Optimal stride frequency computed from the double-compound pendulum of the leg, and verified experimentally as the preferred stride frequency of jogging

Abstract

Observations of long-distance runners reveal that the front-finishing runners invariably have smooth and comfortable running gait. Hence, this study is based on the reasoning that a jogger would naturally feel most comfortable to run at the stride frequency corresponding to the natural oscillation frequency of his leg. Under this condition, the jogger would be least tired, as the leg muscles would need to do minimal work to accelerate and decelerate the leg at the start and end of the leg-swing phase of the cycle. Thus, the jogging motion of a runner will appear to be natural and smooth. To elucidate if the leg motion frequency corresponding to its natural frequency of oscillation about the hip joint is the most comfortable jogging mode (causing minimal fatigue to the jogger), both analytical and experimental studies were carried out to determine these frequency values. Analytically, the leg was modelled as a double-compound pendulum and the expressions for the natural oscillation frequencies were derived to compute the stride frequencies (SFs) based on the anthropometric parameters of the volunteers. Also, experimentally, the SFs of these volunteers were determined under running conditions, using a 50 Hz video camera and Peak Motus software. The regression analysis of the model-based stride frequencies versus preferred stride frequencies of natural running yielded a remarkably high correlation coefficient of 0.94. The results obtained in this study suggest that jogging at the natural oscillation frequency of the leg may invoke the least expenditure of energy.