What factors determine the maximum altitude of an airplane?

Answer 1

Short Answer:

An airplane maintains altitude by producing enough lift to counteract its own weight. So the amount of lift an airplane produces determines how high it can climb. Lift is produced by accelerating air in a downward direction. At higher altitudes the air is less dense so a larger volume must be accelerated downward to produce enough lift to keep flying. This can be done in two main ways; flying faster or having longer wings. The faster you fly the more air you pass through so the more you can accelerate downward which generates more lift. The longer your wings are the more surface area you have to generate lift so you can maintain altitude. You can also make your plane lighter while maintaining its top speed and wing length by carrying less fuel and cargo or using smaller pilots. Given the same speed and wing length a lighter plane can maintain altitude in less dense air so it can climb higher than a heavier plane that is traveling the same speed.

Longer Answer:

Lift can also be generated by an airplanes engine if that engine is pointed towards the ground. In fact some airplanes can fly straight up by generating all their lift with their engine and none with their wings. So with a powerful enough engine there is not limit to how high an airplane can fly. However most airplanes use "air breathing" engines that burn fuel with oxygen supplied by the atmosphere. The higher you go the less air there is in a given volume of sky so the less oxygen is gets sucked into the engine to burn fuel. Pilots have reduce the fuel flow to their engines as they go higher since the extra fuel would be wasted with no oxygen to burn it and it would tend foul the engine with partially burned residue making it run less efficiently or stalling it out completely. With less fuel to the engines the airplane slows down until it produces exactly enough lift to maintain its altitude. It's possible to get a little higher by diving and speeding up then pulling up hard and letting the airplanes momentum carry it to a higher altitude temporarily but when it slows down it will drop back to an altitude where lift equals the planes weight at the highest speed possible given the amount of oxygen in the air at that altitude. If a plane could get going over 25,000 mph (33 times the speed of sound) and and coast out of the atmosphere before it slowed down much below that speed it would keep going since it would be above escape velocity needed to get out of the earth's gravitational field. If it were pointed in the right direction and kept going faster than about 17,000 mph it could go into orbit in space.

Rocket engines carry their own oxidizer which contains the oxygen to burn the fuel so they can run even in the vacuum of space above around 100 km (330,000 feet). The only limitation on altitude for them is how much fuel they can carry before they are too heavy to lift themselves.

So the real answer to the question is that the main factor determining maximum altitude for an airplane is how high the engine can go before the air gets too thin to maintain enough velocity to balance the plane's weight against lift. Longer wings and less drag (a more aerodynamic shape) will help the same engine fly higher as will a lighter plane.

An airplane with a rocket engine that does not breath air is limited by how much fuel it can lift when starting off. Too much fuel weight and the plane won't take off until the excess weight of fuel has been burned. Once the rocket plane lifts off the altitude limit is determined by how fast the plane can get going before running out of fuel. If it can accelerate to 25,000 mph or faster it can go forever. If it can go at least 17,000 mph it can go into orbit in space more than 330,000 feet up (62 miles). Otherwise you can use rocket science equations to figure out how high it can get before it starts falling using the vehicle mass, rocket engine thrust, fuel burn rate and atmospheric drag. This is a complex calculation because the mass, and atmospheric drag change as a function of altitude and the fuel burn rate and engine thrust usually don't stay the same throughout the flight.