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I read an article that described static margin by taking the aerodynamic center and the center of gravity. It explained why the center of gravity has to be in front of the aerodynamic center for a stable aircraft. But how does center of pressure play into this? Couldn't the center of pressure be in front of the aerodynamic center and the center of gravity and still make the aircraft unstable? For example when the aircraft wants to gain altitude.

Then my next question arises, but I kind of have to understand the first problem... I'll just try to explain it the best I understand it right now. Usually the stabilizers have a 'downwards' lift but say it doesn't. Say my aircraft just has two big wings.. where do I center the center of gravity around? How do I take the 'average' of both aerodynamic centers (or centers of pressure, depending on what's actually matters here) from both wings? I have a feeling that with two wings the center of gravity has to be somewhere between the two. And then say the aircraft has a proper stabilizer that has a downwards lift, how do I calculate where my center of gravity is? Or can I just take the main wings aerodynamic center?

If you explain it, feel free to use technical terms and forums. I want to understand this!

I guess my main question is the difference between the aerodynamic center and the center of pressure regarding stability and how it's related to the center of gravity.

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The "Center of Pressure" is an older concept that imagines the lift from the wing, and any uplift or downlift from the tail, as combining to a create a single lifting force acting at a single point on the aircraft.

To a first approximation (ignoring thrust line effects, drag, etc) the airplane can only be trimmed for steady flight at a constant angle-of-attack, if the "Center of Pressure" is at, or directly above, or directly below, the CG. (By "above" or "below", we really mean lying on a line drawn parallel to the direction of the lift vector.)

The Center of Pressure of the wing itself is not fixed-- it shifts forwards at high angles-of-attack and shifts backwards at low angles-of-attack. This is destabilizing.

The Center of Pressure of the whole aircraft must do the opposite, if the aircraft is to be stable. Note that we haven't yet said anything about what configurations or what CG locations make that possible.

The "Aerodynamic Center" is a newer concept that treats the wing's lift vector as acting at a given fixed point on the wing, usually the quarter-chord point, but also invokes an aerodynamic pitching moment.

That's just a start--

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  • $\begingroup$ Good start! To continue: If the quarter point is chosen for the AC, the moment will be constant over AoA. Now your lift may vary but will still act at the same point. And the moment will not be affected by AoA changes. That makes calculations so much easier. $\endgroup$ Mar 25, 2023 at 16:14
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Center of pressure is to aerodynamic force what center of gravity is to gravity force.

Considering an airplane, gravity acts on everything that has a mass inside the airplane (each seat, windshield, landing gear, each blade of the turbofan and each rivet of the structure, payload, cables,... anything) but the whole effect can be ascribed to one single force acting in the centre of gravity of the airplane. The same happens with the aerodynamic force: it acts on every mm² of the surface of the wing but the whole effect can be ascribed to one single force acting on one particular point termed centre of pressure.

Changing the distribution of each mass inside the airplane changes the position of the centre of gravity: if the payload on a cargo aircraft is loaded toward the tail instead the nose, the center of gravity shifts backwards proportionally. The same happens with the centre of pressure: if the angle of attack of the wing or the pressure or speed changes, the aerodynamic force acting on each mm² changes proportionally as well as the location of the centre of pressure.

Having something that changes continuously makes things complicated. But luckily enough, both theory and practice show that, if the wing is thin, there exists a point in respect to which the aerodynamic force can be represented as the sum of a) one lift force linearly proportional to the AoA plus b) one constant moment. That point is called aerodynamic centre and is located at 25% of the chord at subsonic speed and 50% at supersonic speed. Being a well defined point, it is conveniently used as reference point to do calculations.

Regarding stability: this is a quite simple but lengthy concept and there are already many answers about it: I like this one the most.

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The aerodynamic center is a point on an airfoil where pitching moments do not change with Angle of Attack. This holds true for symmetrical airfoil. It moves forward a bit with cambered asymmetric airfoil (like most wings) when AoA increases. This is where "tail feathers" like an arrow help.

A plane can be built with the weight right at the AC, but how do we control it? 2 ways:

  1. Move the weight (hang glider)
  2. Move the center of pressure (center of lift) with aerodynamic controls

for example when a plane wants to gain altitude

Gaining altitude is done by increasing thrust at a given trim speed

BUT, as you perceived, how do we rotate our aircraft to take off? This is where you are rolling down the runway, reaching takeoff speed and you do what ... increase elevator back pressure to increase Angle of Attack.

Easiest to understand when you push the elevator down. More positive lift is created at the tail. The center of pressure moves back. The nose angle of attack reduces. Pull the elevator up. Less lift in the tail, center of pressure moves forward. The nose angle of attack increases.

That brings us to "static stability" or speed control. If you want a glider that is thrown from a hill top, (in free flight) to smoothly glide down for a few hundred feet, set the weight CG a bit forward of AC (usually) < 1/4 chord from the leading edge, and have your tail with less of an angle of attack than the wing.

Experiment with moving the weight around.

Once you have some idea of how the plane glides best (in a straight line all the way down with the greatest distance), you can move on to bringing the weight back and lessening the "downtrim" of the tail. This makes the plane better in gusts$^1$ as long as it is not so far back to make it directionally unstable!.

Now we can have a "lifting tail", which can even "morph" into a tiny canard and a giant tail as weight keeps moving further back.

