Chris Scott
Ten degrees nose UP? That tells us nothing about the AoA, or the position of the THS. Was it already at 13.2? Did pilot cease his initial NU and begin his repeated ND inputs? The 7000fpm suggests the climb was (initially) very rapid, and there is no reason to think the THS was not "UP" having corrected for a chronic descent? Turbulence? There is nothing in this sequence (sic) to base a conclusion of PF chronic NU. BEA say ".......A INPUT....."
How outlandish was the descent that THS needed ten degrees to arrest it, and start to climb? Or more to the point, what was the THS' deflection at a/p drop? BEA don't say. A/P will hang in until 13 degrees Pitch UP before it quits. If the descent was transient, and chronic, why shouldn't the THS react with 13 degrees nose up? FOR TRIM.... Initially, PF may have seen the nose dropping as the problem needing nose up. When he realised his TRIM state, he started his repeated ND?
you say,
So, a likely interpretation is that the PF's nose-up input initiated the climb by increasing pitch to above +10deg. (You may disagree.) That is an extraordinary attitude at high altitude. He may have ceased nose-up inputs at that point, but the new pitch attitude produced a climb VS of 7000ft/min. At that rate, it would only take about 15 seconds to get to the next point, where the PF made his short-term nose-down input, causing the reduction in VS to only 700ft/min with an AoA of +4, which was just below the stall AoA.
What About.....
IOW. If the THS was at 13.2 degrees at a/p handover, and the a/c was sinking, wouldn't the PF input NU to stop descent? When he realizes his THS (can he?), he stops, but the a/c "has started to climb" (Bow Howdy, 7000fpm?) His elevator pushed the a/c past what it needed? Once climbing, furtrher ND input stalled the TAIL AS A UNIT. It could not bite to drop the nose, It was committed to Ballistic trajectory to actual aerodynamic Stall, that dropped the Nose but no energy available to keep the nose dropping so it settled back on its tail., but PF input ND, which restalled the TAIL. Now PF is in a corner. He CANNOT recover, he is bracketed between no energy and a Tail that cannot unstall. The tail is a huge Spoiler, now, and it is stuck deployed full. When the a/c goes NU , it is limited by the drag of the tail from going inverted, but since the Tail cannot unstall the a/c cannot drop. This I believe was the result of what is seen as the initial "recovery" that initiated the STALLSTALL. The AoA was never going to be less than 4 degrees, insufficient to Break the STALL.
This means that the THS may have been responsible for the A/P quitting. 13.2 degrees exceeds its Limit for TRIMMING. Does Airbus want such a huge lifting surface as a TRIM DEVICE? Pending further data, it could well be.
Why did the Pilots not MAN TRIM ND? First of all, they were trained not to, and secondly, How were they to know the THS was at 13.2 degrees NU or at the limit. Actually, BEA have not said precisiely. With elevators, they had horrible nose up, or "almost" a recovery. The Rolling on descent may have been there solution to gain STALL recovery.
There is just such a disconnect between a/c and pilot, is it impossible to entertain "holding back stick all the way down"? Every time they Push, the a/c goes berserk, and refuses to unSTALL anyway. Holding back stick gives a stable, "quiet" ride. Deadly, but quiet.
The LEFT ROLL command? Let's say the Autopilot had been trimming for NU and Right ROLL. Just before a/p quits, the trend intensifies, perhaps with gusto. Serious ND trend and right ROLL. These aspects can be as much as 9 degrees ND and 45 degrees ROLL. The a/p quits with max NU and max left ROLL. PF is not ready for this amount of Trim; his initial (and likely ham handed, as discussed) inputs ask for maximum Left Roll and Maximum NU.
Hell of a way to start flying. In an astonishing climb, where ND inputs stall the Tail, and the trajectory is ballistic. Ballistic because no aerodynamic controls were available to descend, and the climb will only halt when the energy is too small to fly, only ballistic flight,
I am not sure the PF was not trying to keep the nose dropping when the AoA was 4 degrees, but the Plane couldn't get over the last little bump.