Recovery trajectories
 

Since there seems to be consensus that the pitch-down should continue until the stall warning stops, here it is:

N.B. The pitch-up rate has been reduced to 1.5 deg/s to respect stall warning.

http://i.imgur.com/Jvchu.gif?1
http://i.imgur.com/Qfp1h.gif?1

The "crazy speed" comment comes well after selecting TOGA if I recall correctly. There seems to be a significant deterioration in joined-up thinking from the crew - and the PF in particular - after taking manual control.

This is why I am and always have been focused on where the training went wrong (and incidentally, why I get very antsy when others claim I'm arguing for a conclusion that begins and ends with pilot error). The consensus seems to be that the correct course of action would have been to cover the controls, but not actually do anything with them (or indeed leave them alone completely) until the aircraft's response to the conditions had been monitored for at least half a minute. It's all very well saying that from the comfort of our keyboards, but on a psychological level it's another thing entirely to have an aircraft suffer a failure in marginal conditions and retain the willpower to not intervene - especially for less-experienced flight crew.

Holding back and seeing how the aircraft copes is a universal thing, by which I mean it's true regardless of whether one is flying a FBW jet with bells and whistles, or something more traditional - because in both cases the aircraft has been trimmed to remain more-or-less stable. The exception to this rule is of course when a flight surface problem has occurred - but such events are rare enough to be a fair way down the mental list of potential failures.

Hi DozyWannabe,

From Page 88.
"The A/P2 disconnects. The roll angle changes from 0 to 8.4° in 2 seconds whereas the sidestick is at neutral. The pitch attitude is 0°."

I'm sure they would have loved to have waited 30 secs before touching the controls, but with that roll rate, they could have been beyond 30 degs bank within 7 secs. Most pilots would do something before it went beyond 20 degs.

Hi rudderrudderrat :),

This is why I said "cover the controls". The aircraft was in moderate turbulence, enough to give it a nasty bump, but probably not enough to turn it over. My suspicion is that the bump that hit at roughly the same time as A/P disconnect is the cause of that roll. It's a nasty rate, for sure - but if you're in turbulence, it's rare for it it last long enough to turn it over, or even much past 10-15 degrees of bank.

Now here's where I need your input. Airliners are designed to be stable. In layman's terms they "want" to fly straight and level. In roll direct, I suspect that 8.4 degree bank angle would remain when exiting the turbulent air pocket - am I right in thinking that unless something has happened to the flight surfaces that angle will hold until corrected?

In any case, the deviation from straight-and-level on exiting the bump was a moderate roll with a minor nose-down pitch component. Of course the roll will need decisive correction - but I think (and please correct me if I'm wrong) that "decisive" can still be smooth and gentle in execution. The pitch component was barely half a point nose-down and should have corrected itself via trim.

The question is why the sudden aggressive pitch-up command when it wasn't necessary?

[ In case it wasn't clear, 30 seconds was a theoretical average - of course that'll be different depending on the circumstances, but I think most agree that the sidestick commands were well in excess of what was required, and to me hint at the classic signs of a startle response. ]

It was not .5 degree ND. More like 3.5. You assume too much re: bank. The pilot's reactions were necessary. BEA, in #3: "The Pitch reached 10 degrees NU and the a/c began to climb." Have you reviewed how long it took to get to 10 degrees NU? Without horizon, a ten degree input (from outset) is only six degrees NU from cruise.

Whatever the lay analysis; here, at a/p loss, was the beginning of upset, can we agree? In that beginning, a change in LAW and PILOT both became too much to smooth over. I venture that upset began whilst a/p was still latched, for the attitude in PITCH and ROLL needed correction, having begun in auto.

What began as respect for the conditions at hand for 447 has morphed into a mere and casual dismissal of the challenge. c'est la vie..... If only to read a respectful approach to the pilots, I long for the final report.

So back to Alt laws and such
 

Looked up the "laws" and reversion sequence again, and seems the system continues to use "normal gee" as the pitch command, and roll rate, but not roll angle "protection". That right?