But, walking before you run may be best. Build a single wing classic glider. Build many of them. If you make it to flying full scale, the benefits of a glider foundation will be priceless.

$^1$ not as "pitchy"

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You have to separate two concepts; static stability and trim forces.

The weathervane analogy works well for this when conceptualizing static stability. A weathervane points into wind when its aerodynamic center, the point at which all forces induced by the wind is focused, is downwind of its pivot axis. Wind shifts, it points into the new wind direction. It's statically stable; it wants to always point into the airflow.

If I move the pivot axis of the weathervane back to the same spot as the aerodynamic center, it won't point any longer and will just drift. Its static stability is neutral. If I move the pivot axis even farter back, it becomes statically unstable in the original direction, and will seek stability in the opposite direction. It'll switch ends.

Then there's trimming forces. If the weathervane is flat, it points into wind along its axis. But say I want it to be statically stable, but point at an angle off the wind, so that some side force is generated on the pole holding the vane up. I bend the trailing edge to one side. I'm trimming it. The local force created by the bent trailing edge will drive it out of alignment with the airflow until the opposing forces of the wind acting on the rest of the vane reaches equilibrium.

It will now be statically stable, and will point consistently at some angle off the wind depending on the amount of trimming force I applied. I could call that Angle of Attack. So trimming forces modify the angle to the flow at which weathervaning forces (static stability forces) want it to point.

Turn the weathervane axis 90 degrees to horizontal. Same thing is happening. It wants to point into wind in the vertical plane, and trimming forces can influence the relative angle of the body to the wind at which it points, in the vertical plane.

Now take away the fixed pivot, so the weathervane is a free body. The pivot axis now becomes the weathervane's center of gravity. If the aerodynamic center is still behind the C of G, it will still want to point into wind. Absent any trimming forces, being free in space, if I throw the body, it will go in a very statically stable ballistic arc into the ground as it's drawn by gravity, maintaining alignment into the airflow the whole way. Like a lawn dart.

So to make it resist gravity and fly, I have to put lifting foils or wings on it, while keeping the aerodynamic focus point where I want it behind the C of G to keep it statically stable, and trim it to point into the air at an angle that makes the lifting foils operate at a positive angle. Now when I throw it, the body wants to align into the wind with the wings at a positive angle, and if the angle is right, enough lifting force is made to resist gravity and it flies straight instead of going into a ballistic arc.

On the wing, Center of Pressure becomes just one of the various influences that determine where the overall aerodynamic center's point of focus results. Because we need the wing to lift up, we need to apply trimming forces in the direction that forces the airplane to be statically stable - to vertically weathervane - at an angle to the flow that generates an up force. The trimming force therefore has to be opposite to the desired lift force, so it's down. But for stability purposes, the tail's force orientation is as part of the overall weathervaning effect, whatever it takes to maintain the trimmed angle of attack.

The tail is actually doing two separate jobs - contributing to static stability by adding surface area aft of the C of G, and generating trimming (and maneuvering) forces. Like a weathervane turned horizontal with the trailing edge bent up, it generates a down force to trim the aircraft to seek an angle to the flow that angles the wings into the flow to create lift. It also adds its area to the overall footprint of the whole aircraft that determines where the aerodynamic forces in the vertical plane will be focused, which must always be aft of the C of G (static margin). So that when the angle to the flow changes from an external source, being statically stable in its trimmed angle of attack, it will seek to maintain that angle.

Pitching moments, Centers of Lift, etc, are just sub-parts of the set of forces that result in the aerodynamic center, or Neutral Point, at any given time. If the aerodynamic center or NP, the sum of air forces acting on the fuselage, wings, nacelles, and tail is at x, while the C of P is at y, and the C of P of the wing moves aft, the overall aerodynamic center moves aft a little bit, increasing static margin, while also increasing the trimming force required to hold the same angle of attack. And vice versa when the CP moves forward.

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  • $\begingroup$ Lots of great content in this answer-- but -- Re "The trimming force therefore has to be opposite to the desired lift force, so it's down." -- yet aircraft with lifting tails do exist, right? $\endgroup$ Mar 24, 2023 at 16:19
  • $\begingroup$ If it's a conventional tail, to trim to a positive angle of attack, the tail has to provide a downward moment to force the mainplane into a positive AOA. If the trimming moment is up, the mainplane is being forced to stabilize into a negative angle of attack. If the tail is lifting to support the plane, the trimming force balance has to come from somewhere else, probably from the front wing, and you have a tandem wing airplane. Remember that it wants to weathervane into the flow, and you want it to weathervane at a specific angle to the flow by trimming it. Think it through what it takes. $\endgroup$
    – John K
    Mar 24, 2023 at 18:27
  • $\begingroup$ The trimming force comes not only from the tail, but also from the weight. If weight acts behind the center of pressure of the wing, the tail needs to contribute a positive force. This does not mean that stability is lost: Stability does not depend on the forces themselves but their change with angle of attack. For static stability you need to think in their derivatives over AoA, not the forces themselves. $\endgroup$ Mar 25, 2023 at 16:08
  • $\begingroup$ I like to use "weathervaning" to describe the change with angle of attack. But if the weight is acting behind the wing, you have a tandem wing design and to trim it to achieve a stability point at some angle to the flow, the trimming force balance is different, coming from vertical lifting force balance between the front wing and aft wing. $\endgroup$
    – John K
    Mar 25, 2023 at 18:49

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