What information on mechanical parameters can a polynomial model tell about the 100 ​m sprint

Abstract

In this paper for the first time, a simple procedure allowing to obtain all important parameters of the 100 ​m run based only on the measured values for the distance S from the start line and expired time t, was summarized. An example for testing the proposed model were the results for segment values for S and t for elite sprinters, male: C. Lewis, M. Green and U. Bolt, and female: F. Griffith-Jоyner, F. Ashford and H. Drecksler. The distance was approximated by a third order polynomial function, S ​= ​f(t), which is easily fitted from the split (segment) times. This function is a mathematical model which enables, via a standard mathematical treatment, the ability to obtain the equations for determining the point of the maximal sprinter velocity, vmax, corresponding to vanishing acceleration, its distance from the start line (Smax) and corresponding time moment (tmax). The function provides direct reading of the initial velocity (vo) as well as finding the expressions for the sprinter instantaneous velocity (vt) and acceleration (at). It also provides the initial acceleration, enabling the determination the forces acting at the beginning of the run. The results obtained justified the proposed approach for a universal and practical preparation tool and also showed that there were no significant differences in the values of kinematical parameters between analyzed male and female sprinters.