Aerodynamic Center
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I must have somthing wrong in my brain but I still don't get it.
Is it correct if I say that the aerodynamic moment is the moment of the Lift force about a point?
Is it correct if I say that the aerodynamic moment is the moment of the Lift force about a point?
Yes, but.....
In simple terms we use a point termed the centre of pressure, which is the point on the wing chordline where the total lift may be considered to act.
In reality this point cannot exist, but we may make empirical calcultaions based upon its' existence and its' position with respect to percentage of the wing chord.
I am able to supply a diagram showing just how the pitching moments are derived and how they change with changing angle of attack/CL.
Edit to say prolly best done via PM.
In simple terms we use a point termed the centre of pressure, which is the point on the wing chordline where the total lift may be considered to act.
In reality this point cannot exist, but we may make empirical calcultaions based upon its' existence and its' position with respect to percentage of the wing chord.
I am able to supply a diagram showing just how the pitching moments are derived and how they change with changing angle of attack/CL.
Edit to say prolly best done via PM.
Last edited by Lightning Mate; 12th Jan 2011 at 11:18.
There are many different ways in which we could accurately describe the lift forces acting on the aerofoil.
METHOD 1.
One way is to add together all of the individual lift forces to produce a single lift force. This single lift forces acts at the centre of pressure.
Because it acts at the centre of pressure it does not exert any pitching moments about the centre of pressure.
So we have lift expressed as a single force, (but no pitching moment) acting at the centre of pressure.
But if we were to measure the moments about any other point on the aerofoil we would find that the lift exerts a moments that is the product of the lift force multiplied by its distance from the centre of pressure.
This means that a second method of expressing the effect of lift is a force plus a pitching moment, both acting at a point that is not the centre of pressure.
METHOD 2
As LM’s diagram shows, if we measure the moments about the trailing edge we will find that increasing angle of attack produces an increasing pitch up moment.
If we take moments about a point slightly ahead of the trailing edge we will find that the rate of increase of pitch up moments is less than it was at the trailing edge.
If we gradually move forward from the trailing edge the rate of increase of pitch up moments will gradually decrease.
If we take moments about the leading edge we will find that increasing angle of attack increases the nose down moment.
If we take moments about a point slightly behind the leading edge we will find that the rate of increase of pitch down moments is less than it was at the leading edge.
If we gradually move aft from the leading edge the rate of increase of pitch down moments will gradually decrease.
If we repeat this process, gradually moving forward from the trailing edge and aft from the leading edge we will find a point at which the pitching moments do not change with changes in angle of attack. This point is the Aerodynamic Centre of the aerofoil.
So we can express the effects of lift as a single force plus a constant pitching moment acting at the Aerodynamic Centre.
METHOD 1.
One way is to add together all of the individual lift forces to produce a single lift force. This single lift forces acts at the centre of pressure.
Because it acts at the centre of pressure it does not exert any pitching moments about the centre of pressure.
So we have lift expressed as a single force, (but no pitching moment) acting at the centre of pressure.
But if we were to measure the moments about any other point on the aerofoil we would find that the lift exerts a moments that is the product of the lift force multiplied by its distance from the centre of pressure.
This means that a second method of expressing the effect of lift is a force plus a pitching moment, both acting at a point that is not the centre of pressure.
METHOD 2
As LM’s diagram shows, if we measure the moments about the trailing edge we will find that increasing angle of attack produces an increasing pitch up moment.
If we take moments about a point slightly ahead of the trailing edge we will find that the rate of increase of pitch up moments is less than it was at the trailing edge.
If we gradually move forward from the trailing edge the rate of increase of pitch up moments will gradually decrease.
If we take moments about the leading edge we will find that increasing angle of attack increases the nose down moment.
If we take moments about a point slightly behind the leading edge we will find that the rate of increase of pitch down moments is less than it was at the leading edge.
If we gradually move aft from the leading edge the rate of increase of pitch down moments will gradually decrease.
If we repeat this process, gradually moving forward from the trailing edge and aft from the leading edge we will find a point at which the pitching moments do not change with changes in angle of attack. This point is the Aerodynamic Centre of the aerofoil.
So we can express the effects of lift as a single force plus a constant pitching moment acting at the Aerodynamic Centre.
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From what I read on the books, I understand that the Lift of an airfoil can be thought of as the sum of the upper Lift and lower Lift.
In symmetrical airfoils, both upper and lower Lift always act at the same point of the chord and this point, the CP, is always the same regardles of angle of attack, and happens to be at the AC.
In cambered airfoils, these lifts act at different points, so that we have a pair of parallel forces, the resultant of which acts at the CP. The CP location changes with AoA.
The existence of this pair of parallel forces reveals an effect that has an aerodynamic origin. Which exists per se. It is not the moment of any force about any arbitrarily chosen point, but a very phisical twisting torque that can be measured in the wind tunnel and expressed in Newtons-meters or whatever unit.
It is this twisting torque that I am interested in. I don't accept that we consider Lift as acting at the AC because that greatly simplifies calculations. Lift acts at the CP. That's where it acts.
I believed that this twisting moment (pitch down in typical airfoils) was decreasing with AoA, which of course meant a negative effect on airplane's stability. However, when taking the AC as the origin of moments and deriving in the stability equation, this effect is "magically" eliminated, and I can't understand why they do that. I just don't buy it.
