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After answering this question it got me wondering whether there can be a situation where a complete flameout of engines could cause a serious loss of control if the auto-pilot were to continue to try to maintain altitude despite the loss of power. If it did, presumably by raising the nose and losing air-speed, eventually the aircraft would enter a stall.

Which raises the question, does the auto-pilot automatically shut off in the event of engine failure? Though I suppose it depends on the auto-pilot and the aircraft model.

I do realize the pilot and co-pilot should be very aware something is awry, but I can also see them being rather busy trying to figure out what all the alarms are telling them, and or trying to restart the engines and not notice the AP is setting them up for disaster.

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    $\begingroup$ I am not entirely certain whether an autopilot disconnect would be required under all circumstances, as it probably depends on the mode that the autopilot is in, anyway. It is, however, definitely an issue if the autoflight system tries to achieve flight parameters that are outside the performance capabilities of the aircraft. Airbus unfortunately has lost an A330 during flight test in exactly that way, see en.m.wikipedia.org/wiki/Airbus_Industrie_Flight_129. $\endgroup$ – Cpt Reynolds Jan 4 '18 at 0:22
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    $\begingroup$ Not always, see China Airlines Flight 006 $\endgroup$ – Steve Kuo Jan 4 '18 at 0:42
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    $\begingroup$ I'm assuming you are asking about commercial aircraft? The answer is likely "no", at least it doesn't fully disengage. For example an engine failure may disengage the auto-throttle system, but roll control remains enabled. This is the nature of multi-mode autopilots where the modes can be independent. The altitude hold system may not disengage until the trim goes out of limits, so it is a secondary effect of an engine failure, but I don't think an engine failure would affect anything directly other than auto-throttle. $\endgroup$ – Ron Beyer Jan 4 '18 at 1:30
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No, there is no necessary connection between the autopilot and an engine failing on any aircraft that I'm aware of -- which is far from all of them! If you're in an idle descent, one motor failing wouldn't really change the flight characteristics of the aircraft, so in that case there's no great need to get rid of the autopilot. Also, once you have everything trimmed up (i.e. rudder trim in to balance the asymmetric thrust), it's nice to put the autopilot on to let it keep the wings level & hold altitude for you while the pilots sort out everything that comes next -- checklists, ATC coordination, choosing where you'll land, etc.

What DOES come off almost immediately after engine failure, at least on the 737, is the Autothrottle. It will sense that the thrust and throttle position are mismatched, and rather than moving the good throttle around when you may not be ready to compensate with the rudder, it disengages. I'm not certain if that is universally true; the 777 computers are crazy smart, and they may actually leave the A/T engaged in that sort of a scenario (while the A/P flies the rudder for you).

The basic challenge that you mention, an autopilot that will hold altitude even when the thrust is insufficient to maintain airspeed, is a scenario that's not limited to an engine failure. The automation will have some set of rules as far as when to hold, when to go into reversion modes, and so forth. And if you get caught in the wrong spot, the automation can bite you. In the 737, for instance, if you're in altitude hold or glideslope capture, the autopilot will hold that no matter how badly the speed decays. (Stall while on glide path, or follow the speed cursor into the dirt short of the runway... damned if you do, damned if you don't!) On the other hand, if you're in a vertical speed mode or a VNAV climb or descent, there are speed reversions that will change your flightpath rather than accepting a speed above or below safe limits. If everything has been set up correctly and the Autothrottle is engaged (or the pilot is setting the power appropriately), then everything works really well. But if enough things go wrong and you aren't paying attention... well, that's when bad things can happen.

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I can't find a link to an article from the 90s, but there was an article where a Bonanza pilot died in flight (due to health issues), his plane came smoothly down in a field somewhere due to the autopilot keeping the wings level after it ran out of gas.

So as long as the plane has electric power, many autopilots will function when the engine stops.

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    $\begingroup$ If you do figure out which flight that was (there should be an investigation report, if you're willing to do some digging), you might consider adding it to the Beechcraft Bonanza Notable flights section on Wikipedia. It certainly sounds to me like it'd qualify. Neither that section nor the "Accidents and incidents" section lists anything at all from any year in the 1990s. $\endgroup$ – a CVn Mar 30 '18 at 20:17
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On most modern aircraft thrust asymmetry is compensated by the FBW irrespective of the autopilot in the following phases: takeoff(obviously since A/P is not engaged), climb, cruise, and descent; in these phases one active autopilot is managing the vertical and the lateral path, and it will keep engaged.

Another situation occurs in land mode where in most modern aircrafts we have triple redundancy(Boeing has 3 APFD computers, Airbus has 2 doubled computers), and the active computers(left and right in Boeing case)will manage the rudder too. Normally in land mode every AP computer has its own power supply, that is they are electrically totally separated, if the engine failure occurs while the APU is off, the A/P mode could get degraded because of lack of separate power supply but will not disconnect, however if the APU is running, the electrical reconfiguration will prevent the degraded mode.

With respect to old generation aircraft like the B737, I can’t answer.

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