Aerodynamic Forces

[Cyrus]

I need some help from you aerodynamic masters. I am doing a small project for my controls lab course. We get to choose anything we want, and so I decided to make a pitch rate loop for an autopilot. The setup is very basic, I am going to carve a wing out of Styrofoam and attach a servo to a control surface. The wing will have a rod going through the COM that is attached w roller bearings to a stand. So the wing is fixed to the stand and can pivot clockwise/counter clockwise around the COM. The idea is to get a house fan to provide airflow and have Simulink move the servo so that it always keeps the wing level. The angle will be measured either with an encoder or a potentiometer. Once we get that working we can then suspend masses at various points along the airfoil to change the location of the CG. This will cause the wing to pivot forward or aft around the shaft passing through the original COM. Then the control loop can correct this error out by command up or down elevator until the wing remains level once again.

We need to show some simple calculations that this idea is feasible. Since the wing is rigidly attached to the stand, the airflow only has to be sufficient to allow for rotations.

So, what equations would be helpful here? Also, if you know how the control loops should look like, that would be nice to see as well. I am not a fluids person...so my guess would be that the force generated on the elevator would be proportional to the velocity, area and density. I want to make a simple, standard airfoil (Clark Y maybe?). The wing will be small, about 9" x 12" max.

Thanks for your ideas.

 

[AlephZero]

See http://www.dreesecode.com/primer/airfoil3.htm (and the other pages as required) for the basics...

 

[Cyrus]

Thanks, now where can I find a table listing the moment coefficients for differnt airfoils?

I know there's a blue blook with an airfoil on the cover that has lots of information.

 

[Rope]

Blue book with the airfoil on the cover...

Thanks, now where can I find a table listing the moment coefficients for differnt airfoils?

I know there's a blue blook with an airfoil on the cover that has lots of information.

Theory of Wing Sections: Including a Summary of Airfoil Data
by Ira H. Abbott, A. E. von Doenhoff

Also, don't get above the stall angle, or otherwise your controller may not be able to stabilize the motion.

 

[Cyrus]

Yep, that's exactly the blue book with the airfoil on the cover I was thinking of, thanks.

As for the stall angle, don't worry. We want to find out when it does go uncontrollable as well. So it will be interesting to see when this happens.

Would you know where in the book I should be looking?

 

[Rope]

As for the stall angle, don't worry. We want to find out when it does go uncontrollable as well. So it will be interesting to see when this happens.

Would you know where in the book I should be looking?

It will definitely be interesting, but the controllability will depend both on your controller design and on the stall characteristics of your airfoil (and by that I mean the hysteresis loop at large angle of attack (AOA).

Appendix IV has plots of the lift, drag, and pitch moment with the AOA. Clark Y is not in the book.

Cheers // Rope.

 

[AlephZero]

We want to find out when it does go uncontrollable as well.

"Uncontrollable" will probably by the default operating mode, for your first few controller designs

Your wing doesn't have to be stalled to be unstable, depending where the centre of pressure is relative to the centre of rotation.

And yeah I know "unstable" doesn't necessarily mean uncontrollable!

 

[Cyrus]

I want to calculate the force exerted on the elevator due to the airflow.

I semi-derived this equation using dimensional analysis and trying to remember stuff from fluids.

$$F= \rho A V^2$$

Obviously, p = density of air, A= profile area, V= velocity.

I don't know if I should have a coefficient infront because the air flowing over the wing will speed up/slow down depending if the elevator is going up or down relative to the wing. In other words, the velocity would increase from the free stream as it curves over the wing and impacts the elevator.

I guess for now its good enough to assume its 100%.

Looks awful close to KE*A though its missing a 1/2.

 

[Rope]

I want to calculate the force exerted on the elevator due to the airflow.
...
$$F= \rho A V^2$$
...
I don't know if I should have a coefficient infront because the air flowing over the wing will speed up/slow down depending if the elevator is going up or down relative to the wing. In other words, the velocity would increase from the free stream as it curves over the wing and impacts the elevator.

I guess for now its good enough to assume its 100%.

Looks awful close to KE*A though its missing a 1/2.

I'm not sure what your geometry is (a sketch wouldn't hurt). With a wing fixed to the stand, you'll only have pitch moments to control, in which case,
$$M=1/2 * \rho * V^2 * A * chord * Cm$$
If you're trying to control just the flap, that's another story.

 

[Cyrus]

Ok, I have a question about this equation. This seems to be the 'natural' moment of the wing itself.

Im talking about sticking a servo attached to a hinged elevator at the back.

What is the scope of the equation you provided?

Setup: Picture in your mind an airfoil. A ridgid rod goes through the CG. There is a elevator on the back of the wing that can go up or down. It's that simple.

http://img340.imageshack.us/my.php?image=untitleddx2.png

 

[Rope]

Ok, I have a question about this equation. This seems to be the 'natural' moment of the wing itself.

Im talking about sticking a servo attached to a hinged elevator at the back.

What is the scope of the equation you provided?

Setup: Picture in your mind an airfoil. A ridgid rod goes through the CG. There is a elevator on the back of the wing that can go up or down. It's that simple.

http://img340.imageshack.us/my.php?image=untitleddx2.png

The equation was that of the aerodynamic moment (it was rather a definition for the moment coefficient, not an equation...).

Given your sketch though, that's not what you need. Assuming that you want to dimension the servo, you'd probably need the pressure distribution on the flap itself when deflected (not only the magnitude of the force, but its pressure center as well). Section 8.8 and corresponding table in the "blue book" of Abbot and Doenhoff may be of some help, while some basic info is provided in section 8.37 of Milne-Thomson's "Theroretical Aerodynamics".

 

[Cyrus]

In this book, do they publish the MOI for a symmetrical airfoil?

 

[Rope]

Sorry for the delay... what's MOI? If it's the moment of inertia, then the answer is no (you could nevertheless approximate it as a beam (2D) or a plate (3D).