Several questions on the Aviation SE site have dealt with the question: can the rudder alone turn the aircraft:
- This one, which was marked a duplicate of
- this one, which was itself marked as a duplicate of
- this question, with a skilful and detailed answer.
So we know in triplicate that the rudder alone can turn an aircraft. Not very comfortably due to the side forces, wrong way lean, different airspeeds on inside & outside wing etc, that is why the normal way to turn is to bank.
However, the following has been posted in the comments (partial quotes only due to length):
Yaw does not cause aircraft turn. It only causes yaw. Yaw is not turn.
Lift, pointed in a direction other than perpendicular to the horizon, is what creates turn. Nothing else.
With no other yaw force on the aircraft, if you have right rudder, that does create a leftwards force, but it also creates a right yaw (sideslip) which itself creates a rightwards force that opposes the leftwards force from the rudder.
It works in exactly the same way as it does in pitch. The elevator pulls the tail down and, because it's behind the CG, creates a nose up pitching moment (torque). Lift on the wings lifts the aircraft up, and because it's also (generally) behind the CG it produces a Nose down pitching moment. Because the moment arm of the elevator is so much longer the torques balance, but the Up force from wings is much larger than the down force from the elevator and the aircraft is able to fly. The force from the rudder, and the force from the sideslip angle of the fuselage act in the same way.
The nose of the aircraft does not "turn" away from the "direction the pilot ... " it only "yaws" away, and it only yaws away until the sideslip angle reaches the point where equilibrium occurs.
The gist of all this is that the aircraft would behave in yaw in the same way as in pitch: rudder deflection only causes an angle of sideslip, not a continuous turn in heading. That would conflict with the earlier questions posted above.
So the question is: does yaw really behave exactly like pitch? Does deflecting the rudder only cause a greater angle of sideslip but no flight path change?