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With respect to "centering", a yoke only "centers" itself in the equilibrium point where forces on both ailerons and on both top and bottom of the elevator/stabilator are equal. That said, I wouldn't want to let the yoke "center and fly itself" as the forces on the control surfaces can be equal even when the aircraft is not straight and level. If not enough power is applied the plane will pitch down and "center" as you say, and if too much power is applied the plane will pitch up and then "center". As for roll, I find that in light aircraft (Cirrus excluded as the side stick has a spring mechanism) you don't usually want to leave the yoke out of hand as slight wind and light wind shear will cause the airplane to roll somewhat. So - short answer is - yes, it will "center" eventually but you might not like the attitude the plane is in when it's done, much of this depending on power setting and gusts/shear aloft/turbulence. As for autopilot, a roll and pitch (2-axis) autopilot actually continually applies force to the controls to keep the airplane level or turning as commanded, and at a constant altitude or climb/descent/airspeed as commendedcommanded, so I wouldn't say the controls really "center" when on autopilot either. Cheers!

As a bit more of an explanation, a "nice" airplane (one with positive aerodynamic stability) with the appropriate power setting should re-enter and maintain straight and level flight if the controls are disturbed and the yoke is released (but I've always had to input a little roll to keep the wings level). Check out the following picture from the FAA Pilot's Handbook of Aeronautical Knowledge Page 4-14:

PHAK 4-14

Notice that the orange line eventually gets more and more flat. You can expect that in a Cessna 172 or something of the like... not in a more aggressive plan like aerobatic planes and fighter jets - you'll see something a little more like the green or red line. You can read more in Chapter 4 of the FAA PHAK (link here).

With respect to "centering", a yoke only "centers" itself in the equilibrium point where forces on both ailerons and on both top and bottom of the elevator/stabilator are equal. That said, I wouldn't want to let the yoke "center and fly itself" as the forces on the control surfaces can be equal even when the aircraft is not straight and level. If not enough power is applied the plane will pitch down and "center" as you say, and if too much power is applied the plane will pitch up and then "center". As for roll, I find that in light aircraft (Cirrus excluded as the side stick has a spring mechanism) you don't usually want to leave the yoke out of hand as slight wind and light wind shear will cause the airplane to roll somewhat. So - short answer is - yes, it will "center" eventually but you might not like the attitude the plane is in when it's done, much of this depending on power setting and gusts/shear aloft/turbulence. As for autopilot, a roll and pitch (2-axis) autopilot actually continually applies force to the controls to keep the airplane level or turning as commanded, and at a constant altitude or climb/descent/airspeed as commended, so I wouldn't say the controls really "center" when on autopilot either. Cheers!

With respect to "centering", a yoke only "centers" itself in the equilibrium point where forces on both ailerons and on both top and bottom of the elevator/stabilator are equal. That said, I wouldn't want to let the yoke "center and fly itself" as the forces on the control surfaces can be equal even when the aircraft is not straight and level. If not enough power is applied the plane will pitch down and "center" as you say, and if too much power is applied the plane will pitch up and then "center". As for roll, I find that in light aircraft (Cirrus excluded as the side stick has a spring mechanism) you don't usually want to leave the yoke out of hand as slight wind and light wind shear will cause the airplane to roll somewhat. So - short answer is - yes, it will "center" eventually but you might not like the attitude the plane is in when it's done, much of this depending on power setting and gusts/shear aloft/turbulence. As for autopilot, a roll and pitch (2-axis) autopilot actually continually applies force to the controls to keep the airplane level or turning as commanded, and at a constant altitude or climb/descent/airspeed as commanded, so I wouldn't say the controls really "center" when on autopilot either. Cheers!

As a bit more of an explanation, a "nice" airplane (one with positive aerodynamic stability) with the appropriate power setting should re-enter and maintain straight and level flight if the controls are disturbed and the yoke is released (but I've always had to input a little roll to keep the wings level). Check out the following picture from the FAA Pilot's Handbook of Aeronautical Knowledge Page 4-14:

PHAK 4-14

Notice that the orange line eventually gets more and more flat. You can expect that in a Cessna 172 or something of the like... not in a more aggressive plan like aerobatic planes and fighter jets - you'll see something a little more like the green or red line. You can read more in Chapter 4 of the FAA PHAK (link here).

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With respect to "centering", a yoke only "centers" itself in the equilibrium point where forces on both ailerons and on both top and bottom of the elevator/stabilator are equal. That said, I wouldn't want to let the yoke "center and fly itself" as the forces on the control surfaces can be equal even when the aircraft is not straight and level. If not enough power is applied the plane will pitch down and "center" as you say, and if too much power is applied the plane will pitch up and then "center". As for roll, I find that in light aircraft (Cirrus excluded as the side stick has a spring mechanism) you don't usually want to leave the yoke out of hand as slight wind and light wind shear will cause the airplane to roll somewhat. So - short answer is - yes, it will "center" eventually but you might not like the attitude the plane is in when it's done, much of this depending on power setting and gusts/shear aloft/turbulence. As for autopilot, a roll and pitch (2-axis) autopilot actually continually applies force to the controls to keep the airplane level or turning as commanded, and at a constant altitude or climb/descent/airspeed as commended, so I wouldn't say the controls really "center" when on autopilot either. Cheers!