Center of Gravity and Center of Lift stability

I have recently been reading about the center of gravity and center of lift. On the German Wikipedia there are many different graphics about the relation between the center of gravity and the center of lift. The one that struck me the most is the one where the description is the one where the center of gravity is the same as the center of lift:

Image according to: https://en.wikipedia.org/wiki/Wikipedia:Image_use_policy

The article in Wikipedia mentions that having a center of gravity (theoretically) coincide with the center of lift constitutes for a very unstable aircraft. It says that even the slightest turbulence will cause very bad nose attitude changes as the airplane becomes very unstable along the lateral axis.

I am having a really hard time understanding how this is any different from any other CG/CL configuration. Why is the airplane more laterally stable if the center of gravity is in front of the center of lift and the elevator is compensating the ensuing torque around the center between center of lift and gravity?

• I'm wondering if you meant to say the longitudinal axis rather than the lateral axis. Fore and aft are measured along the longitudinal axis. If a sudden gust increases the angle of attack momentarily, a center of lift aft of the c.g. will counter the momentary increase in lift with a nose down force to provide stability by reducing the angle of attack. The rudder is not involved in this resolution of forces. May 12, 2021 at 23:03
• I think the confusion here is because in longitudinal stability we look at rotations (pitch) about the lateral axis (y-axis in the body reference system). So probably the wikipedia article talks about longitudinal stability when it mentions "unstable along the lateral axis" May 13, 2021 at 7:46
• @DeltaLima It would be more clever to talk about the pitch axis. Never mind that this article seems to perpetuate a myth that is untrue. May 13, 2021 at 10:34
• @DeltaLima The Wiki article was even worse, it talked about the "horizontal axis" as if the airplane only has one horizontal axis. I inferred they mean pitch around the lateral axis (i.e. the lateral axis is the axis of rotation). May 14, 2021 at 15:01
• @Terry you're back! Nice to see you!! May 14, 2021 at 15:38

If you ever read something along the line that "even the slightest" cause will result in "very bad changes" when before all was stable, you know that the writer was out of their depth. But you have come to the right place.

The way you formulate the question it concerns lateral stability. The combined center of all side forces (= lateral lift) should be behind the combined center of gravity of all components of the airplane to give it weathervane stability. Since the law of conservation of momentum applies also to a flying airplane, all movements should happen around its center of gravity, so all moments should be summed up there to see what effect they will have. In order to see their effect on stability, it is even better to focus on the force changes effected by a change in sideslip. If they produce a moment which will rotate the airplane away from that sideslip, the airplane is laterally stable.

Why only the changes in sideforce with sideslip? This will become more clear when we look at longitudinal stability, which is implied by the graphic in your question. Here the same principles apply, only that a constant downward acceleration is added, namely gravity. To compensate its weight, the airplane needs to produce an opposite force, namely lift. This lift has to act at the same longitudinal and lateral position of the center of gravity. Any deviation would produce a moment around that center of gravity which would start a rotation. In order to shift the center of lift to the desired location, the pilot will deflect control surfaces to modulate the lift force at the extreme ends of the airplane (tail rsp. canard and wingtips) so that any moment around the center of gravity disappears. This is one meaning of "trimming" the airplane (the other one means to remove all stick forces in order to stay at this state).

Theoretically, the pilot could balance the airplane in the desired state using the control surfaces like you can balance a broom on your fingertip. But that becomes tiring quickly. So it is preferable that the airplane itself will produce moments when the trimmed position is left, without any additional control deflections. This is achieved by having the changes in lift force act at a location behind the center of gravity.

The point where all lift forces can be summed up is the center of pressure, (Auftriebsmittelpunkt) whereas the point where all changes can be summed up is the neutral point (Neutralpunkt). Now you know what the author of the Wikipedia article wanted to say but failed to do so. He is by far not the only person to confuse those two points.

In fact, only when the center of lift coincides with the center of gravity will flight be straight and steady. All other positions will cause the airplane to rotate away from its current attitude. In order to return to its old state, only the neutral point needs to behind the center of gravity.

• I actually think wikipedia was about longitudinal stability, but since that looks at pitching moments which are around the lateral (y-)axis, the OP got confused. May 13, 2021 at 7:49
• @DeltaLima I wasn't sure so I covered both. I tried to find the article but was unsuccessful. May 13, 2021 at 10:33
• I think some of the confusion is over the precise definition of "Center of Lift", where it's generally thought of as applying only to the wing (a fulcrum point representing the forces holding the airplane up so to speak), but in your definition it's the "whole body" center of lift which takes into account the addition or subtraction of other lifting components being used for trim. The pitching force balance that constitutes trim, the "target AOA" that the static stability forces will orient toward, occurs with the whole-body C of L is coincident with the C of G. Is that about right? May 13, 2021 at 13:37
• @JohnK The whole body definition of center of lift is much more useful that that of only the wing, but harder to calculate. That is precisely because as you are rightly saying, when both, the CoL and the CoG, match length- and sidewise the airplane is trimmed. May 13, 2021 at 13:56
• My terms might be a bit confusing, I figured the tendency to (or not to) rotate around the lateral axis could be considered the lateral stability :). I.e. how much the nose of the aircraft moves up or down. May 14, 2021 at 22:35

A quick refresher: the lateral axis runs through the wings and rotates in pitch. The vertical axis runs through the top to bottom and rotates in yaw. The longitudinal axis runs nose to tail and rotates in roll.

So we talk about longitudinal stability around the lateral axis. (Ah ha!) So the relevant control surface is the elevator.

Placing the center of wing lift near the center of gravity is not necessarily a horrible thing if there is adequate surface area behind the center of gravity (for both vertical and horizontal stabilizers) for the aircraft to be directionally stable.

Placing the center of gravity ahead of the center of wing lift allows us to use tail downforce to trim for constant airspeed. The is called static stability.

However, fuel conscious long distance cruisers such as airliners (and gliders) can save a little bit of drag (drag = thrust = fuel = \$) by "relaxing" static stability tail downforce, allowing the wing to most efficiently do all the lifting work.

Pilots flying these aircraft must beware of unwanted airspeed changes, where as staticly stable aircraft can be "trimmed" for a specific airspeed.

Edit for Yanick Salzmann:

Regarding the final paragraph concerning lateral stability (about the vertical axis), which would use the rudder as the control surface, setting the CG forward by default increases lateral stability. Interestingly, control surfaces such as the elevator and rudder introduce instability when applied.

The rudder applies torque to the center of gravity in order to change the direction of flight. It must overcome stabilizing forces to do this.

Making the plane more stable makes it harder to turn, which is why too much is not good.

• I really like this analogy. Turning the airplane upside down and imagining it like a table makes it very obvious why its more stable! May 14, 2021 at 14:58
• Regarding your edit, I probably made it more confusing, I think it might be easier to go down to very simple terms: Making the nose of the airplane go up or down. Thats what I understood from the Wikipedia article (it is very poorly worded). May 14, 2021 at 22:37
• Ah, I realized I mistakenly mentioned the 'rudder' in my question, I meant the elevator. May 14, 2021 at 22:40