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How much do these type of flaps increase drag? 
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#1
Mar1710, 08:05 AM

P: 32

by how much will singleslotted Fowlertype flaps increase the drag coefficient of an aerofoil?



#2
Mar1710, 09:59 AM

PF Gold
P: 959

McCormick [1] mentions, that the increment in wing drag [itex]\Delta C_D[/itex] for a slotted flap as function of flap deflection angle [itex]\delta[/itex] is given approximately by
[tex] \Delta C_D = 0.9 (c_f / c)^{1.38} (S_f / S) sin^2 \delta [/tex] where c_{f}/c is the flap to wing cord ratio and S_{f}/S is the flap to wing surface ratio. He does not specify the source of this approximation, but I presume it is based on theoretical and practical analysis of various combinations of NACA airfoils and flap types. [1] Aerodynamics, Aeronautics and Flight Mechanics, 2nd ed., McCormick, Wiley, 1995. 


#3
Mar1710, 11:52 AM

P: 32

thanks, just what im looking for...
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? 


#4
Mar1710, 12:56 PM

PF Gold
P: 959

How much do these type of flaps increase drag?
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_{D} for a plane at various flap deflection angles). 


#5
Mar1710, 06:18 PM

P: 32

if the flaps are fully retracted and theta is equal 0 that would mean the equation is equal to 0? is sin^2(theta) a trig identity? why am i get syntax error on calculator?



#6
Mar1810, 01:40 AM

PF Gold
P: 959

Note, that [itex]\sin^2 \theta[/itex] or [itex] \sin^2(\theta)[/itex] is shorthand notation for [itex] (\sin \theta )^2[/itex] or [itex] (\sin(\theta))^2[/itex]. Its a very common notation, especially with trigonometric functions.



#7
Mar1810, 02:41 AM

Sci Advisor
PF Gold
P: 9,430

You need to know fuselage aerodynamics before calculating flap affects.



#8
Mar1810, 06:09 PM

P: 261

How can that equation be valid at such large angles? I would expect flow separation to come into play long before you reach 90 degrees of deflection.



#9
Mar1810, 06:36 PM

PF Gold
P: 959




#10
Mar1810, 10:01 PM

P: 4,777




#11
Mar1810, 10:05 PM

P: 4,777

[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 assumed the model is linear for the sake of this example. So one then needs to know two things: (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. References [1] Theory of Wing Sections, Abbot and Von Doenhoff, Dover Press, 1959. 


#12
Mar1910, 03:35 AM

PF Gold
P: 959

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. 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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