A Mathematical Model of the 100m

This paper develops a mathematical model, or formula, of the 100m sprint, which accurately describes the relationship between time elapsed and distance covered in the race. From this are derived formulae for velocity and acceleration. There are four constants in these formulae. They are constant throughout a particular performance of a particular runner, and they vary from performance to performance and runner to runner. The constants have important significance, and describe the maximum speed to which the runner is heading, the acceleration, the extent of loss of speed at the end, and the moment of onset of deceleration. This enables performance to be compared with performance. The model is applied to the men’s 100m event at the 1999 World Championships, for which times at each 10m-point are available for all finalists. From this set of data models are derived for the average performance of the first seven runners, representing archetypal elite sprinter, and for the winner, Maurice Greene. The differences between Greene and the average finalist are identified. The really significant result to come out of the analysis is that Greene is able to accelerate for considerably longer than anyone else.