# Another formula to throw on the fire

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Sent: 	Wednesday, December 10, 1997 9:57 PM
To: 	tesla list
Subject: 	Another formula to throw on the fire

I computed a simple integration for finding out how much tubing or wire
is need for a primary coil that may be of use to those building coils.
The formula is as follows:

For a flat (or slightly banked) spiral primary coil of:

Outside (final) radius of Ro (Both Radii measured from the center of
the tubing)
N number of turns

The total length of wire/tubing (L) required is:  pi * N * (Ro + Ri)
Pretty simple end result, eh?  Independent of units chosen too, as long
as you are consistant of course!

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For completeness, here is my entire calculation:

The integrand was radius as a function of Theta:

R = (W/2pi) * (Ro - Ri)/N + Ri    where W is Theta in Radians

Integrating the radius this over all 2*pi*N turns (henceforth 2piN) we
get L:

_ (2piN)
/
L = / [(W/2pi)(Ro - Ri)/N + Ri] dW
_/
0

L = [(Ro - Ri)/2piN] * [(2piN)^2/2] + 2piN*Ri

L = piN(Ro-Ri) + 2piN*Ri

L = piN(Ro-Ri)    [Q.E.D.]

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