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Mr Optimistic
Is there any circumstance were pushing the nose down can initiate or exacerbate a stall ? You want to point the nose into the wind, more or less so the wing can start working "proper" again. If the wind isn't coming from below it soon will be, assuming you are flying the right way up. Nose down a bit should give you more horizontal velocity too, Going faster horizontally should send the AoA in the right direction. These guys needed a horizontal velocity of over 1000mph if they were going to get out of the stall by "outrunning" it, so to speak, As it was, they had the engines on idle, I believe. |
auraflyer
with the net effect of making the correct input appear to be the wrong one. The guys made a tentative nose down to get out of a stall, got blasted by a warning, and thereafter tried to get out of a dive, |
The Flight Global article and David Learmont blog contain spin, is not factual Perhaps you're trying to inject your own "spin" with your accusation, for which you appear to provide no evidence. |
If the stall warning was perceived as real, you would expect the nose down input to be sustained but with some puzzlement (to be solved later) as to what delayed the warning. If the warning was considered spurious then there is still no reason to pull back on receipt of the warning because it is, erm, spurious. I can't imagine a train of thought which would cause a pull back on receipt of the warning, purely because of the warning.
On the subject of the intial climb, really can't progress without the CVR can we ? If the tape in the early part of the incident happens to record something along the lines of ' I am going to try and get out of this icing' or ' jeez, have you seen the height, how did that happen' the mystery of what was intended evaporates. Mind you, that sort of clarity may also be the reason the CVR hasn't been reported in full at this stage. |
AoA rules!!! Not speed
Thanks for the link Franz, it should help more here to consider stall recovery and recognition and corrective actions.
The first graphic in the file shows the curve for a typical straight wing, large camber wing. Swept wings generally have a lower slope and an extended curve at the top of the curve. So as Franz, 'bird, Smilin' Ed and I have seen, you can fly around up at the top of the curve when you need to, but you have to be very careful!!! Besides, the plane is usually buffeting/shaking like crazy - it's telling you it doesn't like it there, duuuh????? As PJ has noted, the mach buffet and overspeed have a different "feel" than a no-kidding aerodynamic stall. Personal opinion, but I suspect the 'bus is very tolerant of mach overspeed until maybe 0.9M or so. So get the nose down and worry about mach later. Observation: The displays I have seen for the 'bus show a small AoA indication on the left scale. Is that correct? My preference would be a larger range and not worry about the "low" end, but the "high" end. Comments? Edited: the main Pprune forum has this excellent link concerning stalls. I wonder if the AF447 story prompts this... Hmmmm. http://www.ukfsc.co.uk/files/Safety Briefings _ Presentations/Airbus Safety First Mag -January 2011.pdf |
Mr Optimistic
If the stall warning was perceived as real, you would expect the nose down input to be sustained but with some puzzlement (to be solved later) as to what delayed the warning. If the warning was considered spurious then there is still no reason to pull back on receipt of the warning because it is, erm, spurious. I can't imagine a train of thought which would cause a pull back on receipt of the warning, purely because of the warning. In the info released so far there is no mention of what the PF did after that stall warning caused by his nose down inputs. It's just surmise that he stopped nose down inputs at that point. The released statement is obviously a highly selected set of the whole data. I would imagine selected in order to prepare us for a conclusion, which those in the know have already come to. After all, with the voice recorder available, and precise timings of inputs, it may be obvious that the resumed stall warning had a direct reponse from the PF - or not as the case may be. I guess with all the data you could come to a conclusion in the time it takes to listen the the voice recorder. |
Jazz Hands - apart from all the other problems, you can be assured that spatial disorientation was a major part of this accident. The initial pitch up would have been misconstrued by a stressed and distracted pilot handflying in IMC/Storm as both acceleration and pitch down ( somatogravic via decelleration), with the persistence of pitch up commands the likley result in the absence a contribution from instrument scan.
Not knowing which raw data to trust, of which the attitude indicator and the altidude indicator were I presume the most trustworthy, and which stall warning to trust, must have been horrifying.. A best guess approach on known cruise setting perhaps with a very gentle descent.. |
@ t54
Isn't it rather a DOWNWARD wind that would explain pitch = aoa at horizontal flight they had at FL380? Should be about 10 kts for 185 kts airspeed and 3 deg chord angle. Could the down draft also explain the compensating NU sidestick pilot's input, which in turn sent them (without alpha protections and reliable airspeed info) to FL380 with loss of airspeed and finally to a stall?
