Evaluation of the Final Time and Velocity of a 100 m Run Under the Realistic Conditions

The aim of the research was to provide an analytical expression for the final time and velocity at the 100 m run, taking into account realistic conditions of the run, more precisely the effect of the wind and resistance of the medium (air). Combining the polynomial model for the distance vs time with the solution of the algebraic cubic equation, such an analytical expression was derived. The expression allowed to evaluate the dependence of the final time of the race on the wind velocity. This enabled the quantification of the time effect of the mentioned influences on the final time and velocity. It is possible to calculate the dependence of the sprinter’s velocity on expired running time for various wind velocities (from 0 up to ± 10 m/s) as well as determine the maximal running velocity vmax and corresponding time moment tmax. The results obtained were verified using split time data for six top sprinters: C. Lewis, M. Green, U. Bolt and F. Griffith-Joyner, E. Ashford and H. Drechsler. The results confirmed that it was possible to quantify the time effect of the influence of the wind velocity and resistance of the medium on the final time of the 100 m run. Although the applicability of the approach was tested using the data concerning top sprinters, the mathematical expressions involved are simple enough to be used by any coach to estimate the results of a sprinter under various weather conditions.