I recently sent this off as a letter to the editor of the National
Contest Journal. I thought it might be of interest here as well,
although [g] I'm afraid it has nothing to do with reflection
coefficients.

# # #

In recent issues of the National Contest Journal, Eric Scace K3NA
presents a unique way of showing the radiation pattern for an antenna.
He runs a model through NEC to generate far field data across a "sky
hemisphere" of directions (similar to a 3D pattern) and then uses some
post-processor tools to project the far field dBi values onto a flat
sheet for display and statistical analysis. Full details are included
in the article, which is available on the NCJ web site. (See
references below.)

One of the examples included in Part II of the article is a stack of
two 20m Yagis, mounted at heights of 50 and 100 feet and separately
rotatable. The initial configuration has both Yagis pointed towards
Europe, compass bearing 46° from the Washington DC area. Then the
upper Yagi is rotated counterclockwise and the sky hemisphere pattern
is captured at intervals along the way. The final position of the
upper Yagi is 90° counterclockwise from the lower, compass bearing
316° towards Japan.

I thought this example was very interesting and I exchanged several
emails with Eric concerning a follow-up. My idea was to twist the
stack as Eric had done and show the results in a variety of different
ways including 2D plots, 3D plots, and VOACAP area coverage maps.

The original example output is available for downloading but you must
have Microsoft PowerPoint to show it, so the first thing I did was to
extract a subset of the images and assemble them into an animated gif.
The animation shows reduced-size versions of Eric's "Eckert IV" flat
projections of the sky hemisphere, representing the top Yagi twisted
by amounts of 0°, 15°, 30°, 45°, 60°, 75°, and 90°. See
www.qsl.net/ac6la/adhoc/twist_scace.html
(You may wish to open this link and the following links in separate
browser windows so that you can easily switch from one to another.
Note that some browsers do not let you stop a gif animation and some
"ad blocker" software will prevent animations from being shown at
all.)

Then I imported Eric's NEC format antenna model into the MultiNEC
program. MultiNEC has a "Rotate Wire(s)" function and the amount of
rotation can be controlled by a variable. I created a series of test
cases with the rotation amount for the top Yagi set to the 0° through
90° steps mentioned above, and plotted a set of 2D elevation patterns
at the azimuth angle representing the initial bearing towards Europe.
This shows how the original main beam is degraded as the top Yagi is
twisted away. See
www.qsl.net/ac6la/adhoc/twist_2d.html

Next I used the MultiNEC interface to Arie Voor's very nice 4nec2
program. I requested a 3D plot at each twist interval and used the
4nec2 DirectX viewer to show the results, taking care to insure that
all the 3D plots used the same scale for color coding and had the same
XYZ orientation. In this series of plots the initial bearing of 46°
towards Europe is towards the lower left corner of the screen. See
www.qsl.net/ac6la/adhoc/twist_3d.html

Finally I used the MultiNEC interface to the VOACAP program to
automatically create a series of area coverage maps representing a
different twist amount. These maps, like Eric's originals, show
results that are projected onto a 2D surface. But in this case the
surface is the Earth and the parameter shown is not transmitted signal
strength but received signal strength. See
www.qsl.net/ac6la/adhoc/twist_voa.html

All of these animations are just different ways of looking at the same
scenario. Each offers different insights.

Dan Maguire, AC6LA


References:
1. Eric Scace K3NA, "Antenna Interactions, Parts I and II," National
Contest Journal, Jul/Aug and Sep/Oct 2003. Available in pdf format at
www.ncjweb.com/bonus.php. The example discussed above is available as
a PowerPoint slide show in file 'twisting_open_2_yagis.ppt' (5.92 MB).
2. 4nec2 program, see www.qsl.net/wb6tpu/swindex.html.
3. MultiNEC program, see www.qsl.net/ac6la/. File
www.qsl.net/ac6la/adhoc/2stack_Europe.zip contains the 'weq' format
(MultiNEC) model for the above scenario. This format preserves all
Excel formulas, variable definitions, and test case parameters as well
as the wire specifications and other details for a model.