Mathematical model of the influence of the time of start reaction in 100 m sprint run

Abstract

The purpose of this study is to explain the influence of the time of start reaction tR to the results of sprinters in a 100 m run, using a new simple mathematical model based on the measured values for distance s, corresponding time t, and tR. The research is based on IAAF data obtained by measuring the segment length, the time of start reaction, transient times in 100 m run, and final times for the top sprinters C. Lewis (1988); M. Green (2011), and U. Bolt (2009) (men) and F. Griffith-Joyner (1988); E. Ashford (1988), and H. Drechsler (1988) (women). The values of the start reaction tR for both male and female top sprinters indicate that there appear no substantial differences in the values of tR based on gender which would directly favor male or female sprinters in achieving the top results in the 100m run. The influence of the time of start reaction tR decreases exponentially with the time t during the run (t>tR) and ends up at about 30 m, influencing the initial velocity vR although it is not directly related to the result of the run. Due to its applicative simplicity, the presented mathematical model and related conclusions can represent a solid basis for future studies concerning sprint running.