An enhanced toroid shape?

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Original poster: Finn Hammer <f-h-at-c.dk> 

Antonio, all

This wonderfull tool allows me to entertain a favourite pet therory of 
mine: that it might be beneficial to flatten the outside curve of a toroid 
slightly, and thus get a higher breakdown voltage than that offered by a 
stock round sectioned toroid. This flattening of the outside curve would 
inevitably lead to a sharper curve at the top and bottom of the shallow 
curve, where it curves back into the center of the toroid. If the outside 
is a total flat, this transition would be a shatp corner, and obviously, 
this wouldn`t be any good. But somewhere inbetween that, and the circular 
shape, I had a notion that the shielding effect of the major diametre might 
allow some flattening of the minor diametre to totally allow a slightly 
higher breakdowh voltage. And also deliver the shoulder to push the field a 
bit longer out, to deliver longer arcs.
Anyway, I drew up a toroid with these coordinates in the INCA program:,

* Fancy toroid

Lcenter terminal 15 0 1.5 0.14 1.5
Cedge1 terminal 25 0.22 1.50 0.08 90 180
Cedge2 terminal 25 0.22 1.50 0.08 90 270
Eedge terminal 50 0.22 1.5 0.068 0.08 -90 90

In the last line,"Eedge" it is the value 0.068 that determines the 
curvature of the outside face of the toroid.
0.08 is equal to a normal circular toroid, 0 would be a stright line, 
creating a cylinder.
I ran the simulator against a series of values, and got these results.
0.08    509kV
0.075   513kV
0.07    518kV
0.068   519kV
0.065   517kV
0.06    506kV

Not a dramatic difference, by any means, but at least an indication of a 
possible way to follow, and at least the borders of flattening of the 
outside curve has been established.

http://home5.inet.tele.dk/f-hammer/fancytoroid.jpeg

Cheers, Finn Hammer


Tesla list wrote:
>Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
>Tesla list wrote:
>  > Original poster: Finn Hammer <f-h-at-c.dk>
>  >
>  > Antonio,
>  >
>  > I have the tooling for a 160mm by 600mm toroid, and consider having made
>  > the accompanying half sphere, for a Van der Graff terminal.
>  > I now know that it will be able to supress breakdown at voltages below
>  > 31*8*2.19=543kV. That is pretty nice to know.
>For better precision, since the 7.5x2 toroid is missing in my table,
>it's possible to interpolate. Anyway, the exact number would be 509.1
>kV.
>I can simulate also a half-toroid covered by a half-sphere. The
>composition would hold 593 kV.
>If you want to see, the Inca program (I will change this name, since
>there are other programs with this name around) is at:
>http://www.coe.ufrj.br/~acmq/programs.
>In the "general case with axial symmetry" capacitance calculation,
>the description for the toroid with a round cap would be:
>C vdg 80 0.22 0 0.08 180 360
>C vdg 60 0 0 0.3 0 90
>  > You earned your laurels a long time ago, and you add guilding to them by
>  > your work. I feel honoured to be on this list with you.
>Thank you. This list is very stimulating.
>Antonio Carlos M. de Queiroz
>