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Re: Equation 9, Capacitance of a Toroid

>>From oldradio-at-cheney-dot-net Wed Feb 28 20:16 MST 1996
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>From: Jim Watson <oldradio-at-cheney-dot-net>
>To: "'Chips Tesla Board'" <tesla-at-objinc-dot-com>
>Subject: Equation 9, Capacitance of a Toroid
>Date: Wed, 28 Feb 1996 08:11:18 -0600
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>Greetings Everyone,
>
>   My name is Jim Watson.  I am a student (non-traditional) at the 
University of West Florida in Pensacola, Florida;  in the Electrical 
Engineering Technology program.  "Non-traditional" is a euphamism which 
means that I am a bit older than the normal student.  I am writing a paper 
on Nikola Tesla and the Wireless Transmission of Power;  I am designing and 
building a Tesla Coil as part of the same project.
>
>   The equation regarding the capacitance of a toroid. the one contributed 
by Bert Pool, is not entirely clear to me.  There is a numer 2 in the 
numerator of the radicand that I can not place with 100% certianty;  this is 
because the formula has always arrived in a slightly jumbled form, and I 
have to reconstruct it.  
>
>   The two appears to square 2pi;  it appears to be (2pi)^2.  Is this 
correct?  The remainder of the equation is very clear.  I would also 
appreciate any comments on the origin of this formula.
>
>Thanks.
>
>                          Jim Watson
>

Jim, how about a reply from the originator of the formula, Bert himself? :)

I am no mathematician.  I took a formula for calculating the capacitance of 
a sphere and started modifying it.  The formula you have is my attempt to 
substitute the surface area of a toroid (including the center disk) for that 
of a sphere.  Next, I took a large table of KNOWN cpapcitances for several 
different real toroids and using those values I put some "fudge" factors 
into the equation until the equation would give results within 5 % of the table.
The final formula will give you an estimated value of capacitance for almost 
any real-world toroid with an error of less than about 5%.

So that's where the numbers came from that don't initially make sense.

Bert