Quote: t54 its pitch attitude and angle of attack being 16 degrees its geometrie: in still air if the flightpath = chord angle (mayby + 3 deg....) than pitch attitude= AoA You could only get pitch = AoA in horizontal flight if there is an upward wind. Maybe there was and that's what helped to get the plane up there in the first place. |
antpp
Isn't it rather a DOWNWARD wind that would explain pitch = aoa at horizontal flight they had at FL380? |
HN39,
The wording of the FCOM suggests that there is no stall warning in normal law. Alternate law is a low-probability failure condition in which an airplane is not required to meet all requirements that apply normally. While there may be a logical answer I am still wondering about why activation of the stall alarm does not simultaneously prevent further auto-trim induced nose up THS move as does AoA protection activation in normal law? |
Gums, what does Issue 5 have to say on unreliable airspeed ?
|
And the cosine of 61 degrees is 0.4848, so the longitudinal component of 151 kt is 73 knots? I may not see exactly what you’re getting at. If I look at the triangle I think you’re referring to, i.e. aircraft longitudinal axis and FPA and I close it vertically, I get a near equilateral triangle, not a right triangle, so the cosine function of 61 degrees is N/A? If you close it either of two ways to make a right triangle, I’m not sure what that other side represents? For a constant given inertial FPA (in this case -45), with vertical speed along the vertical axis & groundspeed along the horizontal axis, as you increase any postulated headwind component, for a given constant pitch attitude (in this case +16), it has the effect of lowering the existing aero AOA (higher KTAS & consequently higher KCAS for the conditions) while the inertial AOA (in this case 61 degrees, 16+45) remains the same. I think… |
MM43, in re final data:
My browser doesn't always display graphics. Now that the pix display, it is quite clear. Thanks to both you and tailspin. :) OK: roger. |
Airbus Flight Safety mag
Sorry, Opto, but I can't access the directory for past issues. I had to save the file and then upload it to my personal domain so's all here could read, learn, think, theorize, et al
Maybe a 'bus driver here can help, as the magazine has a wealth of data from real folks and not the press or BEA. |
Control Law Mapping Etc
It seems to me that the confusion (here anyway) about the various control
laws could be made a lot easier to dispell if there was a chart showing the rules and input conditions under which each are transitioned to and from. A nice big A3 sheet perhaps, as a picture is always worth more than dry text. To put it another way, to transition from one law to another depends on a variety of input data, logical, boolean and variable. A boolean variable might be something like the ap or ath dropping out (ie: on or off), while a variable might be airspeed, aoa or similar. A logical function being and / or / sum of 2 or more inputs to generate an output. Apologies if this seems a bit abstract, but the transition between the various laws does seem to be key to understanding what happened to af447. From what's been discussed here, it seems to me that the control law logic is not smart enough by half. As someone else said, it looks rule based, when what's really needed is a more fuzzy, or semi ai approach that takes into account history and trends, as well as all the variables to arrive at a conclusion. It then presents this to the pilot as a best effort scenario of where it's going before handing control back. More of a big picture view, rather than the fine granularity of individual system failure alarms. Even with partial system failure, there should still be enough data and history to get an idea of where it's all going. Would guess that there is some of this already, but it does seem to give up just at the point where it most needs to be providing a bit more intelligent reasoning. Before anyone gets excited about the idea of yet more automation, such a system would provide only information, not direct control of the aircraft... |
Chart of Laws
Sounds like a good project for you, SYSENG.
