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I would like to know the lift coefficient with 10 degrees of flaps extended.

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  • $\begingroup$ Why do you want to know this? Under which circumstances; in a windtunnel where everything else remains the same, or during flight where extending flaps happens together with many other parameters changing? $\endgroup$ – DeltaLima Jul 3 '18 at 16:54
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As mostly when questions are vague, the answer is: It depends.

If nothing else changes, the nominal lift coefficient stays the same. A coefficient is referenced to an area, and for aircraft this is the reference area which is derived from the wing area. Regardless of flap settings, the reference area stays fixed, and so does the lift coefficient because neither the mass nor the speed of the aircraft have changed when flaps have been set.

In reality, the aircraft will slow down when flaps are extended, and it can afford to do so because drag is increased and stall speed lowered. Now, with the lower flight speed, the lift coefficient will go up in proportion to the ratio of the speeds before and after squared: $$c_{L_{flaps}} = c_{L_{clean}}\cdot\frac{v_{clean}^2}{v_{flaps}^2}$$ Again, this assumes the same reference area.

In a wind tunnel where the aircraft model is fixed to a sting and the angle of attack is controlled, setting flaps will increase the lift coefficient by the difference in zero-lift angles of the aircraft with and without flaps, multiplied by the lift curve slope of the aircraft.

$$c_{L_{flaps}} = c_{L_{clean}}+ (\alpha_{0_{clean}} - \alpha_{0_{flaps}})\cdot c_{L_{\alpha}}$$

Note that the lift curve slope increases when setting flaps increases the effective wing area. Again, all is referenced to the unchanged reference area.

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With extended flaps, the chord length of the airfoil increases, increasing area of the wing itself. This would decrease the lift coefficient of the wing, thanks to this formula from NASA:

Cl = L / (A * .5 * r * V^2)

Hope I could help, at least partially.

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When an aircraft flap is deployed, it increases the effective camber of the wing airfoil. Thus, the zero lift angle, i.e., AoA at zero lift decreases as a result the cl-a curve shifts to the left.Increase in Clmax due to increase of camber.

As you would know, a cambered airfoil has higher cl than a symmetric airfoil. It is the same concept here. As the camber increases, so does the cl.

To calculate the change wrt flap deflection you need more information. Either you could do this physically on a model of A380 or you could try to plot the curve if you have aircraft aerodynamic data.

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  • $\begingroup$ This would be true if nothing else changed, including AoA. In this case the aircraft would start climbing (initially). But in all practical situations we'd assume that we want to maintain steady flight, and this means that we want to keep lift the same. Which means: either cl must stay the same, by reducing AoA, or we slow down and choose the appropriate cl (and AoA), which can be greater or smaller depending on the chosen airspeed. $\endgroup$ – Zeus Jul 4 '18 at 1:46

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