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Flying in the Coffin Corner--Air France Flight 447


When Air France Flight 447 disappeared in June 2009, it was in the middle of the tropical Atlantic and had likely entered a mesoscale convective complex, a system of strong thunderstorms thought to have been at least four storms deep along 447's flight path.

Flight 447 was also flying at a cruise altitude of 35,000 feet, an altitude where the relationship between an aircraft's stall speed and the speed of sound has gained the name "the coffin corner". The name does not come from "it's deadly to fly there", but from the shape of a plot of stall velocity versus altitude when the velocity is expressed as Mach number, the speed relative to the speed of sound. The curve then resembles the tapered corner of a coffin as shown at the right.

It’s far easier to go fast when you don't have a lot of air to push out of your way. That simple fact motivates modern jet aircraft to fly above 30,000 feet, where the air is thin and fuel economy is high.

Flying that high also has its disadvantages. The same thin air that reduces frictional drag also reduces engine power, lift, and the effectiveness of control surfaces. In a U.K. Times article about Flight 447, former British Airways pilot Roger Guiver is quoted about large, fuel-heavy planes wallowing at such altitudes.

Flight 447's Airbus 330 is also a "fly-by-wire" aircraft, meaning that there is no mechanical connection between the pilot and the control surfaces and hence no physical feedback. Even in a direct-fly mode, the controls are entirely electronic and connected only by copper wire, as the name suggests.

If the lift produced by the flow of air over the wings becomes less than the weight of the aircraft, you are no longer flying, but falling in a "stall". The minimum safe operating velocity (Vmin) for an aircraft is set enough above the stall speed so that normal fluctuations in wind and aircraft altitude won’t cause an airplane to stall.

The lift, however, depends on both air density (kg/m³) and on the plane's velocity, and air density decreases with altitude. So, the higher you go, the faster you have to fly to stay above the stall speed.

As you go higher, temperature also decreases, at least in the troposphere were commercial planes are flying. As the temperature decreases, so does the speed of sound.

A commercial aircraft like Flight 447's Airbus 330 will often cruise at around 82% of the speed of sound. Beyond about 86% of the sound speed, the airflow begins to break away from the wings, becomes turbulent, and lift is reduced.

With stall speed increasing with altitude and sound speed decreasing, the velocity window in which an aircraft can operate becomes narrower and narrower. The figure to the right shows this convergence of the minimum and maximum operating velocities for temperature and pressure vertical profiles typical of the atmosphere in the tropics.

The blue curve shows the type of variation expected for the minimum operating velocity. The red curve shows the maximum operating velocity at 86% of the sound speed. The green curve shows a cruise velocity of 82% of the sound speed. The flat black line across the top shows the "window" of velocities within which the plane can fly.

Under normal conditions, flying in the coffin corner is standard operation. When it entered the mesoscale convective complex, however, Flight 447 left normal conditions, perhaps seeing only the first line of storms and going between them only to find itself in the middle of the complex itself.

Experiencing an airplane stalling is normally a memorable experience. At one time, I soloed in flying a glider. Learning to recognize and recover from a stall was one of the first lessons taught. You pull back slowly on the stick, letting the nose come up and the airspeed fall. The glider gives a slight shudder and the bottom drops out. Suddenly you are falling rather than flying.

To recover, you push the stick forward, letting the craft's nose go down and the speed over the wings increase. You start flying again and can bring the stick back to a straight and (almost) level glide.

With a powered aircraft, recovery from a stall approach can be accomplished either by applying more power to increase the airspeed or by dropping the nose, but you have to know that you are stalling. That means having working air speed indicators or being able to sense the drop in airspeed and lift. Once the plane is actually stalled, dropping the nose is required to recover.

For Flight 447, neither of those conditions may have held. The model of pitot tubes on the aircraft were known to have problems with icing and had been scheduled for replacement. Automatic messages from the aircraft indicated failures just before it disappeared from contact.

For the pilot, sensing a change in flying performance without instruments and without direct feedback from the flight controls may not have been possible, not in the middle of visibility limiting clouds and in the presence of violent wind gusts, updrafts, and downdrafts.

The interim report (pdf) from the BEA, the French Agency investigating the crash of Flight 447 indicated that "Observations of the tail fin and on the parts from the passenger [cabin] (galley, toilet door, crew restmodule) showed that the airplane had likely struck the surface of the water in a straight line, with a high rate vertical acceleration. … Based on the elements recovered up to now, no evidence of fire or explosion has been brought to light."

Was this a plane intact up to the moment of impact? Did the plane stall in the "coffin corner" yet systems failures, turbulence, and lack of visibility caused the pilots to believe it was in level flight until too late?

Theoretically, as a plane descends out of the coffin corner, recovery from a stall becomes easier as the window of possible flight velocities becomes wider, engines become stronger, and control surfaces more effective. It's unknown whether damage or lack of information undermined such recovery for Flight 447. Only now, after two years and with the retrieval of the black boxes will the answers start to be known.

About the Author: Keith Eric Grant is a freelance writer, physicist, and massage therapy instructor. He holds a PhD in Applied Science from University of California, Davis, and has worked as an atmospheric scientist and computational physicist at Lawrence Livermore National Laboratory. Keith is a member of the National Association of Science writers, American Geophysical Union, Society for Industrial & Applied Mathematics, and Associated Bodywork & Massage Professionals. He also writes the "Ramblemuse" column for the trade magazine Massage Today. You can follow Keith on Twitter as @ramblemuse.

The views expressed are those of the author and are not necessarily those of Scientific American.

The views expressed are those of the author and are not necessarily those of Scientific American.

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