Why do airplanes fly so high?

Aerodynamic drag is proportional to air density, and density falls quickly with height. At 11 km (36,000 ft) the air is about 30 per cent as dense as at sea level; at 12 km, about a quarter. An airliner flying at the same true airspeed therefore meets a fraction of the drag it would face low down, and the engines can be throttled back accordingly. Jet engines also prefer cold, thin air: their thrust falls with height, but their fuel consumption per unit of thrust falls too, and the turbine runs closest to its design point near the tropopause. The combination is why a Boeing 787 or Airbus A350 typically cruises at 11 to 13 km (35,000–43,000 ft) and why a long-haul flight climbs in steps as it burns fuel and gets lighter.

The speed of sound falls with temperature, and at cruise altitude it is about 295 m/s (1,062 km/h). Airliners cruise at Mach 0.78 to 0.85, just below the point where shock waves on the wing start to raise drag sharply, so the cold air sets both the efficient altitude and the practical speed.

Most cloud, precipitation and turbulence live in the lower troposphere. Cruising above 10 km puts an aircraft over the tops of all but the tallest thunderstorms, which pilots avoid laterally, and above much of the turbulence generated by terrain and convection. Jet streams, the rivers of fast air near the tropopause, can be ridden eastbound for a tailwind of 150 to 300 km/h or avoided westbound, another reason routes and altitudes are chosen with the day's weather in mind. High altitude also helps air traffic management: a dozen usable levels between 9 and 13 km, separated by 300 m (1,000 ft), let controllers stack traffic on the same route.

Several limits close in above about 13 km. Engine thrust keeps falling with density, so climbing further requires a lighter aircraft or a more powerful engine. The wing needs a higher true airspeed to generate the same lift in thinner air, and eventually the speed needed to avoid a stall meets the speed at which shock waves cause trouble, the so-called coffin corner. The cabin must be pressurised to the equivalent of no more than about 2,400 m (8,000 ft), and the structural load from that pressure difference grows with altitude. Concorde, with its slender wing and turbojets, cruised at 17 to 18 km (55,000–60,000 ft), and the U-2 reconnaissance aircraft flies above 21 km (70,000 ft), but each is a specialised design. For the aircraft that carry most of the world's passengers, the band between 9 and 13 km is where fuel, speed, weather and structure all line up.