Skiing manufacturers depend on the development of new skis on trial and error cycles and extensive product testing. Simulation tools, such as the finite element method, might be able to reduce the number of required testing cycles. However, computer programs simulating a ski in the situation of a turn so far lack realistic ski-snow interaction models. The aim of this study was to (a) implement a finite element simulation of a ski in a carved turn with an experimentally validated ski-snow interaction model, and (b) comparison of the simulation results with instantaneous turn radii determined for an actual carved turn. A quasi-static approach was chosen in which the skisnow interaction was implemented as a boundary condition on the running surface of the ski. A stepwise linear function was used to characterise the snow pressure resisting the penetration of the ski. In a carved turn the rear section of the ski interacts with the groove that forms in the snow. Two effects were incorporated in the simulation to model this situation: (a) the plasticity of the snow deformation, (b) the influence of the ski's side-cut on the formation and shape of this groove. The simulation results agreed well with experiments characterising snow penetration. Implementation of the groove in the ski-snow interaction model allowed calculation of the instantaneous turn radii measured in actual turns, but also caused significant numerical instability. The simulation contributes to the understanding of the mechanical aspects of the ski-snow interaction in carved turns and can be used to evaluate new ski designs.

Alpine ski races are typically won by fractions of a second. It is therefore essential for ski racers to minimize air drag as well as ski-snow friction. In contrast to air drag, ski-snow friction during actual skiing has rarely been investigated so far. Two tasks, forward/backward leaning and edging of the skis, were selected, which (a) were expected to have an impact on ski-snow friction, and (b) could be executed while gliding in tucked position. Two hypotheses were tested: (H1) Run times are affected by forward or backward leaning. (H2) Run times are affected by edging of the skis. Four professional ski testers were recruited, who conducted a total of 68 runs of straight gliding. Execution of the tasks was documented by video recordings and by measuring the force application point on the skis of one tester. The findings of this study support (H2) but not (H1). There are indications that the increased run times for edging are caused by increased ski-snow friction. From a performance point of view, it seems beneficial for ski racers to minimize edging in the gliding sections of a race.

Two outstanding questions of the ski-snow friction are considered: the deformation mode of the snow and the real contact area. The deformation of hard, well sintered snow in a short time impact has been measured with a special linear friction tester. Four types of deformations have been identified: brittle fracture of bonds, plastic deformation of ice at the contact spots, elastic and delayed elastic deformation of the snow matrix. The latter is the dominant deformation in the ski-snow contact. Based on the measured loading curves the mechanical energy dissipation of snow deformation in skiing on hard snow has been determined and found negligible compared to the thermal energy dissipation. A mechanical model consisting of ice spheres supported by rheological elements (a nonlinear spring in series with a Kelvin element) is proposed to model the deformation of snow in the ski-snow contact. The model can describe the delayed elastic behaviour of snow. Coupled with the complete topographical description of the snow surface obtained from X-ray micro computer tomography measurements, the model predicts the number and area of contact spots between ski and snow. An average contact spot size of 110 lm, and a relative real contact area of 0.4% has been found.

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For ski manufacturers, it is important to know how a given ski-binding system performs under different loading conditions. Important performance parameters are the ski deformation and the resulting turn radius. This study focuses on carving turns. The aims of this study were: (1) to investigate the dependence of the turn radius on edging angle, load on the binding, and snow hardness using a finite element (FE) simulation, and (2) to compare the results with predictions of a frequently used model introduced by Howe. The FE simulation used a quasi-static approach (similar to Howe's model), but the ski-snow interaction model incorporated the groove that forms in the snow during a carved turn. Up to edging angles of 40°, the results of the FE simulation agreed well with Howe's model. However, for large edging angles ([50°) the calculated turn radius leveled out, whereas Howe's model tends to zero. This effect was more pronounced for soft snow than for hard snow conditions. Increasing forces on the binding caused a decrease in the calculated turn radii. In summary, the FE simulation showed that particularly at large edging angles the groove in the snow needs to be considered in models of the ski-snow interaction or in computations of the turn radius.