I for one can't understand why there are more than two Laws: Normal and Direct. With more than two Laws available, I also don't understand why the roll automation and protections were given up when the bad data was in the pitch channel. |
Mr. Optimistic
Is there any circumstance were pushing the nose down can initiate or exacerbate a stall ? Result was a very stable inverted spin and a not so beautiful ejection. He had been taught to forcibly "unload" the wing in training.:* For airline flying, the lesson is that you need to be carefull about nose down inputs as well. At very low speed (like AF447), if you generated a high nose down pitch rate, you could go right on through flying angles of attack to inverted stall angles of attack. Suppose they had run the trim full down on AF447 and generated a strong pitch rate nose down. The pitch rate momentum of the aircraft could have easily taken them on through into an inverted stall. By the time you are feeling yourself get light in the seat, it can be too late to stop the pitch rate.:ooh: That is why jets need AOA indicators. So they know where they are in their AOA envelope. |
Control law mapping
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Airspeed
There appears to be some differences as to the definition of airspeed. As far as I know, it's the speed in the direction that the airplane is going because that's what determines lift. By that definition, it's the diagonal of the ground speed and rate of descent vector triangle that I posted before, which is 152 knots. Note that the actual angle of attack and airspeed is dependent on the surface wind speed and direction relative to the airplane's heading. Also, the aircraft airspeed measurement system will not be able to accurately convey this speed to the pilots due to the very high angle of attack involved. Not that it matters, post stall.
Airspeed is not the the relative speed along the horizontal unless the airplane is in level flight (that's ground speed after correction for the wind aloft) or the relative speed along the axis of the body (I don't know what would be called but the hard-core aero guys probably have a phrase for it) unless the airplane angle of attack is zero or thereabouts, depending on the angle of attack reference versus the wing incidence on the fuselage. In other words, if the airplane was in level flight with a 16-degree nose-up pitch and there was no wind aloft, the air speed would be equal to ground speed, not reduced by the body angle relative to the horizon. http://img.photobucket.com/albums/v3...roundSpeed.jpg |
HN 39:
I should have used the term near "isosceles" rather than near "equilateral" earlier. (45, 61, 74) TST: AIR speed parameters (KTAS, KCAS) are sensed by the aircraft onboard systems. You are correct that the aircraft has a trig calculated speed of 151 knots. Your making the assumption that all 151 knots of actual speed would be sensed by the on board systems at a 61 degree AOA. Maybe you're right, I don't know, but the other possibility is that at that AOA (61 degrees) there is some disturbed airflow across the pitot. The pitots are roughly longitudinal. Most "normal" large aircraft flight conditions are flown with the pitots quite a bit less than 60 degrees from the relative airflow. |
Here's another example of wind effect on AOA at a given FPA for HN 39 & TST.
You're flying an ILS in no wind. You've established the proper pitch attitude and power setting at the proper IAS (resulting in the proper AOA) to maintain a 3 degree FPA (Glide slope) on the facility fixed beam which is independent of wind. A headwind component develops. You have two options to maintain an absolute 3 degree FPA. Option #1. You can increase power and pitch attitude while maintaining the same IAS (& same aero AOA, but increased inertial AOA by the amount of the pitch increase) resulting in a lower descent rate at the lower Gnd Spd to maintain the 3 degree FPA. This is what is normally done. or Option #2. You can hold pitch attitude constant and increase IAS with thrust (& consequently TAS & Gnd Spd) which decreases the effective aero AOA, keeping the inertial AOA constant, while maintaining the 3 degree FPA. Thrust level sets a rate of 'potential energy' decay which takes you from altitude XXXX to the runway surface at a constant 'kinetic energy' level in a controlled set of conditions. Kinetic energy is then reduced on the runway by thrust reversing, brakes, drag chute, arresting gear, etc. Just the reverse holds in a tailwind conceptually. (BTW TST, what's getting sensed CAS-wise at 60 AOA may put the sensed TAS somewhere between 89 & 151 knots, I don't know) |
Lets go back to the start for a minute
While there is a lot of conjecture as to what happened when (and the releases so far don't clear much of it up), it seems nobody is disputing that the airspeed sensors shut down (for whatever reason, and for now everybody is saying it was icing, so I will assume for a moment that is correct). While everybody is focusing on the eventual stall, the "for the want of a nail" event was the loss of airspeed data.