So why have to hold back stick? Further, the 'bus has a pitch attitude correction for the Nz the plane tries to maintain with stick neutral. Otherwise, at just a few hundredths of a gee less than 1 gee the thing would continue to go nose up in order to maintain 1 gee. We saw this in our little jet once pitch was above 10 or so degrees, and it was quite noticeable above 30 deg of pitch. What, 0.87 gee for constant pitch angle?

I understand some folks pointing out a rapid roll change just after UAS could be disturbing, but seems about right for a bit of turbulence.

I can also understand a very slight nose up command if worried about overspeed, but only for a few seconds and then back to whatever pitch was before the UAS.

The CVR comment about crazy speed might be explained, as vertical velocity was extreme but indicated speed was what, 107 or 135 knots? So PF wondering about why such a slow speed if descending so fast. Maybe started to question the altitude readings, too, for first 30 or 40 seconds.

As another contributor has opined, this will be a "landmark" report and I think the recommendations as well.

Hi DozyWannabe & salute Gums,

On page 112 Lateral parameters, Estimated side slip shows a distinct asymmetry after the AP disengaged. If I'm reading the trace correctly, it shows a Left Hand side slip DA. Since it was in ALT LAW, the the pilot will have to constantly apply aileron in one particular direction (LH in this case), until the side slip was trimmed to neutral.

I don't think the roll was turbulence induced because the effect lasted too long and would be random L/R. I think the aircraft was out of lateral trim (due some fuel imbalance, or asymmetric thrust, or rudder trim applied by the AP just before disconnect.)

All Boeing pilots are familiar with this problem, because we frequently re-trimmed the rudder during the cruise to keep the ailerons neutral. I've never had to do this on the Airbus, because the AP does it automatically for me.

If the FOs had never flown a Boeing, they would possibly not know about the requirement to re-trim the rudder to facilitate manual flying in ALT Law.

Lyman, I'm referring to the position on the artificial horizon from 0, not the cruise pitch angle. We've gone through this a dozen times or more, but the autopilot did not induce the climb. There was a nose-up trend before the PF took manual control, but it was gradual, minimal and entirely consistent either with the autopilot regaining cruise pitch, or the aircraft attempting to regain cruise pitch via the trim setting.

The abnormal pitch angles that followed were entirely a result of manual sidestick inputs made by the PF.

Gums, our Francophone colleagues have asserted that "crazy" in this sense refers to high speed, not low speed. The PF talks about a sense or feeling of "crazy speed", and he does not refer to the instruments.

Rudderrudderrat - interesting. However I think turbulence had to have been involved even if the rudder trim was slightly off, because there was a pitch component to it. I know that yaw inputs tend to bring the nose down, but not 3.5 degrees off where it was supposed to be, surely? The estimated side slip trace looks to be in excess of what could be expected if the rudder was out of trim in calm air, no?

nor a free-faller ! Kiss
At 02:11:50 Vz=15000 Ft/mn = 148 KTS ; CAS=50 KTS

conclusion is easy :
SPEED VECTOR INTENSITY = (148² + 50²)^.5 = 156 KTS ;)

HOW MUCH IS THE STALL SPEED ?!?!

STALL is a problem of AoA, and never a problem of SPEED !

Giraud did fly to speed near of zero in the airflow without to stall...:ok:

Sorry ! That is "unloading the wing", balistic flight, that all combat pilots know. :rolleyes:

Hi DozyWannabe,

On reflection, I think the side slip trace has some error - I can't see why it would peak at -10 so regularly. So ignoring that:

If you look at Aileron Displacement, before AP disconnect the pattern is symmetrical and seems to include all 4 ailerons.

After AP disconnect, the trace only shows the inner ailerons were active. The deflections show far more LH Inner Aileron around> -10 ( = Left inner UP). It indicates that the aircraft had a continuous desire to roll right, counteracted by a more frequent roll Left command.

The tendency to roll could have been solved with rudder trim.

Thank you Roul and Rat.

I was not looking carefully at the yaw trace on the recorder.

