When you put power into an antenna, a current flows out of one conductor
of the feedline to supply that power. An equal and opposite current
flows into the other conductor. In the case of a grounded vertical, this
means that whatever current flows into the base of the antenna also
flows through the ground -- where the feedline shield is connected. Due
to the resistance of the ground, this results in I^2 * R power loss. If
the antenna's radiation resistance is comparable to or lower than the
ground resistance, the fraction of applied power that's lost is
significant, so it's common to lower the ground resistance by using
radials. Radials become increasingly important as the vertical gets
shorter, because a short vertical has a lower radiation resistance.
However, the feedpoint radiation resistance of a half wave vertical is
very high -- typically higher than the ground resistance. For a given
power input, a relatively small current flows into the base of the
antenna, so very little current flows in the ground. Consequently, the
ground loss is low, and there's no need to decrease its resistance with
radials.

Roy Lewallen, W7EL

Roy, I've always maintained that when I don't know that the ground
resistance is zero, I want as little current flowing in it as possible. My
inverted "L" is a voltage fed half wave on 160 meters, about 70 feet up and
170 feet out courtesy of a couple of strategically placed Oaks . I have
measured that feed impedance as being in excess of 2600 ohms and feed it
with a remotely tuned "L" network. I used it for several years just fed
against 60 feet of 6 inch well casing, and then, bowing to conventional
wisdom as advertised on 1850 KHz, added an elevated counterpoise beneath the
whole thing. (About 12 feet in the air) I didn't notice any change in signal
reports, but that impedance sure changed a lot. Did I change something
besides the ground resistance?

Regards

W4ZCB