Sphericity

Sphericity is the measure of how closely the shape of an object approaches that of a mathematically perfect sphere. For example, the sphericity of the balls inside a ball bearing determines the quality of the bearing, such as the load it can bear or the speed at which it can turn without failing. Sphericity is a specific example of a compactness measure of a shape. Defined by Wadell in 1935, the sphericity, Ψ {displaystyle Psi } , of a particle is: the ratio of the surface area of a sphere (with the same volume as the given particle) to the surface area of the particle: where V p {displaystyle V_{p}} is volume of the particle and A p {displaystyle A_{p}} is the surface area of the particle. The sphericity of a sphere is unity by definition and, by the isoperimetric inequality, any particle which is not a sphere will have sphericity less than 1. Sphericity applies in three dimensions; its analogue in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft, is called roundness. The sphericity, Ψ {displaystyle Psi } , of an oblate spheroid (similar to the shape of the planet Earth) is: where a and b are the semi-major and semi-minor axes respectively.