A ski-snow interaction model is presented. The force between ski and snow is decomposed into a penetration force normal to the snow surface, a shear force parallel to it, and friction. The purpose of this study was to investigate the benefits of a hypoplastic vs an elastic contact for penetration in the simulation of skiing turns. To reduce the number of influencing factors, a sledge equipped with skis was considered. A forward dynamic simulation model for the sledge was implemented. For the evaluation of both contact models, the deviation between simulated trajectories and experimental track data was computed for turns of 67 and 42 m. Maximum deviations for these turns were 0.44 and 0.14 m for the hypoplastic contact, and 0.6 and 7.5 m for the elastic contact, respectively. In the hypoplastic contact, the penetration depth of the ski's afterbody maintained nearly the same value as the part under maximum load, whereas it decreased in the elastic contact. Because the shear force is proportional to the penetration depth, the hypoplastic contact resulted in a higher shearing resistance. By replacing the sledge with a skier model, one may investigate more complex skier actions, skiing performance, or accident-prone skiing maneuvers.

ABSTRACT. In the simulation of skiing the force between ski and snow is a decisive factor. We decompose the reaction force into a penetration force normal to the snow surface, a shear force and friction. Two portable measurement devices were developed to study the penetration and shear forces for compacted snow on groomed ski slopes. The penetration force was assessed by measuring the penetration depth of a ski-tool loaded normal to the snow surface. . In another investigation, skiing turns were simulated using the presented snow reaction forces. Maximum deviations between computed and real trajectories were <1% of the overall length of the runs.

The paper shows the capability of state-of-the-art models and software to predict the fiber orientation distribution (FOD) on injection molded parts with a complex and thick-walled geometry. Predictions by the standard Folgar-Tucker model and the Reduced Strain Closure model were compared to measurements of the fiber orientation distribution obtained by X-ray Computed Tomography. Measurements and simulations were performed under different processing conditions to investigate the influence of injection velocity and packing pressure on the FOD. It was found that the predicted fiber orientation is in good qualitative agreement with the measurements. The measured orientation shows a distinct shell-core structure with high alignment of the fibers in flow direction in the shell layer and a orientation perpendicular to the flow direction in the core layer. While the orientation in the shell layer is predicted fairly well, a significant deviation is found in the prediction of the orientation in the core layer.

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A computer model was developed to simulate consecutive ski turns. The model consists of a segment model for two skis and a single body for the skier. It was implemented in the multibody simulation software LMS Virtual.Lab. The interaction of ski and snow leads to a normal and a shearing force. For the normal force a hypoplastic relation between force and penetration depth was used. Hypoplasticity considers the effect that compacted snow is inelastic and deformations remain. For the shearing force orthogonal metal cutting theory was applied. During turns the skier has to keep balance. He leans inward to compensate centrifugal force. Neglecting angulation the complement of the inward lean angle is the mean value of the edge angles of the left and the right ski. With a suitable choice of the edge angles the skier kept the balance. Using this model the trajectory of the skier was simulated over four and a half turns. The first turn was rather carved, but in the last turn strong skidding was present. Due to increasing speed the centrifugal force considerably exceeded the shearing strength of snow. The hypoplastic force-penetration relation led to a reasonable penetration depth, which is a crucial factor for the shearing force. Based on this reference simulation the influence of edge angle and forward/backward lean was assessed by performing parameter studies. An increased edge angle caused smaller turn radii. Surprisingly, forward lean caused larger and backward lean smaller turn radii. This phenomenon could be explained by the turn moment of the skier. Both effects were more dominant when the skis skidded.