How high do planes fly?

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Cruising altitude: about 11 km, in thin, icy air

In the model, an Airbus A320 of 64 tonnes cruises at 11,000 m (36,100 ft) at 829 km/h (515 mph). Up there a cubic metre of air has a mass of only 0.36 kg, less than a third of the 1.225 kg at sea level, and its temperature is −56.5 °C. These are the values of the standard atmosphere that pilots and engineers calculate with (NASA Glenn, Earth atmosphere model); on a real day they differ by a few degrees.

Lower down, the air gets denser and warmer: at 2,000 m about 1.0 kg/m³ and +2 °C, at sea level 1.225 kg/m³ and 15 °C. Near the ground the air is almost three and a half times as dense as at 11 km. In cruise the A320 burns about 270 kg of fuel per 100 km.

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Is thin air worse for flying?

A common view is that thin air carries a plane worse: the wing finds less air to push down and the engines less oxygen, so flying up there should be harder. Another, often given as the reason for flying high, says the thin air simply has less drag. Both miss what actually happens.

Take the A320 down to 3,000 m, where the air is two and a half times as dense as at 11 km, and fly it at the most economical speed for that height: 591 km/h. The drag there is 44 kN, close to the 40 kN at cruise. So the engines push about as hard and burn only about 10 % more fuel per hour. But down low that hour carries the plane only 591 km, up high 829 km. Per 100 km it needs about 420 kg instead of 273 kg, half as much again. At sea level, at its best speed there, it would be 486 kg.

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Why planes fly so high: the same drag, 40 % faster

Lift grows with the density of the air and with the square of the speed (NASA Glenn, the lift equation). In air with a third of the density, a wing at the same angle needs more speed to carry the same weight. At 11 km and 591 km/h the A320's wing lifts only 319 kN, half its 628 kN weight. At about 830 km/h the lift carries it again.

The point is the drag at that speed: 40 kN, about what the plane met low down at 591 km/h. In the thin air the same push moves it 40 % faster, so each kilogram of fuel takes it further. The drag isn't lower because the air is thin; at the same speed, 829 km/h at 3,000 m would mean 71 kN of drag. It is lower because the plane flies the speed the thin air asks for, and gets it for the same force.

The cold helps as well: jet engines work more efficiently in the cold air up there (BBC Science Focus). Our model leaves that out, so the gain it shows comes from the wing alone.

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Why planes don't fly higher: the wing runs out of margin

If thin air is so good, why not fly at 15 km? Because the higher the plane flies, the harder its wing must work to carry it, while near Mach 0.78 the wing can give less before the air over it starts to shake and break away, called buffet. The stall speed, the lowest speed at which the wing can still carry the plane (explained in our tour on stalls), creeps up towards the speed it flies: 550 km/h at 11 km, 704 km/h at 13 km, only 125 km/h below its 829 km/h. Flying faster isn't possible either, because drag shoots up near the speed of sound. Pilots call this narrowing gap between too slow and too fast the coffin corner.

The margin that counts is for turns and gusts. In a turn the wing must carry more than the weight: in a 40° bank 1.3 times as much. In practice, crews aim to keep at least 1.3 g available before buffet in calm air, and up to 2 g when turbulence is expected (Aviation Week, Learning From Test Pilots). In the model, a 64 t A320 at 12,300 m and 829 km/h has used up exactly that margin: in a 40° bank the stall speed reaches 831 km/h. At 11 km the same turn leaves 155 km/h to spare.

And the gain from climbing further is small: from 11 to 13 km the fuel per 100 km falls by only about 5 %, from 273 to 260 kg in the model. The engines do lose thrust in the thin air (from 58 to 47 kN at full power), but for a 64 t A320 the wing's margin runs out first, not the oxygen. On top of all this, every type has its certified maximum altitude, 39,100–39,800 ft (11.9–12.1 km) for the A320, which it never exceeds whatever the wing could do.

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Heavy planes fly lower and climb in steps

A heavier plane needs more lift, so its wing reaches its limit lower down. In the model at 11 km, 829 km/h and a 40° bank, the stall speed is 558 km/h for a light A320 of 50 t, 674 km/h at 64 t and 822 km/h at its maximum of 78 t: just below the speed it flies. A full A320 has used up its 1.3 g margin at about 11.1 km already.

That's why long-haul flights, which take off heavy with fuel, start lower and climb in steps as the fuel burns off and the most economical height rises; pilots call it a step climb (Wikipedia, Cruise). A light plane's wing would allow much more height, about 13.9 km for 50 t in the model, but no A320 flies above its certified ceiling of about 12 km. That certified limit is different from the service ceiling, the height where a plane can still climb at a small set rate, typically 100 ft/min, or about 500 ft/min for jets (Wikipedia, Ceiling).