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Old 11th Dec 2012, 20:24   #1 (permalink)
 
Join Date: Nov 2008
Location: Bergen, Norway
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Question Aerodynamical center

Good morning all,

I have my FAA CPL and I'm working to convert it into a JAA ATPL. However, the Oxford books are talking a lot about aerodynamical center.
I think I've understood the definition, but I'm not completly sure about the use.

Especialy when the illustrations show's both lift from the wing AND tailplane.

When working with CP (center of pressure) and CG, the CP usally is aft of the CG. But on these illustrations, CG is between the wing AC and the tailplane AC, and they are both producing positive lift.

Both Lw and Lt on this illustration ground in their respective AC.
The CG also seems to be far aft of normal?






This is what I'm used to:



All help is appriciated (and I hope this is the right forum :-) )
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Old 13th Dec 2012, 04:54   #2 (permalink)
 
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I was reading up on this today, so I'll have a stab at trying to explain what I've learned.

The aerodynamic centre of an airfoil (or an aircraft) is a useful concept when considering its pitch stability.

To be stable in pitch, an aircraft that is perturbed nose-up from its trimmed angle of attack must, as a result of the increased angle of attack of wing and tailplane, develop a nose-down moment (and vice versa).

This is achieved by setting the tailplane at a lower aerodynamic angle of attack than the wing; the change in lift of the tailplane exerts a bigger change in moment (from going, say from 1 to 2 degrees AoA - a doubling of lift) than does the main wing (in going from say 3 to 4 degrees AoA - an increase in lift of 33%)

If you look at the centre of pressure of the two airfoils combined you can see that it therefore moves around as their angles of attack change together. This is somewhat unhelpful from an analytical point of view.

Even for a single cambered airfoil, the centre of pressure also moves around somewhat as the angle of attack changes.

If you're familiar with the idea of the coefficient of lift, then you should quickly understand the idea of the pitching moment coefficient. The pitching moment coefficient of a wing (or of two airfoils combined together in an aircraft) relates the twisting force exerted on the wing (or aircraft) to the dynamic pressure, the wing planform area and the chord. Because the pitching moment coefficient is related to a twisting force or torque, it must obviously change according to the point about which we choose to measure that torque. Therefore it is correct to talk about the pitching moment coefficient about a particular point. Also, in general, the twisting force varies with the angle of attack, even for constant dynamic pressure, planform, and chord. So, generally, the pitching moment coefficient is a function of AoA.

It turns out that if we measure the torque generated by the airfoil (or aircraft) about a carefully selected point, the pitching moment coefficient about that point becomes independent of the angle of attack. (In real life this is approximately "exactly" true only for a limited range of AoA, such as not in the stalled regime.)

That chosen point is defined as the aerodynamic centre of the wing (or aircraft).

If you imagine the twisting force of the wing (or aircraft) acting around that point, the torque it generates around that point becomes a function of airspeed alone (physical attributes like planform and chord remaining equal) through the dependence of the pitching moment on the dynamic pressure.

An analysis of the wing and tail configuration, in respect of their relative areas and angles of attack, principally) will tell you where the aerodynamic centre of the aircraft (in this case) is, and from there it's easy to spell out the criterion for positive pitch stability: the centre of mass of the aircraft must be ahead of the aerodynamic centre. Why? If the aircraft pitches nose up, it slows, the twisting moment holding up the nose decreases and the nose drops as a result. And vice versa. You no longer have to consider the change in twisting forces on the airplane caused purely by the change in AoA.

The aerodynamic centre of an aircraft is also called the neutral point. If the centre of mass is located at the neutral point the aircraft has neutral pitch stability. The distance between the centre of gravity and the neutral point is called the static margin. Depending on which way you define it, you can say that the requirement for positive pitch stability is that the static margin must be negative (usually that way around).

Quote:
When working with CP (center of pressure) and CG, the CP usally is aft of the CG. But on these illustrations, CG is between the wing AC and the tailplane AC, and they are both producing positive lift.
Many people incorrectly think that the CG must be ahead of the CP of the wing, and consequently the tail must to exert a downforce, for stability. That's not correct. In fact the CG can go all the way back to the neutral point which is some way behind the CP of the wing. The tail will then be lifting, as shown in your diagram. As the CG retreats rearward the AoA of the tailplane must increase to generate relatively more lift (by trimming). At the point when the AoA of the tailplane becomes equal to the AoA of the main wing the CG has reached the neutral point and the aircraft is neutrally stable. If the CG goes further rearward then the aircraft becomes unstable in pitch.

