Polinomial model revisited -- a simple calculation of the kinematical
parameters of a 100 m sprint
Abstract
We summarize and extend here a simple procedure allowing to obtain all
important parameters of the 100 m run based on the measured values for
the distance S from the start line and expired time t. An example for
testing the proposed model are 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 is
approximated by a third order polinomial function S = f(t), which is
easily fitted from the split (segment) times. This function is a
mathematical model enabling, by using a standard mathematical treatment,
to obtain the equations for determining the point of the maximal
sprinter velocity vdmax, corresponding to vanishing acceleration, its
distance from the start line Sdmax and corresponding time moment tdmax.
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
to determine the force acting at the begining of the run. Results
obtained justified the proposed approach for a universal and practical
preparation tool and also showed that there do not exist so large
differences in the values of kinematical parameters between analyzed
male and female sprinters. The didactical purpose of the paper is to
demonstrate how the combination of (unrealistic) exactly solvable model
with the knowledge of the realistic behaviour can lead to a good
numerical fit.