@ Roul

The technique of "unloading" is maybe foreign to many of the "heavy" pilots. No problem. And my reading of the existing procedures of many airline jets at the time emphasized minimum loss of altitude. Funny, but if you get those wings producing lift quickly, you'll lose less altitude. Worry about the gee limits later when recovering from the lower pitch attitude.

That being said, pilots must realize that you are either approaching a stall or actually in one. Looks to this old dinosaur that the 'bus has excellent yaw stability ( or great dampers) and decent roll characteristics even when the wing is completely stalled. So it comes down to the continued nose up command on AF447. Didn't see drastic roll angles or yaw excursions on the traces. You can pull all you want, but all you'll get is the gee commanded position of the elevators and the THS following to help trim.

What's funny to me was that the primitive FBW system I flew actually moved the stabilizers for nose down when we got to our AoA limit, regardless of our gee command. Gee, imagine using AoA sensors regardless of CAS once weight-on-wheels flipped once airborne.

@Doze

Maybe the overspeed control was what the dude was thinking due to the unusual noise from a fully stalled wing. Dunno.

@rudderrudderrat

Looking at it again, you're right - the estimated sideslip trace shows evidence of partial data recovery, which is not in itself surprising.

The aileron traces are as you say - but prior to autopilot disconnection they are spiky, indicating regular correction. There's no consistency until after autopilot disconnect, when aileron input, which is manual, trends to the left. This does not necessarily prove a right roll condition, however it does show that the PF *believed* he was correcting a tendency to roll right. But because there is no point at which manual input is not being made post-disconnect, it is impossible to say whether that tendency was consistent, or whether it was transitory.

I'm going to need some input from the better-versed here. I know that upon autopilot disconnect, pitch trim remains in auto in Alternate Law. I know that rudder function reverts to a hard-limited yaw-damper mode in Alternate Law. What I need to know is what happens with rudder trim upon autopilot disconnect in Alternate Law - does it hold the last setting prior to disconnect, or does it return to neutral?

Hi DozyWannabe,
It holds the last setting.

OK - next question. Is that behaviour covered in type conversion training? Is there a "CHECK RUDDER TRIM" in the autopilot disconnect procedure?

NB. While this is an interesting line of inquiry, it doesn't explain the magnitude of the roll inputs made by the PF to my mind, or their apparent aggressive reversals. The mantra for manual control on the FBW Airbus is more-or-less "observe and correct and observe and correct". The DFDR traces show a lot of attempted correction, but no significant period of observation.

Dozy, just personal opinion, but she must have been out of trim in yaw.

It kept wanting to turn right and did a 270 turn to the right in increments on its way down. A swept wing bird at high AOA is very sensitive to rudder input. Very insensitive or even contrary to aileron input.

Why out of trim in yaw? Probably a rigging issue. How often does someone actually check this on a flight-probably never, or almost never.

@Machinbird - If you substitute "must" with "may", I'd be happier about getting on board (if only to not rule anything out). If the rudder was out of trim, then you'd see consistent corrections in the traces prior to A/P disconnect - there aren't any as far as I can see.

The consistency, magnitude and frequency of manual inputs post-disconnect occlude any reasonable conclusion as to what the aircraft would have done if left to it's own devices. If the PF was correcting a constant roll to the right, why the sudden reversals of bank input to the sidestick? Surely a gradual and consistent left bank input would have been enough prior to stall - after which, as you say, ailerons become ineffective.

If the yaw damper function requires an airspeed input to properly set the gain, it may have ceased functioning. This would likely put the BYDU on the line (but I think I remember information that the BYDU was not activated). In any case, the yaw damping function is not identical between Normal law and Alternate law (Yaw Alt). I know that we have discussed this a number of times in some detail, but I no longer remember the details. Getting forgetful in my old age I guess.:O:}


Dozy, remember the roll PIO theory? If he had come in gently on the controls, we probably would not be reading about this accident. Instead (probably through inexperience in this flight regime) he came in with ~ 2/3 of full left roll displacement and it took over half a minute before he got the wings settled down. In the meantime, the pitch went to unsustainable levels.

