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I feel that the arrival angle predictions made by VOACAP are not so well founded empirically as, for example, the predictions of signal strength.
George Lane: You are absolutely correct about the takeoff and arrival angle calculations in VOACAP. They are fixed values for simple ray hops. Exotic modes such as N and M are ignored, too. The reason is that there was no measured data which would provide a statistical representation of the angle distribution.
Around 1990, Dr. Leo McNamara invited me to see a demonstration of the SkyLoc system which had been set up at the FCC HFDF site here in Columbia, MD. This system provided full angle of arrival data which was sampled at a very rapid rate. What amazed me was that the data collected over 5 minutes or so was showing strongest signals at arrival angles spanning 10 to 30 degrees and with a azimuthal spread of plus or minus about 2 to 3 degrees. We collected quite a few samples for different stations and then ran VOACAP. It was interesting that the model predicted the arrival angle within a few degrees for the actual angle observed with the highest number of occurrences. But it was very obvious that many angles were being used over a short period of time.
I was invited back to the FCC HFDF site in Columbia after I retired from VOA. It seems that they built a home-brew design for a phased array which obtains full angle of arrival data in real time for any signal you want to look at... not only from Columbia MD but all of the 13 other remote FCC DF sites.
Yes, takeoff and arrival angle predictions are WOEfully inadequate in VOACAP and all other models that I know of. I suspect that the minute-to-minute fading we observe in signal power is a direct result of ever changing angles. I think the effect is very large too... probably 8 to 16 dB. It was my suspicion that the great range in takeoff and arrival angles is why theory and measurement never agreed.
What I saw with the real-time SkyLoc HFDF system is that in a few minutes, an entire envelope of arrival angles were measured. These arrival angles may be clustered around a single median or about several medians for multiple ray hop modes. What would be nice is to have enough worldwide data to develop the statistical window for the takeoff/arrival angles. The current FCC HFDF network might provide that data for a person interested in exploring this issue.
When I was a Lt. in the Army, I was tutored in HF system design by Tim Shaw of the old Radio Propagation Agency. I was responsible for the design of the antennas being installed in SE Asia and Tim cautioned me not to use antennas whose beam widths were less than 10 degrees in either the vertical or horizontal plane. He cited cases where they had used antenna with beam widths as narrow as 5 degrees only to find that they experienced deep fading which he attributed to instantaneous variations in the arrival angle. Nearly 30 years later, I watched in real time as the SkyLoc system recorded the distribution of arrival angles. How I wished Tim was still alive to see that! Time after time we would see plus or minus 4 to 8 degrees around the central angle per mode.