Re: Torroid Formula

To: tesla-at-pupman-dot-com
Subject: Re: Torroid Formula
From: "Mark Broker" <broker-at-uwplatt.edu> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
Date: Wed, 10 May 2000 15:53:42 -0600
Approved: twftesla-at-uswest-dot-net
Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme
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.  Mathcad
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


Tesla List wrote:

> Original Poster: "Jim Lux" <jimlux-at-jpl.nasa.gov>
>
> Just a bit of algebra.. no need for MathCad..
>
> Given X and D2 to calculate D1
>
> square both sides
>
> 1.4^2 *(1.2781^2 - 2*1.2781*(d2/d1) + d2^2/d1^2) * pi  * d2 * (d1-d2) = x^2
>
> multiply through by d1^2
>
> (1.4^2* 1.2781^2 *d1^2 - 2*1.4*1.4*d2*d1 + d2*d2*1.4*1.4)*pi *(d2*d1 -
> d2*d2) = x*x*d1*d1
>
> collect terms
>
> aaa * d1*d1*d2*d1 - bbb * d2 * d1*d2*d1 + ccc*d2*d2*d2*d1 -aaa*d1*d1*d2*d2
> + bbb*d2*d1*d2*d2 - ccc * d2*d2*d2*d2 = x*x*d1*d1/pi
> aaa = 1.4*1.4 * 1.2781*1.2781
> bbb = 2 * 1.4 * 1.4
> ccc = 1.4 * 1.4
>
> rearrange
>
> (aaa * d2)  *d1*d1*d1
>  (- bbb * d2*d2   -aaa*d2*d2- x*x/pi )*d1*d1
>
> (+ ccc*d2*d2*d2 + bbb*d2*d2*d2) *d1
>  - ccc * d2*d2*d2*d2
>
> = 0
>
> now, all you gotta do (hah) is solve the cubic equation in D1..
>
> ----------
> > From: Tesla List <tesla-at-pupman-dot-com>
> > To: tesla-at-pupman-dot-com
> > Subject: Torroid Formula
> > Date: Tuesday, May 09, 2000 11:18 PM
> >
> > Original Poster: "MalikAT" <MalikAT-at-holycross.ac.uk>
> >
> > Hi its Tabraze,
> >       This is the formula i am using to calculate the capacitance of my
> torroid
> > 1.4(1.2781-(d2/d1))*SQRT(pi*d2(d1-d2)) = x. Given x and d2 can anyone
> with
> > MathCad or some other program please re-arange the above formula for me.
> It
> > would be of great help.
> >
> > Thanks in advance
> >
> > Tabraze
> >
> >
> >
> >
> >
> >
> >
> >
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