Re: Torroid Formula (To Mark and Jim)


Although I haven't mathematically checked my work, I'm pretty confident
that what I
came up with is correct.  (I should check that, but I'm getting ready to go
back home
from school for the summer.)  I came up with a trinomial (y = a(a - b)(a - c)
basically).  I think there's a decent series expansion (not Taylor, though)
for it,
though I don't know what it is.  My advise, talk to a math prof, s/he ought
to be able
to help you some more.

Now you have me wondering what a graph of d1 vs cap looks like....  :-)


Tesla List wrote:

> 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
> 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.
> 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