Computer Simulation of Consecutive Ski Turns

摘要

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.