by , Software Developer
Well, you might start by checking your math. You are calculating the drop as 8 inches per mile squared, which is wrong. It’s wrong for a lot of reasons, but the biggest is that the 59 miles is measured along the curved surface of the Earth, not along the straight base of a Pythagorean triangle set on a plane, which only gives you a very approximate number. And it’s the wrong number anyway.
What you really need to know is how high the curvature causes water to protrude upwards between you and the far shore when you look across the lake. The answer depends very much on your viewing height, which your method also has not accounted for.
You would also need to account for parallax, and the fact the objects on the far shore appear smaller than the water at the half way point, but that’s small enough to ignore here.
When you do the math correctly, depending on the exact distance of your line of sight across the lake, it works out to a bulge of 530–540 feet, so you would expect to see only those parts of the distant skyline that protrude above that height (or a little more if we aren’t looking out right at water level):
Of course, what we actually see is…oh yeah, exactly what the math predicts.