Since Giraud has been mentioned:
Something perhaps similar to Giraud's Mont Blanc technique, was taught and used at the French National Gliding Centre at Montaigne Noire, close to Revel, some miles to the east of Toulouse in 1950. This involved landing to the south, up a steep slope and with a tail wind. One aimed to stop near the top so that a short winch launch could be used so a further flight could be made, after turning the glider round and into the wind. Most flights were done taking off and landing along the ridge, to east or west.

@ Machinbird, DozyWannabe;

This Rudder / Yaw Damper problem has been raised in the past. I have been looking carefully at the DFDR traces post stall and find that the heading is changing at a fairly constant rate (clockwise) when the SS is held over to the left for a reasonable period of time. This lead me to looking at the Inner Aileron traces, and I believe that the RH Inner Aileron when down was effectively creating drag, whereas the LH Inner Aileron when up was in the wake vortex and ineffectual. This drag on the right was causing yaw, and the the Rudder/Yaw Damper didn't exactly help, though in the same vein, the Rudder Trim was offset 0.4 degrees to the left which may have helped create the right wing down bias.

Well, MM43, how about "adverse yaw"? Could have been a player.

When Doze tried the sim he used rudder to correct roll, not aileron. Using aileron at extreme AoA will definitely cause the nose to move the opposite way you are used to at low AoA. Retired will tell you that in the Phantom, guys would lock the stick between their legs and use rudder for roll when at high AoA. The A-7 was not as bad, but we used the same technique.

Of course, using rudder trim could have helped, if not cured, the constant turn we see in the traces.

Let's face it. The crew was not prepared to fly the beast outside the envelope they were trained to do. Maybe a cosmic test pilot would have seem what was happening and done real fine, but the crew was not trained for that, nor probably had no experience in high performance jets that routinely flew at the limits or even exceeded them. So I'll cut them a small amount of slack in that regard.

Gentlemen, you are discussing the dynamics of aeroplane falling with low speed and extreme, never-before-achieved AoA for the type, using assumptions valid for normal, unstalled, flight. Your theories might be correct... by pure chance.

Why should they be prepared to fly the beast outside the envelope? Key issue is how the aeroplane got out of the envelope in the first place.

Maybe there are not test pilots but rather ordinary line jocks out there who would keep on flying reasonable pitch+power when faced with unreliable airspeed. Does anyone know any other case of loss of all IAS on A330?

Yup. If only we had some other case of A330 losing all airspeeds for comparison. If only...

As Gums has implied, the Vertical Stabilizer coupled with the Rudder is the only airfoil capable of behaving with any degree of reliability at such an extreme AoA when dropping like a stone with limited IAS.

So when outside the known envelope, some g-estimates are inevitable, and further study of the DFDR gives evidence that some of the roll component is being driven by the Yaw Damper, i.e. the YD is leading the roll by between 1 and 2 seconds.

Clandestino;

Yes, your post is noted, and the input of those with experience in military types may actually be of value in understanding the aerodynamics:eek: experienced by this unlucky A330. http://images.ibsrv.net/ibsrv/res/sr...lies/wink2.gif

Turbulence is not always random and perhaps its effects should not be dismissed so easily. The 'bump' around 02:10 lasted about 10 seconds, as shown below.

P.S. The derivation of the formula for vertical gust velocity can be read here .

http://i.imgur.com/zQ21c.gif?1

i`m no pilot,nor an engineer or pc expert.and english is no my native language as you will easy notice.
and excuse if i am too much OT.
there is sometong i`ve been wondering about from the first time i have read the cvr as everybody has done it a few times:

PNF: you`re going up !

PF: i`m going up ?

how comes that he did not expect the a/c to go up when pulling the stick backwards ?
better said,what was he intending when pulling back
he seemed surprised and not expecting to go up

answers ?

P.s. my only "experience" is, i`ve read about all NSTB and britisch acc.inv.reports from 1950 -2011

Hi,

There are several similar dialogues ... here is another just little time before the end CVR
2 h 14 min 05 4,024 The pitch attitude is 14°.

