Owen Duffy wrote:
. . .
One of the things that intrigues me is the common "expert" advice to
cut radials for 7MHz to 33' long and bury them. It seems to me that
when buried and considering the wire as a transmission line, the
velocity factor will be somewhere between 0.3 and 0.8 depending on the
soil type, so that 33' is likely to be closer to a half wave
electrically, and present a relatively high and reactive impedance at
the antenna base if it were not for the attenuation of the wave on the
radial. It would seem a length more like 17' to 20' would be a better
estimate by the SWAG method (Scientific Wild Arsed Guess), although if
ground attenuation is high enough, it could be cut shorter and the
extra wire used for another radial for a more effective solution.

Modeling clearly shows that using elevated radials which are too long
degrades the efficiency. A quarter wavelength can be determined by
constructing a dipole at the height of the proposed radial system and
adjusting it to resonance. The maximum length of the radials is half the
length of that dipole. If you make them longer, efficiency drops. Very
close to the ground, the length of a quarter wavelength decreases
substantially, so a free-space quarter wavelength can easily be too long.

Modeling presents a very idealized situation, overly so when dealing
with ground. But I believe the general trends and conclusions are
instructive. I modeled a 40 meter vertical over average ground. It had
four 34 foot radials, which were quarter wave resonant when elevated
very high. As I lowered the radials from one foot high to 0.1 inch high,
the gain dropped 4 dB. The main cause of the drop was that the radials
were becoming too long at the low height above ground. Shortening them
to 19.6 feet, the resonant length at that height, increased the field
strength by 2.45 dB. Burying them lowered the field strength to 1.7 dB
below the field strength when 0.1 inch above the ground and of proper
length. There wasn't any substantial change in field strength as the
length was increased beyond about 30 feet, or when the depth was varied
from 0.1 to 6 inches. These changes in field strength are solely due to
changes in efficiency; the pattern shape stays the same.

When modeled at 0.1 inch above the ground, the radial current
distribution is approximately sinusoidal, as in elevated radials. When
buried, even an inch, the current decays in an approximately exponential
fashion away from the center. In the case of the modeled antenna system,
the current was substantially zero beyond about 40 feet.

Conclusions a

1. A small number of radials just above the ground are theoretically a
bit more efficient than the same number of buried radials, providing
that they're not longer than a resonant quarter wavelength at that
height. I say theoretically, though, because I believe it would be
impossible to maintain current balance in the radials at a low height.
So one or two radials would likely hog all the current, resulting in a
less efficient system.

2. Making elevated radials too long, even if the elevation consists of
being just above the ground, can seriously reduce the antenna
efficiency. Buried radials, on the other hand, are insensitive to length
provided they're sufficiently long. This latter fact is well known. I've
found in other modeling I've done that making elevated radials shorter
than a resonant quarter wavelength doesn't negatively impact the
efficiency. So if you have to guess, guess on the short side.

The amount of differences you'll see in real antenna systems will vary
quite a bit depending on ground characteristics, frequency, and number
of radials. And it would be impossible to suspend radials precisely over
a perfectly flat and homogeneous ground as I've done with the models.
But I believe the conclusions are valid.

Roy Lewallen, W7EL