Notes on Terrain Modeling, Reflection Point Distance,

and Reflection Point Migration


From August 1979 to December 1980, a wonderful series of articles authored by Jim Lawson, W2PV, appeared in Ham Radio magazine.  The articles discussed Yagi antenna design and pointed out how Yagis interact with the ground around them to produce various vertical radiation patterns.  Reference was made to the fact that irregular terrain might enhance or degrade performance depending on the specific conditions.

I became intrigued with learning more about this, since my QTH was anything but flat.  I wrote a FORTRAN computer program to calculate vertical radiation patterns of Yagis over not only flat, but uneven and irregular topography.  This program wasn't quite as slick as the current HFTA program, by N6BV, but produced essentially the same results.  Each run required delivering about 1000 IBM cards to the computer center, waiting for the center to run the program, and then picking up a ream of printed output.  My program produced no fancy graphs, only raw angle and gain data that I needed to then plot by hand if I wanted a graph!  HFTA is so much easier.

This work led to some interesting observations regarding the distance from the tower at which reflection occurs for typical signals, and helped answer the question of how much terrain really needs to be modeled when doing a terrain assessment.

On the right is a copy of my original hand-written notes from 1980 (no PC and word-processor for me in those days!) regarding my observation that reflection point for signals arriving (or being transmitted) at a given elevation angle will move significantly closer to the tower when the surrounding terrain is sloping downwards.  The notes show that for an antenna 128ft above the tower base, incoming signals at an elevation angle of 10 degrees will reflect at a point 737 feet from the base of the tower, if the ground is flat.  If the ground slopes downwards at 5 degrees, however, the reflection point occurs only 463 feet from the tower.  For a slope of 10 degrees the reflection point is only 319 feet from the tower, etc.  Similar calculations are shown for a signal elevation angle of 4 degrees.

The modern spreadsheet version of my hand-written notes is shown below.  This spreadsheet shows the reflection point distance as a function of antenna height and signal elevation angles over flat ground and provides the opportunity to calculate the reflection point distance for down sloping ground for comparison purposes.  

Regarding the question of how much terrain really needs to be modeled when doing a terrain assessment, this chart shows that if you have a 100 foot tower on flat terrain and are interested in elevation angles of 5 to 18 degrees, the reflection point will be with 1143 feet from the tower for the 5 degree signals and only 308 feet for the 18 degree signals.  The terrain a mile or more away from the antenna is not going to be a factor unless you are dealing with some rather unique topography.  In fact, you don't even need ground out there (see the Grand Canyon profile example).  Keep in mind, however, if you are working into an upslope, the opposite effect takes place and you will need to consider this when modeling your terrain. 

If you'd like to see the derivation of the underlying formulas, click on See the Math.  

The bottom line is that you can consider elevation data for land a mile or more away from your tower, but it probably will not play a factor in the results of the terrain assessment, unless you're in a valley.  You can check this by removing topography data for land more than 2000-3000 feet from your antenna and seeing if the results of the analysis change for the angles of interest.

Finally, I have two other personal observations that I offer for your consideration.  First, it seems logical that to be a good reflector of signals, the portion of land reflecting the signal must be at least one to several wavelengths in length.  If this is the case, it makes little sense to model the topography every 20ft from the tower.  Perhaps characterizing the topography as a series of planes each 100 feet or greater in length might be a better approach.  Secondly, I've found poor correlation between the topography data I obtain using MicroDEM and the topographic maps produced by my county.  I know others who have had the same experience in other parts of the country, so I'm afraid I don't really trust the MicroDEM data.  I use my county topographic maps to create topographic profiles for HFTA.  


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