Model for assessment of the velocity and force at the start of sprint race.

A mathematical model was developed for the assessment of the starting velocity and initial velocity and force of a 100-m sprint, based on a non-homogeneous differential equation with the air resistance proportional to the velocity, and the initial conditions for [Formula: see text], [Formula: see text]The use of this model requires the measurement of reaction time and segmental velocities over the course of the race. The model was validated by comparison with the data obtained from 100-m sprints of men: Carl Lewis (1988), Maurice Green (2001) and Usain Bolt (2009), and women: Florence Griffith-Joyner, Evelyn Ashford and Drechsler Heike (1988) showing a high level of agreement. Combined with the previous work of the authors, the present model allows for the assessment of important physical abilities, such as the exertion of a high starting force, development of high starting velocity and, later on, maximisation of the peak running velocity. These data could be of importance for practitioners to identify possible weaknesses and refine training methods for sprinters and other athletes whose performance depend on rapid movement initiations.

Model for the determination of instantaneous values of the velocity, instantaneous, and average acceleration for 100-m sprinters.

Temporal patterns of running velocity is of profound interest for coaches and researchers involved in sprint racing. In this study, we applied a nonhomogeneous differential equation for the motion with resistance force proportional to the velocity for the determination of the instantaneous velocity and instantaneous and average acceleration in the sprinter discipline at 100 m. Results obtained for the instantaneous velocity in this study using the presented model indicate good agreement with values measured directly, which is a good verification of the proposed procedure. To perform a comprehensive analysis of the applicability of the results obtained, the harmonic canon of running for the 100-m sprint discipline was formed. Using the data obtained by the measurement of split times for segments of 100-m run of the sprinters K. Lewis (1988), M. Green (2001), and U. Bolt (2009), the method described yielded results that enable comparative analysis of the kinematical parameters for each sprinter. Further treatment allowed the derivation of the ideal harmonic velocity canon of running, which can be helpful to any coach in evaluating the results achieved at particular distances in this and other disciplines. The method described can be applied for the analysis of any race.