Goodness factor

The goodness factor is a metric developed by Eric Laithwaite to determine the 'goodness' of an electric motor.^[1][2] Using it he was able to develop efficient magnetic levitation induction motors.^[3]

${\displaystyle G={\frac {\omega }{\mathrm {resistance} \times \mathrm {reluctance} }}={\frac {\omega \mu \sigma A_{\mathrm {e} }A_{\mathrm {m} }}{l_{\mathrm {e} }l_{\mathrm {m} }}}}$

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:

${\displaystyle G\propto {\frac {\omega \mu _{0}p^{2}}{\rho _{\mathrm {r} }g}}}$

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