How do planes control their altitudes?

No mere academic question

With all the air traffic in the sky, we want to avoid planes colliding with each other or with mountains. So a plane has an altimeter that reads altitude. It has control surfaces on the wings and tail to adjust the lift, that is, the upward force generated by the motion of air over and under the wings. It also has a feedback control system that can compute how the control surfaces need to be adjusted so that the altimeter reading steadies to the desired altitude. Feedback control is a branch of engineering and we can design these systems to perform quite well.

Flying on Planet Placid

Our atmosphere has warm fronts, cold fronts, high and low pressure centers, turbulence, and pressure disturbances from air flowing over hills and mountains. An altitude control system is responding to all this dynamic behavior. But suppose the Earth was Planet Placid, a planet with no turbulence, no mountains, and with sea-level pressure and temperature the same everywhere. The air would still get colder and thinner as we ascend, but we would have a smooth ride. In order to maintain an altitude, the control system needs only to adjust the lift so that the plane follows the curvature of the Earth. The physics of motion on circular paths makes this easy. An object will follow a circular path at a constant speed if there is the right amount of force on it directed toward the center of the circle. This force is called the centripetal force. (The difference between this and centrifugal force is a topic for another post.) For a 700,000-pound aircraft flying at 550 mph, the net centripetal force needed is about 700 pounds directed downward. That means that the lift needs to be 700 pounds less than the weight, that is, a lift of 699,300 pounds. The feedback control system is extremely good at adjusting the control surfaces to find this "sweet spot." If the atmosphere were perfectly placid, this would be a one-time adjustment.

Two forces on the aircraft: the downward force of gravity, which is the weight, and the upward force from the wings, which is the lift. The imbalance creates a net downward force of 700 pounds, providing the needed centripetal force.

Flying on Planet Earth

Now that we don't need to worry about flying off into space, we need to worry about all the dynamic behavior of the real atmosphere. The first thing to understand is that the altimeter is actually a glorified barometer. It doesn't measure altitude, rather it measures air pressure and then does a calculation to convert that to an altitude. We can do this because air pressure drops in a predictable way as we ascend, as shown in this figure:

Planes following contours of constant pressure when the ground pressure is the same everywhere

The air pressure at sea level under "standard conditions" is about 14.7 pounds per square inch, which is also called 1 atmosphere or 1 atm. At the summit of Mount Kilimanjaro, the air pressure is half of this, about 0.5 atm. Atop Mount Everest, it's about 0.33 atm. Commercial aircraft en route don't maintain an altitude, rather they maintain a "flight level," which is a pressure. FL230, for example, is an abbreviation for a flight level of 23,000 feet, but a plane at FL230 is actually maintaining a pressure of 0.4 atm. FL300, which denotes 30,000 feet, is actually 0.3 atm of pressure.

As we go from place to place, there are deviations from "standard conditions." Suppose the plane at FL300 flies from a region where there is a high pressure center toward a region where there is a low pressure center, and the FL230 plane is going the opposite way. As illustrated below, the FL300 plane will descend to follow the 0.3-atm level and the FL230 plane will climb to follow the 0.4-atm level. Their altimeters will continue to display respective altitudes of 30,000 and 23,000 feet, but these are just disguised pressure readings. Their actual altitudes will differ from these values.

Planes following contours of constant pressure when the ground pressure varies because of high and low pressure centers

The pilots don't need to worry about a collision. They are flying at sufficiently different pressures to guarantee a safe vertical separation between them. As long as they are high compared to any hills they don't need to measure their actual altitudes. Both their altimeters can do the same "standard conditions" calculation. This means that there's no need to constantly get updates about the local barometric pressure on the ground.

What about flying low or landing?

When planes descend below a certain level (called the transition level ), the pilot needs to switch the settings of the altimeter so that it does a different calculation. Failing to make that switch can lead to disaster, as we can see from this figure:

Plane following the contour of 0.8 atm pressure when the ground pressure varies because of high and low pressure centers

If the plane shown just maintained an FL060 (6,000 feet) flight level, it would follow the 0.8-atm pressure level -- right into a mountainside. There's a saying among pilots: "High to low, look out below." The pilot needs to be aware of topography and the altimeter needs to maintain updated information about local ground-level barometric pressure. It still calculates altitude based on the pressure it measures, but this calculation takes into account ground level barometric pressure variations to get actual altitude. This is also helpful for landing!

Interested in learning more? This Aviation Theory video walks through all the concepts and the terminology.