Physics of free climbing

TL;DR

This paper applies stochastic process theory to analyze free climbing, identifying optimal rope lengths that minimize climbing time based on noise-induced escape kinetics.

Contribution

It introduces a novel application of first passage time theory to determine optimal rope lengths for free climbing, linking noise dynamics to climbing efficiency.

Findings

Discrete set of favorable rope lengths with shortest climbing times

Optimal rope length exists within the favorable set for minimal climbing time

Experienced climbers can reduce climbing time by using longer ropes

Abstract

Theory of stochastic processes provides theoretical tools which can be efficiently used to explore properties of noise induced escape kinetics. Since noise facilitated escape over the potential barrier resembles free climbing, one can use the first passage time theory in analysis of rock climbing. We perform the analysis of the mean first passage time in order to answer the question regarding the optimal, i.e., resulting in the fastest climbing, rope length. It is demonstrated that there is a discrete set of favorable rope lengths assuring shortest climbing times, as they correspond to local minima of mean first passage time. Within the set of favorable rope lengths there is the optimal rope giving rise to the shortest climbing time. In particular, more experienced climbers can decrease their climbing time by using longer ropes.