Goodness factor

Template:Short description 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

Template:Math is the goodness factor (factors above 1 are likely to be efficient)

Template:Math, Template:Math are the cross sections of the electric and magnetic circuits

Template:Math, Template:Math are the lengths of the electric and magnetic circuits

Template:Math is the permeability of the core

Template:Math is the angular frequency the motor is driven at

Template:Math 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 Template:Math is the pole pitch arc length, Template:Math is the surface resistivity of the rotor and Template:Math is the air gap.