Didn't get a chance to go through all the talking in this thread. But here is my tale:
1- most of what I read can be explained by any 3D object(Cylinder or part of a cone for instance). They only answer the question whether the earth was flat or not.
2- The closest thing I can think of to an answer is sailing with the "complete idiot.":
We will see the home land sinking down and disappearing. Well, that could happen if the ocean was a cyclinder, or a section of a sphere.
Once the land disappears, we see the sea surrounding us in a circule. That scene remains until we reach our distination. Seeing the sea as a disk eliminates the possiblity of a cylinder (sea would look rectangular). However, if earth was flat, we would still see the ocean as disk, but we would keep visual of both home land and distination throughout our trip.
If it was part of a cone, we would have to see an abrupt edge when sailing from home to distination.
A convex palin would still give the same results. But the final way to do it is to ask our "complete idiot" to take an 81-day trip around the world (W-E) and repeat it in the orthogonal direction(N-S). If he doesn't dropp off from the other side of the world, or hit an edge, that would prove that earth is a sphere. If it doesn't, it wouldn't bother with such an idiot any more
By the way, the earth is not really spherical, it has more of an eliptic cross section at the plane of sclipse.