Numerical simulation of a turning alpine ski during recreational skiing

While downhill snow skiing, recreational alpine skiers enjoy making turning motions with their skis. These motions are mainly induced by skidding, while turning by alpine ski racers is made by carving a trace in the snow. In the present study we treat the turning motions by recreational alpine skiers. This "skidding" turning motion is made possible by centripetal forces acting on the ski and skier dynamic motion systems, with these forces arising due to the skier placing the ski's longitudinal axis at an angle that is inclined away from the velocity vector and edging the ski into the snow. When snow is soft, the edged ski creates a snow impacting force, whereas a snow cutting force occurs when it is hard. Here, we calculate the former force using a three-dimensional water jet analogy, while the latter one using conventional metal cutting theory, after which the corresponding equations of motion for each system are derived and numerically solved. This methodology enables simulating the curvilinear and rotational motion of the ski and skier systems. Resultant simulations quantitatively show for the first time that the resultant radius of curvature of a ski track while downhill skiing is strongly dependent on the location of the ski boot on the ski's longitudinal axis and also on its side-cut (midlength taper).