The physics of a climbing rope under a heavy dynamic load

Abstract

In this theoretical article, the force-elongation behaviour of a climbing rope in a heavy fall is investigated and compared with experiments. The experiments show that the state-of-the-art viscoelastic description of a climbing rope with time-independent friction is not able to explain the rope tension as a function of time. A proper description has to take into account time-delayed friction, that is, a transition from a low-friction regime to strong friction near the force maximum which leads to a fast relaxation of the rope into its equilibrium position. Furthermore, a climbing rope has to be described by a nonlinear tension with increased stiffness for large elongations in order to agree with experiments with varying fall masses. Finally, observed second-mode force oscillations are explained by a continuum description of the rope taking into account its mass.