PHYSICS OF A DEEP STALL:So what causes an aircraft to end up in a un-recoverable deep stall? It obviously occurs at high angles of attack but is compounded when the horizontal stabilizer (and the elevators) of the tail are no longer effective in changing the angle of attack. Aircraft are designed to have to certain longitudinal (pitch) stability. Lift produced by the wing actually causes a moment force on the aircraft that pitches it up or down due to the center of lift being some distance from the aircraft center of gravity. To oppose this moment force the lift from the horizontal stabilizer of the tail counteracts this force in order to achieve static and dynamic stability. Essentially the lift of the tail creates an opposing pitching moment force to that created by the wing. In aerodynamics the pitching moment co-efficient (usually referred to as Cm) represents this overall pitching moment of a plane.
The following is a diagram that represents the lift, drag, and pitching coefficients of a particular airplane which represents the complex interplay of how the wing and tail and resulting lift and drag impact the overall pitching moment of an airplane at different angles of attack. This figure represents an airplane with rectangular wings and conventional aft tail.
The first interesting range to point out is where lift (Cl) peaks and then drops (stall) and the resulting effect on the pitching moment (Cm). There's a sharp drop in Cm to be more negative which represents an overall force for the nose to go down. The more negative the Cm, the more the pitching moment to force the nose down. The reason this occurs is because the wing itself stalled out produces less left therefore less pitching moment force while the tail continues to produce lift and causes the nose to pitch down more because the wing stalls before the horizontal stabilizer of the tail does (downwash from the main wing induces a lower angle of attack on the tail h-stab therefore postponing the stall of the stabilizer). It's this change in pitching moment as a reaction to stabilize the plane that helps a plane recover from a stall to reduce angle of attack.
The 2nd area to notice is when the tail also stalls at some higher aoa which is represented by when Cm rises meaning less moment force by the tail to pitch the nose down because it's producing less lift due to stall. However in the case above Cm is still negative (nose still wants to pitch down). Eventually drag creates more stability causing the pitching moment to be more negative again. For this aircraft there isn't a deep-stall point where pitching moment is at equilibrium. This means that an aircraft should be able to recover from a deep-stall because a pitching moment exists to be able to reduce the angle of attack and get out of stall.
The following graph however represents a plane that has different post-stall characteristics.
The graph looks similar except now notice that there are angles of attack where the pitching moment is either at 0 (equilibrium) or even positive. When the plane has not stalled out this isn't an issue, however where this occurs at higher angles of attack into a stall this becomes very important. It is at these points that the pitching moment is essentially zero which means there's no force available to change the angle of attack of the airplane. From the unstable equlibrium point (25 deg aoa in the aircraft above) with the control held in the same position that would result in recovery in a shallow stall, the plane would quickly rotate to this deep stall trim point. In other words, the deep stall trim point is where the aircraft can no longer produce a pitching moment to change the angle of attack of the airplane and the plane remains at this angle of attack. At this point it becomes difficult if not impossible to recover the aircraft with conventional controls and the airplane literally pancakes into the ground.
For the well documented deep stall t-tail cases, the reason this occurs (where Cm=0 at high aoa) is because the turbulent flow behind the stalled wing actually severely interferes with the airflow for the tail and this wake severely reduces the ability of the tail to stabilize the plane by reducing it's ability to create a corrective pitching moment through tail-lift.
Here's a similar pitching moment vs. aoa chart for the F-16 which shows the regions highlighted where pitching moment is at equilibrium which leads to a deep stall where aoa is in the 50-60 degree range either direction.
It should be noted that the deep stall can occur irrespective of the airplane attitude whether it's nose up in the vertical, wings level or wings inverted.
AH DEEP STALL ENTRIES?:Joe Bill Dryden, a test pilot for the F-16 has write-ups regarding F-16 departure into deep stall including inverted deep stalls. The situations leading to deep stall usually occur when the airspeed of the aircraft was at zero in ther vertical or at slow speed with a hard maneuver. In either case the computerized flight control system isn't able to correct quickly enough for the rapidly changing aoa.
I theorize this is basically what is happening in the AH flight model. As Widewing's film of the Mosquito demonstrates as the mossie nears 0 airspeed with nose pointed up the nose begins to drop. This resultant drop whether pitched back or pitched forward represents rapidly changing angle of attack because the free-stream air is striking the leading edge of the wing at angles of attack that increase very rapidly due to the motion of the rotation with the nose coming down.
Very quickly we find that both the wing (and tail) are at high angles of attack passing through the transition zone where a spin occurs and into aoa well in excess of the critical aoa. In this attitude the tail (and elevator) is essentially unable to produce enough lift to create a negative pitching moment to offset whatever lift is produced by the wing inorder to pitch the nose down. Essentially the aircraft is now in state that pitch equilibrium has been reached (like our graph above where Cm=0 at high aoa) and we pancake into the ground either upright or inverted.
I have not seen any film or have I tried reproducing the inverted deep stall of the Spitfire I. I'm guessing essentially something similar is happening where the aircraft is at or near zero airspeed and begins to fall which results again in a very high aoa attitude very quickly passing through the spin zone and into a deep stall.
Whether deep stall trim points exist for each of the AH airplanes in real life is another question. Post-stall dynamics as mentioned are very tricky to estimate and model. The question is does enough pitching moment exists at very high angles of attack post-stall to pitch the nose in order to reduce aoa depending on the configuration and design of the aircraft. But from what I can tell it appears the unrecoverable float downs we are seeing in AH is essentially a deep stall.
Sources:
(1) Mechanics of Flight, Warren Phillips. 2004.
(2) NASA TN86401: Flight Characteristics of a Manned, Lowspeed, Controlled Deep Stall Vehicle, Alex G. Sim. Aug 1984.
(3) Explaning Aerodynamic Stall, Mark McCabe, Aviation Litigation Monthly, Fall 2002.
(4) Formation Flight Model Tested, NASA Dryden Flight Research Center, Aug 1997.
(5) No Excuses, Joe Bill Dryden. Code One Magazine, July 1991.
(6) Concept to Reality: Contributions of NASA Langley Research Center to US Civil Aircraft of the 1990s, Joseph R. Chambers, Oct 2003.
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412th FS Braunco Mustangs
