In large transport aircraft, do we ever encounter the situation where we are unable to maintain a given, low airspeed while banked and turning, because we "run out of elevator travel" (elevator is fully deflected upwards) even though the wing is nowhere near the stall angle-of-attack? Meaning that for a given bank angle, the amount of elevator travel is limiting how slowly we can fly in a steady-state turn, and for a given (low) airspeed, the amount of elevator travel is limiting the steepest bank angle in which we can maintain a steady-state turn?
In more detail:
A) Does this ever actually happen with large transport aircraft?
B) Would it ever happen at any bank angle corresponding to a steady-state turn that is within the allowable G-loading envelope of the aircraft, even if that bank angle is steeper than would normally (or ever) be used in actual practice?
(The question is not intended to be limited to turns where enough thrust is available to maintain altitude. The question is not intended to encompass situations where a computer is limiting the elevator travel to a smaller value than would be available in other flight conditions. The question is not intended to address aircraft being flown outside of their prescribed C.G. envelopes. The question is about steady-state (except for altitude) turning performance, and is not intended to address how quickly any given aircraft can enter a turn.)
In turning flight, the "relative wind" actually curves to follow the path of the turn, at least in any case where the aircraft's rotation rate about each of the three axes is constant (and therefore is appropriately matched to the turn rate.) This is a consequence of the fact that the aircraft as a whole has an instantaneous rotational velocity as well as an instantaneous linear velocity, so at any given instant, a point at the nose of the aircraft is moving through the airmass in a different direction than a point at the tail of the aircraft. Similarly, the outboard wingtip is moving through the airmass faster than the inboard wingtip.
While turning, if the aircraft's tail surfaces are positioned exactly the same as they would be in wings-level flight at the same angle-of-attack, the curving relative wind will tend to "push up" on the tail, tending to make the tail's angle-of-attack more positive or less negative. The end result will be that the aircraft will tend to pitch down to place the wing at a lower angle-of-attack. So for a given position of the elevator (or all-moving stabilizer), the angle-of-attack of the wing is somewhat lower in turning flight than when the wings are level.
(This effect can also be described as "aerodynamic damping" in the pitch axis.)
The magnitude of this effect can range from negligible to very significant. It is most pronounced when the turn radius is not vastly (several orders of magnitude) longer than the length of the fuselage. Therefore it tends to be most pronounced in slow-flying aircraft, such as sailplanes and ultralights. It is very pronounced in radio-controlled model sailplanes. In all of these aircraft, in a steeply-banked turn at low airspeed, it is common for the control stick to be so far aft that the same control stick position would produce a full-blown stall in wings-level flight.
In some full-scale sailplanes where the upward travel of the elevator has been intentionally limited by the designer to help prevent stalls and spins (e.g. Slingsby Swallow), heavy pilots (flying with a CG near the forward end of the allowable envelope) find that while attempting to circle at the angle-of-attack that would give the minimum sink rate for a given medium to steep bank angle, they "run out of stick travel"-- the elevator hits the full-up stop. As a consequence, they are forced to either accept a lower, less-optimal angle-of-attack (and higher airspeed), or to reduce the bank angle. Either approach increases the turn radius.
The present question is asking A) if anything like this ever happens with large transport aircraft. Also, B) if it ever would happen at any bank angle corresponding to a steady-state turn that is within the allowable G-loading envelope of the aircraft, even if that bank angle is steeper than would normally (or ever) be used in actual practice.
Related ASE answers that also address the curvature in the relative wind in turning flight: