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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

enter image description here

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. enter image description here

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 ?

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  • $\begingroup$ 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" $\endgroup$ – user3528438 Nov 26 '18 at 19:25
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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.

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    $\begingroup$ I’d add that it’s called “reference area”, which also simplifies comparing different shapes for their efficiency. $\endgroup$ – Gürkan Çetin Dec 9 '18 at 20:27
  • $\begingroup$ @GürkanÇetin Good suggestion - done! $\endgroup$ – Cpt Reynolds Dec 9 '18 at 20:51
  • $\begingroup$ Capt @CptReynolds, this thing is quite confusing me. In Wikipedia. It is written like this: "The aspect ratio AR is the ratio of the square of the wingspan b to the projected wing area, which is equal to the ratio of the wingspan b to the standard mean chord (SMC)". As surface area affecting the wing area, means that AoA is calculated as the factor affecting the lift force. $\endgroup$ – AirCraft Lover Dec 10 '18 at 2:17
  • $\begingroup$ In my opinion, increase the AoA (before it get stall) definitely will increase thrust, which will accelerate the airplane, which at the end will increase the lifting force. But at the same time the increase of the AoA will decrease the lifting force. Mean, the increase of the AoA is not linearly increase the lifting force. $\endgroup$ – AirCraft Lover Dec 10 '18 at 2:22

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