Dynamics of carving runs in alpine skiing. II.Centrifugal pendulum with a retractable leg

In this paper, we present an advanced model of centrifugal pendulum where its length is allowed to vary during swinging. This modification accounts for flexion and extension of skier's legs when turning. We focus entirely on the case where the pendulum leg shortens near the vertical position, which corresponds to the most popular technique for the transition between carving turns in ski racing, and study the effect of this action on the kinematics and dynamics of these turns. In particular, we find that leg flexion on approach to the summit point is a very efficient way of preserving the contact between skis and snow. The up and down motion of the skier centre of mass can also have a strong effect of the peak ground reaction force experienced by skiers, particularly at high inclination angles. Minimisation of this motion allows a noticeable reduction of this force and hence of the risk of injury. We make a detailed comparison between the model and the results of a field study of slalom turns and find a very good agreement. This suggests that the pendulum model is a useful mathematical tool for analysing the dynamics of skiing.