Skating on slippery ice

Abstract

The friction of a stationary moving skate on smooth ice is investigated, in particular in relation to the formation of a thin layer of water between skate and ice. It is found that the combination of ploughing and melting gives a friction force that is rather insensitive for parameters such as velocity and temperature. The weak dependence originates from the pressure adjustment inside the water layer. For instance, higher velocities, giving rise to higher friction, also lead to larger pressures, which, in turn, decrease the contact zone and so lower the friction. By treating ice as a Bingham solid the theory combines and completes two existing but conflicting theories on the formation of the water layer.

The friction of tilted skates on ice

“…Our calculation is a simplified version of the equations proposed for the upright position [4,6] where heat generation and flows in the bulk are taken into account. In general these extensions are of minor influence except for more special circumstances as very low temperatures.…”

“…2). Our study is an extension of the treatment given earlier for the upright skate [6], which appears here as limit of zero tilt angle. There are many parameters such as temperature, weight, speed, mass and type of skate, which all can be varied, leading to myriad of cases.…”

“…Fortunately a recalculation of the friction of the upright skate with the new boundary conditions, does not give a large difference for the friction. For completeness we give in Appendix B the changes in the equation with respect to the previous calculation [6], due to the changes in the boundary conditions.…”

“…We will now use the layer equation for the generation of the water layer derived in a previous paper [6] reading…”

“…The more conventional school of thought [4,5,6] explains the low friction by the formation of a liquid layer between skate and ice. The friction provides the heat to melt a layer and the layer co-determines the friction.…”