Thanks for your response and explanation. I understand what you are saying about wavelength and it's theoretical application in the disscusion of tracking devices. Although I disagree with your statement that take off angle only applies to horizontally polarized antennas.
http://www.dx-antennas.com/Height versus take off angle.htm
With a horizontally polarized antenna, the image antenna is 180 degrees out of phase with the real antenna so there is complete cancellation at 0 degrees elevation. At very low elevations above ground, it will have a single vertically oriented lobe. As the antenna is raised above ground, the lobe will split into multiple lobes.
With a vertically polarized antenna, the image signal is phased so there is constructive addition at 0 degrees elevation. A quarter wave vertical with its base at ground level will combine with its image to form a virtual half-wavelength long vertical dipole which will have a single broad single lobe with its peak at 0 deg elevation. (This is how a 1/4 wave whip with ground-plane antenna operates, except an it uses its own ground plane (3 or 4 radials) rather than an earth ground plane so it can be mounted well above the physical ground.)
As you raise a vertically polarized (actually any) antenna above ground, its vertical radiation pattern will break into multiple lobes because the antenna and its image will be separated by long distances (eg multiple wavelenths). For a real antenna, the 0 degree elevation lobe can be absorbed by a lossy ground leaving the next lobe (as seen at a distance) as the main lobe at a takeoff angle of >0 degrees.
The above radiation patterns assume a perfectly conducting infinite level ground. Real world antennas exist above imperfectly-conducting, uneven, and tilted grounds. This imperfect ground can alter the phase (and amplitude) of the signal "radiated" by the image antenna which can alter the takeoff angles of all of the lobes. Thus the phase shift can cause the take off angle of the main lobe of a vertical antenna to be greater than 0 deg, but to a first approximation, all vertical antennas will have a main lobe at 0 deg.
The radiation patterns of (non-active) antennas are the same for receive and transmit although they may be easier to understand in one or the other.
Bottom line: the radiation patterns of antennas can be altered in weird and wondrous ways by objects in their near-field.
When analyzing the vertical radiation pattern of any antenna, one must consider both the real antenna and its image. If they are close together, there will be only a few lobes and only one if very close together. If they are far apart, then there will be many lobes will nulls in between them and the directions of these lobes will depend on the antenna locations, signal phasing, and signal amplitudes. (This is related to a 2-slit interference pattern
https://en.wikipedia.org/wiki/Double-slit_experiment https://en.wikipedia.org/wiki/Young's_interference_experiment)
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This is quite a tangent--hope those who are not interested in this level of detail have had the good sense to skip it...
It is actually relevant for getting the best signals between a satellite and a portable device, but sticking to the rules-of-thumb with regard to antenna positioning and orientation is probably the best strategy in the field in most cases. However, the above can explain why a small change in the location of an antenna can sometimes make a significant change in the signal strength.
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Doug
