Department of Applied Mathematics, The University of Leeds, Leeds, UK.
Sports Biomech. 2023 Sep;22(9):1209-1242. doi: 10.1080/14763141.2020.1795236. Epub 2020 Aug 3.
In this paper, we analyse the model of pure carving turns in alpine skiing and snowboarding based on the usual assumption of approximate balance between forces and torques acting on the skier during the turn. The approximation of torque balance yields both lower and upper limits on the skier speed, which depend only on the sidecut radius of skis and the slope gradient. We use the model to simulate carving runs on slopes of constant gradient and find that pure carving is possible only on slopes of relatively small gradient, with the critical slope angle in the range of . The exact value depends mostly on the coefficient of snow friction and to a lesser degree on the sidecut radius of skis. Comparison with the practice of ski racing shows that the upper speed limit and the related upper limit on the slope gradient set by the model are too restrictive and so must be the assumption of torque balance used in the model. A more advanced theory is needed.
在本文中，我们基于滑雪者在转弯过程中受力和力矩近似平衡的假设，分析了高山滑雪和单板滑雪的纯刻滑模型。力矩平衡的近似给出了滑雪者速度的下限和上限，它们仅取决于雪板的侧切半径和坡度梯度。我们使用该模型模拟了恒定坡度上的刻滑运行，发现只有在坡度较小的情况下才能实现纯刻滑，临界坡度角在 范围内。具体值主要取决于雪的摩擦系数，在较小程度上取决于雪板的侧切半径。与滑雪比赛的实际情况相比，模型设定的速度上限和相关坡度梯度上限过于严格，因此模型中使用的力矩平衡假设必须进行修正。需要更先进的理论。
