At what altitude could Air France 447 no longer recover from it’s stall, even if the pilots put the nose down - 5,000 feet? 7,000?
The no-kidding limit case answer depends on a lot of unknown factors. Such as what was their forward & vertical speed, were the engines still running, are we assuming the instruments suddenly started working and the pilots became unconfused Chuck Yeagers, or would this be a tentative effort by confused scared folks in the dark guessing at their true aircraft state?
WAGing heroically, I’d say from 20,000 Chuck would have no trouble recovering. From 15,000 it gets sporty. At 10,000 its probably 50/50 even for Saint Chuck.
The problem is they were in a very deep stall. in that circumstance you need to get the nose pointed almost straight down to get the airplane aligned with it’s direction of motion. Anything less and you’re not unstalled yet.
Once unstalled you have to pull out of the near-90 degree dive. But given that jetliners have very low G limits, that implies a vey large turn radius. And managing airspeed will be tough. At first you’ll be too slow to pull max Gs. But real quickly you’ll be too fast to pull min turn radius. And may get going fast enough to break the jet or have other control problems.
10,000 feet sounds like a lot of altitude. But turning 90 degrees in 2 miles sounds like a high G turn for airliner G capability and airliner flying speeds.
Hint: In fighters our rules were that if you were out of control, always eject no later than passing 10,000 feet above the ground. The odds on recovering control decline so quickly as you get below that altitude that the smart money was to write off the jet & save the pilot(s). And that was in jets with full aerobatic capability, huge powerful control surfaces, lots of G capability, etc.
Conversely, we routinely get close to stalling the simulator at high altitude, say mid 30 thousands of feet. The term of art is “approach to stall” training. We do it every few months.
If we react promptly to the stall warnings and apply max power & judiciously lower the nose, we normally lose 4-6,000 feet building back to a normal speed. And nothing real scary happens unless there was another jet beneath you. But in this case we never actually stalled; we just got real slow and got close-ish to stalling.
Doing the same thing at low altitude results in negligible altitude loss since the engines are so much more powerful down low. We can pretty much just power out of a low airspeed situation at low altitudes.
As a reaction to AF447 and other recent accidents, there is a move afoot in the industry to do much more complete full stall & loss of control training. The problem is the simulators can’t replicate either the logical aircraft behavior (i.e. drive the instruments and visual accurately), nor come anywhere close to replicating the physical sensations (G forces, angle rates, buffeting, etc.)
And training in actual large aircraft is stupid dangerous, whereas training in light aerobatic aircraft may be so dissimilar as to represent negative training.
A lot of debate and effort is ongoing and the industry should see results in a couple more years.
Fantastic answers, thanks.
I thought AF447 was not in a deep stall, though, but rather, a shallow, very-recoverable stall that persisted only because the first officer kept pulling back on the stick? Maybe I’m wrong.
F=v^2/r
v=600mph = 880ft/sec (rough guess)
r=10,000 let’s say. You’d be skimming the waves on the pull-out
F=(880)^2/10,000 = 77.44 ft/sec^2 = 2.42 G’s
Plus gravity. I assume an airliner could survive 3.5G but I doubt it’s a recommended procedure. Plus, that assumes the thing does not exceed the 600mph as it continues on the downward arc. that is also assuming we’re swinging a weight on a string. An airliner just slicing through air probably has to include some drop or slippage, unless it actually generates enough lift to keep 3.5 times normal weight on track.
Plus the time required to get the nose down, assuming they could…
Lots of detailed info in this Popular Mechanics article.
Yes, they functioned properly throughout. Reasonably early in the event the pilots went to TOGA (take off / go around) power - basically max available power.
Because they had substantial engine thrust, the plane’s descent wasn’t close to vertical - it was actually around 40 degrees from horizontal.
And only a small relaxation in the stick-held-fully-aft problem would have led to controlled flight. This actually happened around 2 minutes into the problem, when the junior pilot let his stick go forward a bit, and airspeed increased from 93 to 223 kts. But he then pulled the stick fully aft again, where it stayed for the rest of the flight.
This near-recovery to me suggests that had the pilots become aware of what was happening and put the stick forward, recovery would have been possible even from a fairly low altitude. The airspeed increase mentioned above (which was due only to a relaxation in back-stick position, not a vigorous forward movement) took just 21 seconds. The plane was descending at around 10,000 fpm, which argues that 3500’ would have been sufficient (perhaps less, given that the rate of descent would have slowed during a recovery maneuver).
