Why does an airplane perform a loop?

[jernejk]

Dear all,

I'm a RC-airplane pilot with basic understanding of physics.

Recently I've been studying basic aerodynamics and I think I understand the basics.

However, I don't entirely understand why an airplane performs a loop and I can't find any references about it. Here's my current breakdown:
- for practical reasons, let's have a glider in a vertical dive
- nil wind
- we'll assume that the glider is flying at terminal velocity, so that weight and drag are neutral

My understanding of the situation:
- resultant of weight and drag is zero
- the wings still produce lift, perpendicular to the relative wind, so the lift vector is parallel to the horizon
- there is no opposite force to the lift

What happens (in a very short time frame, of course):
- the lift starts pulling the airplane
- center of mass moves further down and to the side (due to lift)
- the movement perpendicular to the wings generates drag on the horizontal tail, which in turns generates troque an rotates the plane over pitch axis
- because of this rotation, the airplane doesn't change the angle of af attack
- at the end of the time frame the situation is exactly the same as at the beginning, so here we go again.. and again.. and we perform a loop! (I know, the weight vector changes the direction and it needs to be accounted for)

Are my assumptions correct? Could someone provide accurate information?

TIA
Jernej

 

[russ_watters]

- the wings still produce lift, perpendicular to the relative wind, so the lift vector is parallel to the horizon

Why? This is not necessarily true, of course, since an airplane can be stable in a dive if it wants to. The elevators control pitch/angle of attack to cause the wings to produce lift. In the idealized case where 0 angle of attack is defined at 0 lift, there is no lift without input from the elevators (common with aerobatic planes anyway).

- center of mass moves further down and to the side (due to lift)

The center of mass of a physical object of constant physical shape is a physical property of the object. It does not change.

- the movement perpendicular to the wings generates drag on the horizontal tail, which in turns generates troque an rotates the plane over pitch axis

No. The control input at the elevators is what rotates the plane. This must be true, otherwise the plane will be pitch unstable (caveat: many fighter airplanes are pitch unstable). Since the CoG is in front of the center of lift, the lift from the wings acts against the elevator input to try to reduce the angle of attack.

Additionally, since the elevator increases the angle of attack by producing negative lift, its own effectiveness drops as the angle of attack increases.

- because of this rotation, the airplane doesn't change the angle of af attack

No - see above.

 

[jernejk]

Why? This is not necessarily true, of course, since an airplane can be stable in a dive if it wants to. The elevators control pitch/angle of attack to cause the wings to produce lift. In the idealized case where 0 angle of attack is defined at 0 lift, there is no lift without input from the elevators (common with aerobatic planes anyway).

For this example, let's say that our glider has a simple clark y airfoil, which produces lift at 0 aoa. 0 aoa=0 lift for symetric airfoil, which is considered good for aerobatics but I don't think it's considered "ideal".

The center of mass of a physical object of constant physical shape is a physical property of the object. It does not change.

Of course. What I meant is that the center of mass (in rc we just call it CoG) moves relative to the ground, not relative to the airplane.

No. The control input at the elevators is what rotates the plane. This must be true, otherwise the plane will be pitch unstable (caveat: many fighter airplanes are pitch unstable). Since the CoG is in front of the center of lift, the lift from the wings acts against the elevator input to try to reduce the angle of attack.

Additionally, since the elevator increases the angle of attack by producing negative lift, its own effectiveness drops as the angle of attack increases.

I'm not sure about that. The elevator just changes the pitch, which in turn changes AoA and lift. The elevator is not responsible for the loop rotation IMO. Acctually, a model plane with Clarx y profile won't fly straight down, but will start to loop until level with the elevator in neutral. Negative elevator is required to maintain straight vertical flight (up or down).

Jernej

 

[Danger]

I think that you're over-complicating things, jernejk. It essentially just boils down to the fact that the elevators act like any other control surface; they deflect the airflow, and are deflected by it in response, which causes a torque about an axis. That torque affects in which direction the wings provide lift. You can get the same effect by cutting slots in the back of a paper aeroplane's wings and bending the tabs up, without regard to airfoil shape, C of G, or anything else.

 

[russ_watters]

For this example, let's say that our glider has a simple clark y airfoil, which produces lift at 0 aoa. 0 aoa=0 lift for symetric airfoil, which is considered good for aerobatics but I don't think it's considered "ideal".

Ok. That'll work, but as a caveat, 0 aoa is often defined so that an airfoil produces zero lift. Anyway, though...

Of course. What I meant is that the center of mass (in rc we just call it CoG) moves relative to the ground, not relative to the airplane.

Ok, but how is that useful? It doesn't affect what the plane is doing.

I'm not sure about that. The elevator just changes the pitch, which in turn changes AoA and lift.

Right...

The elevator is not responsible for the loop rotation IMO.

I think I agree with Danger that you are overcomplicating things. If you had a Mig-29, you could change your pitch 100 degrees without affecting the direction of flight, but as long as you don't depart from controlled flight, elevator changes pitch, which increases lift. If the lift is greater than the weight, the plane's forward direction starts to angle up, so unless the pilot eases off the elevator (or it is in the part of the envelope where the lift cancels the elevator input), the pitch will continue to increase and the plane will loop.

Acctually, a model plane with Clarx y profile won't fly straight down, but will start to loop until level with the elevator in neutral. Negative elevator is required to maintain straight vertical flight (up or down).

Well, whatever - that's just a matter of trim. It doesn't change anything about the discussion here.

 

[hbannink]

I agree with Danger and Russ you are complicating matters it does a loop because there is a person on the ground iterfering with its flight path. Any plane will only fly straight & level with a certain trim at a certain speed. To keep it level at a higer speed more down trim needs to be applied as more airflow over the wings generate more lift. When the elevtor is pulled up, in a loop, the angle of attack is changed and the aircraft lifts its nose. With a glider this results in a drop in speed and airflow over the wing and to complete the loop more up elevator is required tocomplete the maneuver. After the apex of the loop gravity speeds the aircraft and progressively less elevator is required to comlete the loop.