Induced drag
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and with out a pencil and paper
keep in mind that you can post a link to a graphic hosted elsewhere. If you need to draw a piccy, do so, scan, and link.
I can't believe the number of red herrings here:
one of the minor problems for those with more in depth backgrounds. However, one of the ways for folks to learn is to work through discussions such as we see on Tech Log, particularly if the minor (and sometimes not so minor) errors are challenged and eventually resolved. We are fortunate in that there are some VERY technically competent folk who choose to play in this particular sandpit ...
keep in mind that you can post a link to a graphic hosted elsewhere. If you need to draw a piccy, do so, scan, and link.
I can't believe the number of red herrings here:
one of the minor problems for those with more in depth backgrounds. However, one of the ways for folks to learn is to work through discussions such as we see on Tech Log, particularly if the minor (and sometimes not so minor) errors are challenged and eventually resolved. We are fortunate in that there are some VERY technically competent folk who choose to play in this particular sandpit ...
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I apologise, I should have been more specific in my language:
CJ (et al); I did read the question, I'm coming at it from a slightly different angle - I do appreciate it can be separated theoretically. When I say 'in practical terms', I mean flying an aeroplane. As in: "why care that in some circumstance lowering the flaps will decrease the induced drag, as far as the flying aeroplane goes, it still has more drag."
kenparry: I'll assume we got off on the wrong foot, and I guess I didn't explain myself well - I shall try to rectify..
An l/d curve is a composite of components of induced and parasite drag; and dominated by induced drag in on the left. You can draw 'curves' / graphs for either independantly. The L/d may be the derivative, but they are all very much related - for the l/d curve to change, the induced and / or parasite drag characteristics must have changed. So no it's not irrelevant.
I'm somewhat stumped that you consider that 1) and 2) are "correct, but irrelevant" - if you change the camber of the wing, you have a different wing. Even ignoring total drag and parasite drag (I'll try to word carefully here) you change it's induced drag characteristics, and furthermore, if you reduce the AOA, you put it in a different place on the induced drag plot. How is that not relevant? We all know that fat, cambered wings work better at low speed; flaps and slats allow us to approximate that fat cambered wing when we require.
I don't have numbers, but gut feel tells me that's got to be far more significant than spanwise flow and aspect ratio (else why can a PA28 fly slower with flaps - no change of aspect ratio there).. so I do consider spanwise flow/aspect ratio to be a 'red herring'. Maybe I should call it a second order effect
I'll also throw in a non-sequitur: how about negative flap? I know at least 1 light aircraft (flight design CTsw), and many gliders that use -ve flap settings in the cruise to fly faster (i.e. with less drag). My understanding again is that you're approximating a less cambered wing....
As for my knowledge aerodynamics - bit of an interest, long time glider pilot, and plouging my way through ATPL aerodynamic theory. Please feel free to prove me wrong - I'm happy to learn.
CJ (et al); I did read the question, I'm coming at it from a slightly different angle - I do appreciate it can be separated theoretically. When I say 'in practical terms', I mean flying an aeroplane. As in: "why care that in some circumstance lowering the flaps will decrease the induced drag, as far as the flying aeroplane goes, it still has more drag."
kenparry: I'll assume we got off on the wrong foot, and I guess I didn't explain myself well - I shall try to rectify..
An l/d curve is a composite of components of induced and parasite drag; and dominated by induced drag in on the left. You can draw 'curves' / graphs for either independantly. The L/d may be the derivative, but they are all very much related - for the l/d curve to change, the induced and / or parasite drag characteristics must have changed. So no it's not irrelevant.
I'm somewhat stumped that you consider that 1) and 2) are "correct, but irrelevant" - if you change the camber of the wing, you have a different wing. Even ignoring total drag and parasite drag (I'll try to word carefully here) you change it's induced drag characteristics, and furthermore, if you reduce the AOA, you put it in a different place on the induced drag plot. How is that not relevant? We all know that fat, cambered wings work better at low speed; flaps and slats allow us to approximate that fat cambered wing when we require.
