# Goodness factor

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]

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

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.

## References

1. ^ ER Laithwaite (1965). "The Goodness of a Machine". Electronics and Power 11 (3): 101–103. doi:10.1049/ep.1965.0071.
2. ^ DJ Patterson, CW Brice, RA Dougal, D Kovuri (2003). "The "Goodness" of Small Contemporary Permanent Magnet Electric Machines". Proceedings of the International Electric Machines and Drives Conference 2: 1195–1200. doi:10.1109/IEMDC.2003.1210392.
3. ^ ER Laithwaite (1965). "Electromagnetic levitation". Electronics and Power 11 (12): 408–410. doi:10.1049/ep.1965.0312.