The loss of airspeed information is a big deal, especially in this aircraft. I'm asking myself what was this aircraft doing in a situation where the loss of airspeed was not uncommon? Coming from my experience with aircraft certification, I don’t believe that the reliability of those pitot tubes would have been considered acceptable in the initial certification if they were presented to the type board. The requisite reliability of sensors such as these is 99.99%. The net result is that you can have failures due to old age and part wearing out, but that high reliability requirement limits failures to random events (one sensor at a time, something the control can cope with). The demonstrated reliability of the pitot sensors was much lower than that, and when Airbus realized that it was they should have not just issued a recommendation, but should have had EASA issue an AD for the replacement of the parts, as well as require flight restrictions on the aircraft until the AD was carried out. The was a high probability of multiple sensor failures in these conditions and the impact on pilot workload makes this action, in my mind mandatory. To put it another way, if Airbus went before the type board and said “these sensors are 99.99% reliable, except when they are flown into known icing at high altitude, in which case they are 95% reliable, and OBTW, when one fails you generally get multiple failures”, the type board (when they stopped laughing) would have said “fine, you can fly the airplane, but you aren’t going to fly it at high altitude into conditions where you could get that kind of icing”. If the reliability of the sensors, under specific conditions, falls below the certification standard then the certificate holder has a responsibility to notify the certification authority and issue an AD with a restriction on the flight envelope until the reliability issue is addressed. Hard to believe that Airbus would leave themselves open to this kind of potential liability by not making sure an AD was issued as opposed to the "recommendation" that went out to replace the sensors. |
engine-eer
From another engineer... I thought the basic problem with the pitots was that the certification specs themselves are totally obsolete. |
AIR speed parameters (KTAS, KCAS) are sensed by the aircraft onboard systems. You are correct that the aircraft has a trig calculated speed of 151 knots. Your making the assumption that all 151 knots of actual speed would be sensed by the on board systems at a 61 degree AOA. Maybe you're right, I don't know, but the other possibility is that at that AOA (61 degrees) there is some disturbed airflow across the pitot. The pitots are roughly longitudinal. Most "normal" large aircraft flight conditions are flown with the pitots quite a bit less than 60 degrees from the relative airflow. |
Originally Posted by syseng68k
(Post 6493191)
Before anyone gets excited about the idea of yet more automation, such a system would provide only information, not direct control of the
aircraft... We had experienced such a problem with some medicine doctors and the "expert system" (say) supporting diagnostics - they eventually did not want to write down their diagnoses until they got the systems' ones. |
gums;
As PJ has noted, the mach buffet and overspeed have a different "feel" than a no-kidding aerodynamic stall. After my simulator work last year I wanted to understand how accurate the simulator reproduced the actual stall behaviour. I discussed the matter informally with those who would know, and the comments I received are echoed in the Wainwright papers cited by PerkyPerkins, (the other reason I thought these two papers were important reading, the first being the handling of trim in the stall). Essentially, for reasons now made clear I am led to believe that Level D simulators DO NOT replicate flight and aircraft handling characteristics at, and beyond the boundaries of controlled flight. Therefore my comments on the nature of the A330 at/in the stall regarding buffet and similarities/differences with Mach buffet, would not, I think, apply. Personal opinion, but I suspect the 'bus is very tolerant of mach overspeed until maybe 0.9M or so. So get the nose down and worry about mach later. |
Hope I haven't got this wrong but as the stall warner was working, then if you believed it, wouldn't you just keep reducing pitch until it silenced ?
|
Lest we forget.
ChristiaanJ said......
"...engine-eer From another engineer... I thought the basic problem with the pitots was that the certification specs themselves are totally obsolete..." *********************************************************** I think that is a red Herring, and it puts one in mind of the "As yet and heretofore "unknown characteristics of FUEL in icing at extremely low temps." BA038 was surrounded by such "informed opinion" and the TRENT was modified by addressing its "Insufficiencies in thermal performance" rather than some exhaustive research into "dangerous" fuel. Here, the same artifact of "Tacit" acceptance of what amounts to absolute bs. The weakness of the Thales install was legend, as was (is) shortcomings in powerplants, avionics, etc. For my money, I remember that the USAF has operated large subsonic a/c with swept wings at FL500 and above for more than fifty years. They heated their fuel, and if pitots were killing pilots....... bear is also a cynic. I believe in an honest regulator, and an authority that not only does not give the players the "benefit of the doubt", but carries a small chip in the Public's interest, though they may walk with a "slight limp". All in all, after thousands of pages of comment, the pitots were known junk, and the pilots acted to burn down the "status quo" (:D). AF changed out the junk, and what remains is for even an average attorney to make even a weak case. Air Travel IS safe, so safe I am incensed that weak kneed and less than honest folk chip away at it. end rant. |
OK465;
RE yr post #1341: The diagram in post 1172 implicitly assumes still air and standard temperature. The effect of wind is not shown. There is a line drawn at the pitch angle of 16 degrees to illustrate that AoA=pitch + flight path gradient = 61 degrees. Agreed. The length of the line represents 86 knots, and I assume that 89 is a typo which doesn't bother me. My problem is that I don't understand the significance of that speed.
