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 = ω r e s i s t a n c e × r e l u c t a n c e = ω μ σ A m A e l m l 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 circuitl_m, l_e are the lengths of the magnetic and electric circuitsμ is the permeability of the coreω is the angular frequency the motor is driven atσ 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 ∝ ω μ 0 p 2 ρ 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.