I've explained this to Reg many times before, but somehow it doesn't
seem to sink in. Here's the explanation again.

Reg Edwards wrote:
"Frank's" wrote
W7EL tells us that EZNEC doesn't display the surface
wave which obviously contains power. Would that affect
the efficiency using the integration technique?
======================================

The surface or ground wave is the most important fraction of total
radiated power.

It's important only to AM broadcasters and others communicating at low
frequencies, and to HF operators interested in working distances of only
a few miles. At HF, it decays to a negligibly low value within a few
miles, and so is no importance at all beyond that distance.

The correct radiation pattern of a vertical antenna
shows maximum radiation along the ground. Angle of maximum radiation =
0 degrees.

Let's consider that for a moment. The surface wave decays rapidly. So
the "correct" radiation pattern as described by Reg changes dramatically
with distance. At HF, the pattern at one mile will be strikingly
different from the pattern at 20 miles; the first will be maximum at
zero elevation angle, the latter won't. So if you want this kind of
"correct" pattern, you'll have to specify the distance from the antenna.
Once you're a few miles away, at HF, the pattern becomes constant with
distance, because the surface wave has decayed to essentially zero. Then
you have the pattern which is useful in determining communication beyond
a few miles. (This is the pattern reported by EZNEC and NEC as the "far
field" pattern.) Reg's "correct" pattern isn't useful for anything but
short distance communication, and isn't valid except at the distance
specified.

When deducing efficiency, to omit power radiated along the ground from
the hemispherical integration will result in serious error.

Well, it kind of depends what you lump in with losses when calculating
efficiency. The classical formula for antenna efficiency, Rrad/(Rrad +
Rloss), generally applies only to the antenna itself and near field
losses such as ground system losses. So power in the surface wave is
considered to be "radiation", and if you want to calculate this
efficiency by dividing the power in the radiated field by the power from
the sources, you would have to include the surface wave in the
calculation. However, for people communicating more than a few miles,
the surface wave power, which is dissipated in the ground within a few
miles of the antenna, is just as lost as power dissipated in the wires
or the ground system. So if you consider "radiated power" to be power
radiated beyond a few miles and "loss" to be the rest, then you can lump
the surface wave power into the "loss" portion. If you do that, the
efficiency is correctly reported by EZNEC or NEC's average gain function.

( Efficiency by NEC4 ) / ( Efficiency by formula ) = 0.38

I won't comment on that because I haven't a clue where it came from.

I can imagine other losses in addition to loss in the radials but to
have the other losses several times greater is a bit much. Where are
these large losses? Are they in the soil surface - the only other
candidate?

The surface wave power is indeed dissipated in the soil within a few
miles of the antenna.

Roy Lewallen, W7EL