Richard Fry wrote:
. . .
A typical r-f ground loss even in a set of 120 each, 1/4-wave-long
buried radials is on the order of two ohms. So referencing the
example in the link to Kraus that I posted earlier, the radiation
efficiency of that helically-loaded monopole system with a two ohm r-f
ground would be about 0.6/2.6 = 23%, approximately.

The loss of a radial system using 0.1-0.2 lambda conductors would be
significantly higher, so the antenna system radiation efficiency then
would be significantly less than 23%.

A naturally-resonant, unloaded monopole about 1/4-wave high has a
radiation resistance of around 34 ohms. When it is used with a two
ohm r-f ground, the radiation efficiency of the antenna system is
about 34/36 = 94%.

RF

Although 2 ohms is a reasonable approximation for 120 radial ground
system resistance, it varies not only with ground quality and frequency,
but also antenna height. For example, an NEC-4 simulation for vertical
radiators at 3.7 MHz with 120 radials, each a free space half wavelength
long buried 0.1 meter in average soil, shows 3.25 ohms ground system
resistance when the radiator is 0.24 wavelength high (nearly resonant).
When the radiator is shortened to 0.12 wavelength, the ground system
resistance increases to 4.30 ohms. And with a 0.06 high radiator, the
ground system resistance nearly doubles to 8.06 ohms. This decreases the
efficiency of the very short radiator by about an additional 3 dB beyond
what it would be if the ground system resistance were fixed at 3.25 ohms.

I believe the ground system resistance increase with short radiators is
due to concentration of the field very close to the antenna, resulting
in much higher ground currents in that region. It would probably be
useful to use a larger number of radials, which could be shorter, when
the radiator is very short.

Roy Lewallen, W7EL