Goodness factor

The goodness factor is a metric developed by Eric Laithwaite to determine the 'goodness' of an electric motor. Using it he was able to develop efficient magnetic levitation induction motors.

$G=\frac{\omega }{\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\times \mathrm{r}\mathrm{e}\mathrm{l}\mathrm{u}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}}=\frac{\omega \mu \sigma A_{\mathrm{e}}{A}_{\mathrm{m}}}{l_{\mathrm{e}}{l}_{\mathrm{m}}}$

where

G is the goodness factor (factors above 1 are likely to be efficient)

A_e, A_m are the cross sections of the electric and magnetic circuits

l_e, l_m are the lengths of the electric and magnetic circuits

μ is the permeability of the core

ω is the angular frequency the motor is driven at

σ is the conductivity of the conductor

From this he showed that the most efficient motors are likely to be relatively large. However, the equation only directly relates to non-permanent magnet motors.

Laithwaite showed that for a simple induction motor this gave:

$G\propto \frac{\omega {\mu }_0{p}^2}{{\rho }_{\mathrm{r}}g}$

where p is the pole pitch arc length, ρ_r is the surface resistivity of the rotor and g is the air gap.