# What does a negative moment tell us about the characterisics of the airfoil?

## Main Question or Discussion Point

I've done an experiment lately on the NACA-0012 and I've found that as the angle of attack increases, the moment becomes more negative. I wanted to know what does that negative value say about the characteristics of the airfoil, and what is its importance.

If someone could help me out, this would be greatly appreciated.
Thank you very much.

## Answers and Replies

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A good reason that some aerofoils have negative pitching moment is that lift is concentrated on the forward of the aerofoil that is 1/4 of the chord region.

Ref:
http://www.desktop.aero/appliedaero/configuration/tailless.html [Broken]

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yes, ofcourse as physixlover said, thats sure for good reason, but he didn't really evaluate the importance of negative pitchng moments. As solely its hard to speak about the airfoil alone, but consideration of aircraft as a whole, it is one of the key elements in analysing the longitudinal stability of an aircraft. This negative pitchig moment is for only with the cambered wings, the cambered wings even in straight and level produces some sort of lift, so to counter balance this force, the negative pitching moment comes into act to maintain the aircrafts longitudinal stability. Let discuss, if I've got an Aircraft with maximum longitudinal stabiliy even though I increased the angle of attack and releases the stick, the negative pitching moment from my cambered wing comes into act to get my aircraft again straight and level. with a conventioal aircraft, I can even make use of my horizantal stabilisers.

For further studies, look on how the tailless aircrafts achieves longitudinal stability cos they are tail less.

Ref:
Basic Aerodynamics
My amazing sort of brain

Thx, be in touch if we need to discuss about this in detail......:)

boneh3ad
Science Advisor
Gold Member
yes, ofcourse as physixlover said, thats sure for good reason, but he didn't really evaluate the importance of negative pitchng moments. As solely its hard to speak about the airfoil alone, but consideration of aircraft as a whole, it is one of the key elements in analysing the longitudinal stability of an aircraft. This negative pitchig moment is for only with the cambered wings, the cambered wings even in straight and level produces some sort of lift, so to counter balance this force, the negative pitching moment comes into act to maintain the aircrafts longitudinal stability. Let discuss, if I've got an Aircraft with maximum longitudinal stabiliy even though I increased the angle of attack and releases the stick, the negative pitching moment from my cambered wing comes into act to get my aircraft again straight and level. with a conventioal aircraft, I can even make use of my horizantal stabilisers.

For further studies, look on how the tailless aircrafts achieves longitudinal stability cos they are tail less.

Ref:
Basic Aerodynamics
My amazing sort of brain

Thx, be in touch if we need to discuss about this in detail......:)
Correct me if I am wrong, but in flight dynamics, a positive pitching angle refers to nose-up by convention. With that in mind, a negative pitching moment implies that the nose will be pushed up, not the tail.

Ref:
Basic math

Correct me if I am wrong, but in flight dynamics, a positive pitching angle refers to nose-up by convention. With that in mind, a negative pitching moment implies that the nose will be pushed up, not the tail.

Ref:
Basic math
Don't want to sound condescending but read your statement again, it makes no sense. sweetiebyuty's statement was correct, negative pitching moment is nose down or tail up while positive pitching moment is nose up or tail down.

This is the reason that for a stable aircraft, Cma is negative. Negative delta alpha gives a restoring (pitch up) motion and vice versa. My daily activities require me to have the aircraft stability reference frame in mind...

Hi Viscous Flow, and others What everything said was fine but I have a doubt like see For example as sweetiebyuty said when the pilot pulls the stick and hold in the same angle of attack then how can we say about its Negative pitching moment( I mean i do understand the pressure makes the aircraft down when stick is released but how can we decide that at that point the pitching moment is more any relation or formula that can precisely explain that) and how does this helps to decides the characteristics of an aerofoil.

boneh3ad
Science Advisor
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It makes sense given that I was thinking in terms of a right-handed coordinate system. The problem is that looking at the problem the way I was, the system would have been left-handed, thus the sign error.

It makes sense given that I was thinking in terms of a right-handed coordinate system. The problem is that looking at the problem the way I was, the system would have been left-handed, thus the sign error.
Hi..boneh3ad, sounds weird but good, can u make me clear about those words 'right handed and left handed co-ordinate systems', I never came through those words before in aircraft referencing...Thanks Bone

Hi Viscous Flow, and others What everything said was fine but I have a doubt like see For example as sweetiebyuty said when the pilot pulls the stick and hold in the same angle of attack then how can we say about its Negative pitching moment( I mean i do understand the pressure makes the aircraft down when stick is released but how can we decide that at that point the pitching moment is more any relation or formula that can precisely explain that) and how does this helps to decides the characteristics of an aerofoil.
Hi physics, I couldn't remember the exact formula, to be frank don't have time to search for that at the moment, but if u look at the formula, you'll get the variables which influences the pitching moment on the aircraft, hope it helps you out....Thanks

boneh3ad
Science Advisor
Gold Member
Hi..boneh3ad, sounds weird but good, can u make me clear about those words 'right handed and left handed co-ordinate systems', I never came through those words before in aircraft referencing...Thanks Bone
It is just in reference to the axes of the coordinate system you choose. In a right-handed coordinate system, if you take the cross product of the x-axis with the y-axis you will get the z-axis in the direction indicated by the right-hand rule. In a left-handed coordinate system the z-axis would go off in the other direction.

