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Re: [TCML] inductance Vs diameter Vs height


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 !!


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.
  Tesla mailing list
Phil Tuck

Tesla mailing list