This study is conducted to develop a simplified mathematical model to describe the lift mechanics of downhill skiing and snowboarding, where the lift contributions due to both the transiently trapped air and the compressed solid phase (snow crystals) are determined. To our knowledge, this is the first time that anyone has attempted to realistically estimate the relative contribution of the transiently trapped air to the total lift in skiing and snowboarding.
The model uses Shimizu's empirical relation to predict the local variation in Darcy permeability due to the compression of the solid phase. The forces and moments on the skier or snowboarder are used to predict the angle of attack of the planing surface, the penetration depth at the leading edge, and the shift in the center of pressure for two typical snow types, fresh and wind-packed snow. We present numerical solutions for snowboarding and asymptotic analytic solutions for skiing for the case where there are no edging or turning maneuvers. The force and moment balance are then used to develop a theory for control and stability in response to changes in the center of mass as the individual shifts his/her weight.
Our model predicts that for fine-grained, windpacked snow that when the velocity (U) of the snowboarder or skier is 20 m·s−1, approximately 50% of the total lift force is generated by the trapped air for snowboarding and 40% for skiing. For highly permeable fresh powder snow, the lift contribution from the pore air pressure drops substantially.
This paper develops a new theoretical framework for analyzing the lift mechanics and stability of skis and snowboards that could have important applications in future ski and snowboard design.
1Department of Mechanical Engineering, Villanova University, Villanova, PA; 2Department of Chemical Engineering, Princeton University, Princeton, NJ; 3Department of Mechanical Engineering, The City College of the City University of New York, CUNY, New York, NY; and 4Departments of Mechanical and Biomedical Engineering and New York Center for Biomechanical Engineering, The City College of New York, CUNY, New York, NY
Address for correspondence: Sheldon Weinbaum, PhD, The City College of the City University of New York; E-mail: email@example.com.
Submitted for publication June 2005.
Accepted for publication November 2005.