In other words, I was looking at the z-axis backwards.

What point are you taking the moment about for the airfoil? If you are taking it about the quarter chord point the pitching moment should be zero for the NACA 0012 until stall.

What point are you taking the moment about for the airfoil? If you are taking it about the quarter chord point the pitching moment should be zero for the NACA 0012 until stall.
Moments don't have a point. An airfoil's pitching moment imparts a torque to the fuselage to which its attached, regardless of where it's attached, and the moment remains contant throughout the length of the fuselage. A second moment exists because stability requires the center of gravity to be forward of the center of pressure.

Countering those downward moments (which pitches the tail up) requires the horizontal stabilizer to exert a counteracting downward force. This results in a stable configuration which tends to maintain the same airspeed at any given trim. This configuration exacts a penalty, however, for the horizontal tailplane incurs both parasitic as well as induced drag, while pushing downward, a force the wing has to counter with even more induced drag.

In contrast, canards exert an upward force. They still have parasitic and induced drag, but they're adding to the overall lift, rather than detracting from it, and thereby eliminate the twice the increased induced drag on the main wing. It's one of the reasons Rutan's canards have established many records for efficiency.

Moments don't have a point. An airfoil's pitching moment imparts a torque to the fuselage to which its attached, regardless of where it's attached, and the moment remains contant throughout the length of the fuselage. A second moment exists because stability requires the center of gravity to be forward of the center of pressure.

Countering those downward moments (which pitches the tail up) requires the horizontal stabilizer to exert a counteracting downward force. This results in a stable configuration which tends to maintain the same airspeed at any given trim. This configuration exacts a penalty, however, for the horizontal tailplane incurs both parasitic as well as induced drag, while pushing downward, a force the wing has to counter with even more induced drag.

In contrast, canards exert an upward force. They still have parasitic and induced drag, but they're adding to the overall lift, rather than detracting from it, and thereby eliminate the twice the increased induced drag on the main wing. It's one of the reasons Rutan's canards have established many records for efficiency.
Hold on a moment. A moment in physics is the same at torque. No problem there, but the term 'moment' for engineers is ---well, it's something different, and poorly defined from what I can gather. And I've been doing a lot of time trying to do the gathering. The engineers who explain this "engineering momentum" on Wikipedia are useless (so what's new?) Answers.com has one idiot-answer.com from an individual who doesn't know sine from cosine. Same with Wikipedia. To make things worse, it may even vary from the US to England. If you could possibly clear up what in the blue-blazes an engineering moment is, I would be very grateful.

checkout this non-information:

http://en.wikipedia.org/wiki/Torque#Terminology"

The terminology for this concept is not straightforward: In the US, in physics it is usually called "torque" and in mechanical engineering it is called "moment".[2] However outside the US this varies. In the UK for instance, most physicists will use the term "moment". In mechanical engineering, the term "torque" means something different,[3] described below. In this article the word "torque" is always used to mean the same as "moment".​

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boneh3ad
Science Advisor
Gold Member
Moments don't have a point. An airfoil's pitching moment imparts a torque to the fuselage to which its attached, regardless of where it's attached, and the moment remains contant throughout the length of the fuselage. A second moment exists because stability requires the center of gravity to be forward of the center of pressure.
Moments don't have a point at which they are applied, but they do have a point about which they were taken. In this case, that point is the point at which the airfoil is fixed. This is usually at x/c = 0.25, which corresponds to the aerodynamic center of a symmetric airfoil. About this point, the pitching moment coefficient doesn't vary with lift. about other points it does.

Anderson's "Fundamentals of Aerodynamics" has a good treatment of airfoils, and Abbott and con Doenhoff's "Theory of Wing Sections" is a good comprehensive source on airfoils.

Moments don't have a point at which they are applied, but they do have a point about which they were taken. In this case, that point is the point at which the airfoil is fixed. This is usually at x/c = 0.25, which corresponds to the aerodynamic center of a symmetric airfoil.
Then you would define moment as synonymous with a force couple.
About this point, the pitching moment coefficient doesn't vary with lift. about other points it does.
But now you seem to contradict yourself, or I'm really missing the point.
Anderson's "Fundamentals of Aerodynamics" has a good treatment of airfoils, and Abbott and con Doenhoff's "Theory of Wing Sections" is a good comprehensive source on airfoils.
I have the text. I don't see 'moment' anywhere defined in Theory of Wing Sections.

boneh3ad
Science Advisor
Gold Member
Any moment can be expressed as a force couple. However, the magnitude of that moment (and thus the couple) depends on the point about which it is taken.

