Theory of ice-skating

TL;DR

This paper develops a fluid mechanics and Stefan law-based model to analyze the thin water film enabling frictionless ice skating, deriving equations for film thickness and contact length, and providing insights into the conditions for lubrication.

Contribution

It introduces a coupled equation model for the water film in ice skating, including boundary layer analysis, to predict film thickness and its dependence on skating parameters.

Findings

A boundary layer solution estimates film thickness without complex calculations.

The water layer thickness is always macroscopic for typical skating conditions.

The model aligns well with numerical simulations and explains lubrication mechanisms.

Abstract

Almost frictionless skating on ice relies on a thin layer of melted water insulating mechanically the blade of the skate from ice. Using the basic equations of fluid mechanics and Stefan law, we derive a set of two coupled equations for the thickness of the film and the length of contact, a length scale which cannot be taken as its value at rest. The analytical study of these equations allows to define a small a-dimensional parameter depending on the longitudinal coordinate which can be neglected everywhere except close to the contact points at the front and the end of the blade, where a boundary layer solution is given. This solution provides without any calculation the order of magnitude of the film thickness, and its dependence with respect to external parameters like the velocity and mass of the skater and the radius of profile and bite angle of the blade, in good agreement with the numerical study. Moreover this solution also shows that a lubricating water layer of macroscopic thickness always exists for standard values of ice skating data, contrary to what happens in the case of cavitation of droplets due to thermal heating (Leidenfrost effect).