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

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; r(2)=0.96). Metabolic rate also increased with the fourth power of step length (from 7 W to 379 W; r(2)=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.