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Does the AP (autopilot) essentially detect a rapid change in speed/altitude as a wild maneuver? If so, upon disengaging, if the pilots are not holding the control column in a neutral position, will it move in whatever direction the plane is going?

For example, a steep climb that wasn’t anticipated, and no one holding the Column, will it fall back towards the pilots, ultimately making the steep climb worse?

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    $\begingroup$ Are you asking about a particular aircraft, reversible or FBW aircraft? The answers will differ. $\endgroup$ – JZYL Nov 28 '19 at 11:42
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For non FVW airplanes:

Yes it will disengage if certain pitch and roll attitudes are exceeded. When it disengages, the controls are "let go" if the A/P was applying an input at the time, and the control column will move to whatever its natural trimmed state is at that time if the elevator is manually operated with trim tabs.

If the airplane has irreversible hydraulic controls and an artificial feel system and a trimmable stabilizer, the column will just spring back to neutral and the airplane will seek its existing trimmed speed. If the trim speed is the same as the current speed, pretty much nothing happens, if the trim speed is much different that trim speed, the nose will pitch up or down to try to accelerate or decelerate to the trim speed set by the current state of the pitch trim system.

It's as if your copilot was flying, minding his own business, and you shot him dead. The column will just go to wherever it wants to go when no-one is holding it. The airplane has natural static "stick-free" stability so it will seek its natural trimmed state and if the A/P input was different from that, it'll just start going where it trim state wants it. As if you pulled on the column and then let go.

On an airplane with control cables, the autopilot is a little computer running a bidirectional electric winch (the A/P servo) back in the tail who's winch cables are tied into the elevator cable run. It drives the cable circuit from back there instead of from the column. The autopilot also usually works the pitch trim that same way a human pilot would, to relieve the need for the servo to hold control pressures beyond a small threshold same way a human would.

So if the airplane was more or less in trim when the A/P kicks off, not much happens. If the airplane was in some crazy attitude because of some outside event, the A/P kicking off is like you were flying and got flipped over and you took your hands off the controls to cover your face in fright (that's what I would do lol). The controls will just return to where they are trimmed to go to in that state. On most airliners with powered controls and a moveable stab, the column always springs back to the same neutral position regardless of trim state.

If the a/c is FBW, the A/P is integrated into the computers that actually run things and it gets a lot more complex, although the end results are not that much different.

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    $\begingroup$ Poor Co-Pilot :( $\endgroup$ – Peter Nov 28 '19 at 20:47
  • $\begingroup$ From what I have learned in university and my personal experience as a glider pilot, airplanes are not roll stable. They will fall into a turn at some point and not continue straight forever. The time period for that is really long, could be minutes before the bank angle exceeds 5 degrees if the aircraft is trimmed correctly and flying straight and level. A tiny aileron correction is all that is needed and therefore it is accepted as being unstable but easily controllable.But if you're already at 30 degrees of bank things get worse quickly $\endgroup$ – Jan Nov 30 '19 at 20:50
  • $\begingroup$ Well sort of are, within a range. Gliders on the other hand are designed to be more or less roll neutral, so it tends to hold whatever bank angle you set, for easy thermalling. I've been flying a SZD-51 Junior this summer and it is wonderfully roll neutral. But yes most airplanes are roll stable within a narrow range and if upset beyond that they will naturally start to spiral, a function of sideslip + weathervaning tendency. So in reasonably smooth air an airplane like a 172 will carry on by itself for quite a while until something upsets it enough to overpower its roll stability. $\endgroup$ – John K Nov 30 '19 at 21:34
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It's hard to provide a specific answer because a lot of important context is missing from your question, but here goes.

In a conventional airplane, with any manner of control system, when the stick is released from a held position where there is deflection of the control surfaces, the stick should return to centre.

In salt-of-the-earth cable driven control systems, the act of pushing the stick in any direction causes control surfaces to move up into the airstream. The drag that this produces creates resistance, a weight that is felt in the stick. When you let go, the stick will spring back due to this resistance, and probably over centre into the opposite side and cause an oscillation, but that will dampen out and the stick will rest neutrally.

This self-aligning force can be felt when you're driving a car at relatively high speed. Imagine you're on the highway and to follow the road, you need to make a gentle

Even in systems where there are not direct connections between the stick and the surfaces, engineers add artificial means to produce this feedback. For example, in some fighter jets the stick has an extension under the floor which has a deadweight attached to it, which the pilot has to pull against to hold the airplane at a certain level of G-loading when turning.

This self-aligning force is very important to how the aircraft feels in the hand. It can also be felt when you're driving a car at relatively high speed. Imagine you're on the highway and to follow the road, you need to make a gentle curve. Then imagine you turn the wheel and it's as light as a feather.. it would be very difficult to find and hold the precise input required to produce the required turn.

In your scenario, when the airplane is climbing and the stick is released, it may fall backwards a little bit initially, but it will not accelerate like a dropped object straight to maximum deflection because the airplane itself is resisting the force gravity as it's applying itself to the stick. it will find a neutral point just aft of centre stick

None of this means to say that the airplane will climb or descend, or even maintain the same angle of bank. You haven't defined enough variables in this scenario (Airspeed, pitch angle, power setting, trim setting, engine type) to tell us what might happen next.

I will leave the autopilot part of the question to somebody who's even remotely qualified to talk about that.

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