The kinetic friction of ice

An apparatus based on a pendulum hanging around a revolving drum of ice was developed to measure the kinetic friction between a slider and an ice surface under conditions commonly experienced in ice skating (temperatures from -15 to -1 degrees C and velocities from 0.2 to 10 m s$^{-1})$. The results are explained by a quantitative development of the frictional heating theory of Bowden & Hughes (1939): heat produced by friction raises the surface to its melting point and a small amount of water is produced which lubricates the contact area. The frictional heat used in melting is usually small; most of the heat flows from the contact area at the melting point into the slider and into the ice. This makes it possible to calculate the dependence of the coefficient of friction $\mu $ on the thermal conductivity of the slider, the ambient temperature and the velocity of sliding $v$, without considering the detailed mechanism that produces the frictional force. For sliders of mild steel and Perspex the main heat loss is through the ice and $\mu $ is hence proportional to the temperature below the melting point and to $v^{-\frac{1}{2}}$. For these two materials the magnitude of the coefficient of friction is correctly calculated from measured and known parameters to within a factor of 2. The remaining discrepancy is probably mainly due to the difference between the real and apparent contact areas. For a copper slider the heat loss through the metal is about the same as that through the ice. There is no pressure melting in these experiments; the only effect of the lowering of the melting point by pressure is to reduce slightly the frictional heat needed to keep the contact area at the melting point. On the other hand, at temperatures above about -2 degrees C pressure melting would be expected.