Optimization of the roundness of the soccer ball

Abstract

Most soccer balls are made of stitched leather or synthetic panels with a bladder inside. The initial configuration of the balls can be represented by polyhedra in the three dimensional space. For the numerical evaluation of the sphericity of the ball, a method previously proposed by the first author is used in this paper. Following previous studies on the optimizaton of the initial uninflated configuration of the soccer ball, this paper aims to calculate the shape and the sphericity of the inflated soccerball under given internal pressure and material properties. For this purpose two large displacement mechanical models are applied. The most popular configuration, the truncated icosahedron is considered as the initial shape of the ball, and a parametric study is conducted to determine the optimal shape. Our results show that there is significant difference between the optimal shape of the inflated and uninflated shapes.