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Re: Re: [TCML] Re: Spark models, revisited



On 19/10/2012 22:27, Jim Lux wrote:
On 10/19/12 6:11 PM, Antonio Queiroz wrote:
Em 18/10/2012, às 11:43, "Udo Lenz" <udo_lenz@xxxxxxxxxxxxxx> escreveu:


That poses another question. A thin conductor does not have much
capacitance. The model calculations for a real arc indicate about
10 to 20 pF/m.
That is much more than a 0.2mm wire would have. Possibly a thin
conductor like that would be a perfect breakout point for sideways
arcs or create corona around the main arc, adding capacitance.

Thin conductors have really this range of capacitance. The inductance of a thin wire is approximately 1 uH/m. Adding distributed capacitance, a transmission line is formed. With L being the inductance per meter and C the capacitance per meter, the speed of a signal travelling through the line is 1/sqrt(LC). As this speed must be smaller than the speed of
light c, c^2<1/(LC), C<1/(Lc^2) =/(1e-6 x 9e16) .1 pF/m.

This is very elegant..

I've tried other schemes to approximate it (e.g. capacitance of a wire above a infinite plane, and let the distance go to infinity), but it breaks down.

As a practical matter, too, the inductance does not vary much from that 1 uH/meter, almost independent of shape and size of the conductor. Maybe a 2:1 variation for a 10:1 or 100:1 variation in physical size.

So the 11 pF/m is probably a good working number to use in general, when the "wire" is "thin" When the wire (or spark channel) gets big enough to have significant surface area, then other techniques might give you decent answers.


But I made an error. Replace "<" by ">". The 11.1 pV/m is the lower limit, not the upper limit. Using a better formula for the inductance per meter gives a better formula for the capacitance too.

Antonio Carlos M. de Queiroz

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