Richard Fry wrote:
To determine efficiency you'd have to make some field strength measurements
(usually performed with a calibrated field strength meter) in order to determine
how much of the power going into the antenna terminals is being radiated
into free space.

The radiation resistance present at the base of an electrically short,
linear, monopole (whip) antenna of various ODs can be calculated
rather accurately using equations found in various antenna engineering
textbooks . . .

This is true only if you don't confuse the idealized textbook models
with real antennas. But most of us are unfortunately stuck with using
the latter. In general, the impedance you calculate with the idealized
models doesn't match that of real world antennas. It works pretty well
for AM broadcast installations, where the length and large number of
radials make the impedance relatively independent of ground
characteristics. But this doesn't describe the typical amateur monopole
antenna, either ground or mobile mounted.

An approximation to input resistance can be made by adjusting for an
abbreviated radial system, but this gets increasingly unreliable as the
number of radials decreases. The best readily available modeling program
allowing the inclusion of a buried ground system, which uses the same
well-established equations as textbooks, is NEC-4. It, however, suffers
from a serious shortcoming in doing this calculation -- it assumes that
the ground is homogeneous to an infinite depth. Real ground is typically
stratified, and skin depth at HF is as much as several tens of feet, so
the representation of real ground is very poor. There are many cases
where a single "equivalent" value of homogeneous ground doesn't exist
which gives the same results as actual measurement. I've made very
careful measurements of a simple vertical monopole with various numbers
of buried radials whose impedance couldn't be matched with NEC-4 using
any ground parameters, and I believe this to be a common occurrence. In
no case would I depend on a computer model, let alone an even more
simplified textbook model, to predict the resistance of a real monopole
having an abbreviated ground system with enough accuracy to reasonably
estimate the efficiency.

As a side note, Brown, Lewis, and Epstein's sparse radial results can be
matched reasonably well with NEC-4, but it does require a fair amount of
ground constant adjustment for various numbers and lengths of radials.

Mobile mounted whip antennas fare even worse relative to simple textbook
models. I don't have any experience with comparison of computer models
with actual measurement. Those results should depend on the care with
which the model is constructed and the amount of influence the ground
has on the impedance.

Roy Lewallen, W7EL