Re: Help with this equation!

To: tesla-at-poodle.pupman-dot-com
Subject: Re: Help with this equation!
From: Tesla List <tesla-at-stic-dot-net>
Date: Fri, 30 May 1997 22:26:11 -0500
Approved: tesla-at-stic-dot-net
Subject:      Re: Help with this equation!
       Date:  Fri, 30 May 1997 16:43:41 -0400
       From:  Tom Heiber <theiber-at-lonet.ca>
Organization: Power Surge
         To:  Tesla List <tesla-at-pupman-dot-com>
 References:  1


> Tom,
> 
> Hi from downunder!
> 
> My initial thought, given the nature of the equation, was that you could
> only solve for d1 &/or d2 by an iterative approach, however I have found
> an approach which may suit your needs:
> 
> Taking "Bert's #10" equation and cleaning it up we have,
> 
> C = 1.4 (1.2781 - d2/d1) . sqrt( PI (d1-d2) d2 )
> 
> If we substitute D for d2 and A for the aspect ration of the toroid,
> (i.e. A = d1/d2), we can put the equation in a form where only one
> diameter term exists and it is then easy to solve for D:
> 
> C = 1.4( 1.2781 - D/(AD) ) . sqrt( PI (AD-D)D )
>   = 1.4( 1.2781 - 1/A ) . D . sqrt( PI(A-1) )
> 
> Hence D = C / ( 1.4( 1.2781 - 1/A) . sqrt( PI(A-1) ) )
> 
> Just select a value for the aspect ratio that appeals to you, say 3, the
> capactiance you want and out pops D.  For mathematical reasons A must be
> greater than 1 (or else solution is not real) and should be greater than
> 2 for practical reasons (or the toroid intersects itself.
> 
> Hope this helps.
> 
> What is the origin of this equation?  While it is relatively
> straightforward problem to derive the eqn for the capacitance of an
> isolated sphere (one simple integral), my maths is far too rusty to do
> so for a more complicated shape like a toroid.  Is there a derivation of
> the equation from Bert's list anywhere?  (I would be surprised if it
> came from a textbook in its current form given the number of terms that
> can be cancelled directly or eliminated by simple rearrangement).
> 
> Best regards from one of the many generally silent but avid followers of
> the contents of this list,
> 
> Safe and sucessful coiling to all.
> 
> Ian.
> --
> -----------------------------------------------------------------------
> Ian Holland                               E-mail:   Ian-at-DigIdeas-dot-com.au
> Carnegie, Victoria AUSTRALIA              Callsign: VK3YQN
> -----------------------------------------------------------------------


I got this equation from some Text file I downloaded from the 'net. I
thought it'd give me a ballpark figure on the size of the toroid on my
Tesla Coil.

Tom Heiber