Originally Posted by Tailspin Turtle
...it is almost certain, not just a possibility, that the indicated airspeed was something different than the actual airspeed because of the angle of attack involved.
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Protections
I am glad that we got a good input from PJ on the high speed phenomena.
I would take my chances any day about going too fast versus stalling in a large plane. I am not sure if the 'bus has the "nose down" problem that one plane I flew had. If you got too fast ( beyond critical mach), that sucker was hard to get nose up until you could slow down ( speed brakes/spoilers/reduced throttle). Go read about the P-38 in that regard. I did fly a subsonic design that handled the mach very well, with no pronounced buffet or pitch problems - the A-7D. Nevertheless, at or near the mach the thing was very hard to get any "up" vector without slowing down. I saw about 50 knots over the placard limit one day, and my first clue was I couldn't get a lotta nose up movement pulling off the dive. Glanced at the IAS gauge and I was about 700 knots IAS with a placard limit of 650 IAS or so. Had plenty of altitude and the thing slowed down, pitch control came back and no big deal. It was my first mission over Hanoi in Dec 1972 and I had left the throttle at max while rolling in ( cut me some slack for being a bit hyper at that moment). Didn't make that mistake again, heh heh. The same applied to the F-86, which also has a subsonic wing ( camber and such a lot different than the "diamond" camber configuration for supersonic jets). As with the SLUF, it could pass the mach and not suffer much due to the all-moving stabilizers/elevators. As the Airbus safety pub states, AoA is paramount, and worry about pitch, altitude and speed later. GET OUTTA THE STALL, you dumb a$$, then worry about speed later. And this applies even on short final. Better to hit with more horizontal than vertical vector - a "skip hit". The first Airbus crash shows this. One thing some folks here must realize is that the planes fly in a different coordinate system than one related to the ground. It's the airmass, which is not usually static with respect to the ground. It's called wind, duh? Some are quibbling about the actual velocities at impact. I submit that at 10 feet above the water, that indicated and true airspeed were within a hundreth of a knot. Same for inertial velocities. The really good thing about the HUD I flew with from 1971 to 1984 was it showed me the actual flight path vector with respect to the ground, and not the airmass. I'll try to get my LEF failure landing digitized and you can see its value. |
Mr Optimistic
Hope I haven't got this wrong but as the stall warner was working, then if you believed it, wouldn't you just keep reducing pitch until it silenced ? More likely you'd stick to standard procedures. |
All in all, after thousands of pages of comment, the pitots were known junk, and the pilots acted to burn down the "status quo" (:D). AF changed out the junk, and what remains is for even an average attorney to make even a weak case. Air Travel IS safe, so safe I am incensed that weak kneed and less than honest folk chip away at it. |
Pointing the nose down when you are falling at 123mph requires a certain amount of confidence and the certainty that that is the right thing to do. More likely you'd stick to standard procedures. With AF447, what seems wrong to me is, as I read it, the automatics quit when they reached their limits of trim and control, and quit leaving all the control surfaces at their program-permitted-extreems. It just handed the ship back to the pilots with all control surfaces in maximum and unknown & unexpected configuration. The automatics should have been programmed to return all controls to neutral, trims to zero etc, before quitting. At least leave the pilots with an average aero-dynamic brick, rather than a brick with random control surfaces. |
Need more balance in discussion
Engineers?
