[Amps] Arc distance - see for youself!

[Dr. David Kirkby]

Tom W8JI wrote:
> I wouldn't want people to walk away with the false idea that 
> spacing is the only major parameter that determines arc 
> distance in a given dielectric media. The shape is extremely 
> important, as are any small sharp edges.

Agreed.

Look at this coax

http://atlc.sourceforge.net/jpgs/coax2.jpg

Here is a picture of the electric field around coax cable.

http://atlc.sourceforge.net/jpgs/coax2.E.jpg

The gap between the two conductors is of course uniform all away around. 
But the center has a smaller radius of curvature, so the E-field is 
highest (shown brighter) around there.

White is maximum E-field, black is minimum E-field. The E-field is 
always zero inside a conductor.

> A blunt smooth surface for a given spacing can have several 
> times the voltage breakdown of a similar spacing with a 
> sharp edge or even a very small sharp protrusion.

Agreed.

> People who think they can look at a complex structure and 
> predict where it will break down based on spacing are 
> kidding themselves and fooling anyone else who believes 
> them.

Yes, you are right.

I thought I'd run and show some simulations with a computer program I 
wrote more than a decade ago called 'atlc'

http://atlc.sourceforge.net/

It allows you to see this sort of thing very clearly.

The very basic theory of 'atlc' was published in QEX in December 1996, 
but it is heavy going and not necessary to use the program. See the link 
below if interested.

http://atlc.sourceforge.net/qex-december-1996/atlc.pdf

If anyone wants to download and play with atlc, computing their favorite 
structure they can. You will need a UNIX or Linux computer.

EXAMPLES
-------

Consider this structure

http://www.g8wrb.org/useful-stuff/breakdown/points4.bmp

consisting of a green metal box, with a wall about in the center. (OK 
its a bit to the left, but it will now matter as it is far away from the 
other conductors)

Inside the box are two red conductors which have a high voltage on them. 
(Consider it 10 kV if you like, but it does not matter.)

Red = 10 kV, Green = 0 V, white is air.

Note the gaps between the closest points of the two conductors to their 
surrounding box is the same (it is 13 pixels at the top, 14 at the bottom).

After running 'atlc' on that structure, several results are computed. 
The most relevant to the discussion is this one, which shows the 
eclectic field.

http://www.g8wrb.org/useful-stuff/breakdown/points4.E.bmp

White is maximum E-field, black is minimum E-field.

Note the pixel values are *not* directly proportional to E-field. So 
don't assume one that has twice the brightness (as measured in your 
graphics package or by eye) is twice the E-field. Quantitative data is 
produced by atlc, but I've not bothered uploading that information.

It should be obvious that the areas around the small rectangle are 
larger than around the circle. Feel free to feed them into your favorite 
graphics package and check the pixel values.

Others that might be of interest are the voltage distribution:

http://www.g8wrb.org/useful-stuff/breakdown/points4.V.bmp

(Red is 10 kV, black = 0V and the other areas are somewhere between 0 
and 10 kV).

Looking at the energy distribution it is even more obvious the energy is 
highest around the corners:

http://www.g8wrb.org/useful-stuff/breakdown/points4.U.bmp

The reason this is more pronounced is that energy goes up with voltage 
squared (think of a capacitor - Energy is 0.5 * C * V^2)

Now it gets a bit more complex, so stop here if you want.

Here are the X and Y directions of electric field

http://www.g8wrb.org/useful-stuff/breakdown/points4.Ex.bmp
http://www.g8wrb.org/useful-stuff/breakdown/points4.Ey.bmp

Note this changes sign as you go past the inner conductors. Red and Blue 
indicate signs of electric field this time. (Red is positive, blue 
negative, where E is defined in the conventional way of E = -dV/dx)

Ex = - dV/dx
Ey = - dV/y
E = sqrt(Ex^2 + Ey^2)

There are more examples at

http://atlc.sourceforge.net/examples.html

There's an FAQ on 'atlc' at:

http://atlc.sourceforge.net/FAQ.html


-- 
Dr. David Kirkby