{{Short description|Metric for determining the efficiency of an electric motor}} The '''goodness factor''' is a metric developed by Eric Laithwaite to determine the 'goodness' of an electric motor.<ref> {{cite journal | author = ER Laithwaite | date = 1965 | title = The Goodness of a Machine | journal = Electronics and Power | volume = 11 | issue = 3 | pages = 101–103 | doi =10.1049/ep.1965.0071 }}</ref><ref> {{cite book |author1=DJ Patterson |author2=CW Brice |author3=RA Dougal |author4=D Kovuri |title=IEEE International Electric Machines and Drives Conference, 2003. IEMDC'03. |chapter=The "goodness" of small contemporary permanent magnet electric machines | date = 2003 | chapter-url = http://vtb.engr.sc.edu/vtbwebsite/downloads/publications/IEMDCpaper.pdf | volume = 2| pages = 1195–1200 | doi = 10.1109/IEMDC.2003.1210392 |isbn=0-7803-7817-2 |s2cid=14563810 }}</ref> Using it he was able to develop efficient magnetic levitation induction motors.<ref> {{cite journal | author = ER Laithwaite | date = 1965 | title = Electromagnetic levitation | url = https://ieeexplore.ieee.org/document/5176480 | journal = Electronics and Power | volume = 11 | issue = 12 | pages = 408–410 | doi = 10.1049/ep.1965.0312 | url-access = subscription }}</ref>
:<math>G = \frac {\omega} {\mathrm{resistance} \times \mathrm{reluctance}} = \frac {\omega \mu \sigma A_\mathrm{e} A_\mathrm{m}} {l_\mathrm{e} l_\mathrm{m}}</math>
where :{{math|''G''}} is the goodness factor (factors above 1 are likely to be efficient) :{{math|''A''<sub>e</sub>}}, {{math|''A''<sub>m</sub>}} are the cross sections of the electric and magnetic circuits :{{math|''l''<sub>e</sub>}}, {{math|''l''<sub>m</sub>}} are the lengths of the electric and magnetic circuits :{{math|''μ''}} is the permeability of the core :{{math|''ω''}} is the angular frequency the motor is driven at :{{math|''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:
:<math>G \propto \frac {\omega \mu_0 p^2} {\rho_\mathrm{r} g}</math>
where {{math|''p''}} is the pole pitch arc length, {{math|''ρ''<sub>r</sub>}} is the surface resistivity of the rotor and {{math|''g''}} is the air gap.
==References== {{reflist}}
Category:Induction motors Category:Dimensionless numbers of physics Category:Magnetism