# 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.

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

G is the goodness factor (factors above 1 are likely to be efficient)
Am, Ae are the cross sections of the magnetic and electric circuit
lm, le are the lengths of the magnetic and electric 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, ρr is the surface resistivity of the rotor and g is the air gap.