A search turns up to previous threads on this subject but neither seemed to offer a definitive conclusion either way and both were more general than my case. I have a long running debate with my father-in-law regarding the curvature of the horizon. Please note that I am not referring to the curvature in the medial plane (as one is facing the ocean), but rather in the frontal plane.
The debate is as follows.
At his Miami Beach apartment building on the 8th floor, one can see the ocean. The view is partially obscured by the building itself, as well as the adjacent building, so it is not possible to see all the way down the beach. You can see the building here. The apartment is located in the section of the building directly to the left of the larger of the two pools, across the large patio section. He argues that he can see curvature at the horizon while I maintain that while he may think he does, it is impossible for the human eye to actually perceive the minimal curvature.
Based on my rough calculations, the horizon is approximately 12.4 miles away at that height (~100ft). Estimating the amount of visible horizon (due to the blocking buildings) at that distance as a generous 20 mi, I believe that the difference in “height” between the midpoint of the visible arc and the side points is ~16 ft. I do not believe that it is possible to detect a difference in height of 16 ft at a distance of 12.4 miles. To put it another way, if we were to approximate the horizon as a short, wide triangle, the “slope” of horizon would be 1.6 ft rise for every mile of horizontal distance. Is it really possible for a human to perceive such a minimal slope at a distance of 12.4 miles? I contend that it is not.
I’m afraid I don’t understand your comment about “the midpoint of the visible arc and the side points”. Every point on the horizon is equidistant from an observer.
Giving him the benefit of the doubt regarding the curvature and the various ways that he might perceive it, I’m estimating the curvature for the given arc where the horizon is the chord between the “side points”. I realize that this isn’t really what is seen, but I’m just trying to give a rough approximation of what he is seeing if it were visible at all.
I think I understand what your asking . . . but what your father-in-law is perceiving is curvature in the medial plane, and would look exactly the same on a flat Earth.
As I write this I’m looking out the window of the office behind my cube, about fifty feet away. The office window has a divider in the middle. The horizon “bulges” in the middle in the sense that it clips the divider at a higher point then it clips the sides of the window.
But that has squat-all to due with the curvature of the Earth. It’s a consequence of the foreground: I’m superimposing a flat, vertical, two-dimensional window in front of a three-dimensional background. If my office building were round, I wouldn’t see that effect.
I agree, I think that whatever curvature he thinks he’s seeing is due to that. To make matters worse, my ex-Navy uncle also insists that you can see the curvature when at sea. He also says that the horizon is 11 miles distant for a 6 ft observer, which is clearly false. So much for Navy training.
The problem is, people confuse the curvature of the horizon with the curvature of the earth. The horizon is a circle, because (without obstructions) you see an equal distance in all directions, and the locus of points equally distant from an observer is a circle. It would be a circle even if the earth were flat.
The difference between the flat-earth circular horizon, and our round-earth circular horizon–the only difference–is that the flat-earth horizon encloses exactly 180 degrees of your field of vision, whereas the round-earth horizon encloses a tiny bit less than that, with the “tiny bit” slowly growing as you gain height.
Can you perceive this from the deck of a ship? Sure, if you happen to be watching another ship disappear hull-first over the horizon–which is why the ancient Greeks recognized this as evidence for the sphericity of the earth. Otherwise, no chance.
But people see what they want to see. You get out on a ship and see that big circle of a horizon all around you, and you’re an educated Twenty-First Century Citizen of the World who knows that the world is round, and you blurt out, “Wow, I’m seeing the curvature of the earth!” But you’re not.
Exactly, you can see the the curvature of the earth from a ship if you see things disappearing over the horizon (medial plane), but you certainly cannot see curvature in the frontal plane. I’ve spent a good deal of time on ships myself and I cannot for the life of me figure out what my uncle is talking about. Anyway, I believe that what my father-in-law see as curvature in the frontal plane is, just as you describe, actually curvature in the horizontal plane since the limits of vision in that plane are, logically, a circle, assuming no obstructions.
