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Aerodynamic Center

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Aerodynamic Center

Old 7th Jan 2011, 13:16
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Aerodynamic Center

In simple terms can someone please explain what the Aerodynamic Center of an aerofoil is.

Thanks
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Old 7th Jan 2011, 13:22
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a la wiki

The torques or moments acting on an airfoil moving through a fluid can be accounted for by the net lift applied at some point on the foil, and a separate net pitching moment about that point whose magnitude varies with the choice of where the lift is chosen to be applied. The aerodynamic center is the point at which the pitching moment coefficient for the airfoil does not vary with lift coefficient i.e. angle of attack, so this choice makes analysis simpler [1].

long story short the point where all aerodynamic forces appear to be acting, will move according to configuration, angle of attack, etc.....
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Old 7th Jan 2011, 13:28
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I've always referred to it as the "Center of Pressure". The concept makes more sense when viewed as a cross section.

Center of Pressure


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Old 7th Jan 2011, 15:42
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Originally Posted by zerozero
NASA: Center of pressure moves with angle of attack
Aerodynamic center does not. As rigpiggy explains.

regards,
HN39

Last edited by HazelNuts39; 7th Jan 2011 at 20:40.
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Old 7th Jan 2011, 17:08
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I've always referred to it as the "Center of Pressure". The concept makes more sense when viewed as a cross section.
Hmmm, that could be identical to what is called the aerodynamic cneter but it doesn't have to. In fact usually it isn't.
The pitching moment in the aerodynamic center doesn't have to be Zero.
The trick is the pitching moment remains constant even if Alpha (or Lift being a function of Alpha) changes.

Center of pressure would be the point where the pitching moment is Zero for a given Alpha. If Alpha changes the pitching moment around this point will change, i.e. the center of pressure will move.

Last edited by henra; 7th Jan 2011 at 18:59. Reason: clarified
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Old 7th Jan 2011, 18:11
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Let my try:


When a number of forces are exerted on different points of a body, the net effect of all those forces on the body (both lineal and angular) is the same as the effect of a single force acting on a particular point.

This resultant force is the sum of all the forces, and the moment that this force creates about any point is the sum of the moments of all the forces about that point.

Each air molecule exerts a force on the airfoil. The resultant of all the forces is Lift, and the point at which Lift acts is the center of pressure.

The relative position of the CP with respect to the CG determines the necessary tailplane lift to trim the airplane.

We use the center of pressure for static situations. But it is better to use the aerodynamic center when it comes to non-static situations.

When there is a change in Lift we can think of the Lift after the change as being the sum of the Lift before the change plus the Lift increment. Understand? think of two vectors, one being the "old" Lift and the other the lift increment. The point at which the lift increment is acting is the Aerodynamic Center.

The relative location of the AC with respect to the CG will determine the degree of stability of the airplane.
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Old 7th Jan 2011, 18:46
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I must say you are ALL wrong this is an aerodynamic center...I'll refrain from showing where the Cp is located...
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Old 7th Jan 2011, 19:14
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Yep, they are all wrong.
The original question was related to the aerodynamic centre of an airfoil. This is the point at which the lift due to angle of attack acts. Theoretically, for subsonic airfoils this is at 25% of the chord aft of the leading edge. In practice it is within 1 or 2% of that point up to Mach Numbers where drag rise and shock waves become important. Camber produces a pitching moment even at zero lift so the centre of pressure, which depends on the resultant pitching moment and lift, varies with angle of attack.
The aerodynamic centre of a wing is usually close to 25% of the mean aerodynamic chord.
The aerodynamic centre of the aeroplane depends on tail area and position relative to the wing.
You can find details in almost any standard textbook.

