Sphericity is a measure of how closely the shape of a physical 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.

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.

Definition

Defined by Wadell in 1935,, of an object is the ratio of the surface area of a sphere with the same volume to the object's surface area:

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

, 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.

Derivation

Hakon Wadell defined sphericity as the surface area of a sphere of the same volume as the object divided by the actual surface area of the object.

therefore

as:

Sphericity of common objects

See also

• Equivalent spherical diameter

• Flattening

• Isoperimetric ratio

• Rounding (sediment)

• Roundness

• Willmore energy

References

External links

• Grain Morphology: Roundness, Surface Features, and Sphericity of Grains