# How should control surfaces be modeled in simulations?

I am modeling the lift and drag forces of a wing in software of my own creation.

If I have a wing which fits the profile of (for example) NACA 0024, it is a simple operation to look up the proper coefficients for lift and drag based on the current angle of attack for the wing.

But what happens if I slap an aileron on the trailing edge?

Do I need to re classify the wing based on the new geometry?
Should I treat control surfaces as their own aerodynamic bodies and look for lift/drag tables for them?
Since this is just a simulator, would it make sense to just offset the current coefficients by some value based on angle of deflection?

I am admittedly uneducated in aerodynamics and aviation, so please forgive me if I've come at this problem from entirely the wrong direction.
Any help or advice would be greatly appreciated!

Thanks!

Any control surface changes both local camber and local incidence, so it would be best if you change the coefficients accordingly. If you use a panel code, it would be enough to change the local surface inclination (= the flow direction at the local control point) by the deflection angle.

If you need formulas for the coefficients: A control surface with a cord length fraction d (of total chord length) will change the local lift coefficient $$c_l$$ with $$\Delta c_l = \sqrt{d}\cdot c_{l\alpha}\cdot sin (\eta),$$ where $$\eta$$ is the deflection angle in radians and $$c_{l\alpha}$$ is the lift coefficient gradient over angle of attack of the original airfoil. The additional lift will act at a point between 50% and 25% of wing chord. The higher value is for very short flaps, the lower for all-flying surfaces (technically 100% flap chord), so a control surface deflection will add a torsional load. Drag will not be affected for small deflection angles, but when they get bigger, first drag rises and then the lift increase becomes nonlinear.

If you stay in the linear range (15° with 30% flap chord, 25° with 15% flap chord at moderate angle of attack) you can linearly add the flap effect (offset the coefficients). Going beyond that in both deflection angle and angle of attack will need a reduction in flap effectivity which can (in extreme cases) even become control reversal.

Also note that the aileron especially will twist the wing such that its effectivity is reduced at higher dynamic pressure. The details of this effect depend on the stiffness of the wing.

Your example of a NACA 0024 is already so thick that it will not tolerate big flap deflection angles and show separation on the suction side. Good wing thicknesses for subsonic flight are between 12% and 15%, and the most extreme ones (like the root of highly loaded high aspect ratio wings) will still be below 20%. Supersonic wing thicknesses are generally between 4% and 6%.

If you depend on that control surface for trimming the aircraft, don't let its effectivity decrease (as it would in reality), but give it linear effectivity (without the sine function) into infinity and punish large deflection angles with excessive drag (or whatever runs against your target parameter).

• Wonderful! This is quite a bit to run with. TBH I just picked 0024 to start with because it was easy to make a 3D model of, and 'reads well' on screen. Thanks again for all of the helpful information! Sep 21, 2014 at 15:47
• @Habitablaba: Just one detail: Make sure you do not use the percent value of d in the root, but the fraction. Also, I forgot the lift curve slope. Sorry for the wrong description, this was not my day! Sep 21, 2014 at 18:44