Hirano Y, Tada N
Department of Industrial and Systems Engineering, Faculty of Science and Engineering, Chuo University, Tokyo, Japan.
Med Sci Sports Exerc. 1996 Sep;28(9):1209-13. doi: 10.1097/00005768-199609000-00020.
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).
在进行高山速降滑雪时，休闲高山滑雪者喜欢用滑雪板做出转弯动作。这些动作主要是通过滑行产生的，而高山滑雪比赛选手的转弯则是通过在雪地上划出痕迹来实现的。在本研究中，我们探讨休闲高山滑雪者的转弯动作。这种“滑行”转弯动作是由作用在滑雪板和滑雪者动态运动系统上的向心力促成的，这些力是由于滑雪者将滑雪板的纵轴置于一个偏离速度矢量的倾斜角度，并将滑雪板刃切入雪中而产生的。当雪较软时，刃切入雪中会产生雪撞击力，而当雪较硬时则会产生雪切削力。在此，我们用三维水射流类比法计算前一种力，用传统金属切削理论计算后一种力，然后推导出每个系统相应的运动方程并进行数值求解。这种方法能够模拟滑雪板和滑雪者系统的曲线运动和旋转运动。模拟结果首次定量显示，高山速降滑雪时滑雪轨迹的合成曲率半径强烈依赖于滑雪靴在滑雪板纵轴上的位置以及滑雪板的侧切（中间长度锥度）。
