I had a question regarding the direction of the pitching moment.

To make sure we are on the same page, here is what I know so far (please correct me if I am wrong).

  1. Lift acts through center of pressure
  2. Normally moment is taken around Aerodynamic Center because then the moment does not vary with angle of attack.
  3. In a cambered airfoil, the aerodynamic center and center of pressure are not at the same place, so the lift created also generates a moment at the aerodynamic center.
  4. In a symmetric airfoil, the aerodynamic center and the center of pressure are at the same place, so you do not have a pitching moment.
  5. Location of Aerodynamic Center is fixed for an airfoil, it does not change with speed.

I am trying to understand the concept of longitudinal static stability and in all the diagrams, the pitching moment is shown to be nose up.
enter image description here

But I would imagine that the center of pressure is further downstream on a airfoil than the aerodynamic center, so shouldn't the pitching moment be nose down? As shown in this picture enter image description here

Thanks for your help,

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    $\begingroup$ you can have a moment computed around any arbitrary point. There is a center of gravity, a center of pressure and aerodynamic center. 3 different things, but really, the rotation of an object depends on the moment computed around whatever is the hinge (in this case center of gravity) $\endgroup$ – Radu094 Oct 26 '16 at 18:19
  • $\begingroup$ @Radu094, you are right except that there is no 'hinge' on a flying aircraft. For our mathematical convenience, we may consider all motion as rotations around CG plus whatever translation there is, but if you try to isolate pure rotation, its centre could be anywhere. A delta wing airplane can have centre of controlled pitch rotation outside in front of the craft (which may confuse pilots), due to strong force from elevons. An isolated normal wing, with its initial lift (CP) at ¼chord and CG at ½, will start pitching up about a point midway between the two. $\endgroup$ – Zeus Oct 27 '16 at 2:25
  • $\begingroup$ The diagram above is for an aircraft with the Center of Pressure (CP) IN FRONT of the center of Gravity (CG). in this case the pitching moment is indeed Nose up. But this makes the aircraft statically unstable. Only one aircraft (AFAIK) is like this, (the F-16) and it is only like this when subsonic. It can deal with the instability because it is "fly by wire" - the computer constantly generates stabilator inputs to compensate. Most all other aircraft have the CP behind the CG and then the pitching moment is indeed nose down. $\endgroup$ – Charles Bretana Oct 30 '16 at 16:11

All points you mention are correct (for the nitpickers: Point 5 is only true below transsonic speeds). That the pitching moment of the wing is drawn nose-up is probably because it is positive this way - nothing more. The sketch you posted in your question is rather poor, with the center of gravity located behind mid-chord when it should be closer to the aerodynamic center.

Indeed, if you have positive camber, the center of pressure of the wing is behind the aerodynamic center, so the wing's pitching moment around the aerodynamic center should be nose-down. However, if you assume the center of gravity of the isolated wing to be at mid-chord, the center of pressure is normally between the quarter chord and mid points, so the wing all by itself will pitch up because it pitches around the center of gravity. The moment depends on the reference point.

Did you look at this answer for an explanation of static stability yet? Let me know if something is left unclear.

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  • $\begingroup$ Thanks, for the reply, indeed if you want longitudinal stability, the change in lift at the rear has to be more than at the front! $\endgroup$ – T-REX Oct 27 '16 at 9:03
  • $\begingroup$ @T-REX: Yup. Simple, isn't it? $\endgroup$ – Peter Kämpf Oct 27 '16 at 9:32
  • $\begingroup$ @PeterKämpf "the aerodynamic center is normally between the quarter chord and mid points, so the wing all by itself will pitch up because it pitches are" Did you mean center of pressure here? Or perhaps meant to say something else? Because a pure moment imparts the same direction of rotation no matter where it is relative to the COG. Direction of rotation changes though if it is a translating force being applied at different locations around the COG (ie. not a pure moment). $\endgroup$ – DKNguyen Jan 5 at 20:43
  • $\begingroup$ Or maybe you are referring to the aerodynamic force acting at the aerodynamic center? But then you would need to qualify that the lever arm between the COG and aerodynamic center is enough for the force to overcome direction of the pitching moment at the aerodynamic center. $\endgroup$ – DKNguyen Jan 5 at 20:52
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    $\begingroup$ @DKNguyen OMG, you're right. Stupid mistake, thank you for pointing this out! $\endgroup$ – Peter Kämpf Jan 5 at 21:30

For the pitching moment, two distinct cases need to be considered, the airfoil and the whole aircraft, both over a range of Angle of Attack (AoA). The questions centre around the main wing only, the picture in OP is of an entire aeroplane, creating some confusion.

