I decided to bite the bullet and purchase AutoEZ, which is a front end
to EZNEC which automates building models using formulas, generating
test cases, optimizing designs, etc.

http://www.ac6la.com

One of my first models was a common ground plane antenna with the
variables being the radiator length, radial length, radial droop
angle, and the height of the bottom of the radials over ground.

The first run was to optimize a ground plane for 10M built of 5/8"
aluminum tubing with a droop angle of zero degrees, i.e. horizontal
radials, in free space.

The next run was to optimize the same ground plane with a radial droop
angle of 45 degees, as is more common for elevated ground planes.

The results are shown below with the lengths being in wavelengths.


0 degree radials 45 degree radials

SWR gain radiator radial SWR gain radiator radial
1.01 1.7 0.322 0.086 1.00 2.2 0.231 0.244

Note that the antenna has slightly better gain with a 45 degree
radial droop.


The next step was to run test cases for the two antennas at various
heights above real, average ground, which yielded the following.

Height is in wavelengths above ground for the bottom of the radials
and @ elev is the elevation angle of the main lobe.

0 degrees 45 degrees

Height gain @ elev gain @ elev

0.01 -0.76 24 0.78 21
0.10 0.27 21 1.32 18
0.15 0.61 19 1.50 17
0.20 0.85 17 1.59 15
0.25 1.01 16 1.63 15
0.30 1.09 15 1.63 14
0.35 1.11 14 1.62 13
0.40 1.11 13 1.63 13
0.45 1.12 13 2.02 43
0.50 1.18 44 2.37 40
0.55 1.59 41 2.64 38
0.60 1.91 39 2.86 36
0.65 2.16 36 3.03 34
0.70 2.37 35 3.15 32
0.75 2.52 33 3.21 30
0.80 2.61 31 3.22 29
0.85 2.65 29 3.18 27
0.90 2.65 28 3.16 9
0.95 2.62 27 3.29 9
1.00 2.70 9 3.42 9
1.05 2.83 9 3.54 9
1.10 2.95 9 3.67 9
1.15 3.08 9 3.81 8
1.20 3.20 8 3.95 8
1.25 3.35 8 4.07 8

The very surprising result, at least to me, was that 1/2 wavelengths is
the worst height to mount a ground plane as the elevation angle of the
main lobe is at the maximum elevation of about 45 degrees around that
height for both versions of the antenna.



Special note:

Most people understand that the results of an antenna analysis program
reflect the material used to construct the antenna and the type of
ground, if any, used for the analysis, are an approximation, and are
not accurate to 27 decimal places.

Further, most people also understand that absent them being a part of
the model used for the analysis, objects in the near field of the antenna,
such as, but not limited to, 20 foot prision walls, blimp hangers,
skyscrapers, a deluge of biblical proportions, giant sequoia trees,
hovering 2 mile wide alien spacecraft, hords of locusts, large gold
deposits under the antenna, battles between Autobots and Decepticons,
beached aircraft carriers, and stadium domes may well effect the
actual antenna perfomance.

Your mileage may vary, void where prohibited.

Any spelling mistakes in this article are all entirly my fault. Any grammer
errors spotted in this article were put there because I could.

--
Jim Pennino