Goodness factor

{{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.

{{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

}}

{{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 }} Using it he was able to develop efficient magnetic levitation induction motors.

{{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

}}

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

where

:{{math|G}} is the goodness factor (factors above 1 are likely to be efficient)

:{{math|A_e}}, {{math|A_m}} are the cross sections of the electric and magnetic circuits

:{{math|l_e}}, {{math|l_m}} 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:

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

where {{math|p}} is the pole pitch arc length, {{math|ρ_r}} is the surface resistivity of the rotor and {{math|g}} is the air gap.