[LoveScience]

One of the points of evidence that has been put forward for a 'flat Earth' is the flatness of the horizon.  The clearest view of the horizon you can get I would suggest is when you are at sea. Lets say that a human being standing on a ship is typically a few tens of metres above the sea surface. That means that the horizon as the observer sees lies a few km away. Such a small distance means that any true curvature of the surface of the Earth would not be visible to the observer. This will be true in all directions so the visible flat horizon at sea appears flat in all directions. If the Earth is spherical then this observation will remain true regardless of where we are standing on its surface.

Increasing your height above the surface of the Earth to about the cruising altitude of commerical airliners will make no difference. Your distance above the surface is still very small compared to the actual size of the Earth. Scaling things down observing the surface of the Earth from the height of an airliner is like looking at a beach ball from just a couple of millimetres, if that above its surface. You simply can't see enough of the surface area  to have any direct perception of the surface curvature. So it appears to you that the surface is flat. It is only when your height above the surface is sufficient to make the distance to the horizon comparable to the diameter of the sphere that any direct impression of curvature becomes apparent. This is why the crew of the ISS, orbiting at an average height of 250km see a curved horizon because the horizon distance has increased to just over 1,800km compared to only about 11km for our observer standing on the ship at a height of about 10m. This is not an opinion or a belief of mine, it is simply a fact and I tend to work with facts rather then opinions.

Another point that is often quoted is the apparent flat base of clouds, particularly cumulus clouds. In terms of size the base dimension of an average cumulus has an equivalent surface distance of a few miles at most. In maths there is something called the small angle approximation. A very small angle will produce a very short arc as a proportion of a complete circle. The curvature of the arc is so small that the arc can be considered to be a straight line without any significant loss in accuracy. So if you have two radii (OA) and (OB) where O is the centre of a circle then the length of the arc AB will be very small. OAB can therefore be taken to be a right angled or isosceles triangle.

If the circumference of the Earth is around 38,000km (12,200km x pi) it doesn't take a huge stretch of common sense to figure out that the base of an average cumulus cloud covering just a few km represents an extremely small part of that circumference as a whole. Much less in fact than 1% of 1% of 1% etc.  That means I would suggest that the small angle approximation applies. That would most certainly account for the flat looking cloud bases.

So neither of these above points of 'evidence' prove a flat Earth but neither do they necessarily prove a spherical Earth either. Of the two though I know which one I would put my money on!

[RonJ]

It is very difficult for the tiny human (relative to the size of the earth) to tell by the simple measurement you suggested whether the earth is flat or round.  The needed accuracy is well buried in the noise.  Cumulus clouds sometimes gave me a subtle indication of something during my 20 years working on cargo ships.  From time to time you could see large clouds well ahead of the ship.  They appeared to go all the way down to the visible horizon.  After a while, as the ship approached the clouds doing about 25 knots, the clouds would slowly appear to lift and we always passed under the clouds. This phenomenon has happened to me plenty of times.  The realization was similar to the time when I actually realized that Santa Clause wasn't real. 

[Curiosity File]

It's absolutely impossible to get a sense of whether the earth is flat or round from any viewpoint standing on the surface.
From some view points you can, however, see the things drop out of sight passed the horizon and no matter how powerful binoculars you use you still cant see over the horizon. That's not an optical illusion or mirage. THat's absolute proof that at a given distance in that spot the earth drops below eye sight. But still is not proof the earth is round.
Where the proof comes in is, for example, when you continue to travel forward and the earth continues to drop off from the horizon and you go all the way around the earth and end back where you started with out ever finding an ice wall or edge of the earth or any spot in which you can see from on end to the other of the earth with a telescope like hundreds of thousands if not millions of people been doing for millennia.
That's what's know as solid physical proof.
With the technology and sea worthy vessels and aircraft we have in today's age somebody would have found that elusive edge of the earth if it were flat.           

[RonJ]

You are correct in that it is very difficult to see any kind of evidence of a global earth just by observation of the horizon with your own eyes.  Unfortunately,  circumnavigation of the globe doesn't really work very well either.  I know, firsthand, because I've done it myself a couple of times, in each direction.  If you look on a flat earth map you can clearly see that it would be possible to just get on a ship and sail in a circle and you would come back to the same place you started, but coming from the opposite direction.  That's difficult to do in the Northern latitudes (on a ship) because of the landmasses in the way, but by making detours, you can get completely around the world.  Round earth, or flat earth, the results would be the same.  Without some other evidence the task is difficult to decide which is the correct theory, round earth or flat earth. 

[Curiosity File]

You are correct in that it is very difficult to see any kind of evidence of a global earth just by observation of the horizon with your own eyes.  Unfortunately,  circumnavigation of the globe doesn't really work very well either.  I know, firsthand, because I've done it myself a couple of times, in each direction.  If you look on a flat earth map you can clearly see that it would be possible to just get on a ship and sail in a circle and you would come back to the same place you started, but coming from the opposite direction.  That's difficult to do in the Northern latitudes (on a ship) because of the landmasses in the way, but by making detours, you can get completely around the world.  Round earth, or flat earth, the results would be the same.  Without some other evidence the task is difficult to decide which is the correct theory, round earth or flat earth.

It's in the Knowledge of navigation.
On a flat earth you can spin circles and end up back where you started
But with proper navigation you find your destination.
Spinning circles you will never reach your destination.

But we now have the ability to fly all the way around the world.
This leaves absolutely no questions.

I think we need to give the human race more credit than to be so stupid as to not know they've been spinning circles for centuries