Re: Torroid Formula

To: tesla-at-pupman-dot-com
Subject: Re: Torroid Formula
From: "Jim Lux" <jimlux-at-jpl.nasa.gov> (by way of Terry Fritz <twftesla-at-uswest-dot-net>)
Date: Wed, 10 May 2000 05:26:51 -0600
Approved: twftesla-at-uswest-dot-net
Delivered-To: fixup-tesla-at-pupman-dot-com-at-fixme

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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