Optimization of energy expenditure during level walking

An analytical relationship between the basic variables of walking — step rate, step length, and metabolic energy expenditure — is formulated with the aid of data derived from the only two complete studies in the literature (Atzler and Herbst, 1927; Molen et al., 1972b). The relationship in its hyperbolic form indicates that for any given step length within the normal range of walking speeds (approximately up to 145 m/min) there is a unique step rate which requires minimal energy expenditure per unit distance traversed. Matching the given step length with any other step rate results in greater energy demand. As derived here, the condition of optimality requires that the step rate be directly proportional to the step length with a subject-dependent proportionality constant. Imposing this optimality constraint on the hyperbolic form yields an optimal pattern equation which virtually coincides, up to speeds of about 100 m/min, with an empirical equation of quadratic form, found by a number of investigators to adequately relate energy expenditure to speed under moderate walking conditions.