Static Longitudinal Stability (The study of)

[Superpilot]

In the study of static longitudinal stability, why is it accepted that lift always acts at the Aerodynamic Centre? What are the reasons for this?

I'm sure I'll discover soon but it would aid my learning if I found out now!

Thanks

[JohnFTEng]

As I recall, and its going back a few years to uni. days, the centre of lift does move back and forth as speed varies. A notable example is Concorde where there is huge change subsonic/supersonic so it needed to shift fuel to compensate. The idea of a fixed centre is to make the maths simpler. We fix the centre of lift and have a variable moment - twisitng force - about the same point. So all the forces act at this one point simplifying the equations. For full details you'll need to check a textbook.

[rhovsquared]

JohnFTEng: I don't think it really exist anymore with FBW ????

but the HTBJ explaination is the allowed range of airspeed/Mach no divergence allowed, for a given hands-off trimmed out yoke; I'm paraphrasing and perhaps slightly bastardizing now.

BTW Mad (flt Scientist) covered the other aircraft stabilities and modes thereof wonderfully in another thread...
just can't find it now--- diazapam + codeine --- anyone wonder why I no longer fly (at this time period in life stopped flying

rhovsquared

[Rivet gun]

Originally Posted by Superpilot

In the study of static longitudinal stability, why is it accepted that lift always acts at the Aerodynamic Centre? What are the reasons for this?
I'm sure I'll discover soon but it would aid my learning if I found out now!
Thanks

Basically because "aerodynamic centre" is defined that way.

The "center of lift" does move chordwise with angle of attack. Center of lift is defined such that there is a force but no turning moment about that point.

Because center of lift moves, it is confusing for engineers. Instead of center of lift therefore it is convienent to define a fixed point and consider there to be both a force and a moment acting at this point. It turns out that it is possible to find a point at which the force varies with angle of attack but the moment is nearly constant. This is the Aerodynamic centre.

http://www.grc.nasa.gov/WWW/K-12/airplane/ac.html

[Mad (Flt) Scientist]

Ah - but lift doesn't act at the "aerodynamic centre" (or "center"). If it did there would be no pitching moment at the AC.

The AC is simply the point where d(PM)/d(alpha) is zero, but as the diagram shows, PM need not be zero.

There are two competing ideas stated above, and I'll try to disentangle them if I can.

Originally Posted by JohnFTEng

The idea of a fixed centre is to make the maths simpler. We fix the centre of lift and have a variable moment - twisitng force - about the same point. So all the forces act at this one point simplifying the equations.

What you're talking about there is a fixed moment reference centre. In principle you could choose any given point for an aircraft type, and as long as you're CONSISTENT and stick to that reference point then you can have relative simplicity in how you apply your equations of motion. That reference point is often, for historical reasons now as much as anything, defined to be at the 25% position on the mean aerodynamic chord, but it doesn't have to be, and there's no particular reason why that position should be special for a "real" aircraft.

The Centre of Lift is the point at which the summed lift on the aircraft (or some portion of it: you can have a "centre of lift" for a tail or a fin alone, too) actually may be assumed to act. It's the integration of the pressures over the surface, and as stated moves about all over the place with changes in Mach, alpha, camber, etc. It's a pretty useless thing to use a reference, but the fact that it does move about is of course rather important.

The Aerodynamic Centre is indeed the point where d(Pitching Moment)/d(alpha) is zero. It's important because the position of the cg relative to the AC is important in determining the longitudinal stability of the aircraft. The idea of the Neutral Point is closely related to the concept of the AC.