  1. Airfoil. A positively cambered airfoil indeed contributes a nose-down pitching moment, as mentioned by @quietflyer. The magnitude of the pitching moment varies with AoA, as depicted in the graph below. From old paper format uni book on stability & control

    • Note that the graph plots $C_m$ as function of $\alpha$ (AoA), and moment M = $C_M \cdot \alpha$.
    • A constant $C_M$ means that the pitching moment varies linearly with AoA.
    • For this wing and for many others, $C_M$ is constant when the moment axis point is chosen in the Mean Aerodynamic Chord of the wing. The sign of $C_M$ is negative: nose down. The moment axis point can be chosen anywhere on the wing, but the point where $C_M$ is constant proves to be a very convenient definition point and is called the Aerodynamic Centre.
  2. The whole aircraft. The aircraft must be longitudinally stable, meaning that the aeroplane returns to a trim position after it encounters an aerodynamic disturbance. The moment equilibrium of the whole aeroplane is considered around the Centre of Gravity (CoG), because this is where the response movement hinges around. There are many more parts of aircraft contributing to the pitching moment equilibrium, as the picture below from this answer illustrates - for clarity reasons, the X-axis origin point is chosen in front of the aeroplane.enter image description here

    • The M.A.C. is depicted away from the CoG. The M.A.C. is also the imaginary centre point for the wing lift force $N_W$, which increases with AoA. For the total aeroplane, that equates to a nose up pitching moment contribution of the main wing in flight, where $N_W$ is not zero.
    • The horizontal tail contributes to the pitching moment with force $N_H$. In the picture this force points up, contributing a nose down pitching moment. This answer states the situation where a horizontal tail upforce results in a longitudinally stable aeroplane.
    • For the aeroplane in trimmed position, the total pitching moment is zero. If it encounters an aerodynamic disturbance its AoA changes, and return to the trimmed position means that $C_M$ as function of AoA must be negative.
    • Longitudinal stability must be considered in the complete range of AoA and sideslip, including stall. In and around the stall the moments and forces cannot be considered linear. It is vital that should the horizontal tail partially stall, for instance in a tight sideslip, the nose pitches down - so at low speed, the aeroplane is trimmed around the CoG such that the tailplane delivers a downward force.

But I would imagine that the center of pressure is further downstream on a airfoil than the aerodynamic center...

Introducing centre of pressure confuses the whole picture, since it changes with AoA and we cannot construct a pitching moment situation that is valid for a wide range of AoA. Best forget use the Aerodynamic Centre instead in generalised considerations of stability and control.

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In steady state flight Center of Pressure is at Center of Gravity. If center of gravity/pressure is ahead of aerodynamic center the aircraft will be staticly stable. Looking at it purely aerodynamicly, increasing speed will increase lift, pitching up and slowing the aircraft.

The longitudinal stability nuetral point is at the aerodynamic center for tailless aircraft (Vt = 0), ergo, further back when a "tail" is added! As explained here , and illustrated in the design of a common arrow.

So why bother having a tail? It is the movement of the Center of Pressure of the wing, when AOA is changed, that be-deviled tailless proponents, particularly at higher speeds. Combined with the tendency of swept wings to stall at the tips first, and lower control surface torque lever arm, as compared with a conventional fuselage boom and empennage, made many "tailless" designs less desirable.

The forward movement of CP at higher AOA, and the rearward movement of CP at lower AO creates the need of a balancing mechanism to hold CP in place. This is tail "downforce" at lower AOA and tail "upforce" at higher AOA. With proper design the tail torque perfectly cancels out CP shift in the wing. Symmetrical or "reflexed" airfoils also are helpful here.

So placing, and keeping, your CP at AC gives nuetral static stability. If we want to move CP ahead of AC to create positive static stability, we must move CG forward as well.

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