Jim Brown wrote:
> On Tue, 07 Oct 2008 04:53:25 -0700, jimlux wrote:
>
>> Why not put them hundreds of feet apart then?
>> In lightning protection, though, you also want to minimize the length of
>> the wires to the rods (because of the R and L of the wire). And, wire is
>> expensive.
>
> I haven't read the Polyphaser language. BUT: the fundamental reason for
> wide spacing between earth electrodes is that the mutual inductive coupling
> between them reduces their effectiveness. I've seen math developing the
> recommendations for spacing, but don't recall what those guidelnes are.
> Jim's logic is correct -- it's a compromise between inductance in the wire
> connecting the electrodes and the mutual inductance of the rods themselves.
> That's where the Polyphaser recommendations come from, and I'd bet they're
> pretty good.
>
A lot of the analysis has to do with looking at current distributions in
the soil surrounding the rods. Think of a rod as being a connector to a
hemispherical or hemi-elliptical equivalent electrode (at some
equipotential contour in the soil). If the two hemispheres overlap, the
current density is higher, so the voltage drop is more.
The mutual L between two buried rods some meters apart is pretty small,
and unlike in the above ground case, the resistive effects are probably
much larger in magnitude.
For those interested in the details IEEE Std 144 has all stuff you'd
want to know. Probably the most useful thing is a table that shows a
couple dozen multiple rod configurations and tells what the equivalent
impedances are.
However, for all practical purposes, it's easier just to remember,
separate by twice the rod length. If you've got a special deal on low
inductance superconducting wire or exotic foamed silver electrodes, then
you've got an opportunity to reoptimize the situation for what you have.
FWIW, from a lightning dissipation standpoint, I suspect a set of fairly
small buried radial wires would do a better job than almost any
combination of driven rods. Since lightning's dominant components are in
the hundreds of kHz, low MHz area, that famous impedance data from Brown
Lewis and Epstein for AM broadcast stations is actually applicable.
BTW, the antenna and tower system itself acts as a filter (mostly series
L) to change the current pulse shape from a lightning strike, so the
current recorded at the bottom of a tower might be somewhat different in
pulse shape from that recorded by a lightning researcher. There has been
some research in accurately modeling this sort of thing using NEC and FFTs
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