There is a table in ON4UN's book, table 9.1 which I
think addressed your interest. This is reproduuced
from that book.
9-1 Resistance of buried radial systems
radial # of radials
length(lambda)
2 15 30 60 120
.15 28.6 15.3 14.8 11.6 11.6
.2 28.4 15.3 13.4 9.1 9.1
.25 28.1 15.1 12.2 7.9 6.9
.3 27.7 14.5 10.7 6.2 5.2
.35 27.5 13.9 9.8 5.6 2.8
.4 27 13.1 7.2 5.2 0.1
If you study this table you will I think be able to
draw your own conclusion. My experience is that to
get the antenna effectively coupled to the "ground"
takes about 15 .2 wavelength radials regardless of the
radiator that I place above the "ground". I have
fooled around with short loaded radiators, full 1/4
wave and up to 5/8 wave antennas, and have found in
the case of short loaded radiators there is a point
where the inefficiency of the radiator overwhelms the
inefficiency of the ground. I have also found that it
takes about 15 radials for the coupling to the
"ground" to become predictable in terms of impedance
measurement.
I think in vertical parlance less than 15 radials is
basically like using a random wire. The antenna
becomes unpredictable in its performance. It may work
really well, it may not. You may have common mode on
the coax, you may not etc etc. It seems after around
15 radials you can start to see stability and
predictablilty in your measurements. My experience is
over Florida sand and Illinois clay using #14 solid
copper.
You will note the ratio of 2 .15 radials compared to
60 .25 radials is 4.69:1. The ratio of 2 .15 radials
to 120 .4 radials is 286:1 and the ratio of 60 .25
radials to 120 .4 is 79:1
This gives you a way to rapidly estimate the relative
"goodness" of a ground system vs the amount of work
your willing to put in. Its not much work to string
out 2 radials and the result is you don't get out much
signal, that is your system efficiency is low. At one
extreme if you go to all the trouble to put up an
efficient radiator you do yourself a diservice to put
in a lousey ground. Likewise if you put in 120 .4
lambda radials you do yourself a diservice putting up
a hamstick as your radiator. But in the end I think
you need at least 15 radials to even get to the point
where you can maesure what the heck is going on. Its
really not that much work to string out 15 radials for
a portable station (like a field day station).
Another interesting asect of this table is that you
can see the effectiveness of putting in radials v
going up and dowm in freq. 30 .2 wave radials on 80M
become 30 .4 radials on 40M for a nice increase in
efficiency, but 2 .2 radials on 80M are virtually
identical in performance on 40M. You also see why
putting in a bunch of short radials makes virtually no
difference in performance.
Another table worth taking a look at is table 9-3
which describes Optimum length v Number of radials.
73 W9OY
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