# Re: [TCML] inductance Vs diameter Vs height

```Scott:

I came across this post the other day while looking for something related:  http://www.pupman.com/listarchives/2009/Mar/msg00178.html
I do not know if it is correct though !!

Phil

It says "The ABSOLUTE MAXIMUM Inductance from a given length of wire, the section should be circular and the with a ratio of a = 2.575r where a is the radius of the circular axis of the coil and r is the radius of the cross-section - eg a torus...
The inductance is  L = 5.35 * PI * N² * a * 10-³ microhenries
where N = total turns

For a SINGLE LAYER coil (ie classic tesla coil) where the turns are close wound, the maximum inductance for a given wire length is:
diameter/ breath = 2.415
which is probably why tesla's magnifier was so fat and squat - maximum inductance and hence maximum coupling and energy transfer to the secondary before being fed to the extra coil...?

For a FLAT CIRCULAR COIL - the lowest resistance - and hence max time constant/maximum inductance of a flat circular coil is is obtained when inner radius r1 is about 0.4 of the outer radius r2.
This coil has 99% of the maximum efficiency when r1/r2 < 0.7.

I have not verified these sizes and shapes and equations personally - but they should be easy enough to plot on a spreadsheet.. the best way to do this would be to have a constant turns per inch ration and this simplifies the terms need to plot. then the basic inductance equation adopts the form D²*Length with everything else being constant..... "

From: Scott Bogard
Sent: Tuesday, August 10, 2010 9:01 PM
To: Tesla Coil Mailing List
Subject: [TCML] inductance Vs diameter Vs height

Hey all,
Off the top of your heads can anybody tell me the most efficient
surface area to inductance ratio of single winding solenoids?  What I
mean is the most efficient surface area to volume ratio for cylinders is
1 to 1 diameter to height, I am wondering if this applies to inductors
also, or if a single turn of huge diameter is better, or perhaps zero
diameter and infinite turns or somewhere in between.  So for a given
wire length, what configuration yields the highest inductance for single
layer I guess is what I am asking, just curious and thought someone
might know a short answer, and have any thoughts as to if this could
apply to coiling in any way.

Scott Bogard.
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Regards
Phil Tuck

www.hvtesla.com
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