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## Main Question or Discussion Point

by how much will single-slotted Fowler-type flaps increase the drag coefficient of an aerofoil?

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by how much will single-slotted Fowler-type flaps increase the drag coefficient of an aerofoil?

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Filip Larsen

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[tex]

\Delta C_D = 0.9 (c_f / c)^{1.38} (S_f / S) sin^2 \delta

[/tex]

where c

[1]

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is sin theta the flap angle?

it says the change in drag coeffcient is equal to, so do i add this on to the original drag of the aerofoil?

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Filip Larsen

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Theta is the deflection angle, with theta = 0 meaning fully retracted. The maximum angle depend on the precise construction but the given approximation should be valid up to 90 degrees, I believe. McCormick notes that the optimal (maximum Cis sin theta the flap angle?

Yes, you add the flaps drag to the total drag coefficient you have for the airfoil wing, or plane in question.it says the change in drag coeffcient is equal to, so do i add this on to the original drag of the aerofoil?

I may also add, that McCormick gives similar drag expression for plain flaps where only the initial factor is different (1.7 instead of 0.9). This suggests that you in general can model drag for a specific flap construction by fitting that factor to measured drag (like if you have C

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Filip Larsen

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Chronos

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You need to know fuselage aerodynamics before calculating flap affects.

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Filip Larsen

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I can only comment that McCormick have plots of measured and theoretical values up to 90 degrees with no (visible) discontinuities and that this approximation is for the drag coefficient, not the lift which would be a different matter. That said, I too would be surprised if the approximation were to be just as accurate at 90 degree as at, say, 10, but that is just a hunch. And who would want to allow flap deflection over, say, 40 degrees anyway.

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Typically it is the drag curves that are in error, not the lift (because of the estimation of drag due to shear stresses). So if the drag agrees well, the lift is probably very good too. The equation you provided is interesting. It appears to apply to a wing, not a wing section, but doesn't account for wingspan, or how far outboard the flaps extend. So, use with caution.I can only comment that McCormick have plots of measured and theoretical values up to 90 degrees with no (visible) discontinuities and that this approximation is for the drag coefficient, not the lift which would be a different matter.

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Yes and no. We need to clear up some general misconceptions here in several of the posts. There is an aerodynamic interaction effect between the wing and fuselage. As a result, the total drag can be written as:You need to know fuselage aerodynamics before calculating flap affects.

[tex]C_D= C_D_{wing}+C_D_{fuse}+C_D_{inter}[/tex]

[1]

Note, I have assumed a linear model structure for the simplicity, which may not be valid. We can break down the wing drag as:

[tex]C_D_{wing} = C_D_0 + \Delta C_D_{flap}[/tex]

[2]

where the first term is the wing in a clean configuration. Again, I

-(a) How well is the linear perturbation assumption in Eq. [2] valid?

-(b) Does the interaction drag in Eq. [1] change significantly due to the perturbation?

Note also, that while not explicitly shown, the values in Eqs. [1,2] are generally a function of angle of attack, sideslip, and airspeed.

If the aspect ratio of the wings are large, then one can approximate the increase in drag based on sectional data from any good source, such as Ref. [1], and assume the perturbation found in the table applies to the entire wing.

[1]

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Filip Larsen

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By "lift ... would be a different matter" I was referring to CTypically it is the drag curves that are in error, not the lift (because of the estimation of drag due to shear stresses). So if the drag agrees well, the lift is probably very good too.

Another point to make to argue for the validity of high deflection angles in the approximation, could be to say, that the flap deflection angle is not the same as angle of attack and that high deflection angles not necessarily imply equally high AoA for the flap airfoil since it lives in the downstream from the wing airfoil.

I must admit, after thinking about it I am not sure what the surface area ratio SThe equation you provided is interesting.

It appears to apply to a wing, not a wing section, but doesn't account for wingspan, or how far outboard the flaps extend. So, use with caution.

It seems to me that this approximation is somehow extended to apply to a wing sections that include both flapped and unflapped parts, but if that then means the surface area ratio should be set equal to the chord ratio when applying the approximation for a flapped airfoil, I don't know. And this also seems to imply that flapped sections induce drag on unflapped sections which, in general, doesn't make sense.

I see that Theory of Wing Sections (which McCormick references for some of his airfoil data) has some drag data that maybe could be used to verify this drag approximation.

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Ah, I see what you meant now - quite right.By "lift ... would be a different matter" I was referring to C_{L}for simple unflapped airfoils not having an accurate analytical model for AoA above the AoA for maximum C_{L}. There you would not expect such analytical models to be valid for high AoA.

Another point to make to argue for the validity of high deflection angles in the approximation, could be to say, that the flap deflection angle is not the same as angle of attack and that high deflection angles not necessarily imply equally high AoA for the flap airfoil since it lives in the downstream from the wing airfoil.

That is an excellent point.I see that Theory of Wing Sections (which McCormick references for some of his airfoil data) has some drag data that maybe could be used to verify this drag approximation.

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