ISTR that airliner wings (at least some of them) were designed to take 4 g’s, but with fly-by-wire, it’s questionable whether the plane will actually let you do that to it.
600MPH is a bit excessive. I assumed 200 MPH; together with a 2.42-g pullout (plus 1 g of gravity, so 3.42-g wing loading), that gives a turn radius of 1120 feet, much more comfortable. This is of course after you have gotten the aircraft pitching downhill and achieved the required 200 MPH. If you assume they go to 30 degrees downward pitch, and full thrust, then they’re getting maybe ~.25 g’s of forward acceleration with the engines, and 0.5 g’s of forward acceleration due to gravity. With that kind of accelertion, to get the forward speed from 50 MPH up to 200 MPH it would take just 7 seconds. Average speed along the 30-degree-descent flight path during that time would be 125 MPH, so average vertical speed would be 63 MPH. For a duration of 7 seconds, that means they’d only lose about 650 feet of altitude before they could begin cranking back on the yoke. So from the moment they achieve a nose-down attitude to the moment they restore level, controlled flight, they might need as little as 1770 feet of altitude. This assumes the aircraft is capable of 2.42 g’s at just 200 MPH. Not sure about that.
Also, all of this is after having gotten the aircraft from a deep stall into a steep nose-down attitude. Not clear how long that transition would take, as they probably didn’t have much pitch authority when they were in deep stall. Speaking of which, yes, they were in deep stall:
So the time/altitude required to achieve a nose-down attitude is a bit murky. Wikipedia claims they had a vertical speed of 124 mph (108 kts); if we SWAG that it takes ten seconds to get the nose pointed down, then they lose about 1819 feet of altitude during this time.
So it seems like a bare minimum, skimming-the-waves recovery might be possible with just 3600 feet of altitude, depending on assumptions:
-is 3.42 g’s of wing loading allowed by the FBW system?
-is 3.42 g’s of wing loading even possible at 200 MPH airspeed?
-how long does it take to get from 40 degrees nose-up to 30 degrees nose down with double-digit forward airspeed?
200 mph is ~ approach speed. The jet will very quickly accelerate through that, really quickly. I’d expect it to be on the barbers pole if not faster during the pull, so 330 knots indicated air speed, plus about 50 knots because the higher your altitude the greater the difference between true air speed and indicated air speed. 440 mph would be close to the mark IMO.
So where exactly is the treadmill in this scenario?
From the PM article, it looks like the relaxation of the stick early on would have kept them from entering the stall; once they were in the stall and flying like a set of car keys, I wonder where they were in the flight envelope so they could regain speed and get above Vs (especially with 10K fpm rate of descent). My experience is all propellers, but in my world, power on stall speed is pretty low and harder to recover from than a power off stall.
I have never read much about the details of the accident that came out after the data recorders were recovered & read out. So it’s interesting for me to finally see the facts about AOA, airspeed, & flight path angle.
Taking the various details as others give above as true, and putting the pieces together we see a flight path angle of more or less -40, and a similar AOA, implying a more or less level flight attitude. And engines running which gives us full thrust, plus normal electrical & hydraulic power.
Given that, the turn radius required is just a few thousand feet. And paradoxically, the lower they are, the smaller the turn radius would be.
As to structural G limits, 2.5 is the certification limit. Which means the main structure has to be able to do 115% of that without permanently bending and 150% of that without breaking. That does NOT mean the entire aircraft must be totally undamaged at 150% of 2.5G = 3.75G. Having minor parts, which can include engines, break off somewhere above 2.5G and below 3.75G is totally acceptable. I think you can see how something like that *might *complicate the rest of the recovery
The next thing to consider is the concept called “radial G”. That’s the fact that we’re always maneuvering in a 1G gravity field courtesy of the Earth. That fact was ignored in md2000’s radius calculations which are otherwise completely valid Physics 101.
Imagine doing a loop: During the over-the-top part, gravity is pulling the same direction as the aircraft pitch rate is trying to go. So if the aircraft “feels”, say, 3G acceleration, the actual turn radius is equivalent to 4G due to gravity helping. Conversely, if the aircraft is at the bottom of the loop and “feels” the same 3G of acceleration, the actual flight path is only getting 2G worth of turning; 1G of felt acceleration is going just to offset gravity.
