Running on flat turns: experiments, theory, and applications

Theoretical and experimental results are presented which demonstrate the mechanical effects of running along a circular turn. The theory is a simple one-parameter model, requiring only the top speed Vo of the runner as an input. The dimensionless parameter (Rg/v2o), a reciprocal Froude number or dimensionless parameter (Rg/v20), a reciprocal Froude number or dimensionless radius, appears as a natural result of the theory. This radial Froude number allows for the comparison of the theory and experiment for a large number of individuals on the same set of axes. The parameters of speed, foot contact time, ballistic air time, step length, stride length, and stride time are all predicted and measured for 23 different subjects. The agreement between theory and experiment is good. Exact solutions and approximate asymptotic results for the speed-radius relation are presented. Applications are made to the practical problem of the design of indoor and outdoor running tracks for athletic competition.