I think you're right on paper except that the height of the antenna was such that maximum detection range and the horizon matched up.
So while it's possible to detect SJ-1's beams out to 50 miles or so on paper, it can only actually start picking up the top of a BB at 12 miles and vice versa due to line of sight through the surface of the ocean..
Then again, depending on how the beams bounce... I don't actually know the answer to that at all.
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