How does flight control surface authority change with AOA?

I am working on semi-realistic (let's just call it "believable") flight simulation component set for a game engine. One of the topics that I tried to research but could not find reliable information on is the authority or effectiveness of flight control surfaces over AOA. I would prefer to see some graphs or some approximate math expression. I've found more or less enough information on other topics (e.g. lift coefficient over AOA) but I cannot really come up with reliable information (even just theory) regarding flight control surfaces. Gut feeling tells me that they would probably behave similar to wing, but on the other hand elevators should really not lose much authority even past stall AOA.

• I think you may be misunderstanding the dynamics, the effectiveness of flight controls varies with airspeed. Maybe what you are asking is how much force is generated by flight surfaces at different angles?
– GdD
Commented Jun 11, 2015 at 9:51

Control authority is a function of the local dynamic pressure (the product of air density and speed squared), geometry (the product of control surface area and lever arm), local angle of attack $\alpha$, the angle of deflection $\eta$ and the relative flap chord. Generally, the control surface works fairly linearly in a range between $-15° < \eta < 15°$ for a relative flap chord of 25% rsp. $-25° < \eta < 25°$ for a relative flap chord of 15%. Interpolate for values in between. Note that flap effectiveness is proportional to the square root of the relative flap chord, such that a flap of 15% needs twice the deflection angle to effect the same control authority than a flap of 60% relative chord.

Bigger deflection angles reduce flap authority, and here it becomes complicated, because local flow phenomena can make a big difference, up to control reversal. For a simple model you may just assume that control authority is cut in half for all deflections exceeding the limits mentioned above.

This all is only valid for moderate angles of attack, when forces change linearly with angle of attack changes. Once you approach the lift force limits of the particular control surface, authority suffers. Now it is important to know the local flow field: Elevators fly in the wake of the wing, which in effect reduces the angle of attack changes at the elevator compared to those at the wing. This means that most elevators still have a healthy lift margin when the wing starts to stall. But stall they will, eventually. To give you an idea how a wing performs over the first 180° of angle of attack, see the plot below. A plot for a control surface should look similarly. It is taken from a book which should exhaustively answer all your questions about control surface authority, be it subsonic or supersonic, for all conceivable configurations. It has been written by Sighard Hörner half a century ago and is still the best you will be able to find on this topic.

For an example of an airfoil's flap effectiveness over AoA, see the plot below of the XFOIL calculation for a Wortmann FX71-L-120 symmetric airfoil with a 25% flap at a Reynolds number of 1 Million and with a fixed boundary layer transition at 60% of chord. Note especially the hysteresis close to the maximum and minimum lift angles of attack at higher deflection angles (own work; c$_a$ is the lift coefficient).

ALL flight control surfaces lose authority at lower speeds and/or in less dense air (heat/altitude). In most cases, this can be compensated somewhat by increasing the deflection until the max is reached.

Some aircraft with fly-by-wire can compensate for the 'sloppy' controls somewhat by doing the increase in deflection automatically.

Although I can't help you with formulas or graphs, I can tell you that the reduction in effectiveness can be very significant.

However, by design, the elevator stalls much later than the main lifting surfaces for stability reasons and to have the ability to get out of a stall (naturally or by pilot input).