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let's assume an aircraft flies in straight level flight in the direction of an x-axis with an angle of attack of 3°. When the pilot pulls the flight stick, an additional lift is produced which acts perpendicular to incoming air direction. But in order to fly a looping, the lift force should always be perpendicular to the body axis/attitude of the aircraft?

So the thing is, to my understanding when we increase the angle of attack, the lift force increases (drag also increases a little bit). This should only mean that the aircraft climbs now, but the attitude or to be precise: the aircraft flies still into the x-direction but has now also an y-component (altitude). But there must happen something with the forces so that a pilot can fly a turn.

Can you follow me?

Thanks for your help in this!

Lucas

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  • $\begingroup$ You forgot to consider what directly happens when you pull the stick (which is not producing additional lift with the wing) 😉 $\endgroup$
    – sophit
    Jan 27, 2023 at 10:27
  • $\begingroup$ Dou you mean: When I pull the stick then "directly" the tail goes down and the nose up. $\endgroup$
    – Lucas
    Jan 27, 2023 at 13:14
  • $\begingroup$ Consider: looping always involves pulling the stick back (well, could think of a few exotic exceptions such as a very rapid roll to wings-level from a steep fast spiral dive, but that's the general rule), but pulling the stick back doesn't always make a loop. Hmmmm.... $\endgroup$ Jan 27, 2023 at 13:29
  • $\begingroup$ Yep, your tail goes down (i.e. the nose up) and you gain incidence. Afterwards it's just a matter of equilibrating the forces acting upon the aircraft. $\endgroup$
    – sophit
    Jan 27, 2023 at 14:06
  • $\begingroup$ In any turn, forces do not equilibrate. As you pull the stick back, your nose changes direction. A loop is a turn in the vertical. As you turn, the wing is constantly pulling in a new direction. As @quietflyer said, the physics are similar to a level turn, but you need enough energy to turn past 90 degrees vertical, of the plane will fall backwards. In considering what an elevator control input does, it is a rotational torque about the pitch axis and a change in direction of the plane. $\endgroup$ Jan 27, 2023 at 16:13

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You might as well ask why an airplane doesn't just start sliding sideways, rather than flying in a horizontal circle, when it banks (while increasing lift as needed so that the flight path remains in the same horizontal plane.) The two situations have a lot in common. The key attribute of a circling flight path, be it a horizontal or a vertical circle, is that there is constantly a net centripetal force acting perpendicular to the instantaneous direction of the flight path. This net centripetal force makes the flight path curve, or change direction. Meanwhile the aircraft has an inherent tendency to stay generally aligned with the instantaneous direction of the flight path, albeit with some offset angle. (Oversimplifying a bit, we call the offset angle the "sideslip angle" in the case of a horizontal turn, and it tends to stay near zero in most aircraft, while in the case of a vertical turn we call the offset angle the "angle of attack".)

By the way, keep in mind that in a linear climb, as opposed to during the initial pull-up or during the start of a loop, lift is less than aircraft weight, not more. For more see related ASE answer Does lift equal weight in a climb?.

Keep in mind too that though you are right to point out that the lift vector is defined to act perpendicular to the flight path, not the longitudinal axis of the aircraft, it would be possible to re-define the lift vector so that it was tied to the "body frame" of the aircraft, but that wouldn't fundamentally change our view of what is happening during a loop.

You may find it helpful to first think through the problem with the simplifying assumption that the aircraft's rotational moment of inertia about the pitch axis is zero. This basically means that the aircraft is going to instantly assume whatever angle-of-attack the pilot is "setting" with the control stick, which is fundamentally an angle-of-attack controller. You can seen that it is impossible for the flight path to stay linear if the net force is not zero, i.e. if there is a net centripetal force on the aircraft. Once you are thoroughly comfortable with this concept, then you may wish to also consider how the aircraft's actual non-zero rotational moment of inertia about the pitch axis might slightly complicate the stick inputs required of the pilot in various maneuvers.

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  • $\begingroup$ TL;DR it may be useful to consider what happens when the aircraft has rotated 90 degrees and is pointing upwards. Perhaps the OP considers that it will be ‘stuck’ here and won’t rotate further, although it should be obvious that the control surfaces and relative airflow rotate more or less with the aircraft. $\endgroup$
    – Frog
    Jan 27, 2023 at 20:17

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