# Inductance (fwd)

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---------- Forwarded message ----------
Date: Tue, 31 Mar 1998 06:01:40 -0500
From: Alan Sharp <AlanSharp-at-compuserve-dot-com>
To: "INTERNET:tesla-at-pupman-dot-com" <tesla-at-pupman-dot-com>
Subject: Inductance (fwd)

Erik:

It checks!
Erik wrote:
>L : inductance in uH, r : radius in inches, N : number of turns,
>b : length of coil in inches, d : turns per inch, w : length of wire in
inches

>L = (r * r * N * N) / (9 * r + 10 * b)

Nasty Maths omitted here :)

>So the most inductance for a cylinder coil is when
>r = sqrt((5 * w) / d) / (3 * sqrt( Pi ))
>or
>w = r * r * Pi * d * 9 / 5

Daune Bylund goes through this in his "Modern Tesla Coil Theory"
and you can go one step further:

b = w / ( 2 * pi * r * d )

the hieght of the coil is the length of wire divided by the circumference
and
the number of turns per inch:

so:

b=  (r * r * Pi * d * 9 / 5) / ( 2 * pi * r * d ) = 0.9 * r
gives
b = 0.9 * r

Just having fun with some old fashioned algebra. :)
(the bit of my brain that used to do differential equations burned out on
tensor
calculus twenty years ago - just when I'ld almost reconciled Quantum
Mechanics
with General Relativity :)

So the most inductance for a cylinder coil is when the hieght is nine
tenths
of the radius. Make them short and fat everyone!

I checked this using spreadsheet and graph and the results for different
height radius ratio's are shown on the maths page of my web site:

http://ourworld-dot-compuserve-dot-com/homepages/AlanSharp

Have fun,

Alan Sharp (UK)

Message text written by INTERNET:tesla-at-pupman-dot-com
>Maximizing the inductance for a cylinder coil.

L : inductance in uH, r : radius in inches, N : number of turns,
b : length of coil in inches, d : turns per inch, w : length of wire in
inches

L = (r * r * N * N) / (9 * r + 10 * b)

Using this and solving for L in terms of r. and using
(N = b / d and b = w / (2 * Pi * r * d))

we get

L = w / (4 * Pi * Pi * (9 * r + (10 * w) / (2 * Pi * r * d)))

Now I took the derivative in respects to r

- (d * w * w * (9 * d * Pi * r * r - 5 * w)) / (4 * Pi * (9 * d * Pi * r *
r +
5 * w) ^ 2)

Set this to 0 and solve.

So the most inductance for a cylinder coil is when
r = sqrt((5 * w) / d) / (3 * sqrt( Pi ))
or
w = r * r * Pi * d * 9 / 5

Can somebody check to see if this is right?
Just having fun with some old fashioned calculus. :)<

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