Induced drag

[KristianNorway]

I have been taught that there is more induced drag from a clean aircraft with high alpha than the same plane with flaps extended at the same speed.
At the same speed and the same weight there has to be the same amount of lift, so I can't see why there should be a difference in induced drag.

Can anyone explain?

[Mark1234]

Quite frankly, I don't know if that's true or not(1), however the relationship between lift and (induced) drag is not a constant factor - it depends upon the aerofoil.

For instance, if one takes a flat sheet, it will generate lift - but it will be somewhat inefficient at doing so - If you curve that sheet into an 'aerofoil' section, it will become somewhat more efficient at generating lift - the drag per unit of lift will be less.

Different aerofoil shapes will have a different lift/drag curve. When you start sticking out flaps, slats and suchlike, you change the aerofoil, and change it's L/d ratio.

(1) I'm don't think it's that useful to consider just the induced drag - it's only a small part of the picture, hanging flaps out dramatically increases the parasite drag. In any practical terms, you need to consider the combined effect of induced and parasite drag.

[Mad (Flt) Scientist]

It all depends what you mean.

Firstly, by talking about "induced" drag there are complications introduced by the higher profile drag of the flaps down case.

By not defining "high alpha" anything is possible.

Certainly, at alphas where the clean wing is starting to see flow separation, the flaps down case will win the drag comparison.

But also, certainly, at some lower alpha the clean wing must win, otherwise you'd cruise with the flaps down, and someone might conclude that your wing design was "non optimised".

So there must be a cross-over alpha. It all depends if that's above or below your definition of "high" alpha

[mathy]

And induced drag is pretty much proportional to the square of the lift coefficient and inversely proportional to effective aspect ratio. Lift coefficient with flaps may be about 2.0 whereas on retraction 0.5 is nearer the mark. Depending on loading of course. Effective aspect ratio is the square of wing span divided by [wing area x fiddle factor]. For a well designed passenger transport aircraft the fiddle factor is about 0.85 with flaps retracted and maybe 0.5->0.7 with flaps. So you may indeed want to have the same lift but by modifying the shape of the wing you change aspect ratio and by dangling bits you change the effective aspect ratio. The effect is more induced drag.

[captaan]

higher the speed more is the induced drag.....
so when you got flaps extended it is obviously low speed.& hence low induced drag.
depanding upon aerofoil shape and air flow speed determines various kind of drags.
for every perticular situation, drags varies....total drag comes in picture.

[saman]

Induced drag is the drag induced by the lift and, from memory,

Cdi = kClsquared / Pi AR where :

Cdi = Induced drag coefficient
k is a constant dependant upon the span-wise lift distribution with k=1 for a perfect elliptical distribution,
Cl is lift coefficient
Pi is Pi
and AR is Aspect Ratio

So flap deployment will change the span-wise lift distribution - assuming the flaps are not full span (the form drag will certainly increase) - thus changing k and thus changing Cdi

Flap deployment will change the wing area (assuming some type of area-increasing flap such as Fowler or dropped hinge) and thus the Cl and thus Cdi

Methinks induced drag will change with flap deployment!

[MerlinV8]

More simply could it be that with flaps extended you have a nose pitch down moment, in turn a lesser angle of attack to the relative airflow at the wingtips which in turn would produce less induced drag with the flaps down.

Remembering induced drag is the result of the pressure difference of the air at the wingtips.... air wanting to move from higher to lower pressure at the wingtips.

The flaps are producing the extra lift and drag at low airspeed but is this is not induced drag.

Not an expert, Just putting it out there.

[kenparry]

captaan - no.
You have it the wrong way round. Induced drag is greater at low speeds, form drag greater at high speeds. Really I need to draw a graph to illustrate how it works, but that is probably beyond my PPrune posting skills.

Form drag, for a given body and attitude and atmospheric condition, and ignoring compressibility, is proportional to speed squared.

Induced drag is inversely proportional to speed squared. You can show mathematically that an aircraft's min drag speed is the speed at which induced drag and form drag are equal. You can fly more slowly - that's when you are "on the wrong side of the drag curve" and speed is unstable - you need a whole armful of thrust to recover from a speed reduction.

For a given span, induced drag is minimum if the spanwise distribution of lift is elliptical - again that can be shown mathematically. You can achieve that with an elliptical wing (e.g Spitfire) or by more subtle means of changing thickness and wing section.

Yes, flap extension will change the spanwise lift distribution, as remarked by previous contributors, and since the wing (on a transport aircraft) will be optimised for cruise, you can say with some certainty that induced drag will then increase.

[MerlinV8]

I agree totally, low airspeed and high angle of attack equals high induced drag, math, graphs and formulas are great but just to help our friend out here, I always try to visualize what the actual little air particals would be doing in different situations.

[ChristiaanJ]

saman,
Thanks for refreshing my memory.

You said:
Methinks induced drag will change with flap deployment!I noticed you said "change", not "increase" or "decrease".
Made me think...

Take an untwisted rectangular wing planform, so the span-wise lift distribution is definitely not elliptical. Now simply lower the inboard part of the trailing edge as a simple flap, increasing the lift over the inboard part of the wing.

The span-wise lift distribution will now be closer to the elliptical than before, so under otherwise the same conditions (same speed, so same Cl, and AR unchanged) the induced drag should actually decrease (k closer to 1).

That's what KristianNorway mentioned in the first post.

On the other hand, of course, if you do the same thing in the Spitfire, you move away from the ideal lift distribution, so the induced drag increases.

Do you agree?

