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, , of an object is the ratio of the surface area of a sphere with the same volume to the object's surface area:
where is volume of the object and is the surface area. The sphericity of a sphere is unity by definition and, by the isoperimetric inequality, any shape which is not a sphere will have sphericity less than 1.
Ellipsoidal objects
The sphericity, , of an oblate spheroid (similar to the shape of the planet Earth) is:
^Wadell, Hakon (1935). "Volume, Shape, and Roundness of Quartz Particles". The Journal of Geology. 43 (3): 250–280. Bibcode:1935JG.....43..250W. doi:10.1086/624298.
External links
Look up sphericity in Wiktionary, the free dictionary.
Grain Morphology: Roundness, Surface Features, and Sphericity of Grains