How does the increase of body mass and ageing affect sprinter's results in a 100 m run? / ¿Cómo afecta el aumento de la masa corporal y el envejecimiento a los resultados del velocista en una carrera de 100 m?

SUMMARY: The career of a sprinter is analyzed with U. Bolt achievements as an example. The effects of the increase of body mass and ageing are discussed within the framework of the polynomial models for the velocity, muscular isometric force and age. The analysis presented demonstrates the influence of the BM factor in analyzed racing. The nonlinear increase of the BM for 9 kg in the period 2009 - 2017 in was one of the reasons of Bolt's unsuccessful attempt to repeat or confirm the time 9.58 s. Another limiting factor was the fact that due to the age, Bolt was not able to increase isometric muscular force which, after the year of maximal efficiency (2009) decreased.

RESUMEN: La carrera de un velocista se analiza con los logros de U. Bolt como ejemplo. Los efectos del aumento de la masa corporal y el envejecimiento se discuten en el marco de los modelos polinomiales de velocidad, fuerza isométrica muscular y edad. El análisis presentado demuestra la influencia del factor MC en el análisis en las carreras. El aumento no lineal de la MC para 9 kg en el período 2009 - 2017 fue una de las razones del intento fallido de Bolt de repetir o confirmar el tiempo 9,58 s. Otro factor limitante fue el hecho de que debido a la edad, Bolt no fue capaz de aumentar la fuerza muscular isométrica que disminuyó luego del año de máxima eficiencia (2009).

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.

A Model for Determining the Effect of the Wind Velocity on 100 m Sprinting Performance.

This paper introduces an equation for determining instantaneous and final velocity of a sprinter in a 100 m run completed with a wind resistance ranging from 0.1 to 4.5 m/s. The validity of the equation was verified using the data of three world class sprinters: Carl Lewis, Maurice Green, and Usain Bolt. For the given constant wind velocity with the values + 0.9 and + 1.1 m/s, the wind contribution to the change of sprinter velocity was the same for the maximum as well as for the final velocity. This study assessed how the effect of the wind velocity influenced the change of sprinting velocity. The analysis led to the conclusion that the official limit of safely neglecting the wind influence could be chosen as 1 m/s instead of 2 m/s, if the velocity were presented using three, instead of two decimal digits. This implies that wind velocity should be rounded off to two decimal places instead of the present practice of one decimal place. In particular, the results indicated that the influence of wind on the change of sprinting velocity in the range of up to 2 m/s and was of order of magnitude of 10-3 m/s. This proves that the IAAF Competition Rules correctly neglect the influence of the wind with regard to such velocities. However, for the wind velocity over 2 m/s, the wind influence is of order 10-2 m/s and cannot be neglected.

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.

Comment on "Improvement of the Davydov theory of bioenergy transport in protein molecular systems".

The validity of the recently proposed tentative improvement of the Davydov theory of intramolecular vibrational transfer is discussed. It is shown that it contains a few principal shortcomings and cannot be a sound ground for studies of the transport processes in molecular systems.