Calculate Wire Length for Rectangular Former/Bobbin

Here:

Understand that in practice the number of turns worked out this way will never fit in the winding space. There will always be gaps in between turns and layers and the actual number of turns you can fit in will be somewhat less than the theoretical value.

Example: Say the dimensions of the bobbin are Outer sides - 2" x 2.5" Inner sides - 1" x 1.5" Winding depth = 0.5" Winding length = 1.5"

and you want to fill it with 24 AWG enamel wire wire diameter ? 0.022"

Theoretically, you can fill it with 1550 turns at 7" per turn. This gives a total wire length of 904 ft. In practice, the total number of turns will be less, much less if you wind it by hand.

Note that assumes square wire and paths. Square packing is probably optimistic for scramble winding, reasonably close for flat layers with tape (tape rigid enough to support the next layer, mind), and pessimistic for flat wound no tape (hexagonal packing).

Square paths underestimate the lower layers (that poof out a little because of wire stiffness) and mostly overestimate the upper layers (because the corners round off).

There's also a contribution from the wire not being infinitely thin -- the difference between a summation and an integral. This weighs the perimeter(layer number) slightly differently.

Note that a winding factor of 0.5 or so is very typical. That is, take the winding area, halve it, and fit the wire in there. That accounts for the wire not laying flat, and layers of tape.

If you need an exact length, this method should be pretty close without going under. If you're okay with an overestimate, go with the outer perimeter rather than the average. To then get an exact number, cut off the excess, and subtract that from the initial measurement. Or wind one part, unwind it and measure it (make sure you straighten the wire though).

Tim

The OP asked for the math and I gave it while being careful to point out some of the pitfalls and you added some useful information.

There are two sides to the effect of winding with round wires. On the one hand, the winding space can never be fully utilised even with a perfect winding pitch. On the other hand, successive layers can be offset by one-half wire diameter and adjacent layers can partly occupy the depression between adjacent turns.

This is not just theory. I occasionally wind my own transformers when I can't find what I need in the market. I find that offset layering can save a significant amount of depth, especially with thick wires, and partially compensates for imperfections in pitch. A factor of 0.8 works very well for me.

To the OP: There is no magic formula that will work precisely in practice due to the various factors we've pointed out. There will also be variations in the departure from ideal windings with technique, skill, wire gauge and the tools used. Rules-of-thumb gained from others' or one's own experience can be very useful.

Thank you. This is exactly what I was looking for.

Steve Morris

For an approximate value: length of wire times cross section area of wire-plus-insulation is strictly less than volume available.

For a better approximation, allow for packing density (