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 ?
TL; DR: It depends on the specific assumptions of the aerodynamic model, but normally wing area is considered constant.

Wing area normally is defined as fixed, and the CL is given so that any control surface deflection results in a change in lift curve, i.e. CL, only. One could equally attribute the change in total lift following a control surface deflection to an associated change in surface area, and then the resultant new CL to go with the deflection would accordingly be of different magnitude, so as to yield the same total lift.

It is a convenient general convention as far as I know, to consider wing area (also very appropriately dubbed as reference area) as constant, because it essentially eliminates one variable from the model.