Qianhong Wu1, Qingjie Sun. 1. Cellular Biomechanics and Sports Science Laboratory, Department of Mechanical Engineering, Villanova University, Villanova, PA 19085, USA. qianhong.wu@villanova.ed
Abstract
PURPOSE: Lift mechanics of downhill skiing or snowboarding is a new theory developed by the corresponding author and colleagues in 2006 and published in Medicine & Science in Sports & Exercise®. This theory, hereafter called the Wu-Weinbaum theory, captures the lift contributions due to both the transiently trapped air inside a snow layer and the solid phase (snow crystals) for the first time and examines the stability and control of skiing/snowboarding. However, it has two major shortcomings. First, it only predicts a single equilibrium position for a given gliding condition because of its limitations on the numerical simulation. Second, it is only applicable to rectangular boards. In the current study, we shall treat these limitations by improving the numerical methods as well as extending the Wu-Weinbaum theory to more complex planar shapes. METHODS: A modified mathematical model is developed where a width factor, f(x), which characterizes the variation of width from the leading to the trailing edge of a ski/snowboard, is introduced. RESULTS: We have performed a thorough reexamination of the force and moment balance on a rectangular board on the basis of an improved numerical scheme and obtained multiple equilibrium positions for a skier or snowboarder gliding over a compressed snow layer at a certain speed. Furthermore, the performance of a commercial ski/snowboard with a specified shape was studied on the basis of our revised model, which revealed different pore pressure distribution underneath the sliding surface compared with a rectangular board. CONCLUSIONS: This study, along with the Wu-Weinbaum theory, has laid the foundation for the optimization of a ski/snowboard from a lift generation point of view.
PURPOSE: Lift mechanics of downhill skiing or snowboarding is a new theory developed by the corresponding author and colleagues in 2006 and published in Medicine & Science in Sports & Exercise®. This theory, hereafter called the Wu-Weinbaum theory, captures the lift contributions due to both the transiently trapped air inside a snow layer and the solid phase (snow crystals) for the first time and examines the stability and control of skiing/snowboarding. However, it has two major shortcomings. First, it only predicts a single equilibrium position for a given gliding condition because of its limitations on the numerical simulation. Second, it is only applicable to rectangular boards. In the current study, we shall treat these limitations by improving the numerical methods as well as extending the Wu-Weinbaum theory to more complex planar shapes. METHODS: A modified mathematical model is developed where a width factor, f(x), which characterizes the variation of width from the leading to the trailing edge of a ski/snowboard, is introduced. RESULTS: We have performed a thorough reexamination of the force and moment balance on a rectangular board on the basis of an improved numerical scheme and obtained multiple equilibrium positions for a skier or snowboarder gliding over a compressed snow layer at a certain speed. Furthermore, the performance of a commercial ski/snowboard with a specified shape was studied on the basis of our revised model, which revealed different pore pressure distribution underneath the sliding surface compared with a rectangular board. CONCLUSIONS: This study, along with the Wu-Weinbaum theory, has laid the foundation for the optimization of a ski/snowboard from a lift generation point of view.
Authors: Anthony J Robinson; Robert P Carter; Jonathan D Browne; Jonathan Hu; Michael T Arnold; Jaxon T Baum; Eric V Neufeld; Brett A Dolezal Journal: Int J Exerc Sci Date: 2020-12-01