Frank,

Having used NEC4 to derive the input impedance of a single radial, it
is now in your hands to settle the discussion about attenuation along
radials and the distance at which a radial becomes ineffective. The
spectators are waiting!

We already have the input impedance of a single radial of length 10
metres at 7.0 MHz, with resistivity = 150 and permittivity = 16.

Using our standard set of data, I suggest you increase the SINGLE
radial length in increments of 3 metres until the input impedance Zin
stops changing and becomes relatively constant. That value of Zin
will be equal to Zo = Ro + jXo, the complex characteristic impedance
of the equivalent transmission line.

It might never become absolutely constant because NEC4 will take into
acount the effect of current flowing in the soil which, although it is
decreasing, eventually it will be substantially greater than that in a
long radial. ( My program does not do this.) But you should be able to
judge the distance at which radial attenuation is about 18 or 20dB,
ie., when Zin = Zo.

The question of efficiency is of less importance. It doesn't matter
what the efficiency is because you are using the antenna input
impedance plus radial input impedance only to deduce radial input
impedance in the same way as if you were measuring it. Be careful
with the signs of reactances. ;o)

At your leisure you may find a way how to do 36 and other numbers of
radials, at different frequencies. A 1/4-wave resonant antenna is
always best. The optimum length of a radial will decrease as
frequency increases. At 14 MHz the effect of permittivity kicks in
quite strongly. And with 120 or more radials you might be able to
demonstrate BL&E were quite correct when they concluded that a
virtually perfect ground. at MF, is independent of soil conditions.
----
Reg.