Un modelo matemático para la bola de fútbol

Abstract

This work refers to the analysis, study and resolution of the mathematical problem involved in the design and construction of the cover of a ball, such as the ones used in sports, in order to achieve a ball with optimal roundness and sphericity factors.The design of well distributed ball structures has grown in importance in the last years, most of all in the field of sports, such as soccer. The current trend is directed mainly towards finding a fast ball that will give more dynamism to the game. In order to achieve a greater velocity of the ball during its movement it is important that it has not only an adequate distribution of panels, that give it a greater sphericity, but also that it has a structure that allows for a good distribution of the existing tension between the panels.

Starting from an initial design, we define a process of readjustment of the panels in the ball cover, which will lead us to obtain optimal sphericity factors. Then, through a “twisting” process, we can add area to the surface without altering the sphericity factors, and solving the Missing Area Problem (or MAP). Finally, by redefining the final form of the panels, we propose tessellate strategies that will optimize the ball’s spherical structure.