Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking

TLDR

During single‑stance walking the center of mass behaves like an inverted pendulum, yet mechanical work is required to redirect its velocity between steps, and a collision model predicts that the negative work—and the compensatory positive work—scale with the fourth power of step length, implying a proportional metabolic cost. We tested whether the predicted fourth‑power scaling of mechanical work and metabolic cost with step length holds in humans. Nine participants walked at a fixed step frequency while varying step length; limb external mechanical work was measured with force plates and metabolic rate with indirect calorimetry. Both negative and positive external mechanical work and metabolic rate increased with the fourth power of step length, and metabolic rate scaled linearly with mechanical work, indicating that step‑to‑step transition work is a major determinant of walking energy cost.

Abstract

SUMMARY In the single stance phase of walking, center of mass motion resembles that of an inverted pendulum. Theoretically, mechanical work is not necessary for producing the pendular motion, but work is needed to redirect the center of mass velocity from one pendular arc to the next during the transition between steps. A collision model predicts a rate of negative work proportional to the fourth power of step length. Positive work is required to restore the energy lost, potentially exacting a proportional metabolic cost. We tested these predictions with humans (N=9) walking over a range of step lengths(0.4-1.1 m) while keeping step frequency fixed at 1.8 Hz. We measured individual limb external mechanical work using force plates, and metabolic rate using indirect calorimetry. As predicted, average negative and positive external mechanical work rates increased with the fourth power of step length(from 1 W to 38 W; r2=0.96). Metabolic rate also increased with the fourth power of step length (from 7 W to 379 W; r2=0.95), and linearly with mechanical work rate. Mechanical work for step-to-step transitions, rather than pendular motion itself, appears to be a major determinant of the metabolic cost of walking.