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What happens if an airplane's engines shut down in flight?
Short answer
If an airplane's engines shut off in flight, it doesn't fall: it glides. A commercial jet travels about 15-17 km for every 1,000 m it descends, so from 11,000 m it has over 150 km and about 20 minutes to restart the engines or reach a runway. Flight controls, instruments and radio keep working on backup systems.

An airplane without engines is a heavy glider
When people say a plane "shuts off" in the air, they usually mean its engines shut off. When that happens, lift doesn't disappear: the wings keep generating it as long as the aircraft keeps moving forward, and what's lost is the ability to maintain altitude. The aircraft enters a glide, a controlled descent that trades altitude for speed. A passenger jet has a glide ratio of between 15:1 and 17:1: for every 1,000 m it descends, it travels 15 to 17 km forward. From a cruise altitude of 11,000 m, that gives a radius of over 150 km and about 20 minutes of flight.
The controls keep working. Hydraulic and electrical systems are powered by the auxiliary power unit (APU), a small turbine in the tail that can be started in flight, and by the ram air turbine (RAT), a propeller that deploys into the airstream and generates power from the wind created by the descent itself. With it, an Airbus A320 retains flight controls, basic instruments and radio.
What the crew does
The first thing is to fly the aircraft: set the best-glide speed, around 400 km/h on a jet. The second is to attempt a restart; most engine stoppages are due to a transient cause, such as water in the fuel, ice or volcanic ash, and the engines restart once clear of the affected area. Only after that is where to go decided: an airport within glide range or, if there isn't one, the most favorable surface available.
Cases that ended well
In 1982, a British Airways Boeing 747 lost all four engines flying through an ash cloud over Indonesia; after about 13 minutes of gliding, the engines restarted and it landed in Jakarta. In 1983, the "Gimli Glider," an Air Canada Boeing 767, ran out of fuel at 12,500 m due to a unit-conversion error and glided to a former air base. In 2001, an Air Transat Airbus A330 glided 120 km to the Azores with no engines. And in 2009, US Airways Flight 1549 ditched on the Hudson River after ingesting geese in both engines at just 850 m of altitude, with no casualties. None of those aircraft fell: they all flew to the very end.
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