Application point of the lift force and pitching moment

In summary, the aerodynamic center is a point at which the pitching moment does not change significantly with angle of attack. It is located at a quarter chord distance from the leading edge, and transferring the lift force to the aerodynamic center results in a non-varying moment.
  • #1
fog37
1,549
107
Hello

As the angle of attack of an airfoil changes, the lift force ##L## changes both in magnitude and position (not in direction, always upward). The force location is a point called the center of pressure ##x_{cp}##. It is possible to transfer the force to any another different point along the chord (even if it is always physically applied to ##x_{cp}##). But that transfer implies that we add a pure couple moment ##M##. However, as we change the AoA, the pure couple moment ##M## varies, i.e. it is dependent on the AoA even if we keep the reference point about which we calculate the moment fixed.

However, there is a special point called the aerodynamic center ##x_{ac}##, located at a quarter chord distance from the leading edge ##LE##. If the lift force ##L## is transferred to ##x_{ac}## as its application point, this pure couple moment ##M_{ac}## does NOT vary with AoA. Is that correct? This pure couple moment is always nonzero, even when ##L=0##, for any AoA, and always equal to zero for a symmetric airfoil.

246356


I believe, not sure if correct though, that if we leave the lift force ##L## at the center of pressure ##x_{cp}## and calculate the moment of the lift force ##L## about the aerodynamic center, with the lever arm being the distance ##|x_{cp} - x_{ac}|##, the resulting moment
##|M|## = ##L |x_{cp} - x_{ac}|## remains constant and is independent of the angle of attack even if both the distance ##|x_{cp} - x_{ac}|## and ##|L|## change with AoA . Is that correct? Also, this moment happens to be equal to the constant pure couple moment ##M=M_{ac}## described in the first paragraph...

Thanks and any clarification and validation!
 
  • Like
Likes CFD_Wiz
Physics news on Phys.org
  • #2
Hopefully, just to add clarity to my question, here another picture illustrating the lift force ##L## applied at the center of pressure ##CP##, which varies with AoA. If the pitching moment due to ##L## is calculated about the aerodynamic center ##AC##, the moment remains constant: even if the magnitude of ##L## increases from ##L_1## to ##L_2##, the lever arm ##d## decreases from ##d_1## to ##d_2## keeping the moment constant...

246452


The second figure shows how the force can be moved to different points of applications causing the moment ##M## to change depending on the application point. But only when the force is applied at c/4 the moment remains constant with AoA.
246451
 
  • #3
fog37 said:
However, there is a special point called the aerodynamic center xacxacx_{ac}, located at a quarter chord distance from the leading edge LELELE. If the lift force LLL is transferred to xacxacx_{ac} as its application point, this pure couple moment MacMacM_{ac} does NOT vary with AoA. Is that correct?

Yes. In fact the definition of the aerodynamic centre is the point at which the pitching moment does not change significantly with angle of attack.

See also..

https://en.wikipedia.org/wiki/Pitching_moment
fog37 said:
This pure couple moment is always nonzero, even when L=0L=0L=0, for any AoA, and always equal to zero for a symmetric airfoil.

Typically it's negative (nose down) for "normal" cambered wings. Zero for symmetrical wings and can be positive for wing sections used on tailless aircraft.

There is an interesting intro to stability here..

http://www.mh-aerotools.de/airfoils/flywing1.htm
See the table below "Equilibrium". It explains why conventional wing sections need a tail and how sections with a positive pitching moment are used on tailless aircraft. Its been awhile since I looked at this stuff so might not be able to answer all questions.
 
  • #4
Thank you CWatters!

I found figure that may be useful for other readers like me. For the same aerofoil, the figure shows how the pitching moment ##C_m## is constant if the moment is calculated choosing AC as the reference point (lever arm is distance from ##AC## to the lift force ##L##). In other cases, the coefficient varies linearly with AoA:
1563543060727.png


"...Yes. In fact the definition of the aerodynamic centre is the point at which the pitching moment does not change significantly with angle of attack..."

