RE>Inductance len<.8r bound

From:  Malcolm Watts [SMTP:MALCOLM-at-directorate.wnp.ac.nz]
Sent:  Sunday, April 05, 1998 6:32 PM
To:  Tesla List
Subject:  Re: RE>Inductance len<.8r bound

Hi Dale,

> From:  Dale Hall [SMTP:Dale.Hall-at-trw-dot-com]
> Sent:  Friday, April 03, 1998 1:03 PM
> To:  Tesla List
> Subject:  RE>Inductance len<.8r bound
> RE>Inductance len<.8r bounds limit  (Lmax -at-H/D=.5) 
> Erik/List,
> Assumption check: (math valid but application boundary validity question)
> I believe a derivation of the single-layer air-core coil formula maybe necessary
> due to assumptions for the use of  L = (r * r * N * N) / (9 * r + 10 * b):
> The '78 ARRL handbook states this formula to be a CLOSE APPROXIMATION
> for coils having a length => .8 radius.  Mathematically determined conclusions near/beyond boundary are likely to be flawed. 
> Additionally some lab confirmation could be performed as a check.
> Malcom, what was your purely iterative means, basic formula/assumption ?
> Dale


Start with a length of wire of known diameter. Start with a former 
that has h/d = 25 and d = 1"  (for example). Now calculate turns and 
hence inductance and save this value. Next, reduce height and increase
d. Recalculate. Compare this value with the previous one. Somewhere 
along the way you will hit a maximum for L. At this point, coil shape 
for Lmax is known. It really does work. Basically I am getting the 
computer to do a piecewise differentiation.