How much can falling down due to a stall influence the angle of attack?

Question

I am trying to understand the af447 incident, more precisely, how a professional pilot having an attitude indicator available failed to understand that the angle of attack was too high. Was it that the angle of attack may be too high at the horizontal attitude, or close to that? As I understand, the aircraft stalled due to pilot error.

Over the longer range it cannot be just a free fall; the air friction would stabilize even a round ball to some stable falling velocity.

Knowing the downward velocity, as well as forward velocity, we can compute the angle of attack for horizontal attitude, and various different attitudes. Seems that if it falls with the same speed as it moves forward, the angle of attack would be 45 degrees just for a normal horizontal orientation. Is this situation realistic?

Answer 1

In AF447 the falling motion most definitely affected the angle of attack. Due to the fact that the pf did keep the stick pulled back for all but the last few seconds of the fall the aircraft was so steep that, although the aircraft was falling at a slight pitch up, angles of attack actually reached as high as 60°.

The descent was so steep that the air was passing over the pitot tubes at such an angle that it was reading below 40 knots, although the plane was moving far faster then that. The computer required that the airspeed be of a certain value to consider the aoa plausible so the stall warning stopped sounding even though the aoa was between 30° and 60° during the fall. When it hit the water the forward ground speed and the vertical speed were both 107 kts.

As far as why the pilot did not realize he was stalled, that's the question of the century. Much effort has been put into figuring that out, and there are numerous things that are at play. But in the end I don't think anyone has come up with a satisfactory answer for that.

If you want to dig into the causes of this crash and get a good understanding of Airbus systems in general I highly recommend this book and it's companion website. The author is uniquely qualified and gives the most thorough explanation yet is not as technically challenging as reading the BEA report.

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All of the numbers mentioned in this answer come from the linked book.

Answer 2

Your understanding of the situation is correct: The angle of attack was beyond stall and the aircraft was in a descent which reduces the pitch attitude, so the resulting acceleration felt to the pilots close to that in normal flight.

Now it is important to understand that the aircraft produced lift equivalent to its weight. It was in a steady state - if lift had been too small, it would had accelerated downwards. Let's calculate how big the descent angle could have been: The minimum speed of an A330 in clean configuration is 166 KIAS at the maximum landing weight, which is 396,800 lbs or 182 t. Since the aircraft had just flown for less than four hours, I would estimate that it weighed 205 t at the time of the accident, which makes its stall speed 176 KIAS or 90.6 m/s. In about 3½ minutes it went from 11,600 m to sea level, which gives us an average sink speed of 55 m/s. For a very rough estimate we use the mean between the stall speed at 11,600 m, which is 175 m/s, and the stall speed at sea level: 132 m/s. The resulting angle is 22.5° (note that the flight speed is along the flight path, so you need the arctan of 55 / 132.6). The real value was probably a little lower since the aircraft flew a little faster than its stall speed to compensate for the lower lift coefficient in the stalled state. Modern supercritical airfoils have a very benign stall behavior, and I would estimate that the speed was not much above stall speed. Also, it did not fly constantly at the same attitude, but the copilot released his pitch-up command twice, only to resume it seconds later.

When I use the cited values at the time of impact (107 kts ground speed and 108 kts sink speed), the airspeed is 78.2 m/s. Assuming standard atmospheric conditions, this gives a lift coefficient of 1.48 - way more than any stalled wing can manage. This can only be explained by a strong headwind, of which there is no word in the Wikipedia article. Since the plane was flying through a storm, strong winds should be expected, and then the figures become credible again. Tom's value of 60° sounds very unlikely to me - at that angle the wing produces mostly drag and the aerodynamic forces act at mid chord, producing a strong pitch-down moment which cannot be compensated by a tail surface at those 60°, regardless of elevator position. Around 20° to 30° angle of attack the whole situation becomes much more plausible.

