For those interested in a more sophisticated approach, one starting
point is the 1994 paper by Breakall, et al.
J.K. Breakall, J.S. Young, G.H. Hagn, R.W. Adler, D.L. Faust, D.H.
Werner, "The Modeling and Measurement of HF Antenna Skywave Radiation
Patterns in Irregular Terrain", IEEE Trans. Ant. Prop. V42, #7, July
1994, pp936-945
Abstract is below..
Basically they used GTD with the current distribution in the antenna as
the source. They also (as expected) found that for horizontal
polarization, you can just assume that the terrain is perfectly
conducting (which I believe HFTA does), while for vertical pol, you need
to know what the dielectric properties are.
It's true that this work modeled the terrain in sort of a 2 1/2 D way..
that is, the terrain was a row of strips with the long axis of the strip
perpendicular to the direction of propagation.
Of course, computational horsepower available now is a LOT more than
they had in the early 90s, so some of the analysis they couldn't do for
compute time reasons might well be feasible and reasonable today.
Likewise, getting the terrain model is probably much easier today, what
with downloadable DEMs.
One of the authors (J.S. Young) was developing codes to do the combined
MoM and GTD, and maybe if someone can track him down, it might be
productive. Gerry Burke published a paper in the same year about using
Physical Optics for looking at HF propagation in irregular terrain. A
google for "Burke Physical Optics 1994" will probably find it.
All in all it's a pretty complex area, and one would have to ask whether
the work involved in doing the more sophisticated model (and it would be
a lot... I'd say multiple work years off hand, by the time you get it
working and validated) would be worth it.
Jim, W6RMK
-----------------
Here's the abstract for the Breakall paper.
"The Method of Moments (MOM) was used in conjunction with the Geometric
Theory of Diffraction (GTD) for predicting the elevation-plane radiation
patterns of simple high frequency (HF) vertical monopoles and horizontal
dipoles situated in irregular terrain. The three-dimensional terrain was
approximated by seven connected flat plates that were very wide relative
to the largest wavelength of interest. The plate length along the
terrain profile was the longest possible that still adequately followed
the shape of the path on the azimuth of the elevation pattern of
interest and no shorter than 1 wavelength at the lowest frequency of
interest. The MOM model was used to determine the antenna currents under
the assumption that the terrain was planar (i.e., locally flat) over the
distance pertinent to establishing the input impedance. The currents
thus derived were used as inputs to the GTD model to determine the gain
versus elevation angle of the antennas for HF skywave when situated in
the irregular terrain. The surface wave solution for groundwave was not
included since this does not appreciably contribute any effect to the
skywave far-field patterns at HF in this case. The model predictions
were made using perfect electric conducting (PEC) plates and using thin
plates made of lossy dielectric material with the same conductivity and
relative permittivity as measured for the soil. These computed results
were compared with experimental elevation-plane pattern data obtained
using a single-frequency helicopter-borne beacon transmitter towed on a
long dielectric rope in the far field on a linear path directly over the
antennas. The monopoles and dipoles were situated in front of, on top
of, and behind a hill whose elevation above the flat surrounding terrain
was about 45 m. The patterns of all of the antenna types and sitings
exhibited diffraction effects caused by the irregular terrain, with the
largest effects being observed at the highest measurement frequency (27
MHz). The results for the PEC plates and the lossy dielectric plates
were essentially identical for the horizontal dipoles, whereas the lossy
dielectric plates were required to properly match the measured results
for the vertical monopoles. The gain of the antennas in irregular
terrain and the gain of the same antennas situated in flat, open terrain
differed by up to 20 dB at the lower elevation angles (e.g., 3'4"). This
difference in gain is significant for most HF systems.
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