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.

Isometric force development of some muscle groups in athletes.

In a large sample of both male and female athletes, subdivided by age and sex, a development curve of isometric muscule force (F) was analyzed for hand flexors, upper-body flexors and extensors, and knee extensors (PDS). A sample of 1,857 male and 1,009 female athletes, aged 8-30 years, subdivided by their age and sex, was used to measure the mean values of isometric muscle force of certain muscle groups by way of 5 topologically defined tests. Based on the results, isometric muscle force (F) development curves are shown and analyzed for the right-hand and left-hand (PLS) flexors, upper-body flexors (PTR), upper-body extensors (OTR), and knee extensors (ONO). The application of certain statistical programs gave rise to equations of the relationship between isometric force and age. The maximum mean value of PLS was chosen as the reference value or "the gold standard," with which PTR, OTR, and ONO were subsequently compared. The relationships were 1:1:1:2.8:5.9 (for male athletes), and 1:1:1.3:3.2:5.2 (for female athletes). The newly derived relationship was recognized as "the canon." The results may have practical application in athletes' fitness and conditioning. Every topologically defined muscle force has its own patterns and rules that should be closely followed in the training process, because any generalization may lead to false conclusions.