Okay, so I'm not a mathematician!
Calculating the angular size of the Earth to determine the horizon drop DOES NOT WORK!!!!
Therefore the first three lines of my last post are totally wrong! :down:
The reason it doesn't work is because with altitude, you can see a larger and larger percentage of the Earth's surface that approaches the maximum of 50%.
In reality, the horizon drop associated with altitude is actually rather pronounced.
At 100,000 ft the horizon drop is 5.59°. 11 full moons could fit in that much drop.
That's plenty enough to be noticeable, but you'd likely still need a reference point because of the way your brain works. Your brain has spent it's entire life with the horizon at eye level and when you look at a horizon, your brain is going to tell you that it's at eye level unless you have something to reference that tells you otherwise. There are instruments on aircraft that serve this exact function because without it, pilots tend to loose altitude while thinking that they are flying flat and level.
The drop in the horizon really starts to be noticeable at around 40,000 ft where it drops by about 3.5°.
The math involved in figuring this out has to do, once again, with right triangles....
View attachment 26541
So, go
HERE and input the known factors...
Side B = the radius of the Earth in feet = approximately 20,900,000 feet (trust me, any more accurate than that won't change the angle enough to worry about).
Side C = the radius of the Earth plus the altitude.
Hit the calculate button and whatever value you get for angle A is the angle at which you'd have to look down to see the horizon line (see above diagram).
Clete