Measure.Length.Form.Sphericity

MeasureDimensional

Sphericity is a measure of how closely the shape of an object resembles that of a 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,[1] the sphericity, {\displaystyle \Psi }\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 {\displaystyle V_{p}}V_p is volume of the particle and {\displaystyle A_{p}}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.