# RE: Torroid Formula (To Mark and Jim)

```
Tab -

There is a much simpler way to solve this problem. That is by making a graph
of the variables involved. This is standard engineering practice for
difficult equations.

I show a Toroid/Sphere Capacitance graph in one of my books. The graph was
also shown in the TCBA Newsletter based on equations from engineering texts.

The graph covers spheres 10 to 60 inches diameter and toroids 3 to 20 inches
small dia and 10 to 80 inches large diameter. If you would like on of these
graphs send me a stamped self addressed envelope and I will send it to you.

John H. Couture

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-----Original Message-----
From: Tesla List [mailto:tesla-at-pupman-dot-com]
Sent: Thursday, May 11, 2000 3:51 PM
To: tesla-at-pupman-dot-com
Subject: Re: Torroid Formula (To Mark and Jim)

Original Poster: "MalikAT" <MalikAT-at-holycross.ac.uk>

Hi guys it's Tab,
firstly thanks for all your help. I've been trying to do this for quite
some time. Let me fill you in on what i keep getting. (by the way I have
used the solver function in excel to do this for me, the reason i need to
do it because i'm writting a computer program to design tesla coils as part
of my computing course, i've been allowed 1 year to complete it) Because
i'm making a program all i need to do is substitute values for d1 that give
me lower and higher values for x then just check every value between until
it gets the right one. It will probably be some sort of iteration formula.
Because i have found a way to do this, the problem i posed just really
became something to do because i was interested in seeing if i could get
it. There may also be a mistake in jims work - when you multiplied by d1^2
you left the 2nd bracket out. Anyway...
This is what i do..
1.4(1.2781-(d2/d1))SQRT(pi*d2*(d1-d2))=x
/ by 1.4,
(1.2781-(d2/d1))SQRT(pi*d2*(d1-d2))=x/1.4
square both sides
((1.2781-(d2/d1))^2)*(pi*d2*(d1-d2))=(x^2)/(1.4^2)
Expand the first bracket
(1.2781^2 - 2*1.2781*d2/d1 +
(d2^2)/(d1^2))*(pi*d1*d2-pi*(d2^2))=(x^2)/(1.4^2)
Expand again, then put everything over a common denominator. The result is
that the numerator looks like a binomial expansion. I have tried to
factorise this but it never seems to work. You get some binomial over your
denominator. I think once i have this, all i would need to do is multiply
by the denominator, take the nth root of the binomial, bring the denomintor
back as some root then simplify to leave d1!!! but the number crunching
just gets harder until you reach the correct binomial. Like i said it looks
increadibly like a binomial. Just a bit more algebra then we're there.
Good luck and Thanks again

Tabraze

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----------
> From: Tesla List <tesla-at-pupman-dot-com>
> To: tesla-at-pupman-dot-com
> Subject: Re: Torroid Formula
> Date: 10 May 2000 22:53
>
> Original Poster: "Mark Broker" <broker-at-uwplatt.edu>
>
> Jim and Tabraze,
>
> Ouch!
>
> I  plugged the original equation into MathCad2000 Professional, and it
pretty
> much gagged.  So, I simplified it a little by hand, plugged THAT into MC,
and
> it still gagged.  Simplifying by hand, I get this:
>       (x^2 / d2) + d2^3  =  d1(d1 - 1.2173d2)(d1 - .6656d2)
>
> substituting,
>        y = a(a-b)(a-c)
>
> MathCad doesn't like that one (the greatly simplified one), either.
> can copy the result to the clipboard, but the lines are too long and
terse to
> really make too much sense.  However, you can choose your "x" and "d2"
and use
> Excel's Solver to find d1.  For that matter, you should just be able to
plug
> the original into Solver....
>
> That was a good waste of about an  hour trying to solve a cubic function
in
> terms of the cubic.  I thought I remembered a way to do so, but maybe
that was
> under different conditions.  Oh well, hope that this is of some use to
someone.
>
> Mark

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