Calculation of the contact pressure between ski and snow during a carved turn in Alpine skiing

The macroscopic contact area between ski and snow and the contact pressure are crucial influencing factors for carved turns in Alpine skiing. In the present paper, a simulation model is developed to quantify these factors. The ski is modelled as an Euler-Bernoulli beam with variable cross section, camber, bending and torsional stiffness using measured data from skis. The reaction forces of the snow are decomposed in penetration and shear forces. For the penetration forces a hypoplastic constitutive law is applied incorporating elastic and plastic deformation of the snow at the contact area. For the shear forces metal cutting theory is used. Ski deformation, contact area and contact pressure are computed based on quasi-static equilibrium between forces exerted by the skier and snow reaction forces. Parameter studies are performed to investigate the influence of edging and distributing the load between the inner and outer ski. Higher edging angles as well as loading both skis affected the contact pressure positively by increasing the resistance against shearing. The results of our study agree well with measurement data taken from literature. Based on the results, the importance of actions of the skier during carved turns is concluded.