One of the standard stories that is given for this (and is mentioned in Aristotle) is that the hull of a ship disappears first as it sails towards the horizon on a calm sunny day. Is this a myth, or is it possible? After all, at the time no telescopes were available.
Scenario: Assume, for instance the hull of the ship rides 1 metre above the surface of the sea, with a sail whose height is 3 metres (I am going by 'Min of the Desert', a replica of a 3800 years old oceangoing Egyptian ship, so about the right time period.)
- How far must it travel before the curvature of the earth completely hides the hull?
- How far must it travel (assuming a flat earth) before visual acuity of a normal naked eye can no longer discern it?
I get an answer for question 1 of around 120km, this seems too distant (by my unaided intuition) for the naked eye to resolve. Also it seems wrong from general observation of the horizon from the coast, as one of the commenters has pointed out it looks like only a few kilometers. And surely at that kind of distance atmospheric efects begin to kick in, especially in the mediterrean where its generally warm.
Its been a very long time since I've done geometrical optics, so the answer to question 2 is beyond me. Can someone help. Also a verification of 1 would be nice (I've used a radius of the earth as 6000km).