I accept empirical evidence, but I don't like when mathematical tricks are used. Then I get lost not because of my mathematical ability (I was very good at that years ago) but because they (not you, the books) are cheating.
I know well what the CP is and what the AC is. But I think the aerodynamic pitching moment is unduly simplified by everybody.
In symmetrical airfoils, both upper and lower Lift always act at the same point of the chord and this point, the CP, is always the same regardles of angle of attack, and happens to be at the AC.
In cambered airfoils, these lifts act at different points, so that we have a pair of parallel forces, the resultant of which acts at the CP. The CP location changes with AoA.
The existence of this pair of parallel forces reveals an effect that has an aerodynamic origin. Which exists per se. It is not the moment of any force about any arbitrarily chosen point, but a very phisical twisting torque that can be measured in the wind tunnel and expressed in Newtons-meters or whatever unit.
It is this twisting torque that I am interested in. I don't accept that we consider Lift as acting at the AC because that greatly simplifies calculations. Lift acts at the CP. That's where it acts.
I believed that this twisting moment (pitch down in typical airfoils) was decreasing with AoA, which of course meant a negative effect on airplane's stability. However, when taking the AC as the origin of moments and deriving in the stability equation, this effect is "magically" eliminated, and I can't understand why they do that. I just don't buy it.
I accept empirical evidence, but I don't like when mathematical tricks are used. Then I get lost not because of my mathematical ability (I was very good at that years ago) but because they (not you, the books) are cheating.
I know well what the CP is and what the AC is. But I think the aerodynamic pitching moment is unduly simplified by everybody.
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Thank you Keith
Now I start to understand better.
So we are substituting
Lift-acting-at-the-CP by
Lift-acting-at-the-AC-plus-a-pitching-moment (which is convenient because it is constant with AoA).
The net effect would be the same as they are equivalent concepts.
I have always accepted that demonstration of the existence of a point with such a property, graphically expressed in the sketch by LM.
hmmmmm
But Is this pitching moment the same as the aerodynamic moment? Or is the sum of the AM plus the moment of Lift about the AC?
To find the required tailplane lift to trim the airplane in steady flight, we need to know the value of the Lift, the location of the CP and the value of the aerodynamic moment (which should be independent of any point we consider, if we are talking about a couple of forces).
Or, alternatively, we can consider Lift as acting on the AC without forgetting to add the pitching moment with respect to AC.
Still don't understand how the effect of the AM "magically dissapears" in the stability equation.
Now I start to understand better.
So we are substituting
Lift-acting-at-the-CP by
Lift-acting-at-the-AC-plus-a-pitching-moment (which is convenient because it is constant with AoA).
The net effect would be the same as they are equivalent concepts.
I have always accepted that demonstration of the existence of a point with such a property, graphically expressed in the sketch by LM.
hmmmmm
But Is this pitching moment the same as the aerodynamic moment? Or is the sum of the AM plus the moment of Lift about the AC?
To find the required tailplane lift to trim the airplane in steady flight, we need to know the value of the Lift, the location of the CP and the value of the aerodynamic moment (which should be independent of any point we consider, if we are talking about a couple of forces).
Or, alternatively, we can consider Lift as acting on the AC without forgetting to add the pitching moment with respect to AC.
Still don't understand how the effect of the AM "magically dissapears" in the stability equation.
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Microburst,
Can I suggest you 'Google' AA241 which will put you into a Stanford University site that gives course notes for Aircraft Design.
You will find the answers to all your questions there (and much more besides)
CliveL
Can I suggest you 'Google' AA241 which will put you into a Stanford University site that gives course notes for Aircraft Design.
You will find the answers to all your questions there (and much more besides)
CliveL
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Constants such as Cmo which are independent of incidence disappear when the equation is differentiated with respect to alpha. It's not a trick or anything, it's just that some engineering equations couldn't be solved at all unless you set them up in an elegant way. Choosing a subtle point about which to take moments, which has the effect of putting a number of nasty terms to zero later on, is part of the art.
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I know, but many times the physical meaning of something is lost while making it easier to be calculated mathematically.
This is what happens in this case, to me. I can't see through the equations.
You know what I mean? There are many who understand the equations of Einstein's theory of Relativity, but not so many who actually understand that theory.
CliveL, thank you. Probably Stanford notes are too much for a humble pilot like me. But I will take a look at it anyway
cheers
This is what happens in this case, to me. I can't see through the equations.
You know what I mean? There are many who understand the equations of Einstein's theory of Relativity, but not so many who actually understand that theory.
CliveL, thank you. Probably Stanford notes are too much for a humble pilot like me. But I will take a look at it anyway
cheers
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Nah! there are lots of diagrams and even a nice little Java applet that lets you change AoA and see what that does to pressure distributions, lift and pitching moment.
CliveL
CliveL
Constants such as Cmo which are independent of incidence disappear when the equation is differentiated with respect to alpha. It's not a trick or anything, it's just that some engineering equations couldn't be solved at all unless you set them up in an elegant way. Choosing a subtle point about which to take moments, which has the effect of putting a number of nasty terms to zero later on, is part of the art.
I shall now leave the thread because it's becoming silly, but before I go - ZERO LIFT!
