MECHANICS OF A TURNING SNOW SKI

Modelling the turning motion of snow skis is simulated via a single-ski representation followed by numerically solving the associated differential equations of motion. The forces applied to the ski are assumed to be gravity, the longitudinal friction occurring between the ski and snow, and a skidding force (snow resistance force) corresponding to a system centripetal force and making curvilinear motion possible. The skidding force is calculated via a water jet analogy. Our model quantitatively shows that a ski's side-cut, i.e. its midlength taper, remarkably effects the radius of curvature of a ski trail made when skiing down a ski slope.