smooth sphere vs unsmooth sphere

From:  Greg Leyh [SMTP:lod-at-pacbell-dot-net]
Sent:  Tuesday, April 07, 1998 5:24 AM
To:  Tesla List
Subject:  Re: smooth sphere vs unsmooth sphere

Antonio C. M. de Queiroz wrote:

> 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.

I believe that the broken sphere has the same effective
C as a smooth sphere, or very nearly so, since the gaps
in the surface are quite small compared to the distance
to ground, so the overall e-field should look similiar.

Your explanation of how to de-rate the voltage holdoff 
rating based on the pipe size and spacing seems quite 
reasonable to me, and if the sphere is breaking out at
1.5MV, the effective outer surface of the pipe elements
would be about 130 degrees, which also seems believable.