Parametric modeling of human gradient walking for predicting minimum energy expenditure

Abstract

A mathematical model to predict the optimum gradient for a minimum energetic cost is proposed, considering previous results that show a minimum energetic cost when gradient is -10%. The model focus on the variation of mechanical energy during gradient walking. It is shown that kinetic energy has a marginal role in low speed gradient walking. Therefore, the model takes in consideration only potential energy. A mathematical parameter that depends on step length is introduced, showing that the optimal gradient is a function of that parameter. Consequently, the optimal negative gradient depends on the individual step length. The model explains why recent results do not suggest a single optimal gradient but rather a range around -10%.