I don't have numbers, but gut feel tells me that's got to be far more significant than spanwise flow and aspect ratio (else why can a PA28 fly slower with flaps - no change of aspect ratio there).. so I do consider spanwise flow/aspect ratio to be a 'red herring'. Maybe I should call it a second order effect
I'll also throw in a non-sequitur: how about negative flap? I know at least 1 light aircraft (flight design CTsw), and many gliders that use -ve flap settings in the cruise to fly faster (i.e. with less drag). My understanding again is that you're approximating a less cambered wing....
As for my knowledge aerodynamics - bit of an interest, long time glider pilot, and plouging my way through ATPL aerodynamic theory. Please feel free to prove me wrong - I'm happy to learn.
Also, you have perhaps not done much in-depth study of aerodynamics. Induced drag is not related to L/D curves.
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I don't know why most of the posts do not even attempt to answer the question?
The question (KristianNorway, post #1) was: "What happens to the induced drag (Cdi) when I lower the flaps, everything else being equal?"
saman (post #5) mostly already answered the question by reminding us of the formula *) for Cdi.
Cdi = k* Cl_squared / pi * AR
Here k is a factor depending on the spanwise lift distribution. For an elliptical lift distribution k=1, in all other cases k>1.
AR is the aspect ratio of the wing.
If we start with basic flaps (simple trailing-edge flaps), and "everything else equal", i.e., speed, height, weight and wing surface, Cl is unchanged, and so is AR.
The only thing that changes is k.
Whether k increases or decreases depends on the change in lift distribution between the clean wing and the wing with the flaps down.
An 'ideal' clean wing would have a near-elliptical lift distribution, but in practice this is not necessarily the case, so whether Cdi increaes or decreases will depend on the design of the wing.
'Complex' flaps, such as Fowler flaps, increase the wing area. However, both Cl and AR will decrease proportionally to S (wing area), so Cdi remains the same for 'basic' and 'complex' flaps.
*) BTW, before somebody contests the use of a simple-looking formula : while the formula is derived from theoretical wing flow analysis, the experimental results are so close to the theoretical ones, that to all practical extent and purposes they are the same.
Most of the other points raised in the various posts, while not necessarily wrong, do not answer the original question. Matters such as total drag, AoA, L/D curves, low or high speed, wing camber, and others, do not "enter into the equation".
CJ
The question (KristianNorway, post #1) was: "What happens to the induced drag (Cdi) when I lower the flaps, everything else being equal?"
saman (post #5) mostly already answered the question by reminding us of the formula *) for Cdi.
Cdi = k* Cl_squared / pi * AR
Here k is a factor depending on the spanwise lift distribution. For an elliptical lift distribution k=1, in all other cases k>1.
AR is the aspect ratio of the wing.
If we start with basic flaps (simple trailing-edge flaps), and "everything else equal", i.e., speed, height, weight and wing surface, Cl is unchanged, and so is AR.
The only thing that changes is k.
Whether k increases or decreases depends on the change in lift distribution between the clean wing and the wing with the flaps down.
An 'ideal' clean wing would have a near-elliptical lift distribution, but in practice this is not necessarily the case, so whether Cdi increaes or decreases will depend on the design of the wing.
'Complex' flaps, such as Fowler flaps, increase the wing area. However, both Cl and AR will decrease proportionally to S (wing area), so Cdi remains the same for 'basic' and 'complex' flaps.
*) BTW, before somebody contests the use of a simple-looking formula : while the formula is derived from theoretical wing flow analysis, the experimental results are so close to the theoretical ones, that to all practical extent and purposes they are the same.
Most of the other points raised in the various posts, while not necessarily wrong, do not answer the original question. Matters such as total drag, AoA, L/D curves, low or high speed, wing camber, and others, do not "enter into the equation".
CJ
