A theory of energy cost and speed of climbing

Paolo Tosi,Alessandro Rosponi,Federico Schena,Leonardo Ricci

doi:10.1063/1.3646533

Abstract

Climbing is an interesting form of quadrupedal locomotion on vertical substrates, and also a popular recreational activity. However, a theory of locomotor energetics of climbing has not been devised yet. Here we discuss an analytical model, based on simple physical principles, that gives the energy cost as a function of the vertical speed. We found that the energy cost monotonically decreases with speed, so that to minimize the energy spent to climb one should ascend at the highest possible speed. We propose that the actual climbing speed derives from the requirement of minimizing simultaneously the work per unit time as well as the work per unit length. Our predictions are in excellent agreement with measurements carried out on elite climbers.

Highlights

Climbing is an interesting form of quadrupedal locomotion on vertical substrates, which has played a critical role in the hominoid locomotor evolution.[1]
The expansion of the dissipative power into two terms permits a straightforward physical interpretation: g + Kis the force necessary to lift an unit mass sliding along a vertical surface with kinetic friction K
The term g + Krepresents the minimum work at per unit length and mass to be done against gravity and friction

Summary

Introduction

Climbing is an interesting form of quadrupedal locomotion on vertical substrates, which has played a critical role in the hominoid locomotor evolution.[1]. For climbing a vertical length L, a subject of mass m performs a work W that is composed of two terms: the increment in gravitational potential energy mgL, and the dissipative work E for generating the friction necessary for hanging and climbing. By expanding the dissipative power per unit mass k(v) in series and retaining the first two terms we obtain k(v) = k0 + kv Substituting in equation (3), we get EC = g + k + k0 (5)

Results

Conclusion