A fact of basic perspective is that the line of the horizon is always at eye level with the observer. This will help us understand how viewing distance works, in addition to the sinking ship effect.
Have you ever noticed that as you climb a mountain the line of the horizon seems to rise with you? This is because the vanishing point is always at eye level with the observer. This is a very basic property of perspective. From a plane or a mountain, however high you ascend - the horizon will rise to your eye level. The next time you climb in altitude study the horizon closely and observe as it rises with your eye level. The horizon will continue to rise with altitude, at eye level with the observer, until there is no more land to see.
Here's a text about horizon line and eye level, from Chapter 5 from the Perspective Drawing Handbook:
Anyone who has ever been to the seaside will have seen a horizon (as long as it wasn't foggy). This is the line you see far away, out to sea. It's the line where the water stops and the sky starts. There are horizon lines everywhere, but usually you don't see them because something like a hill or a tree or a house is in the way. You always see the horizon line at your eye level. In fact, if you change your eye level (by standing up, or sitting down) the horizon line changes too, and follows your eye level. Your eye level always follows you around everywhere because it's your eye level. If you sit on the floor the horizon is at your eye level. If you stand up, it's at your eye level. If you stand on top of a very tall building, or look out of the window of an aeroplane, the horizon is still at your eye level. It's only everything else that appears to change in relation to your eye level. The fact is, that everything looks the way it does from your point of view because you see it in relation to yourself. So if you are sitting looking out of the window of an airliner everything is going to look shorter than you because at this moment you are taller (or higher) than everything else.
In Zetetic Cosmogony by Thomas Winship we read a real world test:
If the world be a ball, as Sir R. Ball gravely informs us, the aeronaut should be one of his most ardent supporters, as the highest part of the "surface of the globe" would be directly under the car of a balloon, and the sides would fall away or "dip" down in every direction. The universal testimony of aeronauts, however, is entirely against the globular assumption, as the following quotations show. The London Journal 18th July, 1857, says: -- "The chief peculiarity of the view from a balloon at a considerable elevation was the altitude of the horizon, which remained practically on a level with the eye at an elevation of two miles, causing the surface of the earth to appear concave instead of convex, and to recede during the rapid ascent, whilst the horizon and the balloon seemed to be stationary."
Another easy experiment you can do for yourself to demonstrate this effect is find a computer game which can render large 3D maps. Move your character to one end of the map, center your crosshair on the line of the horizon, and turn on noclip. Without moving the mouse, ascend in height and notice how the line of the horizon will stay centered on the crosshair until you run out of land to see.
This simulated perspective effect is enough to satisfy the observer as to its workings and should be apparent and visible in most modern computer games.