# Re: Sphere/Toroid Comparison Chart

```Original poster: "Kurt Schraner by way of Terry Fritz <twftesla-at-uswest-dot-net>" <k.schraner-at-datacomm.ch>

John, Matt, Luc -

the equations, used to equate the respective capacitances of toroids vs.
spheres, must have been:

The well known Bert Pool's eqn. for toroids:
C = [1 + (0.2781-d2/d1)] x 2.8 x { pi x [(d1-d2) x (d2/2)] / 2 }

And for spheres:
C =  epsilon x 25.4 x d / 9

with relative dielectric constant epsilon for air set to 1.0 (instead of
1.0006).

d1  sphere diameter in [inch]
d2  sphere diameter in [inch]
d   sphere diameter in [inch]
C   capacitance in [pF]

This compares to about 3 decimal fractions in C.

Kurt Schraner

Tesla list wrote:
>
> Original poster: "John H. Couture by way of Terry Fritz
<twftesla-at-uswest-dot-net>" <couturejh-at-worldnet.att-dot-net>
>
> Matt -
>
> Your table agrees closely with a Sphere/Toroid Graph I show in one of my
> books. The graph covers spheres up to 60 inches diameter and toroids up to
> 80 inches large diameter. We must have used the same equations. The
> advantage of a graph is that if you only know the capacitance the graph will
> quickly show you several different size toroids that will have the
> capacitance you need and you do not have to do any calculations.
>
> John Couture
>
> -------------------------------
>
> -----Original Message-----
> From: Tesla list [mailto:tesla-at-pupman-dot-com]
> Sent: Thursday, May 03, 2001 7:50 PM
> To: tesla-at-pupman-dot-com
> Subject: Sphere/Toroid Comparison Chart
>
> Original poster: "by way of Terry Fritz <twftesla-at-uswest-dot-net>"
> <Mddeming-at-aol-dot-com>
>
> Hi All!
> I found this on an old paper spread sheet.
> No reference as to source. I think
> the relative sizes are right, but can't swear to it.
> C-C        Chord Nom.
> Toroid     Toroid     Cap       Equiv.Diam. Equiv.Diam.
> d1(inches) d2(inches) pf       sphere (in.)  sphere (m)
>
> 8              4.00 7.723          5.47  0.1390
> 8              6.00 4.540          3.22  0.0817
> 10             4.00 10.675         7.56  0.1921
> 10             6.00 8.243          5.84  0.1484
> 12             4.00 13.262         9.40  0.2387
> 12             6.00 11.585         8.21  0.2085
> 14             4.00 15.574         11.04 0.2803
> 14             6.00 14.605         10.35 0.2629
> 16             4.00 17.675         12.53 0.3181
> 16             6.00 17.359         12.30 0.3125
> 18             4.00 19.607         13.89 0.3529
> 18             6.00 19.893         14.10 0.3581
> 20             4.00 21.402         15.17 0.3852
> 20             6.00 22.245         15.76 0.4004
> 22             4.00 23.083         16.36 0.4155
> 22             6.00 24.444         17.32 0.4400
> 24             4.00 24.668         17.48 0.4440
> 24             6.00 26.512         18.79 0.4772
> 26             4.00 26.170         18.55 0.4711
> 26             6.00 28.469         20.18 0.5124
> 28             4.00 27.601         19.56 0.4968
> 28             6.00 30.329         21.49 0.5459
> 30             4.00 28.969         20.53 0.5214
> 30             6.00 32.103         22.75 0.5779