I am not questioning the current airworthiness, I understand the issue has been addressed. I don't think that the system was airworthy at the time. What I am saying is, if they were known to be junk Airbus had an obligation to have an AD issued to insure they were changed out and they didn't do it until after this crash. Like all systems, even with those with redundancy, it is necessary to assume failure conditions. So the pitots fall off due to birds hitting them or clogged up in volcanic ash or even ice up because the heating system fails. There should be a presumption of some sort of backup to fly the plane to the nearest airport. From my read this presumption was met The problem with assumed failure rates is the limited verification that they are valid to within a 10 power magnitude. This comes about by both certification standards as well as historical experience under wide ranging conditions. I can't yet find fault with the design assumptions in this instalation. The certification was valid as well based on what was known at the time. But there is a problem to be further explored. Once the actual failure rate becomes obvious in the historical useage of the system (they iced up more often than expected) then the system interaction with the ability to continue safe flight and landing needs to be examined. From my read so far, that includes the crew actions and their failure rate (to take appropriate action). I really don;t know how this was taken into account (presumably it was at least considered). If the crew failure rate combined with the pitot failure rate was taken into account then supposedly the risk should have been minimized to a reasonable level. Somewhere in all this is where the corrective action should have been taking place. I don't see how you can fault Airbus for not mandating a balance between all the contributors since all they can do is recommend a course of action based on their own knowledge. Anything the operator does in the use of the product is outside of their ability to control. I think it's best to let the BEA investigation identify the critical paths and develop recommendations accordingly. |
TOGA actions by the system?
I am having trouble finding all the things the plane does if the pilot moves the throttles to the 'TOGA" position. There may be another switch/button, but only one I can find is the throttle position.
Could use a list of all the things the jet does in "TOGA" mode, and I fully understand that "TOGA" is not an autopilot function ( well, think I do). |
Ref PickyPerkins at 1307:
So now we have training to possibly ignore stall warnings on cruise, possible training to pitch up and apply more thrust to abort the impending stall, a possibly massively out of trim aircraft as a result of the pitch up, and training that specifically eliminates reference to the trim wheels. This was at the demands of the airlines. This does not precisely match events in this situation. But it explains important parts of it. (And I hope AF decides to add the RHS to its FDR records. I'm thinking that RHS and LHS did not see the same thing at all. Is this possible? I thought the units were supposed to talk to each other and vote. When this all finally visits a courtroom it does not look at all good at this moment, to me, for Air France. It certainly is not the pilot's fault if he follows his training, perhaps a little too well. It will be interesting to see of appropriate parties pick up on Perky's message and notice similarities between actions apparently taken and the training issues discussed. |
Originally Posted by TiiberiusKirk
(Post 6493586)
With AF447, what seems wrong to me is, as I read it, the automatics quit when they reached their limits of trim and control, and quit leaving all the control surfaces at their program-permitted-extreems. It just handed the ship back to the pilots with all control surfaces in maximum and unknown & unexpected configuration.
Where exactly did you read that the automatics quit when they reached their limits of trim and control ??? They quit right at the beginning of the sequence due to unreliable Airspeed Readings (possibly/probably due to icing).. The trim limit was reached much later after continuous Sidestick Nose Up inpuit by the PF. |
Re gums message 1326:
The whole URL includes the space "Safety" and "Briefings" and others: "http://www.ukfsc.co.uk/files/Safety%20Briefings%20_%20Presentations/Airbus%20Safety%20First%20Mag%20-January%202011.pdf" If it works you can click on this to get it. (I hope.) |
lomapaseo
If the crew failure rate combined with the pitot failure rate was taken into account then supposedly the risk should have been minimized to a reasonable level. Somewhere in all this is where the corrective action should have been taking place. Rgds. |
Better Timeline (FDR format)
FDR formatted chart based on timeline I posted 60 odd pages ago.
Notes: Times are approximate Gray indicates graduated values Chart starts immediately after A/P and A/T disconnect @ 02:10:05 Ends @ 02:12:05 with 2 minutes of data per BEA Transcript Prior: 01:35:15 Radio:TO ATLANTICO - @ INTOL 01:35:46 Radio:FROM ATLANTICO - Maintain FL350...eta TASIL? 01:55:xx Captain awakens #2 co-pilot 01:59:32-02:01:46 Turbulence & WX Briefing 02:06:04 PF notifies CC turbulence ahead 02:08:07 PNF "Go left a little" 02:10:05 A/P and A/T disconnect Transcript post-chart: 75 Seconds elapsed: ================================================= 02:12:17 (approx from BEA) PF commanded pitch down AOA decreased Stall warning (upon valid speed inputs-BEA) ================================================= 56 Seconds elapsed: ================================================= 02:13:32 PF "...arrive at level 100" (10,000ft) 02:13:47 (approx from BEA) Both sidesticks recieved "inputs" AOA "when valid" remained above 35 degrees ================================================= 02:14:28 End of recording V/S -10,912fpm GS 107kts Pitch 16.2 degrees nose-up Roll angle 5.3 degrees L |
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