The apparently contradictory energetics of hopping and running: the counter-intuitive effect of constraints resolves the paradox.

Metabolic rate appears to increase with the rate of force application for running. Leg function during ground contact is similar in hopping and running, so one might expect that this relationship would hold for hopping as well. Surprisingly, metabolic rate appeared to decrease with increasing force rate for hopping. However, this paradox is the result of comparing different cross-sections of the metabolic cost landscapes for hopping and running. The apparent relationship between metabolic rate and force rate observed in treadmill running is likely not a fundamental characteristic of muscle physiology, but a result of runners responding to speed constraints, i.e. runners selecting step frequencies that minimize metabolic cost per distance for a series of treadmill-specified speeds. Evaluating hopping metabolic rate over a narrow range of hop frequencies similar to that selected by treadmill runners yields energy use trends similar to those of running.