The mechanics of running: How does stiffness couple with speed?

Abstract

A mathematical model for terrestrial running is presented, based on a leg with the properties of a simple spring. Experimental force-platform evidence is reviewed justifying the formulation of the model. The governing differential equations are given in dimensionless form to make the results representative of animals of all body sizes. The dimensionless input parameters are: U, a horizontal Froude number based on forward speed and leg length; V, a vertical Froude number based on vertical landing velocity and leg length, and K LEG, a dimensionless stiffness for the leg-spring. Results show that at high forward speed, K LEG is a nearly linear function of both U and V, while the effective vertical stiffness is a quadratic function of U. For each U, V pair, the simulation shows that the vertical force at mid-step may be minimized by the choice of a particular step length. A particularly useful specification of the theory occurs when both K LEG and V are assumed fixed. When K LEG = 15 and V = 0.18, the model makes predictions of relative stride length S and initial leg angle θ 0 that are in good agreement with experimental data obtained from the literature.