Copper Area Ratio Approximation (Electric Motors)

1.10.3

With a winding density factor C of 0.70, the following values of the copper area ratio KA can be used. A winding density factor of 0.70 is conservative, because most coils can be wound with a higher winding density. Therefore, a coil designed with this approximation will be manufacturable.

Copper area ratio	Valid wire	Number of
KA,for C = 0.70	gauge range	installation layers
0.50 ± 0.04	10 < AWG < 38	Single build
0.45 ± 0.07	10 < AWG < 38	Double build
0.40 ± 0.10	10 < AWG < 38	Triple build
0.35 ± 0.13	10 < AWG < 38	Quadruple build

The copper cross-sectional area can be obtained by rewriting Eq. (1.407) and including the effect of different values for the winding density factor, as follows.

The copper cross-sectional area can also be calculated from the number of turns N and the bare wire diameter dB, as follows.

Equations (1.408) and (1.409) can be combined to determine the number of turns or to determine the bare wire diameter. In the case of a dc coil design, the number of turns N can be determined from Eq. (1.410) without needing to use the set of diameter equations Eqs. (1.370) to (1.373) and Eq. (1.385). In the case of an ac coil design, the bare wire diameter dB can be determined from Eq. (1.411) without needing to use equation (1.400), the set of diameter equations Eqs. (1.370) to (1.373), and Eq. (1.401).