Effect of load, ski and snow properties on apparent contact area and pressure distribution in straight gliding

Modeling of ski friction requires an in-depth understanding of the ski-snow contact. For this aim, we imple-mented the Euler-Bernoulli beam equations for an embedded cross-country skating ski. Apparent contact area and pressure distribution were calculated from the ski's penetration depth using a hypoplastic force-penetration relation of snow. In a static validation experiment on an elastomer foundation, the difference between measured and calculated pressure of a loaded ski was below 5.1 kPa. For cross-country skis gliding on snow, the apparent contact area increased for increased normal load, softer snow, and decreased ski stiffness and camber. The pressure along the ski showed separated parts. The maximum pressure increased for increased normal load and harder snow. Overall, we observed an apparent contact area between 23.6 and 57.8% and a maximum pressure between 27.4 and 110.7 kPa. Concluding, a model for the ski-snow contact in straight gliding ski was developed. Apparent contact area and pressure distribution was affected by normal load, snow hardness, and ski stiffness and camber. Effects on the pressure should be considered in applications like ski construction, waxing, and modeling friction along the ski.