Maximum message count rate?

At the extreme distances, the angle that you “see” the plane above horizon is very small. Objects in the path, even if smaller than your antenna height, will block that direct line of sight (or at least partially, some diffraction might pass around).

I’m in the same situation - I can “see” planes past Washington Dulles airport (less than 150 miles), if they are at 28-40,000 ft. I see nothing of the actual IAD traffic, it’s too low.

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