# Does a rotating control surface change the wing area?

It might seem like a silly question, but bear with me.

I am using the standard formula to calculate the lift force of a wing.

L = (1/2) d v2 s CL

My question related to the s part of the formula. According to what I can find this area is calculated as if the wing was completely flat. This would be from the leading to trailing edges.

Wing Area = Wing Span x Average Chord

I am currently doing exactly this, to calculate the lift force of the wing on a computer model while model is flying. It is done at regular intervals along the wing span and added up. The sections that include control surfaces have different chord lines when the control surfaces rotate as expected causing the desired affect on lift.

BUT I noticed that the wing area also changes with the change of control surface angle. As the control surface moves closer to its upper or lower limits the surface area changes too.

Control surface at 0 deflection and at max

Red part is a control surface.

Obviously on a simple wing, the rotating control surface cannot affect the (3d) surface area of a wing. Or should not. Yet using the formula to calculate the s part the wing now has a smaller area.

To get to the point, I would like to know if this makes sense. Does the ...effective wing area change during operation of a control surface ?

• This is like "does speed change the meaning of time" or "does inflatation of a tire to different pressures affects its weight". Answer is "yes but depending on what you are working on it may or may not be meaningful" – user3528438 Nov 26 '18 at 19:25