West Caribbean Airways Flight 708 which crashed in 2005, fell victim when their plane encountered a deep-stall. From my understanding, only certain planes can 'deep-stall'
How can pilots recover their plane to recover from a deep stall?
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A deep stall or a super stall is a condition where the wake of the wing impinges on the tail surface and renders it almost ineffective. The wing is fully stalled, so the airflow on its upper surface separates right after the leading edge, which produces a wide wake of decelerated, turbulent air. Consequently, the dynamic pressure at the tail surface is much smaller than in unstalled flight, which is the main reason for the reduced effectiveness.
Consider this case: The aircraft flies in a nose-up attitude, but on a downward flight path. Consequently, the angle of attack of the wing $\alpha$ is much beyond its normal operating range, causing a fully separated upper surface flow. Due to the T-tail configuration, the wake is hitting the elevator such that all of it is shielded from the regular airflow.
The pitching moment of this configuration over angle of attack (blue line) looks something like this. First there is a stable region with a negative gradient at low values of $\alpha$, followed by a minimum when the wing stalls, and then a region with a positive gradient, where the separation unfolds and the tail moves into the wake from above. This region is unstable in pitch, so without control input the aircraft will not stay there, but either pitch down or up until it reaches a stable region again. At high angles of attack follows another stable region with a negative gradient: Note that we have two trim points, one in the regular range of the angle of attack, and one way out to the right. In both cases the aircraft has a stable trim condition, so small disturbances are answered with force changes which will keep the aircraft at one of these points. Between the two, there is another equilibrium point, but here the airplane is unstable. If it pitches up slightly there, the pitch up will accelerate until it reaches the upper trim point.
Now consider the control power of the horizontal tail. When it flies in undisturbed air, it can trim a wide range of angles of attack. In the deep stall condition, however, its control power is much reduced, resulting in a much smaller range of trimmable angles of attack. If the lower end of this range is right of the point where the pitching moment crosses into positive values (here at $\alpha$ = 24°), the aircraft cannot escape with elevator deflections!
Please note that the control power is not sufficient to enter the deep stall with quasi-stationary trim changes. The pilot needs to pitch up quickly and has to overshoot the static trim range in order to cross into the stable region above 30° angle of attack. There, his range of trimmable $\alpha$s is too small to achieve the same overshoot backwards.
To get out of this trap needs other changes: Either shift the center of gravity forward, or try to drop one wing. Unfortunately, both the ailerons and the rudder will also be much less effective due to the massive separation and the wake. In a number of cases, even experienced test pilots could not escape this condition.
A deep stall is a stall where the pilot is unable to pitch down due to either loss of clean airflow over the elevator (typical in T-tails) or the canards still producing lift while the wing behind it is stalled.
Depending on the aircraft the pilot may be able to bank and use the rudder to get the nose down to correct the stall. If possible the pilot may be able to move/ditch cargo to move the Center of Mass forward.
The article on stall in Wikipedia talks of one instance where a B727 recovered from a deep stall by "rocking the plane to higher bank angles" till the nose dropped and normal control response was recovered.
It's assumed that deep stall mainly affects T tails, but high angles of attack may lead to a more conventional low tail design having the tail stalled. If you look for the accident investigation animation of AF447 (youtube), you will see that there was a lot of ineffective stick movement. Finally, when the stick went forward, the nose lowered to about 10 degrees down, but the flight path angle was close to -45 degrees, so the angle of attack was roughly 35 degrees. Both surfaces were deeply stalled and this manoeuvre was survivable with conventional stall recovery.
There are recovery techniques which may work. I used to air test a large T tail design and the briefed manoeuvre was to roll to induce side-slip which would reduce the angle of attack. On a T tail design, this would mainly be accomplished by rudder. But a low tail design may have the rudder blanked by the tail at these angles of attack. The only way to induce roll from yaw in this case would be the use of asymmetric thrust.
The AF447 pilots were not equipped with this knowledge which may have saved the aircraft. I have asked my colleagues their opinion and I get the impression there is not much appreciation of this situation. With the recent Air Asia accident investigation follow a similar approach to the events leading to the loss of AF447, perhaps now is the time.