Re: An enhanced toroid shape?

["Tesla list" <tesla-at-pupman-dot-com>]

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, 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

Cedge1 is not necessary (doesn't change much the result, however).

 > 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

There is really a degree of flattening that flattens the electric field
peak that happens at the major diameter of a regular toroid, changing
it to a double peak if you continue the flattening. In the program,
you can look at this happening if you list the fields (you can cut
the listing and plot it using another program to see the profile),
or zoom the area around the maximum diameter and click the mouse to
measure the field. There are also solutions that spread the maximum
to a wider area, but the curves would more complicated than
ellipses. There are some known optimal profiles for some cases. I
don't know if optimal profiles for a toroid are known.
Your discovery has practical uses, because it can save
some metal in corona rings for high-voltage equipment.
When making these simulations, always see what happens if you
increase the number of rings. If the fields don't change much,
the simulation is correct (yours is correct).

Antonio Carlos M. de Queiroz