smooth sphere vs unsmooth sphere

From:  Antonio C. M. de Queiroz [SMTP:acmq-at-compuland-dot-com.br]
Sent:  Monday, April 06, 1998 6:01 PM
To:  Tesla List
Subject:  Re: smooth sphere vs unsmooth sphere

Jim Lux wrote:

> > I was wondering if the charge density limit can be used
> > for de-rating a sphere with a broken surface, such as the
> > ones I am using, made out of concentric rings.
> > The 7ft sphere is made up of 1.5" dia pipe, spaced on 3.5"
> > centers, and appears to breakout around 1.5MV.
> > A smooth 7ft sphere would breakout at 1.06m x 3MV/m = 3.2MV.
> > -GL

> Off hand, I wouldn't think so, except by a fortuitous circumstance. What
> you really need to do is look at the field from a parallel set of
> cylinders. Perhaps you might find something in a heat transfer book (like
> in a boiler or condenser).

There is the complication caused by the other conductors of the sphere,
than cancel the field inside the sphere.
If this sphere has approximately the same capacitance of a closed sphere,
the breakout voltage is proportional to the ratio its effective surface
to the surface of a closed sphere. In this case, considering the outer
surfaces of the wires (180 degrees) uniformly charged (approximation), 
this results in:
Vbreak=3.2e6*(pi*wire diameter/2)/center spacing=2.1 MV.
Using 120 degrees of the wire instead of 180 degrees, Vbreak=1.4 MV.
Antonio Carlos M. de Queiroz