Analysis of climbing accidents

Abstract

The fall of a climber is analyzed by realistic and comprehensive model calculations. Various parameters that define such a fall and the action of the belaying system to stop it are included in an equation describing the balance between the energy gained by the fall and the various channels of dissipation. The result is a representative overview about the interplay between the various parameters. From this understanding, important consequences and recommendations for safety in climbing are deduced.

Introduction

Mountaineering and, in particular, sport-climbing have become increasingly popular sports during the last two decades (Alder and Glick, 1994). Several factors stimulated this development. Increased availability of leisure time in industrialized countries together with a higher mobility but also significant improvements of safety standards made these sports more attractive to a broader public. The required level of mental commitment altered from the historical heroic climbing to a more relaxed modern approach which was made possible by technical developments of the climber's safety equipment. The unwritten law of the past—‘the leading climber never falls’—was motivated by the unpredictable and often lethal risk arising from any violation of that rule. Important improvements of the belaying system's key components like ropes, harnesses, belaying devices and, maybe most important, the development of fully reliable protection anchors made climbing much safer. The increased safety allowed a change from the ‘never fall’ to the ‘let's try’ approach which characterized the advent of modern sport-climbing. Unsuccessful trials still result in falls but now they can be stopped safely provided that both the climber and belayer are trained in the proper use of their gear. Accident statistics (Schubert, 1979, Mägdefrau and Schubert, 1984), however, tell that climbing still has considerable risks which is due to several reasons. First, mountaineering is a multifaceted sport whose subdivisions (e.g. high altitude mountaineering) do not always have the high safety standards of sport-climbing. Second, since climbing is typically done on natural rocks, the climber is confronted with ever changing situations which require a high degree of alertness and flexibility in belaying. There is no standard safety recipe which works well under all circumstances. Therefore, safe climbing requires much experience. However, most of the experience is still collected empirically which cannot be the best approach to safe climbing, considering the risks of a fall. The aim of this paper is to elucidate the physics of a climber's fall using model calculations that take into account all relevant parameters. Unlike worst-case-scenarios which, for instance, are employed for official rope tests and do not have much in common with the typical dynamic situation of a realistic fall, the modeling presented here is designed to describe realistic situations as closely as possible. The outcome is some very instructive interdependencies of parameters like braking force, length of the fall and the influence of protection points. The following sections will first give the reader who is unfamiliar with this sport the necessary background of the technical aspects of climbing, thereafter introduce the model and the necessary formulae followed by the main section containing the important results of the calculations and the discussion of their practical consequences. The concluding remarks concentrate on the main recommendations that follow from these calculations.