Clarifications about the aerodynamic centre of an airfoil

[greg_rack]

Hello,

when dealing with longitudinal stability calculations of an aircraft/airfoil we are considering all aerodynamic forces relevant to the generation of moment around the c.g.(lift) as acting at a point we call aerodynamic centre which is, by definition, a point where the pitching moment of the wing stays constant with varying angle of attack.
Even though I'm not convinced of how such a point could exit, I might be okay with the definition and trust the professor who says this point just "exists"... but how can we approximate lift as acting there, when we know in reality it acts at the center of pressure? I know that the cp varies with varying angle of attack, so considering lift acting there would be a pain and involve integration and so on, so I'm wondering if maybe it is maybe just an approximation for small angle of attacks, since the cp is usually close to the ac for such values? Because, if not, how wouldn't this affect our moment calculations?

 

[FactChecker]

Moving forces and torques to other locations are done all the time. The forces of the engines, landing gears, gravity, aerodynamics, are all most conveniently thought of individually at different locations and are moved to standard reference locations to determine the overall motion of the aircraft. Similarly, the measured effect of the forces is moved to other locations to determine the net effect at the pilot location, accelerometers and gyros, stress on particular airplane components, etc.

 

[Lnewqban]

It is an aproximation in order to simplify analysis.
Please, note that the aerodynamic center (AC) concept applies to one airfoil of one rectangular shape wing only, which can't fly in a stable manner or with longitudinal stability (except for a symmetrical airfoil with zero AOA).

For swept wings, and for any tandem wings airplane, the concept of mean aerodynamic center (mac) should be instead used.

Please, see:
https://www.grc.nasa.gov/www/k-12/airplane/ac.html

https://www.physicsforums.com/threa...of-the-lift-force-and-pitching-moment.974522/

:)

 

[greg_rack]

Moving forces and torques to other locations are done all the time. The forces of the engines, landing gears, gravity, aerodynamics, are all most conveniently thought of individually at different locations and are moved to standard reference locations to determine the overall motion of the aircraft. Similarly, the measured effect of the forces is moved to other locations to determine the net effect at the pilot location, accelerometers and gyros, stress on particular airplane components, etc.

But how is it done effortless, without extra adjustments? Moving a force out of its line of action, would require adding an extra couple moment to the body in order to get to an equivalent system... wouldn't it?

 

[FactChecker]

But how is it done effortless, without extra adjustments? Moving a force out of its line of action, would require adding an extra couple moment to the body in order to get to an equivalent system... wouldn't it?

I wouldn't call it "effortless, without extra adjustments", but it is routine. F=mA applies only to the acceleration at the CG, so it is virtually certain that a force is not applied in direct line with the CG and also produces a rotation. Moving calculations to a standard reference location does not add any complexity to the motion. Some calculations are required to get the inertial moments around the reference location, but once that is done the calculations are reasonably routine. And using the same inertial moments for all forces, regardless of the location and direction of the force helps to keep things simple.

 

[greg_rack]

I wouldn't call it "effortless, without extra adjustments", but it is routine. F=mA applies only to the acceleration at the CG, so it is virtually certain that a force is not applied in direct line with the CG and also produces a rotation. Moving calculations to a standard reference location does not add any complexity to the motion. Some calculations are required to get the inertial moments around the reference location, but once that is done the calculations are reasonably routine. And using the same inertial moments for all forces, regardless of the location and direction of the force helps to keep things simple.

I am not really understanding the point... which are those calculations required to get moments around the reference location? Do you mean that these exist, but are treated implicitly and in some way "standardized"?

 

[ergospherical]

Have a read through chapter 2 of this document (specially sections 2.3 & 2.4):
https://courses.cit.cornell.edu/mae5070/Caughey_2011_04.pdf

It's interesting stuff, although I have only just gone over it so please don't ask me any difficult questions!