I know that the drop is six feet at three miles but I dispute the .04° figure because a right triangle with one side being 72 inches and the long side opposite the hypotenuse being 15800 feet yields and angle opposite the 72 inch side of .0261° not .04°.
As for the bulge, it is only relevant past the horizon and only then if you are trying to calculate how much of the object is hidden below the horizon.
Yes, that sounds correct.
I agree.
Quite so. You can see ships disappear behind the horizon. Under normal conditions the ship (or land mass or whatever) is seen to drop behind the horizon in a manner that is completely consistent with what one would intuitively expect. The object is hidden from the bottom up just as if it were going over a hill and disappearing down the opposite side. The times when this perception is altered is when there is some atmospheric effect on the path of the light on it's way to your eyes, which we've already discussed at length.
The important point here is that, because the Earth is so large, the small section of it that we can see with our eyes (a circle with a three mile radius) is practically flat and the horizon drop is too small at that distance to detect by the normal person under normal circumstances.
Just to give you an idea of how small something is that has an angular size of .04° (again using the larger figure for argument's sake), a tennis ball at 298 feet, (99.3 yards) away would have an angular size of .04°. A 1/4 inch ball bearing held at arm's length (3 feet away) is just over ten times that angular size!
Incidentally, if we use the real number, which is .0261° the tennis ball would need to be 548 feet (182.6 yards) away and the 1/4 inch ball bearing at three feet away would have an angular size 15 times that of the horizon drop.
Clete
P.S. I wanted to mention that my last post could have actually added to the confusion because I stated that the website was flipping the triangle over, which is not the case. They have the triangle situated just fine, they just have the terms flipped. The hypotenuse, it seems to me, should not be the "distance" figure because the calculation to determine the drop is not based on the length of the hypotenuse but rather the side opposite the hypotenuse and thus it is that side that would rightly be referred to as the "distance". Again, it doesn't really matter so long as one keeps it straight in their head because the real pertinent figure for this particular discussion has to do with the angle the two line make, which is the same regardless of what you call them or which way the triangle is situated.
View attachment 26537
P.S.S. The angle calculation of .0261° is approximate. Before I was getting .0217° and now I'm getting .0261°. I'm sure I've changed the inputs somehow but the point is that it's really really tiny and about half of the .04° that the other site is reporting probably because they are failing to realize that the horizon drop would only be 1/2 of the angular size of an object at that distance. (see above image)