In the case of recovering from a post-stall dive, radial G is not your friend. In that situation cos(dive angle) times 1G is wasted offsetting gravity. So if in fact you can only pull 2.5G, you’ve only got on the order of 2 to 1.5G available to turn the aircraft. You’ll have more useful G available when diving steeply and less once more-or-less level again.
The next complication is something called “corner velocity.” It’s not technically a velocity, it’s a speed, but somehow that term got stuck in the lexicon.
At low speeds an aircraft will stall before it can pull the structural maximum G force. The maximum AOA before stall results in less than structural limiting G forces. In fact the traditional concept of “stall speed” in straight and level flight is exactly when you’re so slow that you can’t pull the 1G necessary to offset Earth’s gravity and maintain level flight.
Conversely, at high speed you can pull structural maximum Gs and not stall; the AOA needed to do so remains below the stall AOA.
Putting these two endpoints together, there is an intermediate speed which results in the minimum possible turn radius. It’s the speed where at just-below-stall AOA you’re at just-below-max structural G forces. If you fly any slower, your turn radius is larger because you can’t pull as much G before stalling. And if you fly any faster, your turn radius is larger because you’re pulling all the G you can without breaking the airplane.
Applying corner velocity to our post-stall dive recovery means we can’t assume they can pull max Gs the whole time. At first when they’re slow they’ll be AOA-limited and will have much less G available. As they accelerate due to both thrust and being pointed steeply downhill, G available and therefore turn radius will improve until they pass through corner velocity. Unless they can stop the speed increase at that point their turn radius will begin to increase and will continue increasing as they go faster & faster.
Finally, putting radial G and corner velocity together, we see that as they get closer to level and faster, both those factors work together to increase turn radius. The upside is that at shallower descent angles their rate of altitude loss is also decreased at cos(descent angle).
Naturally, managing radial G and speed versus corner velocity is the fundamental foundation of air combat maneuvering and of show aerobatics. These things aren’t normally considered in routine airliner (or lightplane or bizjet) flying, but they’re fully applicable. And awareness of this knowledge and the corresponding approach to flying is at the core of the debate about training professional pilots for edge-of-the-envelope and loss-of-control scenarios.
Another factor is how accurately the crew can pull max Gs either above or below corner velocity. We have no G meters, nor AOA gauges. It’s been 25+ years since I pulled serious Gs. My butt used to know the difference between 2 and 4 and 6Gs. Even back then feeling the difference between 2.4 and 2.8 was pretty fuzzy. AFAIK none of the guys on AF447 had any high G experience ever. Knowing the penalty for excess Gs is the airplane comes apart, most pilots will approach those limits pretty timidly.
This is one area where the Airbus has, arguably, an advantage over Boeings. Once un-stalled, and assuming their instruments and computers wee working right, which they emphatically were NOT on AF447, then simply pulling full aft stick and trying to minimize airspeed gain above corner produces a near optimal recovery with little danger of breaking the jet.
I fly Boeings. In contrast to Airbus, even given a perfectly healthy airplane I can rip the wings off any time I want with injudicious control inputs. Or deeply stall it & keep it there. Thereby precluding recovery.
So overall on this War and Peace-sized post, we see 3 obstacles to calculating or performing an optimal minimum altitude recovery: Radial G, corner velocity, and the pilots’ difficulty in making optimal control inputs given incomplete or misleading instrumentation.
IMO …
What ultimately killed those guys, and all their passengers, was a malfunctioning airplane coupled with Airbus’s training which drills into the pilots the idea that the airplane never malfunctions is such a way that full aft stick isn’t the best possible recovery for any upright loss of control event. So the one pilot tunnel-visioned on what had been drilled into him: max thrust, max aft sick, and HAL will save you.
Which works absolutely perfectly, and much better than it does in Boeings. Unless HAL has gone stupid. Which he had in their case.
My bottom line on the accident: they all died because the pilot didn’t break out of “trust the computer” mode into “this is, at base, still a real aircraft with real aircraft behaviors”. And Airbus training does their damndest to ensure pilots NEVER think the way those guys needed to to save themselves.
Thanks for LSLGuy’s high-quality answers.
