I just ran a few analyses which are relevant to this discussion. They
were done with EZNEC/4 using an NEC-4 calculating engine (although NEC-2
will give the same results), using MININEC-type ground to simulate a
lossless ground system, and with surface wave included. The antenna is a
0.25 wavelength high vertical. The intent was to look at the vertical
pattern characteristics at various distances.

Before discussing the results, let me point out that radiation very
close to a vertical antenna is maximum at the horizon, as Rich has said.
However, the field propagating in proximity with the ground (the surface
wave) gets attenuated with distance much more rapidly than the normal
attenuation of a wave in free space (or the sky wave, discussed
shortly), which is attenuated only because it expands to cover an
increasing area with increasing distance. At a distance beyond which the
surface wave has decayed to a negligible value, the remaining field is
known as the sky wave. This has the pattern characteristics you'll see
with EZNEC (unless using EZNEC pro with ground wave enabled) or NEC
without ground wave enabled. Because of ground reflection, the sky wave
has zero amplitude at an elevation angle of zero except for perfectly
conducting ground. For typical ground conditions and in the HF range,
the maximum field strength occurs at an elevation angle on the order of
20 degrees. Remember, this is the sky wave, which is what's left beyond
the distance at which the surface wave has been attenuated to
essentially zero.

The rate at which the surface wave is attenuated with distance is a
function of ground conductivity, and a very strong function of
frequency. That's why AM broadcasters successfully use surface wave
propagation, while it's of little use to amateurs operating at HF and
above. Rich's original posting showed how some of the surface wave from
a broadcast station can (presumably) even reach far enough for the
Earth's curvature to allow it to escape and reach the ionosphere for
longer distance communication. As the following results will show, this
doesn't happen at HF and above.

Here are results of the analyses.

The initial runs were at 1 MHz, which has been the focus of Rich's
comments on this thread. The reported field strength includes the entire
field, or in other words, the sum of the sky and surface waves.

At 1 km, with either average or very poor soil, the elevation pattern
shows a monotonic decrease as you go up in elevation, like in the plots
referenced in earlier postings and resembling the plot of the pattern
over perfect ground. Changing the ground type attenuates both the sky
and surface waves (although not necessarily by the same amount), which
tends to reduce the dependence of pattern shape on ground
characteristics. So the same general pattern shape occurs with a range
of soil types.

However, the pattern shape is profoundly affected by both distance and
frequency because both these determine the amount of surface wave
attenuation. For example, with average ground at 10 km (rather than 1
km) from the antenna and 1 MHz, the field strength is relatively high at
zero degrees elevation, and drops as the elevation angle increases, as
it does at 1 km. But at about 2 degrees it hits a minimum and begins
increasing again, reaching a maximum at about 20 degrees elevation,
which is the angle of maximum sky wave. At that point, the field
strength is about 1.24 times (about 1.9 dB greater than) the field
strength at zero degrees elevation. This is because the surface wave is
attenuated much more rapidly with distance than the sky wave, and at 10
km the surface wave has already decayed to less than the sky wave field
strength. At 100 km, the ratio of sky to surface wave (that is, field
strength at 20 degree elevation compared to zero degrees) is 13.6 dB,
because of course the surface wave has decayed a great deal more.

At 3 MHz, the attenuation of the surface wave is much more dramatic.
Just 1 km from the antenna over average ground, the field strength
*increases* monotonically (at least above 0.1 degree, which is the
lowest I checked) as the elevation angle increases, until it reaches the
sky wave peak at about 24 degrees. At that angle, the field strength is
more than 40 dB greater than the strength at the horizon (which is the
remaining surface wave). At 10 km, the field strength at 24 degrees is
more than 60 dB stronger than that at the horizon. And of course, this
effect becomes stronger with increasing frequency and distance.

So even at 10 km distance from the antenna at 3 MHz over average ground,
the sky wave is more than 60 dB stronger than the surface wave. The
difference becomes greater at higher frequencies and greater distances.
This is why the surface wave is of little practical interest to most
amateurs. And it's why you'll never see the wonderful low-angle
ionospheric propagation effects Rich predicted in his original posting
on this thread.

The EZNEC/4 results are just what we should expect, given a knowledge of
how the surface wave and sky wave are attenuated with distance.

I caution people to take care in extrapolating propagation or antenna
performance results at AM broadcast frequencies to the higher
frequencies more commonly used by amateurs. If done carelessly, it can
lead you to reach some pretty seriously wrong conclusions.

Roy Lewallen, W7EL