Simulation of a sprinter. Part I. Development of a model

The two horizontal forces acting on a sprinter are ground reaction driving him forward and air resistance impeding him. The driving force starts off at a maximum value but decreases with increase in velocity, whereas the resisting force varies as the square of velocity. Mathematical models of these two forces have been incorporated in Newton's Second Law to yield a second order nonlinear differential equation to describe the sprinter's motion. This equation may be numerically integrated, and validation of the model has shown there is good agreement between theory and experimental data. The model may be used to characterise a runner's performance (a so-called 'sprint profile'), to pinpoint his strengths and/or weaknesses, and to predict what his time might be for a particular distance if he were able to maintain maximum velocity.