If you look in the POH for many aircraft the rear CofG limit is way way aft of the quarter-chord point which is where the CP of the wing is, approximately. Clearly the tailplane is able to provide significant lift and still be stable.

Last edited by photofly; 13th Dec 2012 at 04:57.
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Old 13th Dec 2012, 08:16   #3 (permalink)
 
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Thank you for your answer,
I got most of it, but some stuff is still not making any sense.

- AC is not the same as neutral point for an aircraft? Isn't that the most aft point for the CG with the aircraft NOT beeing unstable? The point where the tailplane arm is to short to create enough pitching motion?
- You say that "the centre of mass of the aircraft must be ahead of the aerodynamic centre." I wish, but even the fwd limit of CG is aft of AC in my book.
- I know that it's possible for the tailplane to create lift in some situations, but in these illustrations it will produce lift even at fwd CG limit. The camber of the tailplane is also positive in these illustrations...
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Old 13th Dec 2012, 12:02   #4 (permalink)
 
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Each airfoil has its own aerodynamic centre. When you have a wing and a tailplane you have a single "aerodynamic system". Just like you define the AC of a wing as the point about which the pitching moment coefficient becomes independent of the AOA, you can also find the point about which the pitching moment coefficient of the whole system (the aircraft) becomes independent of pitch attitude. That's the neutral point. The CofG must be ahead of the neutral point.

I'm new at this so I don't know if the experts use the term aerodynamic centre in respect of the entire aircraft. Your diagram shows the AC for each wing separately. For a flying wing design - one wing with no tailplane, the neutral point is at the AC. When you have a second wing you have to take into account its effect on stability (that's what it's there for). So the same concept of aerodynamic centre can be applied to the aircraft (and ought to take into account the fuselage aerodynamics, undercarriage aerodynamics, when extended etc), and that's when it's called the neutral point.

Quote:
I know that it's possible for the tailplane to create lift in some situations, but in these illustrations it will produce lift even at fwd CG limit. The camber of the tailplane is also positive in these illustrations...
I'm reaching the limits of my knowlege here, but if you're designing a large aircraft you're looking for every ounce of efficiency which means never flying with the tail producing a down-force. I don't have any experience with the actual figures involved for big planes though.
Quote:
Isn't that the most aft point for the CG with the aircraft NOT beeing unstable? The point where the tailplane arm is to short to create enough pitching motion?
The rear CofG limit isn't particularly linked to how much pitching motion the tail can create. If that were the case then a CofG out of limits to the rear would always cause the nose to pitch up. The stability of the aircraft is actually related to how the pitching moment changes with a disturbance, not to how big it is. A CofG out of limits to the rear will cause the nose to pitch up if it's disturbed in a nose-up direction, but will cause the nose to pitch down further if it's disturbed in a nose-down direction.
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Old 13th Dec 2012, 15:51   #5 (permalink)
PJ2
 
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Bluescan, photofly, great questions. Take a look at the "Theory of Lift" thread in Tech Log - you might find some info there. Also, take a look at "Pitching Moment".

For a good discussion on the aerodynamic center, find a book entitled, "Fundamentals of Flight" by Richard Shevell or take a look at this book by Darroll Stinton.

PJ2
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Old 18th Dec 2012, 08:00   #6 (permalink)
 
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The aerodynamic centre is the point on the wing chordline where the pitching moment remains constant with changes in AoA/CL.

For a normal positively cambered aerofoil it is nose-down.

Diagram available.
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Old 18th Dec 2012, 09:11   #7 (permalink)
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Remembering that it is technically very unlikely the PM will be absolutely 'constant', particularly for cambered sections..
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Old 19th Dec 2012, 11:03   #8 (permalink)
 
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There's a very good and clear discussion of AC and longitudinal stability beginning on p 47 of this book, Aerodynamics For Naval Aviators:

http://www.askacfi.com/wp-content/pl...load.php?id=15

Also from page 250 onwards.

Last edited by photofly; 19th Dec 2012 at 11:07.
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Old 20th Dec 2012, 07:18   #9 (permalink)
 
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Old 22nd Dec 2012, 16:19   #10 (permalink)
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Thank you for the link, photofly. - PJ2
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