The curvature of the earth is about 200mm each 1600 metres. If you imagine that is in the least bit significant, you are deluded. Well, you are anyway. Modern aircraft have instruments to fly by. These include radio altimeters that are extremely accurate. Auto pilot enables the aircraft to track the height above the earth with no problem whatsoever.
Height variations are continual anyway. Wind and turbulence move the aircraft around. And no pilot ever has come to the edge of the earth, said, "Oh it's flat" and returned to prove it.