What's the View Like?

Watching RotK got me to thinking that I definitely don't describe my world well enough. Usually my players are in a forest and see... trees and bushes. Or they're in mountains and see the path they are and maybe the valley below them. The sweeping vistas of RotK (especially the lovely view from Minas Tirith) got me to wondering about the equations for how far people can see based on their altitude.

So.. anyone know what the equation would be for an Earth-sized world?

How about a completely flat world?

On the accompanying picture, d is the distance you can see, h is the height above ground, and r is the radius of the Earth (or whatever planet you're on).

From there, it's just a matter of applying the old Pythagorean theorem: the sum of the squares of the (short sides, not sure what the English term is) is equal to the square of the long side:

d²+ r² = (r+h)²
d²= (r+h)²- r²
d = SQRT ((r+h)²- r²)