Mechanical determinants of the minimum energy cost of gradient running in humans

The metabolic cost and the mechanical work of running at different speeds and gradients were measured on five human subjects. The mechanical work was partitioned into the internal work (Wint) due to the speed changes of body segments with respect to the body centre of mass and the external work (Wext) due to the position and speed changes of the body centre of mass in the environment. Wext was further divided into a positive part (W+ext) and a negative part (W-ext), associated with the energy increases and decreases, respectively, over the stride period. For all constant speeds, the most economical gradient was -10.6 +/-0.5% (S.D., N = 5) with a metabolic cost of 146.8 +/- 3.8 ml O2 kg-1 km-1. At each gradient, there was a unique W+ext/W-ext ratio (which was 1 in level running), irrespective of speed, with a tendency for W-ext and W+ext to disappear above a gradient of +30% and below a gradient of -30%, respectively. Wint was constant within each speed from a gradient of -15% to level running. This was the result of a nearly constant stride frequency at all negative gradients. The constancy of Wint within this gradient range implies that Wint has no role in determining the optimum gradient. The metabolic cost C was predicted from the mechanical experimental data according to the following equation: [formula: see text] where eff- (0.80), eff+ (0.18) and effi (0.30) are the efficiencies of W-ext, W+ext and Wint, respectively, and el- and el+ represent the amounts of stored and released elastic energy, which are assumed to be 55J step-1. The predicted C versus gradient curve coincides with the curve obtained from metabolic measurements. We conclude that W+ext/W-ext partitioning and the eff+/eff- ratio, i.e. the different efficiency of the muscles during acceleration and braking, explain the metabolic optimum gradient for running of about -10%.