Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part I: Modelling of forces and torque, and theoretical prospects

Abstract

A model of the forces and the torque operating on a ball that is flying with rotation in the atmosphere of the Earth, and the resulting system of ordinary differential equations, are derived from mechanics and aerodynamics.The system of equations allows the theoretical aspects of the flight of a ball, such as the boundedness of its kinetic energy, the curvature of the orbit or the velocity function, to be investigated using certain transformations of the variables.The solutions of the corresponding ordinary or boundary value problems, computed numerically, are used to treat certain tasks in international ball games, for example, the maximum and minimum velocities of a volleyball service.

Effect of altitude on football performance

“…Although most of the focus in the medical literature is on the physiological effect of altitude on performance, the physical effects of altitude (Fuchs 1991, 1995) may actually be equally or even more important, especially for sports for which success depends substantially on a high degree of technical skill with a ball, as opposed to aerobic power and endurance. In the United States, it has been often discussed that altitude resident teams in Denver, Colorado at 1609 m have much better home records than they do away records.…”

Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part II: Theoretical aspects in the case of vertical angular frequency and applications

“…In the following, we shall only discuss the case tThis 'second' velocity u2 is specific for the ball game as well as u1 (cf. part I, [9]). Examples will be given in the final section 3.…”

“…The physical modelling of the forces and torque operating on a ball that is flying and rotating in the atmosphere has been derived in Part I, section 2, of this paper [9] from the principles of mechanics and aerodynamics. The ball's velocity function will be denoted by v = ( u x , uy, u , )~ and its angular frequency function by o = (ox, o,, o , )~.…”

An Approach to Quantify the Float Effect of Float Serves in Indoor and Beach Volleyball

“…Therefore, the prediction of the unstable airflow conditions causing the ball to float is rather unreliable, even when the initial conditions are well known (Wei et al, 1988). The exact mechanical description of floating balls is complex and has been a matter of debate in physics and mathematics for many decades (Mehta, 1985;Fuchs, 1991;Kao et al, 1994).…”