Experimental and theoretical simulations of climbing falls

Abstract

A modern rock climber attempting difficult routes will expect to take a number of falls. Typically the falls will be from the same point on the climb, for example at a particularly difficult series of moves, therefore the same part of the climbing rope will be damaged by each fall. Since the consequences of rope failure are serious, it is important that the climber should be aware of the number of falls the rope can withstand. The work described in this paper was carried out to understand the mechanics of climbing falls so as to enable predictions to be made of the tension developed in the rope. Once the value for this tension is known, an estimation can be made of the life of the rope measured as the number of falls to failure. A theoretical simulation of climbing falls has been developed which includes the nonlinearity of the rope behaviour and friction where the rope runs through `karabiners,' the metal clips used to anchor the climbers to the rock. The results of the simulation have been compared to experimentally measured rope tensions. The number of falls to failure has been measured experimentally for various lengths of fall and fall factors (the ratio of the length of fall to the length of rope). Failure of the rope invariably occurs where the rope runs over the most heavily loaded karabiner; therefore, the karabiner edge radius has also been varied. The experimental data have been used to derive a failure curve for the rope that may be combined with the theoretical simulation to predict the number of falls to failure.