Coil from a wire gauge

Wind this coil from this wire: how many turns fit, and what does it measure?

L = \frac{31.5 \cdot a^{2} \cdot N^{2}}{6 \cdot a + 9 \cdot ℓ + 10 \cdot c}

Method

1. Look up the gauge: its insulated diameter (heavy-build enamel), its bare copper diameter, and copper's resistance per metre at that diameter.
2. Turns per layer is the winding length times the packing factor, divided by the insulated diameter, rounded down — a fraction of a turn does not fit. Multiply by the layers for N.
3. The winding depth is the layers times the insulated diameter, and the mean radius is the former's radius plus half that depth.
4. Wire length is N turns of circumference at the mean radius; resistance is that length times the gauge's ohms per metre.
5. Wheeler's multilayer formula, 0.8 a²N² ÷ (6a + 9ℓ + 10c) in microhenries with a, ℓ and c in inches, is used here with the lengths in metres, which turns 0.8 into 0.8 ÷ 0.0254 = 31.5.
6. The continuous current is the bare copper's cross-section times 4 A/mm², the usual figure for a coil in air that is allowed to run warm but not hot.

Assumptions

• Orthocyclic-ish winding: each layer is the same number of turns laid side by side, and the layers stack one insulated diameter apart. A scramble wind packs worse and stands off further; the packing factor absorbs the first, not the second.
• Wheeler's 1928 multilayer formula is good to about 1 % while the winding depth and length are of the same order as the radius. For a winding much deeper than the former's radius, or a single layer on a long tube, it drifts; the single-layer form on the Wheeler page is better for the latter.
• Air core. The tube and the medium it carries are not in the inductance; a magnetised slurry raises it by about (1 + χ) of the medium's susceptibility, which the solenoid-field page carries.
• Copper at 20 °C. The resistance rises 0.39 % per degree, so a drive coil at 60 °C is 16 % higher than this.
• The 4 A/mm² ampacity is a rule of thumb for still air and continuous current — a figure to keep the enamel below its class temperature, not a limit the copper cares about. Pulses at a low duty can go several times higher; the current-rise page reports the pulse's resistive power so the two can be compared.
• Nothing here is Meyer's. The estate photographs show coils on tubes and dividers between them; no gauge, turn count or layer count is given anywhere the archive holds, and these are the numbers a reader would have to choose for themselves.