Calculating the length of wire in a flat, slender coil

[kelticwizard]

Suppose I wanted to build a flat, slender coil using 40 gauge wire, (.0078 in).

The air core will be 0.25 in diameter. The ouside diameter of the coil is 2.0 in diameter. The depth of the coil will be 0.0078 inch-just the width of a single strand of wire.

How would I go about calculating the length of the 40 gauge wire necessary for this coil?

[kelticwizard]

Just thought I would put an illustration to what I mean. The coil is only a single strand deep, but 2 inches across.

Since the winding in this example is 40 gauge, that is 0.0078 in diameter. The winding is 0.75 inches on each side of the air gap. If I am figuring correctly-this is the first time I have attempted to calculate such things-that means the coil has 75 / 0.0078 turns. That is 9, 615 turns of 40 gauge wire. But since each turn requires a different length of wire, I don't know the total length required for the winding.

Any help would be appreciated.

[SmarmyDog]

It's 96 turns and you'll need about 379 inches (plus lead length). You can approximate it by multiplying the number of turns by the average diameter (1.25 inches in your case), and then by pi.

Cheers, Casey

[kelticwizard]

Much obliged.

Thank you.

[AudioFreak]

KW,

Just noticed that your description in your first post does not match your description in your second post. In your First post you list ID as 0.25" and in your second post you list ID as 0.5" ... I'll assume that your second post is infact correct since it matches your illustration but I though I would mention it "just incase".

[kelticwizard]

Audio Freak:

See what happens when you do things late at night, lol?

We'll use the 0.5 in for the calculations, even though the 0.25 in would be more desirable. I'm just trying to arrive at a method, I honestly don't know what gauge wire I'll be trying, anyway.

Besides, I just looked up a different website and got a different measurement for the the diameter of 40 gauge wire, so that throws things off even more.

[AndrewT]

Hi,
I think there are at least two ways to get your wire length.
1. the complicated (for me) calculus method.
2. the area method.
I also think these two alternatives give the same answer.

Using method 2.
Calculate the area of the coil [D^2-d^2]*Pi/4=[2^2-0.5^2]*3.14/2=2.945 sqin.
Now take the area and divide by the wire thickness.
A/Thk=4.7/0.0078=378inches. Allow for the thickness of the insulation.

Now it's easy to arrive at the wire length used to form any thickness of coil. Just multiply by the number of turns per layer.

Caution,
when winding this or any coil, it is more important to get the number of turns consistent than the wire length, but good technique should give fairly close tolerance on length.

[Conrad Hoffman]

Well I'm curious. It appears you want to make a "pancake" coil similar to what they used on ancient radios. They used to interweave them on radial spokes. Is this for a crossover, or something completely different? IMO, nobody makes these because they're so difficult, and I don't know if the properties are better or worse or the same as the usual multilayer design, but it should be really interesting to find out.

[AudioFreak]

I would imagine that they are a less perfect inductor than the standard multi-layer type.

[rabbitz]

See the pic for some numbers.