As I already pointed out several times .. these are very strange dialogues
And they only add lanes and deadlocks in the maze leading to the discovery of what happened to those pilots that night

I was referring to the theory being put forward by Machinbird that this *particular* A330 was poorly-rigged. I don't see it myself, but on the other hand, don't want to appear dismissive of possibilities just because I don't happen to agree with them**.

[** - Unless they're *really* stupid and/or offensive... :E ]

Been there done that versus training
 

Thanks for nice words, mm43.

Only reason I joined the discussion was my interest in any FBW system that had a crash or unusual flight condition.

Once the wreckage layout became available, my first impression was a fairly level impact at relatively slow speed. The Viper deep stall came instantly to mind. But I soon found out that the 'bus did not have the area of negative pitch moment coefficient that we had. Back to what happened. I then figured that the jet was very stable in yaw and roll at extreme AoA. So why hold the sucker there? Why not either let go or push forward a bit and see what happens? Never happened.

My point is that we folks here ( 'bird, Smilin', Retired and I) have seen the phenomena and are here to talk about it. And to contribute to an understanding of how many swept-wing jets behave at "abnormal" AoA, and some possible recovery techniques. Our second input has to do with recognition of the jet's actual flight condition.

The AF447 crew did not recognize their condition. Period. Whether they figured the system would prevent a stall or provide warnings (which it seemed to do), was prolly due to their training and experience at "normal" flight conditions.

I certainly do not advocate the same training that we had in our actual jet, but seems the carriers could get the crews up in a trainer such as NASA used for the Shuttle and let them see what it feels like ( jump on that comment Doze and Cland and...), and then what to do.

respectfully submitted

@linktrained

Vous êtes un connaisseur !

Giraud did not officialy nor not officially teached low-g flying. But among his many many glaciers and mountain pilot-pupils, some copied his complex way of doing, without really understand wath he was doing. I only discovered that in 1999, and discussed with him about that : He looked around him if nobody could listen what he was saying, and told me about 3th "regime"...

Great great ART of Monsieur GIRAUD !:D:D:D

Jump on it? In an ideal world I'd be 100% behind it!

I think more realistically (on cost grounds), putting line crew back in a Cessna to revise the basics immediately after hiring, and thence one every couple of years would be a good start. The bean counters would probably have an aneurysm going even that far, and some experienced pilots may even balk at the idea, finding it demeaning.

However - the status quo at the moment is that even fresh recruits may not have actually practiced recovery from a real stall since they got their PPL - which can be months or years before they're put into the right-hand seat of an airliner, and then training becomes all about mastering the systems of these wonderfully complicated beasts (I'm not just talking about Airbus FBW types here), and practicing rote drills using those systems to avoid trouble.

This is fine to some extent, because there's no doubt that automation and modern systems have by and large improved safety. What bothers me is that because basic flying skills are rarely revised once an ATPL is granted, the piloting "instinct" seems to suffer. In the case of AF447, at no point did the crew do the basic calculation:

I would hope that most pilots with an understanding of the principles of flight should be able to perform that calculation, but the truth is that these skills need to be exercised fairly regularly to stay current in the ol' grey matter - and the longer you do a job without needing that information the more likely the knowledge will disappear further into the recesses of long-term memory if not forgotten altogether.

Take my job as a software engineer - we have these wonderful tools and languages these days that abstract away all the nitty-gritty of understanding how these machines work underneath, and except for very specialised parts of the industry, the basics of understanding low-level code and the principles of a von Neumann machine are never used, because all the business is interested in is the speed of delivery and quality of the final product. The tools turn out final code that's *almost* as good as properly hand-optimised assembler, and because machines are so fast these days "almost as good" is usually more than enough. But on the rare occasion that it isn't, you can find yourself galloping up Diarrhoea Drive without a saddle as you try to remember all that stuff about memory pointers and opcode cycles. This has only happened to me once, but from then on once or twice a year I fire up a C64 or Amiga emulator and make myself do some rudimentary assembler just so it's relatively fresh in my head - and the first time I did I was genuinely aghast at how much I'd forgotten.