CliveL
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Old 7th Jan 2011, 20:30
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The location of the airfoil where, if an aerodynamic force was to be applied, the resultant pitching moment would be the same for all angles of attack. For low speed airfoils, 1/4 back from LE. For Supersonic airfoils, about 1/2 back from LE

WSA
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Old 7th Jan 2011, 21:32
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This is the point at which the lift due to angle of attack acts.
Hmm, I'm afraid that is not universally correct.
That would be the Center of Pressure.
The Aerodynamic Center is the Point at which the moment is constant, independent of AoA, but not necessarily Null.
Yes, generally that is close to the Quarter Chord Line but it depends on the Airfoil (mainly on the Camber) where it is exactly.
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Old 7th Jan 2011, 22:29
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Agree 100% with Henra. Thin aerofoil theory in an ideal fluid shows that the pitching moment coefficient Cm is independent of the lift coefficient CL at the quarter-chord point. For finite thickness wing sections in a real fluid, the point (which will be near to the quarter-chord point) can be found such that Cm about this point is independent of incidence. This point, where d Cm / d CL is zero, is called the aerodynamic centre. Note that this is where the first differential, the rate of change of pitching moment with incidence, is zero. The pitching moment coefficient itself at that point will have a constant value, denoted by the term Cmo.

The aerodynamic centre is useful because when you construct the equations of longitudinal static stability for the whole aircraft, taking moments about that point eliminates any variation in the wing pitching moment with incidence. It makes the equations simpler, although when you see them you'd be hard pushed to believe it.

Acknowledgements to the wonderfully clear 1963 lecture notes from the late F.G. Irving (1925-2005).
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Old 8th Jan 2011, 06:46
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Hmm, I'm afraid that is not universally correct.
That would be the Center of Pressure.
The Aerodynamic Center is the Point at which the moment is constant, independent of AoA, but not necessarily Null.
Sorry guys, but that is not what I said. If you take moments about the point where the lift due to incidence acts then you will get a constant pitching moment as incidence varies and this point is generally close to 25% chord. So the aerodynamic centre is the location where the lift due to incidence acts and is independent of incidence (more or less).

Centre of pressure on the other hand varies with incidence. At zero lift the centre of pressure is at plus/minus infinity if there is any wing camber, because the pitching moment at zero lift is produced by a couple. As you increase incidence (and lift) the centre of pressure will move towards the 25% chord point but it will never get there.
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Old 8th Jan 2011, 09:36
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So the aerodynamic centre is the location where the lift due to incidence acts and is independent of incidence (more or less).
Hi CliveL,
As D120A already pointed out, there is a moment Cm0 in the aerodynamic center. This in turn implies that it is not exactly the point where the Lift is excerted, otherwise you wouldn't have a moment at this point. Normally the aerodynamic center is somewhat in front of the Center of Lift (i.e. Center of Pressure). The pitching moment of Airfoils usually increases with increasing AoA.
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Old 8th Jan 2011, 09:50
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henra;

As pointed out already in the first response to OP, lift is represented by a force acting in the aerodynamic center AND a moment. The lift force then increases with AoA while the moment is approx. constant. Alternatively, lift can be represented as a force acting in the center of pressure without a moment.
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Old 8th Jan 2011, 10:01
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Hi, CliveL

I think I understand what the CP and the AC are, at least for practical purposes. Basically the first is where Lift can be considered to act, the second is where changes in Lift can be considered to act. More or less.

But I have always had difficulties in grasping what the Aerodynamic Moment is. I see that you talk about lift due to AoA or incidence, as it is different than the lift due to camber. That is what I don't understand well.

Symmetrical airfoils have no aerodynamic moment because their camber is null, but I don't understand why camber does creates it and AoA alone does not.

What is the origin of the aerodynamic moment? I thought that the circulation around the airfoil created an equal and opposite "circulation" of the airfoil, as I read in a nice Darroll Stinton book. I mean, it is not a "theoretical" moment of a force about a point, but a "pure" moment, like that of a pair of forces with zero net force but a given resultant moment which "phisically exists".

However I can't explain why the circulation due to camber is different to the circulation due to AoA.

I hope you can enlighten me with this thing that has always puzzled me.

