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Another formula to throw on the fire
From: Adam[SMTP:absmith-at-tiac-dot-net]
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:
Inside (starting) radius Ri
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!
---------------------------
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.]
-Adam
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Adam Smith
absmith-at-tiac-dot-net
Epoch, Inc. Digital Music Project
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