All this, and at no time was I in danger of injuring anything more than my pride. Airline pilots are risking considerably more than that, even if it's unlikely they'll draw the short straw.

When the PF made that remark his PFD was on ADR3 and had no airspeed display. Shortly after that the angle of attack 2 was temporarily valid at 41°, and the stall warning was triggered. That means that ADR2 speed was temporarily greater than 60 kts. His PFD on ADR3 indicated temporarily also above 60 kts. The actual speed was then about 140 kts CAS.

http://i1081.photobucket.com/albums/...setresults.jpg

MM43,

Sorry, I have to disagree with you on fin and rudder remaining effective at high AoA. In fact the increased sweep coming from the geometric sweep plus the AoA means that the fin and rudder lift curve slopes fall sharply as AoA get large - see Fig9 on the figure. OK, this is obviously a Boeing design, but fifty plus years in aerodynamics tells me that the A330 isn't going to be a mile different. So although the yaw damper was working the rudder pretty hard, I doubt it was really driving anything since at 40 deg AoA it was down to about 1/3 power.

In addition, when a swept wing aircraft gets to that sort of AoA the lateral behaviour changes from a classic dutch roll to something more like a simple roll oscillation. This isn't sudden, and (of course:D) the A330 at 30~40 deg AoA lies in the transition zone. But a feature of this change is that the relative phasing of yaw rate and roll rate alters, so it is impossible to say that the yaw damper is driving roll - it is more likely to be lagging it considerably.

Clandestino;

You are right to express caution on using classical unstalled equations to explain AF447 behaviour when stalled, but there are other theories that may throw some light on it - but treat with care! - and they will only give an indication of what might be happening.

Amongst other things there is a little matter of asymmetric shedding of vortices off the forward fuselage at high AoA (see picture), and this can be time variant, so it is a brave man who says he can explain what is happening (or one with a lot more data and computing power than I possess)

I think what mm43 was saying was that rudder is *more* effective than aileron in the stall regime, which is undoubtedly true. Obviously at extreme AoA this effectiveness will decrease - possibly rapidly.

That graphic you've posted (thanks by the way - very illuminating) shows that rudder effectiveness on that design approaches 0 at around 60deg AoA. AF447 maxed out in the 40s. Fig. 9 suggests that rudder remains significantly effective at that point.

Giraud
 

Roulishollandais #228

Hi,

Thank you for your praise - I wish that it was deserved. At Montaigne Noire this technique was taught and practiced without MY understanding, I think - but that was 62 years ago. I was to make my longest duration flight without FOUR engines whilst there. (I had seen the eight engined 100 Passenger "Trans Atlantic" Bristol Brabazon at Farnborough in 1949. Things have changed !)

Hopefully no pilot will get into a situation like this again. Losing airspeed at FL350 should not put you into a 14 degree nose up attitude because the overspeed was sounding putting you into a full fatal stall. All airliners have UAS charts to set power and attitude to deal with that. I am sure AF did too. I am sure they do now.

To clarify, no airliner at FL350 can go over 2 degrees nose up at cruise power without stalling. What they did was way out of the envelope. We need to hire pilots that can fly and not just button pushers that can't handle a simple autopilot disconnect.

Two degrees nose up?
 

@Bubbers

C'mon, two friggin' degrees nose up or you fall outta the sky? BEAM ME UP!

A nice, slow pull without violating the control law AoA limits or gee limits can be done, then a gentle nose down should not be a big deal. The situation you describe reminds me of a U-2.

If the 'bus or any other airliner design requires that much attention and skill, then we're outta luck as SLF.

Sorry to be harsh, but I think the 'bus design and other jets have a lot more tolerance in attitude and such.

Not 2 degrees but 14 degrees nose up at FL350 doesn't work at FL 350. Anything much over 2 degrees will catch up with you rapidly and put you in a stall at that altitude. These two managed to do it in less than a minute with their maneuver. I think they really screwed up. Competent pilots don't do that.

Thanks for the graphics (think HN39 posted a link to them some time back) and your explanation.

