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We look at lift,drag and L/D at multi element wing with slots and same wing shape just without slots.

wing without slots:

Completly top side is stalled, so here is all low pressure(blue at picture),more low pressure area then on wing with slots

bottom side= pressure more higher then on wing with slots

Lift and drag higher, L/D lower ..compare to wing with slots (that is how I think, maybe I wrong) enter image description here

With slots:

top side= less area with lower pressure compare to wing without slots

botttom side= reduction in high pressure compare to wing without slots

Lift and drag lower, L/D higher... compare to wing with slots (just my oppinion, maybe wrong) enter image description here

My conclusion:

Wing with slots is more efficient in producing lift(better L/D) compare to same shaped wing without slots, but that doesnt mean it produce higher lift at same fixed AoA compare to same wing without slots.(maybe wrong)

Main question: Does wing without slots has lower lift and higher drag compare to wing with slots? (Confirm your answer with pressure distribution arund wing for both cases, CFD would be ideally)

If answer is yes, we have situation Lift down=drag up,isnt that brake rule for induced drag which in short tell: Lift up = drag up, Lift down=drag down,

Notes before answer:

  1. This is case where lift dont have to be equal weight

  2. Stall is caused by closing slots,not by increasing AoA, AoA is fixed in both case, so we basicaly just change pressure distribution around wing.

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  • $\begingroup$ Your diagrams aren't sufficiently detailed. What about the lift on top of the open slats? What about the flow separation above the closed slats? $\endgroup$
    – Jim
    Nov 13, 2022 at 0:16
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    $\begingroup$ Hello Jurgen M, could you please not change the subject of the question after people have answered? It is annoying for people who put effort in helping you, only to see that you invalidate all their work by changing the question. And also, please don't address single users in your question; everybody who is willing to help you should feel equally invited to do so. That being said, I see you put a lot of effort in improving the question over the last 24 hours, and I think it is much better than where it started. Thank you for that. $\endgroup$
    – DeltaLima
    Nov 13, 2022 at 21:07
  • $\begingroup$ @DeltaLima Ok. Question is just edit and ask on different why same thing.. $\endgroup$
    – user707264
    Nov 14, 2022 at 14:35

4 Answers 4

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are you 100% sure that multi element wing with close[d] slots [show] reduce[d] lift compare[d to] when slots are open, (for same/fixed AoA)?

Yes, I am.

For more see this answer, or better yet, this paper by a renowned expert (A. M. O. Smith, McDonnell-Douglas) - he gets the physics of flaps right!

EDIT:

First you ask about lift, then, after I answer, you change the subject to drag. More consistency would be nicer.

Closing the slats means flow will separate. This increases pressure drag and lowers lift. Yes, induced drag will also drop in parallel with lift, but the increase in pressure drag far outweighs this drag reduction, so overall drag will increase (same speed, same AoA).

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  • $\begingroup$ @JurgenM: Pressure drag is not induced drag, otherwise there wouldn't be two different names. Pressure drag is anyway a broad term which encompasses induced drag. $\endgroup$
    – sophit
    Nov 13, 2022 at 19:41
  • $\begingroup$ @sophit there is only two type of drag, pressure and firiction drag, there is no other way how fluid can exert force on body. So what is induced drag? $\endgroup$
    – user707264
    Nov 13, 2022 at 19:50
  • $\begingroup$ @JurgenM: as said, in that categorisation, induced drag is pressure drag. But in that category also wave drag will fit or form drag. Be aware anyway that there are a lot of drag terms which might overlap in their definitions and that unfortunately don't make the whole story about drag universal. And induced drag is a pure mathematical concept that can only be calculated, not measured. $\endgroup$
    – sophit
    Nov 13, 2022 at 20:09
  • $\begingroup$ @sophit OK forget about induced drag,it doesn't exist in reality anyway, I am ineterested in overall drag, drag that sensors in wind tunnel show....maybe I need to note in text...hmm $\endgroup$
    – user707264
    Nov 13, 2022 at 20:14
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    $\begingroup$ @JurgenM: induced drag does exist and at low speed is unfortunately the highest contribution to total drag. It can be calculated measuring the airflow's speed behind the wing at a specific location called Treffz plane and then making some complicated calculation with that. In a wind tunnel, drag is measured with a scale in the mounting structure of the model, but that measures the total drag and not its single components. Anyway if you are interested in drag in general, maybe you can post a specific question. $\endgroup$
    – sophit
    Nov 13, 2022 at 20:25
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I don't have any crayons handy, but we must understand the whole point of slotted designs such as Fowler flaps is to maintain lift on an area of the wing where flow would separate and produce only drag at a given AoA.

