On Mon, 23 Jan 2006 15:55:52 +0000 (UTC), "Reg Edwards"
wrote:


"Owen Duffy" wrote
One good pickup was the functions for predicting the low frequency
resistance of shallow buried radials (which is relevant when radial
wires are required to provide a level of power / lightning
protection.
I created a graph to add to an existing web page from the functions
for 3mm (bare) wires buried 0.1m, the graph is at
http://www.vk1od.net/post/earth02a.gif . (For avoidance of doubt,
this
graph does not predict the RF characteristics of the radials.)
=========================================

Owen, I assume the curves in your graphs have been obtained by
treating the conductors as transmission lines. As far as I am aware
there's no other way of doing it. Except perhaps EZNEC
number-crunching mathematical modelling methods.

Let me quote again:
(For avoidance of doubt, this
graph does not predict the RF characteristics of the radials.)

The graph uses the functions in the paper identified by Richard (
http://www.usda.gov/rus/telecom/publ...s/1751f802.pdf
). Looking at the functions, I think they just calculates the DC /
low frequency resistance of the electrodes immersed in the soil which
is a high resistivity medium, by modelling the geometry of the
equipotential "layers" around the electrode as is done with a single
straight earth electrode. The functions for 6+ radials (or all of
them) may just be a fit to experimental data.


At VLF the inductance of the conductors and the capacitance due to
relatively high permittivity of the dielectic material (soil) can be
neglected.

I think these functions are for the resistance at power frequencies
(ELF?) and are not applicable to RF. Nevertheless, most lightning
protection texts seem to deal with the earth system as a DC resistance
with some lumped series inductance to model the above ground
connection, though clearly, lightning spikes are a double exponential
with components up to VHF depending on the way in which the network
modifies the waveshape.


This leaves only conductor resistance and conductance (or resistivity)
of the soil. It is then quite simple for single wires.

To predict performance at RF it is necessary to take inductance and
capacitance into account. What is unknown is the way in which soil
permittivity and resistivity change with frequency. But this hardly
matters as the uncertainty at 60 Hz is sufficient to swamp it.

I won't ask you what you did about calculating the effects of multiple
radial wires, and the interaction between individual wires, which
causes "The Law of Diminishing Returns" to be followed.

See above.


There is sufficient information in your graph to demonstrate that
Magician Marzipan's magic high number of 120 is never necessary for
amateur purposes.

I am guessing that the magic 120 was from BLE's paper, and it was
talking about performance at 1MHz or so, so it is RF performance that
is being considered.

The graphs I produced certainly suggest that at DC / 50Hz / 60Hz, that
there is insignificant benefit in installing more than 6 or 8 radial
wires. The reasons will be the same as why installing two vertical
electrodes close together achieves almost no improvement.

Owen
--