RE: breakout voltage

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

Original poster: "Luke" <Bluu-at-cox-dot-net> 

I have checked out the Inca program.  Not very intuitive at least for me
but once I got the hang of the part I was looking for I must say Very
Cool.


May I ask where I could find the math for the break out voltage of a
toroid? Preferably a version that is geared toward someone that is not a
rocket scientist.  Or maybe a version of the math that uses a few well
educated assumptions in it?

Even if it is the complicated version I would like to see it.

I am working on an idea and would like to see how the calculation for
breakdown voltage of a toroid is actually done

Thanx

Luke Galyan
Bluu-at-cox-dot-net

-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Friday, January 23, 2004 7:09 PM
To: tesla-at-pupman-dot-com
Subject: Re: breakout voltage

Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>

Tesla list wrote:

  > Original poster: "Luke" <Bluu-at-cox-dot-net>

  > Field strength = Voltage / Radius.
  > The break down voltage for air is approximately 76KV / inch.
  > This value varies with humidity, frequency, temperature, barometric
  > pressure etc.
  > So combining these gives:
  > Max Voltage (before air breakdown) = 76KV * Radius (in inches)
  > Is this correct for a close approximation?

This is exact for a sphere, far from other objects. Can be used
approximately also for rounded parts of other shapes.

  > When applying this to a toroid I was assuming the minor radius should
be
  > considered since it is the smallest curve on the toroid so the field
  > strength would be strongest there.
  > Am I correct in assuming this formula could be applied to the minor
radius
  > of a toroid to get it's approximate break out voltage?

This doesn't work for a toroid. The actual "effective radius of
curvature" is somewhere between the minimum and the maximum radii.
The exact expression is known, but is a complicated series.
Max. Voltage = 3000 x radius in meters kV:
Example: A 50x20 cm toroid should break down at a voltage between
3000*0.25 = 750 kV and 3000*0.1 = 300 kV.
An exact analysis results in 512.5 kV.
50x10 cm:
Maximum=750 kV, minimum=150 kV. Exact: 367.5 kV
50x5 cm:
Maximum=750 kV, minimum=75 kV. Exact: 249.6 kV

See the Inca program, that can calculate these things, at:
http://www.coe.ufrj.br/~acmq/programs

Antonio Carlos M. de Queiroz