Any moment can be expressed as a force couple. However, the magnitude of that moment (and thus the couple) depends on the point about which it is taken.
You have no idea do you? This is a science forum. What is you source?

boneh3ad
Science Advisor
Gold Member
My source is the definition of a moment. A moment, like a torque, is a force acting about a point from a distance. In other words, it is defined as $\bar{M} = \bar{r} \times \bar{F}$ Where r is the vector from the point about which you are taking the moment to the point where the force is applied and F is the force vector. A couple is very much the same in that it exerts a moment on the body.

In the case of a wing, the lift and drag represent continuous force distribution on the surfaces of the airfoil. Each point contributes to the whole moment on the wing, but how much depends on the point about which you are taking the moment.

The aerodynamic center is the point at which the moment coefficient doesn't change with the lift coefficient, or:

$$\frac{dC_m}{dC_L} = 0$$

In other words, as you change angle of attack, your lift coefficient is changing but the moment coefficient doesn't change about the aerodynamic center. For a symmetric airfoil, the aerodynamic center is located at the quarter chord location, and for that reason, that is the point that us used to attach airfoils when used in wind tunnel tests.

Now, let me ask you, why on earth are you suddenly attacking me and my knowledge of the subject? What would motivate you to do this?

EDIT:Apologies if my LaTeX isn't working. It is sometimes a bit buggy on this forum.

Twas brillig, and the slithy toves did gyre and couple in the wabe.
All mimsy were the borogoves, and the moment raths outgrabe.

boneh3ad
Science Advisor
Gold Member
I fail to see how Lewis Carroll is relevant, but that's cool anyway.

Hold on a moment. A moment in physics is the same at torque. No problem there, but the term 'moment' for engineers is ---well, it's something different, and poorly defined from what I can gather. And I've been doing a lot of time trying to do the gathering. The engineers who explain this "engineering momentum" on Wikipedia are useless (so what's new?) Answers.com has one idiot-answer.com from an individual who doesn't know sine from cosine. Same with Wikipedia. To make things worse, it may even vary from the US to England. If you could possibly clear up what in the blue-blazes an engineering moment is, I would be very grateful.
An engineering moment is both a torque and a force which propogates along a physical body in the form of a shear stress. The term is usually used while describing a loaded beam fixed at one or both ends.

For example, if you twist a screwdriver, it's pure torque. You're applying forces around the circumference of the handle, but the forces in one direction are countered by equal forces in the opposite direction (a couple).

With a beam, however, it's different. Discounting the mass of the beam for the purpose of simplification, if you fix a beam of length L at one end, then apply a force F at the unsupported end, you're creating a moment in the beam where M=F*L

Force
V
---------------- Supported end

Both the moment and the force are countered by an equal but opposite moment and force at the supported end.

I was taught that torque and couple were interchangeable. It's been nearly thirty years since I took Statics, though!

A moment can be just about anything.

The nth moment of A about p over the volume V:

$$\int^V Ar^n dV'$$

where r is the displacement vector from the point p.

For an extended body, mass is the zeroth moment of density about a point p.

$$M = \int^V \rho r^0 dV'$$

One of the unfortunate variants is the first moment of pressure, P about a point p over the surface A, of a volume. This is the aerodynamic moment. This is the moment under discussion.

$$\tau = \int^A P \hat{n}\ x \ r dA'$$

This can be resolved to a torque. It is an unfortunate fact that this object is simply called 'the moment' when there are infinite others.

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Now, let me ask you, why on earth are you suddenly attacking me and my knowledge of the subject? What would motivate you to do this?
Because you were mistaken in your statement, so I asked for a source--meaning a credible reference, rather than more equations.

All first moments of force, or pressure about a point can be resolved as a numerically equal to torque. A torque about a point can be resolved as a force through the point and a force couple. However, not all torques are force couples are usually not. A torque couple exerts no net force; the zeroth moment of force is zero.

boneh3ad
Science Advisor
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When last I checked this was an aerospace engineering forum and I was answering a question about this particular application. The OP did no ask about the zeroth moment of density or the second moment of force or any less commonly used quantities. He asked about the pitching moment on an airfoil. I answered the question in terms of his question. It was a correct answer.

Sure there are different types of moments. However, only a select few are actually useful in engineering practice. This thread asks about the one commonly called a "moment" in basically every engineering field. The other moments that are useful are generally referred to by their informal names such as "moment of inertia."

When last I checked this was an aerospace engineering forum and I was answering a question about this particular application. The OP did no ask about the zeroth moment of density or the second moment of force or any less commonly used quantities. He asked about the pitching moment on an airfoil. I answered the question in terms of his question. It was a correct answer.
That may be, but you threw me off in identifying a moment with a force couple, which it is not. In the mean time, I've resolved the problem and no longer need any clarification.

However, you may care to look at various wing sections where the first derivative of moment is not a constant with either angle of attach or lift as you seem to believe. NACA 747-415 is a good example. This seems to go by the name static marginal.