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J Theor Biol. 2001 Apr 21;209(4):445-53.

Multiple walking speed-frequency relations are predicted by constrained optimization.

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Department of Nutrition, Food and Exercise Sciences, Florida State University, Tallahassee, FL 32306, USA.


A person constrained to walk at a given speed v on a treadmill, chooses a particular step frequency f and step length d=v/f. Testing over a range of speeds generates a speed-frequency (v-f) relationship. This relationship is commonly posited as a basic feature of human gait. It is often further posited that this curve follows from minimum energy cost strategy. We observed that individuals walking under different constraint circumstances--walking to a range of fixed metronome frequencies (fixed f) or over a range of spaced markers (fixed d)--produce speed-frequency relations distinct from the constrained v relation. We show here that three distinct speed-frequency curves, similar to those observed, are predicted by the assumption that a walking person optimizes an underlying objective function F (v, f) that has a minimum at the preferred gait. Further, the metabolic cost of transport is a reasonable approximate candidate for the function F.

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