Needing a break from the exceedingly excruciating task of preparing income
taxes, I took a break to investigate what EZNEC/4 has to say.

To facilitate checking and to use an antenna with more vertical pattern than
that of a dipole, I used as an antenna the 14.2 MHz five-element Yagi
provided with EZNEC. I looked at the first and second peak and the first
null (above the horizon) for three types of ground. I also used three
heights.

---We all know the uncertainties with estimates of the characteristics of
ground, so let us not replay the issue.---

The conductivity in SI units and the relative dielectric constant
immediately follow the height in meters. Angles are in degrees above
horizon.

H = 22 meters
0.005 13
peak 12.5; null 28.3; second peak 41.6
0.01 14
peak 12.6; null 28.3; second peak 41.6
0.002 10
peak 12.5; null 28.4; second peak 41.6
Use of equation:
N = 1: 13.9; N = 2: 28.7; N= 3: 46.0

H = 33 meters
0.005 13
peak 8.7; null 18.5; second peak 27.8
0.01 14
peak 8.6; null 18.5; second peak 27.6
0.002 10
peak 8.6; null 18.6; second peak 27.7
Use of equation:
N=1: 9.2; N = 2: 18.7; N = 3: 28.7

H = 44 meters
0.005 13
peak 6.6; null 13.8; second peak 20.7
0.01 14
peak 6.7; null 13.8; second peak 20.7
0.002 10
peak 6.6; null 13.8; second peak 20.7
Use of equation:
N = 1: 6.9; N = 2: 13.9; N= 3: 21.1

-------
One could conclude that the farther above ground one is and the smaller the
relevant angles are, the better the fit with the equation. Think about why
the first peak above real ground occurs at a smaller angle than what would
be the case with a perfect ground.

As several have commented, what counts is to have gain at the angles to be
used for propagation. The equation provides some useful information but it
needs to be understood. No substitute exists for having a horizontally
polarized antenna at heights that are appropriate for the task.

One extensive project that I worked on involved distances less than one hop.
A significant issue was the desire to minimize gain at low angles where
interference resided. Among other things, it was important to suppress
vertical radiation as much as possible by choking the transmission lines and
by having the wires be close to horizontal.

A point in engineering is to know/learn what the desired end results are and
then to use tools that are to-hand to approximate the desired end results.
In the case of HF systems, as many have observed, a statistical knowledge of
propagation plays a large role.

Back to taxes. Any man-made system of such complexity is inherently
inequitable.

73 Mac N8TT

P.S. For receiving purposes, combining a high antenna with an identical
antenna about 0.5 WL lower can almost cancel the second lobe and thus
attenuate much of the first hop (strong) QRM. Such a scheme does little for
transmitting effectiveness. Compare the placement of the null using H= 33
with the second peak using H = 44.

--
J. Mc Laughlin; Michigan U.S.A.
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