CJ

[Pugilistic Animus]

these thread make me --at times-- wish for better mathematical facilities--I love to expand and illustrate a little more of some of the very good points in thread like this [as I'm sure others here may desire]:8---the biggest problem is pitching it in a reasonable way so those without the appropriate math and physics background could also understand--so it would be useful---perhaps that is the reason we don't have such a facility---and with out a pencil and paper personally I'd make tooo many math errors to be forgiven---In fact I had to stop a little thing I was doing on thermodynamic because I realized it would soon lead [no matter what ] to pure gibberish to the un initiated--and I would just be "preaching to a choir"---as I'm always amused when folks get a simple explanation by folks such as MFS or Christaan J. ---amongst others--- and still choose to add complexity all I can say is that--whatever you can think of in the subject has been intensively treated in the past--so my advice--KISS--trust me:\-:\-:\ I'm not talking about this thread explicitly I mean in general

PA

[kenparry]

"Take an untwisted rectangular wing planform, so the span-wise lift distribution is definitely not elliptical."

No, but nor is it linear across the span - downwash affects the distribution, and the lift is biased towards the inboard sections. Don't try to get too deep into this: if you want to do it fully you will end up with pages of highly complex equations, and probably wish you had not started.

[Pugilistic Animus]

Kenparry---I see you know what I mean:}

[ft]

Lift coefficient with flaps may be about 2.0 whereas on retraction 0.5 is nearer the mark

With the same wing (same reference area), the same airspeed and the same weight?

Even if the wing reference area is indeed changed to reflect the flap extension (if it was me, I wouldn't bother and just change the coefficients) I somehow doubt the factor four change in lift coefficient.

Back to the original question.

As is way too usual when asking very general questions, the answer is: "it depends".

What is high alpha? For which wing? Which flap configuration and setting? You will be able to find cases where induced drag is lower with flaps and there will be cases where the induced drag is lower clean.

We know that wing load distribution will change radically. As ChristiaanJ pointed out, we also know that this will affect the wing efficiency factor in the induced drag equation significantly. However, there is no general answer to just how this factor will change.

Now, if you specify it to a L1011 at 18 degrees of AoA I'm sure someone will be able to provide you with a definitive answer. :)

[Pugilistic Animus]

Theory of wing sections by Abbott and VanDoenhoff---that the easiest reference you can get--to answer the questions actually posed:oh:

[Semu]

Actually, there is a simpler, if less technically elegant solution. Extending the flaps on most (older anyway) transport category aircraft causes a large number of disturbances in the airflow, including the lateral airflow around the wingtip. Aircraft with 'smoother' flaps have a stronger wake with flaps extended. The poster child for this is the 757, and is part of the reason it is considered a heavy for wake turbulence separation. Boeing (and presumably Airbus) have researched having slight displacements in the flight controls in some phases of flight to break up the wake. It works a charm, I am told, but the certification was problematic. Having said all that, I am very interested in the all other things being equal technical answer.

[Mark1234]

wtf :confused:

I can't believe the number of red herrings here:

Spanwise lift distribution and elipsis.. full span flaps still work (see some gliders), so no (secondary effect).
aspect ratio.. plenty of types have flaps that do not vary the aspect ratio, so no, secondary at best

I'm pretty sure we covered it in the first 2 replies:
1) Flaps change the *camber* of the wing. That changes the lift / drag curve for the wing
2) Generally, flaps increase the lift at the penalty of increased (total) drag. At a given lift that will translate to a reduction in required AOA.

If for some circumstance the more cambered wing section, at a lesser AOA produces less *induced* (not total) drag than the flatter wing section at a higher AOA, the original posters scenario is complete. Right at the stall would seem a likely candidate, but it's simply a matter of comparing L/d curves.

However, the induced component of drag would seem slightly irrelevant, as it's rather impossible to separate from total (induced + parasite) in practical terms.

[kenparry]

Mark1234:

It does help if you read the question.

Also, you have perhaps not done much in-depth study of aerodynamics. Induced drag is not related to L/D curves.

Your points under 1) and 2) are true but irrelevant.

Your final sentence shows you have not understood the question put.

[ChristiaanJ]

...the biggest problem is pitching it in a reasonable way so those without the appropriate math and physics background could also understand.... I agree.
Sometimes you have a simple analogy at hand to explain things, like a stone and a rowboat in water to explain the sonic bang. Sometimes you just do need the basic math and physics.

Take an untwisted rectangular wing planform, so the span-wise lift distribution is definitely not elliptical."
No, but nor is it linear across the span - downwash affects the distribution, and the lift is biased towards the inboard sections. Don't try to get too deep into this: if you want to do it fully you will end up with pages of highly complex equations, and probably wish you had not started.I know what you're saying... I was just trying to visualise a situation where inboard flaps could actually decrease induced drag. Not total drag, obviously.

However, the induced component of drag would seem slightly irrelevant, as it's rather impossible to separate from total (induced + parasite) in practical terms.You're right in general terms, I would say, but I think you are missing the point...
Induced drag, i.e., drag due to lift, may be difficult to separate from total drag at first sight, but it can generally be computed quite accurately and the computations usually match real-world measurements very closely. So it's a valuable tool to separate the drag due to lift from the rest.

CJ

[cwatters]

Simple answer..

If you want high lift at slow speed choose a thicker wing section with more camber rather than a thin wing with less camber.

[ChristiaanJ]

cwatters,
What are you talking about?
Did you read the original question at all?

[john_tullamarine]

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 ...

[Mark1234]

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.

[TURIN]

Also, you have perhaps not done much in-depth study of aerodynamics. Induced drag is not related to L/D curves.

Huh???Shurly shome mishtake (http://www.auf.asn.au/groundschool/index.html#drag) :ok:

[pineridge]

Captaan said........




"higher the speed more is the induced drag.....
so when you got flaps extended it is obviously low speed.& hence low induced drag."


Wrong.

[ChristiaanJ]

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