Dale Parfitt wrote:
It includes ground gain. However if they want to play this game, an
isotropic antenna has a gain of 6dBi, which gets you back to 3.9dBi, but
even that is pushing it for a 1/2 over a 1/4 , unless you can get it up at
a few hundred feet. :-)

Brian GM4DIJ

How does a vertical benefit from ground gain?

Dale W4OP

An isotropic antenna always has a gain of 0 dBi, by definition. Also by
definition, it always radiates equally in all directions. So 0 dBi is
always a fixed field strength for a given power input and distance, and
this field strength doesn't depend on the presence or absence of a
ground or other environmental characteristics. This constancy is what
makes dBi such a useful reference. Any other antenna, such as a dipole,
used as a reference should be placed at exactly the same position and,
if over ground, at the same height as the antenna being analyzed.

Antenna field strength automatically increases 3 dB when you place it
over a perfect, infinite, flat ground plane(*) as opposed to being in
free space. That's because the radiated power is concentrated in one
hemisphere rather than being radiated in all directions. The isotropic
reference, 0 dBi, is always referenced to an isotropic antenna in free
space, that is, one which radiates equally in all directions. So gain
expressed in dBi increases 3 dB as a result. Ground reflection also
modifies the antenna pattern due to reflection, so the gain increase
from placing an antenna over ground is often greater than 3 dB,
typically around 4 - 5. A little experimentation with EZNEC or other
modeling program will illustrate this.

Which gives me an opening for one of my favorite soap box topics: dBd.
If you simply accept, as most amateurs do, that 0 dBd = 2.15 dBi, then
any old dipole over ground exhibits several dBd gain. The gain of a
dipole relative to a dipole at the same place over the same ground is of
course really zero dB. But the field strength of a dipole over ground is
considerably greater than a dipole in free space (~2.15 dBi) and
therefore its gain is greater than a free space dipole. This is the
danger of using dBd as a reference except in free space. At least one
major antenna manufacturer used this ambiguity to their advantage to
give their antennas several apparent dB gain over their competitors'.

(*)A dirt ground isn't much different from a perfect ground for low
angle radiation from horizontal antennas.

Roy Lewallen, W7EL