes to this goal. In performing a carved turn the pressure distribution along the running surface of the ski is an important factor. In order to avoid skidding as much as possible an "optimal" pressure distribution is necessary. By comparing the pressure distribution at turns with small turn radii to the pressure distribution at turns with large turn radii conclusions about an "optimal" pressure distribution can be drawn. Beside the turn radius and the pressure distribution the running time is another important factor in competitive skiing. Effects of the bending stiffness on the running time were not included in the investigations, but will be considered in future.