A unified theory for the energy cost of legged locomotion

Abstract

Small animals are remarkably efficient climbers but comparatively poor runners, a well-established phenomenon in locomotor energetics that drives size-related differences in locomotor ecology yet remains poorly understood. Here, I derive the energy cost of legged locomotion from two complementary components of muscle metabolism, Activation-Relaxation and Cross-bridge cycling. A mathematical model incorporating these costs explains observed patterns of locomotor cost both within and between species, across a broad range of animals (insects to ungulates), for a wide range of substrate slopes including level running and vertical climbing. This ARC model unifies work- and force-based models for locomotor cost and integrates whole-organism locomotor cost with cellular muscle physiology, creating a predictive framework for investigating evolutionary and ecological pressures shaping limb design and ranging behaviour.

Keywords: biomechanics; energetics; locomotion.

Figure 1.

(a) AR and cross-bridge costs versus contraction cycling frequency, as a percentage of the cost of continuous contraction, from in situ studies; energy is normalized to muscle force (electronic supplementary material, text S3). (b) E_COT and V_muscCOT for running. Following equation (2.5), AR cost can be calculated from the slope of regression equation, 0.6V_muscCOT. Cross-bridge cost is given by the regression intercept, or as E_COT−AR cost. (c) Mass-specific metabolic cost, E_COT, and mechanical work, k, per metre versus body size and estimated stride cycles m⁻¹; redrawn from [3].

Figure 2.

(a) Observed E_COT and ARC predictions (equation (3.1)) for level running. Shaded regions for AR and cross-bridge costs reflect varying z and w ± 20%. The darker shaded region for the ARC E_COT prediction reflects varying AR : cross-bridge ratio −33 to +50%; the light shaded region for extends ARC E_COT an additional ± 20% (electronic supplementary material, text S6). (b) Observed E_COT and ARC predictions (equation (3.2)) for vertical climbing. Shaded regions as in (a) and (c). Observed E_COT and ARC predictions (equation (3.3)) for a range of species and slopes. Data in electronic supplementary material, table S1. (Online version in colour.)