Not being an aerodynamics expert by any stretch of the imagination, I had concluded that the lateral/transverse stability of the aircraft at such a high AoA and low IAS was balanced on a knife edge, and even with the reduced efficiency of the rudder it would still be possible to induce a roll moment. You doubt that that was the case, but as I stated in my earlier post, the DFDR data is pointing toward it doing just that.

To emphasize what I am getting at, I have blown up part of the Roll trace and and superimposed the Rudder trace on top of it. In addition, an expanded (replotted) 30 second section is shown where (if the traces have been synchronized by the BEA) the rudder is constantly leading the roll and not the other way.
http://oi47.tinypic.com/2wncs20.jpg
I'm still puzzling over the constant yaw to the right and its cause. Were the ailerons responsible, asymmetric drag, or a side-slip component? Though the more I look at it, I have come to realize that the PF had one hell of a fight on his hands just keeping the wings level, though through mostly of his own doing.

http://i1081.photobucket.com/albums/...onlaterals.jpg

Dozy
Since the aileron effectiveness is just about zero in fully stalled conditions this has got to be true.;)
But I didn't mean to say that the rudder was completely useless, just that it was operating at about 30% effectiveness relative to normal conditions.
Incidentally, I forgot to mention that the effectiveness is further reduced by the fin being swept by the low energy wing wake at some AoAs

MM43
Yes, I see where you are coming from and understand how you might have come to that conclusion; but I am coming, quite literally, from the opposite angle.:)

When you put an aircraft up at those sort of AoAs funny things start to happen to the lateral behaviour, of which perhaps the most important is that you develop a direct kinematic interchange between roll and sideslip - bottom left in the graphic. When this really gets going the dutch roll disappears and is replaced by an oscillation which depends on roll-sideslip-rolling moment due to sideslip- roll - sideslip. This oscillation really doesn't involve any significant yaw motion. The top right picture in the graphic is the nearest I can find to an A330 situation - the relevant CL would be in the range 1.2~1.4.

I don't think that AF447 got fully into this state, but if you look closely at the estimated sideslip trace then when it is not saturated the peaks in sideslip coincide timewise with the peaks in bank angle, so there is an element of this phenomenon present I think.

Again, if you look at the rudder traces you see that in the timeframe you cite there was no rudder pedal movement worth a damn and that all the rudder movement was commanded by the yaw damper. Philosophically, the yaw damper is a follower and shouldn't be driving the motion unless the system designers really fouled up and produced an unstable system (which they did not).

More practically, the yaw damper is just what it is called - it applies rudder proportional to rate of yaw, so in this case if you are thinking about the relationship between rudder angle and bank angle you really need to consider the relationship between bank and rate of yaw.

In a conventional dutch roll the rate of roll lags the rate of yaw by about 160deg, so that bank angle will lag rate of yaw (or yaw damper input) by 250 deg. When you get into the roll oscillation mode this may increase a little.

I don't want to sound dogmatic about this because we really don't know where the A330 might sit in the spectrum of possibilities, but it seems to me that the observed relationship between rudder angle and roll could be a big lag rather than a small lead (which would anyway imply some sort of system malfunction).

So in the time interval you quote I see an aircraft with saturated, but ineffective, roll control operating without any effective pilot contributions so that the response is something like the 'natural' one, which in this case is a very lightly damped oscillation more or less confined to roll/sideslip variations. Experience with other aircraft suggests that although the roll oscillation is lightly damped, it won't go unstable.

So far as the drift to the right is concerned I share your puzzlement. It looks like some sort of out of trim coupled with slightly negative spiral stability and if you digitise the estimated sideslip trace ignoring the obvious saturation errors you see an intriguing drift from zero to about -1 deg (left slip) over about 3 minutes. At the same time the rudder trim trace shows a constant 0.5 deg right turn deflection which is at least consistent.

So it is possible that there was a standing out of trim which was being held by the A/P, but whether the numbers stack up I just wouldn't know.

It didn't. It went to 60 - 70 but became NCD above 40.