The energetics of human walking: is Froude number (Fr) useful for metabolic comparisons?

Velocity and body mass have well-known influences on the amount of metabolic energy that animals require to walk. This relationship could stem from the fact that both are key variables in calculating the mechanical energy of a system in motion. Other variables, like leg length, are also important in mechanical energy calculations and two mechanical formulations that incorporate leg length, Froude number (Fr) and the LiMb model, have been shown to correlate with human metabolic energy expenditure. Both, however, include velocity as a key variable in their calculations, so we wondered if the correlation might derive solely from their relationship with velocity rather than leg length. Using the energetic data and gait parameters from 24 human adults and 48 children, we tested several variables - velocity (V), V(2), body mass, leg length, Fr and LiMb - to see which combinations best explained the variation in oxygen consumption, a proxy of metabolic energy expenditure. An equation with V(2), body mass and leg length as covariates produced the highest R(2), explaining 88% of the variation when all subjects were combined. No significant differences in the predictive power of velocity, V(2), Fr or LiMb were detected, prompting us to conclude that neither Fr nor LiMb compensate for the effect of leg length. Leg length does influence the energetic expenditure of walking humans, but Fr and LiMb do not appear to adequately reflect that effect. The development of another method to compensate for the effect of leg length on metabolic energy consumption is essential.