Goodness factor

 ( Induction Motors ) 

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 .

$G\; =\; \backslash frac\; \{\backslash omega\}\; \{\backslash mathrm\{resistance\}\; \backslash times\; \backslash mathrm\{reluctance\}\}\; =\; \backslash frac\; \{\backslash omega\; \backslash mu\; \backslash sigma\; A\_\backslash mathrm\{e\}\; A\_\backslash mathrm\{m\}\}\; \{l\_\backslash mathrm\{e\}\; l\_\backslash mathrm\{m\}\}$

where

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

, are the cross sections of the electric and magnetic circuits

, are the lengths of the electric and magnetic circuits

is the permeability of the core

is the angular frequency the motor is driven at

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:

$G\; \backslash propto\; \backslash frac\; \{\backslash omega\; \backslash mu\_0\; p^2\}\; \{\backslash rho\_\backslash mathrm\{r\}\; g\}$

where is the pole pitch arc length, is the surface resistivity of the rotor and is the air gap.

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