Originally Posted by
Microburst2002
Regarding the shape of the CL vs AoA curves for clean and flaps down:
They are always parallel to each other. Is this a simplification or that reflects the wind tunnel tests?
If so, What is the meaning of that? Why do these curves not have different slopes?
Theoretically, any "thin" aerofoil has a lift curve slope - rate of change of CL with AoA - of 2 * pi per radian. Which works out to 0.1097 CL per degree. So any two dimensional, infinitely long wing would have the same lift curve slope, and that would apply even if the aerofoil was changed - such as by putting down the flaps. So, in an ideal or perfect sense, the lift curve slopes should be perfectly parallel, and of the value mentioned.
In practice, even a 2D section doesn't quite achieve that perfect 2*pi value, but numbers in the range of 0.105 are typical. Once we start to have three-dimensional effects, the slope changes again, but importantly for this discussion the 3-D effects are dominated by the effect of the finite span, which is pretty much the same effect for a given wing whether flaps are extended or retracted.
As a result of all this, the slopes are
slightly different for different flap configurations, but perhaps not more than 5% variable between the different configurations for a given aircraft. As a result its a reasonable simplification to say that the slopes are parallel. The same kind of simplification we make when saying that slats extend the slope. The following two pictures compare the idealised and typical situation. (With even the "typical" one having simplifications)
Unless you are really getting into the weeds, that first picture is good enough to understand the basic effects, and it's a great deal easier to sketch too!!