Wire Gauges Question

[Tristan Lall]

Originally Posted by Richard Wallace

In my country, we use units that are more convenient for small ratio calculations. American Wire Gauge (AWG) is a good example. 10 AWG wire at standard temperature adds one Ohm per thousand feet to its circuit. Increasing the AWG number by three doubles the per-length resistance; e.g., 13 AWG is two Ohms per thousand feet. This system makes wire size selection much more straightforward than other systems, such as wire diameter in millimeters.

Interestingly, increasing AWG by one unit increases per-length resistance of that wire's circuit by a factor of the cube root of two (~1.26). Wire used to wind electromagnet coils in motors, actuators, and transformers is typically available in size increments of one-quarter AWG, so the per-length resistance ratio of successive (i.e., +0.25 AWG) wire sizes is the twelfth root of two (~1.05946), which musicians will recognize as the ratio of fundamental frequencies of successive notes on an equitempered chromatic scale -- this increment is also called a half-step, or semitone; e.g. stepping from A to A#.

Based on that example and others, I think American engineering units are more like those used by artists, rather than by scientists. I think our system of units promotes creative thought.

That's a creative approximation with useful implications, but the truth is that AWG isn't defined that way. Instead of ³√2 ≈ 1.259, the ratio between AWG sizes is ³⁹√92 ≈ 1.229. And the resistance per length depends on using a solid copper conductor in a DC application (no skin effect) under certain environmental conditions—and even then, it's approximated.

In many practical use cases (FRC included), the distinction between approximation and definition doesn't really matter. But the fact that approximations are necessary to make the numbering system meaningful substantially dilutes the rationale for adopting AWG as a standard, especially for use cases that don't derive value from those approximate relationships.

Aside: The ISO paper sizes (A0, A1, A2, A3, A4, etc.) do something similar with ²√2, except that's actually the ratio between sizes (rounded to a whole number of millimetres).