# How do airplane designers determine flap deflection angles for flaps of various % wing chords?

How do airplane designers determine flap deflection angles for flap chords of various % wing chords? E.g. flap chord of 30%, 40% or 50% of wing chord.

I understand most flaps' chords are about 25% of the wing chord, but I understand Rutan's Grizzly had a flap chord of 55% of wing chord.

I assume you could use theory to figure this out, but that doesn't mean it works like that in the real world.

Is this information readily available in graph or chart form?

I thought I saw a link in a post on StackExchange re this from Peter Kaempf, but I can't find it.

• First with tunnel data or CFD which is later refined in flight test. – Peter Kämpf Sep 2 '20 at 17:52
• @Fred, your edits have cleared this up for me, but I still think you are thinking about this in reverse. For example, almost every plane I've flown has flap settings in 10 degree increments. (One is 15 degrees...) I think the designers prefigure standard settings, then by calculation and test derive the performance obtained. – Michael Hall Sep 2 '20 at 18:37

As a rule of thumb, flap effectiveness (that is lift coefficient change per flap deflection angle or c$$_{L\eta}$$) is proportional to the square root of the flap's percentage. A more precise formula was derived by Hermann Glauert (search for the name and you will find that elusive answer by me)

What also changes is the hinge moment needed per degree of flap deflection; this, however, changes with the square of the flap's percentage. By trading off effectivity versus force, a designer will find the best flap percentage for each control surface.

Next, wind tunnel data is used for finding the effectiveness over deflection, because this value decreases with higher deflection angles and is hard to catch by CFD because viscous effects are strongest near the trailing edge and need lots of effort to model correctly. The desired control response and trim should be achievable with maximum deflections of below ±15° (the useable range is wider for smaller percentages) and the flight test will reveal whether the calculations were correct.

If by % flap chord you mean the fraction of the wing chord occupied by the undeflected flap, then the bigger the % flap chord, the smaller the angular deflection needed to achieve the same effective camber.

Specific cases depend, of course, on the airfoil, the AoA envelope, unusually large or small flaps, flaps that extend aft, flaps with slots, etc. That would be more plots and tables than could fit into an answer here.