Thanks
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Old 8th Jan 2011, 10:07
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Originally Posted by microburst2002
However I can't explain why the circulation due to camber is different to the circulation due to AoA.
It isn't.

regards
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Old 8th Jan 2011, 12:15
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As D120A already pointed out, there is a moment Cm0 in the aerodynamic center. This in turn implies that it is not exactly the point where the Lift is excerted, otherwise you wouldn't have a moment at this point. Normally the aerodynamic center is somewhat in front of the Center of Lift (i.e. Center of Pressure). The pitching moment of Airfoils usually increases with increasing AoA.
I don't know what you mean by "in" the aerodynamic centre. Cmo is by definition the pitching moment at ZERO lift and the concept of centre of pressure in conjunction with zero lift is meaningless. As I said, Cmo is produced by a couple, which has no centre of pressure.
You can't talk of airfoil pitching moment without also specifying the point about which the moments are being measured. Usually this is taken as 25% chord for the precise reason that as incidence (AoA) changes the pitching moments about 25% chord don't vary much because the lift acts near there.

Most airfoils have positive camber (mid-thickness line above the line joining LE and TE) and this produces a negative Cmo, so if you measure pitching moments about 25% chord when the airfoil is lifting and that lift acts at the aerodynamic centre (also at 25% chord) then the pitching moment will remain equal to Cmo and the effective centre of pressure will be located at Cmo divided by lift coefficient aft of the measuring point. This means, as has been said, that the CP is behind the aerodynamic centre but that it moves towards the aerodynamic centre as lift increases.

How the pitching moment varies with increasing AoA depends entirely on the datum you assume for pitching moment. If you choose somewhere between the leading edge and 25% chord then the pitching moment will become more negative as AoA is increased. If you choose a point aft of 25% chord the moment will become more positive (nose up).
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Old 8th Jan 2011, 12:32
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HazelNuts,
As pointed out already in the first response to OP, lift is represented by a force acting in the aerodynamic center AND a moment. The lift force then increases with AoA while the moment is approx. constant.
That is exactly what I was trying to point out.

Hoped that was clear from my post !?

CliveL
You can't talk of airfoil pitching moment without also specifying the point about which the moments are being measured.
The point at which the pitching moment is measured would be the aerodynamic center

Re: Cm0 and Center of Pressure: Yes indeed for Zero Lift it is true, there is basically no Center of Pressure. Was an incorrect over-simplification, as happens often when trying to simplify things- Should not try to simplify too much.


regards,
henra
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Old 8th Jan 2011, 13:19
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Originally Posted by henra
The point at which the pitching moment is measured would be the aerodynamic center
Not true I'm afraid. The wind tunnel guys can choose any reference point they like. For convenience they usually use 25% mean aerodynamic chord, but that is not the aerodynamic centre for a complete aircraft or a wing/fuselage combination and may not be the aerodynamic centre for an airfoil or wing if they are testing at moderately high Mach Numbers

Regards

CliveL

Last edited by CliveL; 8th Jan 2011 at 13:19. Reason: addition
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Old 8th Jan 2011, 14:25
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The point about which we choose to take moments is not an irrelevant thing.

We choose one point or another for a reason.

We can try to find about which point a given force has zero moment. If we find it, we can consider the force to be acting exactly on that point.

In the case of Lift, if we find the point about the moment of Lift is zero, we have found the CP

M = L * arm
(if we are in the point where Lift acts, the arm is zero, therefore M is zero)

If we find the point about which pitching moments are constant irrespective of lift, we have found the point about which the moment created by changes in lift is zero.

dM = dF * arm

When this arm is zero, the change in moment due to a change in Lift is zero. Therefore we have the point where changes in Lift are acting. That is the AC. I don't remember the mathematical formulae that show that theoretically this point is at the 25% of the chord (subsonic).

As for the aerodynamic moment, which confuses me:

- This moment is like that of a couple of forces, isn't it? the moment is always the same no mater what point you choose, right? It's like a "pure" moment.

- Why is it always zero when the airfoil is symmetrical?

- Does it changes with Lift in cambered airfoils? Why?
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