I still think it is so cool that there is such a point AC such that the pitching moment due to the lift force F remains constant as the AoA changes. This constancy derives from the fact that the lift force magnitude, the lift force location and lift force distance from AC all change with changing AoA but the product ##M=L d## stay constant.

I guess there is a similar point for the rolling moment such that the rolling moment stays constant as the AoA changes?
1563542467616.png
 
  • #5
It has never been clear to me why using the AC would simplify calculations. Doesn't the AC move when the flight condition changes and how can its position be determined? How hard can it be to add a linear function of AOA? Many people who use the data use a reference position for moments that is not at the AC. I think that the wind tunnel measurements are not done at the AC.
 
  • #6
My understanding is that the AC is a fixed point about 0.25 chord distance from the leading edge of the airfoil and stays there. Mathematically, the moment due to lift force calculated about AC is constant (approximately) with varying AoA.

Like you, I am not sure about the real value of using the AC but those who make serious aerodynamic calculations seem to think it is very convenient...
 
  • #7
Like I said before. The definition of the AC is the point at which the pitching moment is (reasonably) constant with angle of attack.

Consider an all moving rudder on an aircraft or boat (eg no fixed fin). If its not balanced eg its just a plate hinged at the front edge, then there is a massive pitching moment that tends to keep it centred and requires large forces to overcome. The pitching moment varies with angle of attack and changes sign at the centre.

As you move the hinge point back, so that some area is in front of the hinge, it becomes more and more aerodynamically balanced until there is a point where the pitching moment approaches zero and independent of the angle of attack. That's the AC.
 
  • Informative
  • Like
Likes fog37 and anorlunda
  • #8
CWatters said:
As you move the hinge point back, so that some area is in front of the hinge, it becomes more and more aerodynamically balanced until there is a point where the pitching moment approaches zero and independent of the angle of attack.
Yes indeed. In boating, we call that a balanced rudder.
 
  • Like
Likes fog37

What is the lift force and how does it apply to applications?

The lift force is a force that acts perpendicular to the direction of motion of an object in a fluid, such as air or water. It is caused by differences in pressure between the top and bottom surfaces of the object. In applications, the lift force is often used to generate lift on aircraft wings or to create lift and propulsion in propellers and turbines.

How does the lift force affect the stability and control of an aircraft?

The lift force plays a crucial role in the stability and control of an aircraft. It is responsible for keeping the aircraft in the air and providing the necessary lift for takeoff and landing. The magnitude and direction of the lift force can also be manipulated to control the pitch, roll, and yaw of the aircraft, allowing for stable and controlled flight.

What is the relationship between the lift force and the pitching moment?

The pitching moment is a rotational force that acts on an object, causing it to rotate around a specific point. In the context of an aircraft, the pitching moment is caused by the lift force acting at a distance from the center of gravity. The magnitude and direction of the pitching moment are directly related to the lift force and its location on the aircraft's surface.

How do engineers design aircraft to optimize the lift force and pitching moment?

Aircraft designers use various techniques to optimize the lift force and pitching moment for different types of aircraft. This can include shaping the wings and other aerodynamic surfaces to create more lift, adjusting the angle of attack, and strategically placing control surfaces to manipulate the pitching moment. Advanced computer simulations and wind tunnel testing are also used to fine-tune the design and achieve the desired performance.

What are some real-world examples of the application of lift force and pitching moment?

The principles of lift force and pitching moment are used in various applications, including aircraft design, wind turbines, and hydrofoils. In aircraft, the lift force and pitching moment are essential for achieving stable and controlled flight. Wind turbines use the lift force to generate power, and hydrofoils use it to lift the hull of a boat out of the water, reducing drag and increasing speed.

Similar threads

Replies
6
Views
2K
  • Aerospace Engineering
Replies
34
Views
7K
  • Aerospace Engineering
Replies
2
Views
2K
  • Aerospace Engineering
Replies
6
Views
2K
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
820
  • Classical Physics
Replies
30
Views
3K
  • Introductory Physics Homework Help
Replies
7
Views
238
  • Aerospace Engineering
Replies
4
Views
16K
  • Introductory Physics Homework Help
Replies
11
Views
168
Back
Top