zero lift and induced drag

[pjc102]

hi. this may seem a stupid question, but i have gone through a couple of books now (dubs, hoerner, schlichting, crowe)and i still don't quite get it. according to the basic formula, induced drag coefficient of a wing is proportional to lift coefficient squared:

C(draginduced) = C(lift)^2 / Pi*aspectratio

therefore, if a wing generates zero lift it must also generate zero induced drag. but the literature seems to be quite vague about this. schlichting says induced drag occurs with all finite wing spans. but he also states that "within the range of small lift coefficients, the drag of airfoil sections is predominantly frictional..."(fluid-dynamic drag, 1969).
aleyev states that induced drag is "significant when there is hydrodynamical lift" (nekton, 1977).
but they don't clearly say that zero equals zero induced drag.
could anybody help me understand this or at least point me in the general direction of literature that would help me?

 

[AminG]

Hello,

The induced drag is more accurately called "lift induced drag". You are correct that at zero lift (cl = 0), the lift induced drag would be zero. But the total drag will not be zero.

Also, the formula for lift induced drag is more accurately:

Cd(lift induced) = cl^2/(Pi * e * AR), where:

cl - coeff. of lift
Pi = 3.14159
e - Oswald's efficiency factor
AR - Aspect Ratio.

I hope this helps.
-Amin

 

[pjc102]

and therefore the wing tip vortices "induced" by pressure differentials between upper and lower side of the wing would also not appear?

 

[rb1957]

in a nutshell

 

[InteroperabilityFix]

for an entire aircraft, you will always have some form of induced drag, because you have to factor in the control surfaces which generate their own lift

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[btrueblood]

Also, the upper and lower surface pressure distributions are never precisely equal, unless you have a symmetric airfoil, thus there is always a little bit of 3-d flow ("tip vortex").

 

[pjc102]

i am testing foils that are crescent-shaped (like fish caudal fins). they are upper/lower side symmetrical, but the form (extended wing tips) induces a lot of vortices. i am finding it quite difficult to find theories of fluid dynamics for these kind of effects. thanks for the help.

 

[MadSplinter]

You may check in literature for the "D'Alembert Paradox".
For an unviscid flow, you will obtain zero drag for a zero lift finite wing.

Everything should be made as easy as possible, but not easier

Albert Einstein