Should the pitching moment be up or down?

Question

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.

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

Thanks for your help,

Answer 1

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.

Answer 2

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.

   • 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.

   • 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.

Answer 3

the pitching moment is shown to be nose up

Peter alluded to it in his answer, but let's explicate it:

In the cases I have encountered, the clockwise (nose-up) circular arrow drawn just indicates the direction of a positive $M$.

However, the actual moment is negative in typical flight regimes, so, as you say, nose-down.

Just like the tail lift $L_t$ is drawn with an arrow pointing up, indicating that positive $L_t$ corresponds to upward tail lift, even though for many aircraft the tail lift in typical flight regimes is downward, ie negative.