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 e A m l e l m {\displaystyle G={\frac {\omega }{\mathrm {resistance} \times \mathrm {reluctance} }}={\frac {\omega \mu \sigma A_{\mathrm {e} }A_{\mathrm {m} }}{l_{\mathrm {e} }l_{\mathrm {m} }}}}
where
G is the goodness factor (factors above 1 are likely to be efficient) Ae, Am are the cross sections of the electric and magnetic circuits le, lm are the lengths of the electric and magnetic 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 ∝ ω μ 0 p 2 ρ r g {\displaystyle 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.
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