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)
 * $A_{m}$, $A_{e}$ are the cross sections of the magnetic and electric circuit
 * $l_{m}$, $l_{e}$ are the lengths of the magnetic and electric circuits
 * $&mu;$ is the permeability of the core
 * $&omega;$ is the angular frequency the motor is driven at
 * $&sigma;$ 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, $&rho;_{r}$ is the surface resistivity of the rotor and $g$ is the air gap.