A model for the turning snow ski

Abstract

A model is developed to investigate the steady-state solutions of a turning snow ski. In computing equilibrium of the skier/ski system, two types of forces are assumed along the ski bottom: skidding forces, which arise when shearing a virgin snow surface, and carving forces, which maintain the curvature of the ski when it slides in its own track. Turn radius and speed are insufficient to specify a unique turn solution. To quantify the effects of different ski designs on the model, a range of possible solutions is calculated for each turn radius and speed and compared using two indices, one measuring the mechanical efficiency of the turn resulting from the energy dissipation of shearing the snow surface, and the second measuring the equilibrium solution sensitivity to human control and regulation. When possible solutions are mapped onto the plane of these two indices, a characteristic solution behavior emerges corroborating experimental results found using a model ski turning on astroturf. This behavior provides a quantitative basis for comparing different ski designs and proposing new design strategies.