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Re: Help with this equation!



Subject: Re: Help with this equation!
  Date: Fri, 30 May 1997 23:18:00 -0700
  From: "Norman F. Stanley" <nfs-at-midcoast-dot-com>
    To: Tesla List <tesla-at-pupman-dot-com>


At 12:41 AM 5/27/97 -0500, you wrote:
>Subject:      Help with this equation!
>       Date:  Mon, 26 May 1997 21:37:07 -0400
>       From:  Tom Heiber <theiber-at-lonet.ca>
>Organization: Power Surge
>         To:  tesla-at-pupman-dot-com
>
>
>This is an equation I got from Bert Pool's file.
>
>   
>=======================================================================
>    EQUATION 10: CAPACITANCE OF A TOROID
>                                                    ___________________
>                                                   /    2
>         C =(1+ (0.2781 - d2/d1)) x  2.8  x      /  2 pi  (d1-d2)(d2/2)
>                                               /   -------------------
>                                            \/      4 pi
>
>
>     C = capacitance in picofarads (+- 5% )
>    d1 = outside diameter of toroid in inches
>    d2 = diameter of cross section (cord) of toroid in inches
>
>    Equation courtesy of Bert Pool
>   
>=======================================================================
>
>
>CAN ANYONE help me solve for D1 as in D1=........
>I have been trying to do this without any results (I suck at math)
>
>Thank You
>
>Tom Heiber

Bert's equation could be written more compactly than as presented.  To
solve it algebraically, first square both sides to get rid of the
radical
term.  This gives you a cubic equation in d1 which can be solved
symbolically in terms of trigonometric functions.  However this explicit
solution is rather complicated and not very convenient for practical
computation. Furthermore, being a cubic it has three solutions, of which
only one is appropriate for the original radical equation.  It's best
handled by approximation methods.  Back in the BC (before computers) era
this would be done by, say, Horner's Method using pencil and paper or,
at
most, a mechanical calculator, but, as someone else just pointed out,
math
packages such as Derive do it painlessly.

Norm