On the hydrodynamic lubrication of skiing - Larsson, R.; Sandberg, J.; Hindér, G.; Almqvist, A. (10th International Congress on Science and Skiing, January 28 - February 1, 2025, Val di Fiemme, Italy, 2025)
INTRODUCTION: Can friction form a thick, low-friction film in the contact between ski and snow? Is the melting rate sufficiently large for that? These are questions to be discussed in this paper. Lubrication theory can be applied to the ski friction problem, since proper lubrication of the ski requires that the melting rate must balance the amount of water pushed out from the contact between a ski base asperity and the snow. If we assume that the base of the skis is ground with longitudinal ridges and valleys and is placed in contact with a smooth snow surface, then the flow balance equation reads: (U+03B4 /U+03B4 y) * h^3 (U+03B4 p/U+03B4 y) = -12U+03B7 (U+03B4 hm/U+03B4 t) = -12 (U+03B7^2 * u^2 / hLU+03C1 (1) where p is water-film pressure, h is the thickness of the water film, u is the speed, and U+03C1, U+03B7, and L, are water density, viscosity, and latent heat, respectively. The RHS of (1) can be interpreted as a "melt squeeze effect" since U+03B4hm/ U+03B4t is the melting rate.