Your first diagram more accurately shows lift and drag of a slotted wing. Closing the slots will produce a lifting region (blue) similar to your second diagram, with drag similar to the first.

Now, which has a higher Lift/Drag ratio, slotted or non-slotted?

you can't increase lift without increasing induced drag

Try increasing airspeed and lowering Angle of Attack. Now you're better off with a solid, rather than slotted wing.

A comparison of albatross and vulture/eagle wing tips confirms this.

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Is increase in lift always follwed by increase in drag and vice versa?

No. Think about a stalled wing: drag increases but lift decreases. Or a wing at 90° AoA: drag is at its maximum but lift is null.

Aerodynamicists use to subdivide drag in several terms, like profile drag, parasite drag, wave drag, interference drag or induced drag. Not all these components of drag are correlated with lift so an increase in lift doesn't automatically implies an increase in drag. Furthermore these terms are in general not even related to each other and being one smaller doesn't imply that another one gets bigger.


Regarding the slotted wing of your picture: closing the slot neglects the main advantage of this configuration, which is twofold:

  1. each flap gets a brand new fresh boundary layer and;
  2. each flap is invested by the downwash of the previous flap/wing and therefore it can be set at an higher AoA.

The combination of these two effects is what makes a wing with slotted flap more "efficient": without the slot, the flap (or the rear part of the wing) would have a quite thick and sensible turbolent boundary layer and it would be possibly already stalled, both things incrementing drag and decreasing lift.


Regarding induced drag, its value is:

$D_i = \frac{L²}{q \pi e b²}=\frac{W²}{q \pi e b²}$

and it does not depend on the particular geometry of flap being used (if not indirectly via $e$ but if a fair comparison has to be done, then also $e$ should be as similar as possible among the different configurations).

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  • $\begingroup$ Can you confirm your answer with pressure distribution around wing for both case? Dont have to do CFD, maybe just your own sketch or graph find on internet that is related to question $\endgroup$
    – user707264
    Nov 13, 2022 at 16:21
  • $\begingroup$ Mmh, we should find a plot for an high cambered airfoil and compare it with a similar slotted wing $\endgroup$
    – sophit
    Nov 13, 2022 at 16:32
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An increase in lift is always followed by an increase in drag. More lift = more induced drag.

https://en.wikipedia.org/wiki/Lift-induced_drag

But not vice-versa. An increase in drag is not always followed by an increase in lift.

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  • $\begingroup$ Consider making clear whether or not you are assuming constant airspeed. If not, consider this case -- glider-- in steady-state flight, lift= weight * cosine glide angle and drag = weight * sine glide angle. (Link: aviation.stackexchange.com/a/81831/34686). So, if you transition from high-speed flight (at a steep glide angle and poor L/D ratio) to lower-speed flight (at a shallow glide angle and good L/D ratio), L increases (very slightly), and D decreases (potentially quite a lot). $\endgroup$ Nov 14, 2022 at 15:02
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    $\begingroup$ Hi, welcome to aviation. We're looking for full answers which include the main detail within the answer itself. Links to other resources are fine as supporting material. Please consider improving your answer otherwise you might see it downvoted and/or removed by the community. $\endgroup$
    – Jamiec
    Nov 15, 2022 at 7:30

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