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EDIT: Now I spent some time reading the BEA report (thank you @mins for the link!) and are deeply troubled by some details. In FL360 (figure 65) and with 1g (figure 66), the airplane was supposed to have flown at only Mach 0.4. This translates into a post-stall lift coefficient of 2.09, which is physically impossible. Some lift is contributed by the engines due to the positive pitch angle, granted, but by far not enough to make this low speed possible. At least BEA agrees with my mass estimate.

The dynamic pressure at this point is only 2660 N/mm², and in clean configuration this is too little to prevent the plane from dropping like a stone at any angle of attack. The same goes for the condition right before it impacted the ocean surface: 78.2 m/s is too low; at least 95 m/s would be needed for a barely credible post-stall lift coefficient of 1.0. If I add 17 m/s wind speed, things get back into normal territory. Unfortunately, the only wind information in the plots is in figure 64, when the stall begins. Headwind is around 0, but crosswind is between 20 and 30 m/s. If the airplane had sideslipped so badly during the stall, it would had entered a spin. It just does not make sense.

In the text we get a headwind information at the time of the autopilot disconnect (page 91):

Prior to the disconnection of the autopilot, a constant headwind component of 15 kt had to be added in order to make the simulation’s ground speed match the recorded parameter. This value was consistent with the wind parameters recorded.

But the most important line is at the start of the analysis, hidden away at the bottom of page 90. It should be bold and underlined, but isn't:

The validity of the model is limited to the known flight envelope based on flight tests.

Airbus did some more flights at the same configuration and loading as AF447 had at the time of the accident, but it appears that buffet limited their flown angles of attack to below 10°.

It must be concluded that all angle of attack values exceeding 10° are purely speculative and not backed by flight test data.

Answer 3

You are exactly right that the pilot should have noticed he was in a stalled configuration due to (among other things) that the attitude indicator would be showing nose up.

Your guess about a 45-degree down angle is not quite right. That would cause a large increase in speed and constitute an uncontrolled dive. Not good, but definitely better than stalling.

If you pull the nose up and hold it there, then what happens is that the aircraft loses speed steadily until it stalls, then it falls rapidly. In a semi-stalled condition (what occurred to the AF447 flight), the aircraft will be buffeted from side to side as it slides to the ground in a nose up configuration. When this happens the controls become "mushy" and the aircraft becomes difficult to control. This happened to AF447 and that alone should have told them they were stalled.

When there is no visual horizon and the pilots are flying blind it is easy to ignore or misinterpret the controls or focus on the wrong instrument. The pilots involved simply failed to realize they were stalled. The problem was compounded by poor command skills. Normally only ONE person is allowed to have the controls and that control can only be switched using an explicit protocol. The pilots of AF447 were not obeying this rule and both pilots were working the controls at the same time. The response of an Airbus to this behavior is to average the two inputs. Obviously this created more confusion.

One additional issue with the A330 is that it has what is called a "supercritical" airfoil shape to its wings which give it poor stall recovery characteristics, especially when fully loaded. When they tested the A330 in a simulator using the same conditions as in AF447 it took an expert pilot 23000 feet to recover from the type of stall they were in. So, once they had fallen below that altitude, they were dead and situation was unrecoverable.

Answer 4

Not very, I'm afraid.

First of all,it is the angle of attack (once it goes beyond a certain value) that influences (causes) stall and not the other way around.

You're correct that any body will reach terminal velocity while falling through atmosphere. But the stalled aircraft is not a free falling body- the engines are still producing thrust.

Another thing is the stalled aircraft rarely falls like a stone- the pilot is trying to regain control; the aircraft usually rolls or enters into a spin. Depending on the condition, the nose dips, decreasing the angle of attack. The only way for the aircraft to follow a trajectory described by you is if the pilot is holding the wing at a stalled attitude the whole way down.

Even in a (highly unlikely) case where the aircraft falls so that the horizontal and vertical velocities are the same, it will be the trajectory that will be at $45^{\circ}$, not the angle of attack, which can be any value be over the stalling angle.