# Pitching Moment Acting on a Wing

• fog37
In summary, pitching moment acting on a wing is a crucial factor in determining the stability and control of an aircraft. It is calculated by multiplying the lift force by the distance between the wing's aerodynamic center and its center of gravity, and is affected by factors such as the wing's shape, size, and angle of attack. The pitching moment can be controlled through various methods such as adjusting the wing's angle of attack, using flaps or other control surfaces, and shifting the aircraft's center of gravity. A well-designed wing will have a stable pitching moment, allowing for controlled flight.
fog37
Hello, I am learning about the pitching moment acting on a wing that is immersed in an airflow hoping to clarify some key concepts. In general, the moment of a force depends on:
• Location of moment reference point ##o##
• Force magnitude
• Lever arm (distance between force application point and moment reference point ##o##)
A positively cambered wing always experiences a nonzero, constant, pure and negative (nose-down) moment ##M_{camber}## even when the net lift force ##F_{lift}=0##. However, when the lift force ##F_{lift}\neq 0##, which happens for increasing angles of attack ##\alpha##, an extra moment ##M_{lift}\neq 0## due to ##F_{lift}\neq 0## must be included and the total pitching moment ##M_o## about the arbitrary point ##o## is equal to: $$M_o = M_{camber}+M_{lift}$$ When ##M_{lift}=0## then ##M_o = M_{camber}##. I think this discussion presumes that the lift force ##F_{lift}## is applied at the aerodynamic center ##a.c.## and generates a moment ##M_{lift} = F_{lift} x## where ##x## wis the distance between the moment reference point ##o## and ##a.c.##. When the moment reference point ##o=a.c.##, the total pitching moment becomes $$M_O = M_{a.c.}= M_{camber}$$ since ##M_{lift}=0## because the lever arm ##x=0##. So ##M_{lift}## is always zero when either ##x=0## (which happens when ##o=a.c.##) and/or ##F_{lift}=0##. Is that correct?

The same total moment ##M_o## should be obtained when, for a certain angle of attack ##\alpha##, when we consider the force ##F_{lift} \neq 0## and to be applied at the center of pressure ##c.p.## instead of at the aerodynamic center ##a.c.##. I can see how the total moment ##M_o## about a reference point ##o## would be nonzero when ##F_{lift} \neq 0## since $$M_o =F_{lift} x^{*}$$ where ##x^{*}## is the distance between ##c.p.## and the point ##o##. The moment can be positive or negative depending on if ##o## is before or after ##c.p.##.
But when ##F_{lift} = 0##, the moment ##M_o=0## always regardless of the lever arm ##x^{*}##. However, the total moment ##M_o## should always be nonzero due to camber moment contribution ##M_{camber} \neq 0## existing even when ##F_{lift} \neq 0##...

Is it correct?

Yes, that is correct. When the lift force ##F_{lift}=0##, the total pitching moment ##M_o## about a reference point ##o## is equal to the camber moment ##M_{camber}##. Even when ##F_{lift}\neq 0##, the camber moment contribution ##M_{camber}\neq 0## must be included in the total pitching moment ##M_o## and the total pitching moment ##M_o## is equal to the sum of the camber moment and lift-induced moment: $$M_o = M_{camber}+M_{lift}$$

Yes, your understanding is correct. The total pitching moment is always a combination of the camber moment and the lift moment, and the lift moment is only present when the lift force is non-zero. When the lift force is zero, the total pitching moment is equal to the camber moment. Additionally, the location of the force application point (aerodynamic center or center of pressure) does not affect the total moment when the lift force is zero. However, it does affect the total moment when the lift force is non-zero, as it changes the lever arm of the lift force.

## 1. What is pitching moment acting on a wing?

Pitching moment acting on a wing is a measurement of the force that causes an aircraft to rotate around its lateral axis. It is caused by the aerodynamic forces acting on the wing and is a crucial factor in determining the stability and control of an aircraft.

## 2. How is pitching moment calculated?

Pitching moment is calculated by multiplying the lift force acting on the wing by the distance between the wing's aerodynamic center and its center of gravity. It is also affected by the wing's shape, size, and angle of attack.

## 3. What factors affect the pitching moment on a wing?

The main factors that affect the pitching moment on a wing include the wing's shape, size, angle of attack, and airspeed. Other factors such as the location of the wing's center of gravity, the wing's thickness, and the presence of flaps or other control surfaces can also influence the pitching moment.

## 4. How does the pitching moment impact an aircraft's stability?

The pitching moment is one of the key factors in determining an aircraft's stability. A positive pitching moment (nose-up rotation) can result in unstable flight, while a negative pitching moment (nose-down rotation) can lead to over-stability. A well-designed wing will have a stable pitching moment that allows for controlled flight.

## 5. How can the pitching moment be controlled?

The pitching moment can be controlled through various methods, including changing the wing's angle of attack, using flaps or other control surfaces, and shifting the aircraft's center of gravity. These methods allow pilots to adjust the aircraft's pitch and maintain stable flight.

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