The model suggests that as the 3 radial system is lowered, efficiency
(meaning total power radiated in the hemisphere divided by power input)
changes little until the radials are 100mm above ground, and the
efficiency drops quickly, more quickly as the height approaches zero.

All monopoles need an electrical reference point to be "driven
against."

Using a symmetrical arrangement of two or more 1/4-lambda-resonant,
horizontal wires elevated sufficiently above the earth provides that
by acting at their junction under the base of the monopole as a point
with constant electrical characteristics with respect to the current
flowing in the antenna system.

NEC shows the peak free-space gain of such a system using a 1/4-wave
monopole to be the same as that of a 1/2-wave dipole in free space,
e.g., 2.15 dBi. When that system is operating within a few electrical
degrees above a perfect ground plane then the peak gain rises to 5.15
dBi, because all of the radiation is re-directed/confined to one
hemisphere.

Horizontal wires lying on, or buried several inches below the surface
of the earth do not have the same electrical characteristics or
function as when they are elevated. Instead, they serve to collect
the r-f currents generated by the displacement field radiation of the
monopole -- which currents flow in the earth out to about 1/2
wavelength from the base of the monopole.

If the earth was a perfect conductor then those currents could travel
through the earth without loss, and a single, short ground rod would
serve as an electrical reference point for the r-f current flowing in
the antenna system. The sum of those r-f currents flowing in the
earth around the monopole, and collected by that ground rod will be
equal to the base current in the 1/4-wave, series-fed monopole. The
gain of this configuration is 5.15 dBi, the same as when using a few
elevated, resonant wires as a counterpoise.

But the earth is not a perfect conductor. For that reason it is
necessary, when using buried radials, to install enough of them in the
surface area out to about 1/2 wavelength to collect those r-f currents
before they have traveled through much of the lossy earth to reach
those wires.

The benchmark 1937 I.R.E. paper of RCA's Brown, Lewis and Epstein
showed that 113 x 0.412-lambda buried radial wires used with monopoles
of about 45 to 90 degrees in height produced a radiated groundwave
field when measured at 3/10 of a mile that was within several percent
of the theoretical maximum for a perfect monopole radiator with a zero-
ohm connection to a perfect ground plane -- and this despite the fact
that earth conductivity at/near their test site was not better than 4
mS/m.

As an aside: NEC analyses for far-field conditions show an elevation
gain of zero in the horizontal plane for a monopole over real earth,
and peak relative field gain at some elevation angle above the
horizontal plane. However the radiated, relative fields that exist
at, and relatively close to the edge of the near-field boundary of the
radiation hemisphere of all monopoles of 5/8 wavelength and less are
very nearly equal to the cosine of the elevation angle -- which value
is 1.0 at zero degrees (the horizon), and zero at the zenith. If they
were not, then the fields measured by BL&E would be much different
than they recorded in their 1937 paper.

It is only after those fields propagate a significant distance over a
real earth path that they depart significantly, and progressively more
significantly with distance, from the relative fields described by the
cosine value of the elevation angle.

RF