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Since the two axes of a two-axis autopilot are pitch and roll, when the autopilot executes a turn, is it uncoordinated since the autopilot is not controlling the rudder (yaw)?

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  • $\begingroup$ In larger aircraft, the autopilot is usually still 2-axis, but the yaw axis is controlled by separate yaw damper that is simply trying to keep the ball centered (approximately; the control logic is slightly more complex). It's main purpose is to damp the Dutch roll, but as a side-effect it also coordinates turns. Since it is separate, it can be used even when hand-flying. $\endgroup$ – Jan Hudec Apr 24 '17 at 18:34
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Absent other control factors, potentially. It is up to the pilot to maintain coordination with the rudder. However, autopilot turns typically happen at cruise speeds and at gentle bank angles, so the ball won’t get terribly far outside its cage. Even for airplanes with aileron-rudder linkage designed to automatically compensate for adverse yaw, Jan Hudec enumerates other contributors such as P-factor that add slip or skid in a turn.

That’s just for a single-axis autopilot. Your question asks about dual-axis autopilots that have another dimension in which to go “uncoordinated,” viz. pitching up too steeply for the current power setting and causing an aerodynamic stall or pitching down so as to exceed $V_{NO}$, $V_{NE}$, $V_{FE}$, etc.

Being outside sweet spot of the flight envelope is a significant factor behind why many POHs and checklists call for the autopilot to be disengaged below certain altitudes and in critical phases of flight. Cockpit automation when properly understood, used, and monitored is great for reducing pilot workload, but no mechanism should be treated as fool-proof.

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