It beats me that the AF447 pilots didn’t see the high AOA on the artificial horizon indicator, the plummeting altitude, and put two and two together and say, “high AOA, losing altitude, this is a stall.”
Plus, of course, the blaring stall warning alarm.
LSLGuy hits another out of the park.
Plus the easiest and most concise way to understand corner velocity I’ve ever seen.
At 30,000, 20,000 and 15,000 feet how long would you have to recover before you past irrecoverable altitude.
There is no AOA indication on the artificial horizon. What they could see is they were more or less level but with zero airspeed and an insane rate of descent. And warnings that the airspeed indication was inaccurate somehow.
Because the instruments were malfunctioning, the stall warning was also malfunctioning. When they pulled back, the stall warning signals stopped. When they pushed forwards, the stall warning lights & horns started. The exact opposite of their correct behavior.
At night, in the clouds, having just transitioned from total routine boredom to “holy shit, we’re in deep kimchee!!”, the sum of all this was more than they could handle in the time available.
Whether it was more than they *should *have been able to handle is not a topic I’m going to entertain. There but for the grace …
Thanks for the thorough explanations and opinion, LSLGuy.
Curious, what did you fly in the military?
The whole thing started with an iced-up pitot tube, but that resolved itself after about a minute, at which point all instrumentation was behaving as designed by the engineers. The problem was that they ended up in a situation with extremely low forward airspeed (and a high AoA) so that the computer decided “this cannot possibly be real,” and so it silenced the stall warning horn. When the pilot pushed forward on the stick, the AoA decreased enough to where the computer decided “OK, now it’s a real stall,” and turned on the stall warning horn. This confused the crap out of the pilots, who then released the stick (at which point the system was only receiving the input from Bonin’s pulled-back stick, so resumed the plane’s high-alpha orientation). Between Bonin’s stick-back shenanigans and the plane’s turn-on-the-stall-horn-when-the-plane pitches-down, they had no idea WTF was going on.
Thanks, LSLGuy!
My late father in law was an Airbus flight instructor (last working in 2009). He arranged for me to “fly” the A320 simulator, and another time the A340. Man, what amazing video games! I successfully flew the 320 under the Golden Gate Bridge. At least, my altitude would have cleared us under the span. But the visual simulation had a glitch. No matter how low the altitude, even right into crashing in the water, you were always looking “down” onto the bridge deck.
He complained frequently that today’s generation of pilots relied too heavily on their fly-by-wire computerized controls and they had lost all “feeling” (his word) for their aircraft. He would tell me about various exercises he was required to put crews through, and their inability to “get it” despite being marvelously adept at manipulation of the actual technology. When confronted with some novel failure mode, the crew would run through check lists and seek a by-the-book solution. Sometimes the search was fruitless (he liked posing problems that weren’t covered in the pro forma) and the search might go on for an extended period, during which complications would ensue. He’d say “I want to scream at them GODDAMNIT, just FLY THE FUCKING AIRPLANE!”
He never mentioned an Airbus edict along those lines. I assumed it was indicative of today’s pilots coming up in the digital age of sims and computer games. But perhaps corporate philosophy reinforced that. He’s gone now, where I can’t ask him.
I think this is a trifle harsh (though fundamentally on target). As MachineElf notes, the iced-up pitot problem cleared itself soon, after which the plane performed as designed. And the pilots had at least nominally been trained that when control shifts from “standard law” to “alternate law” - the announcement of which was clearly audible - the scheme of “hold stick fully aft” is no longer appropriate.
But I think there can be no doubt you’re correct that Airbus promotes the “trust your airplane” attitude to the point where it can strongly contribute to this sort of problem. And I seriously question a cockpit design that doesn’t make one pilot’s control inputs evident to the other.
The single thing that most amazes me about this crash is that the senior Captain, summoned to the flight deck where it was obvious that a serious problem was underway and clearly not being solved by the two pilots at the controls, would not have taken the place of one of them and tried to do better - you’d think at least he’d want the voice recorder to show that he “went down fighting”. Had he done so, it would likely have been Bonin that he replaced, which would have immediately solved the “stick held fully aft” problem.
It’s a sobering thought that if the three pilots had decided to get up and walk off the flight deck, the plane would have been fine.
Flying level, what is the lowest altitude a passenger aircraft is allowed to fly at?
Playing chicken with a T-6. (NB: Page cluttered with cheesecake of girls in bathing suits; sorry.)