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First heading

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Flaps may also be used when taking off - perhaps this should be mentioned.

This has been taken care of. Jadias 19:03, 11 January 2007 (UTC)[reply]

Someone eliminated the increase in lift coefficient (and therefore lift force via L=½ρSCL) due to flap deployment on takeoff. Someone said that flaps don't increase the lift force, only the lift coefficient. If flaps change CL, they must change the resulting force (see the equation). Their argument is L = W. This is ONLY true for steady level unaccelerated flight. It is possible for aircraft to accelerate, else they wouldn't get anywhere! Thus, there is the "ballooning" effect on flap deployment, caused by an increase in lift force (yes, I said force). 128.211.248.83 00:58, 26 September 2007 (UTC)[reply]

The parenthetical note regarding minimizing induced drag through an elliptical planform has been eliminated due to its irrelevance. This information should be included in the induced drag article. This article is about flaps, not the overall shape of the airplane wings.

It should also be noted that I refer to "wing airfoil." Wing and airfoil are NOT the same thing. A wing refers to a 3D object. An airfoil refers to a 2D shape, specifically the 2D shape of the wing, as one looks from the wingtip to the root of the wing, near the fuselage. Jadias (talk) 05:05, 17 December 2008 (UTC)[reply]

Hi Jadias. I agree that a wing and an airfoil are not the same, but I disagree that an airfoil is a 2D shape. Some authors write that an airfoil is a body capable of developing an aerodynamic force with a component perpendicular to the velocity vector. (Therefore a flat plate can be an airfoil.) Other authors write that an airfoil is a body capable of developing a significant component of aerodynamic force perpendicular to the velocity vector. When referring to a 2D shape, most authors use the expression airfoil section.
A wing is an example of an airfoil, but so too is a propeller, fin and rudder, stabilizer and elevator. These are all 3D bodies. Dolphin51 (talk) 05:31, 17 December 2008 (UTC)[reply]


This wing section/profile business is all semantics and different authors treat them differently. Therefore, I am disinclined to dispute this. However, I do wish to raise an issue regarding the general aircraft lift equation. I described the equation as pertainging to an airplane in a flow. It was changed to "in flight." However, this is creating undue restrictions on this equation.
As we often do, one could use this equation to calculate a takeoff trajectory and associated discreet velocities. A ground roll does not imply flight. For example, consider an airplane on takeoff roll. Until the airplane reaches a speed where it may rotate and takeoff (see V1, V2 and Vr), its wings do generate lift, although the amount of lift generated will not overcome the airplane's weight. Similarly, on a rejected/aborted takeoff (RTO) procedure, pilots of GA airplanes are often instructed in the Approved Airplane Flight Manual to retract flaps on the RTO roll in order to reduce the amount of lift generated at speed and keep the aircraft on the ground.
My point is this: At any non-zero airspeed, the wings will generate a finite amount of lift (however miniscule). Why restrict this equation, therefore, to only "in flight?"
However, if someone was trying to clean up the the way it sounded, I agree that improvement is there to be made. Can you think of a way to rewrite that sentence without restricting that equation to flight? Jadias (talk) 07:28, 11 January 2009 (UTC)[reply]

History

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Does anyone know anything about the history of flaps? I was thinking about this on a flight to CDG today - who is credited with first developing them? When? I'm pretty sure that the Wright Flyer didn't have any... Duncan (talk) 20:38, 20 June 2008 (UTC)[reply]

Seconded. No one wants to address this over 10 years?? --BjKa (talk) 12:01, 12 April 2017 (UTC)[reply]

Drag

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I'm concerned that the issue of drag is not well dealt with. For most planes, the initial few degrees of flap extension increase lift and drag while adding full flap produces mainly drag with little extra lift. To build on this idea, split flaps are mainly drag devices where as Fowler flaps are more efficient lift producers. Would someone like to try to capture these ideas? Cheers MarkC (talk) 23:50, 1 May 2009 (UTC)[reply]

I've added this a few times. People keep changing the article and posting their gross over-simplifications instead. I've given up on re-adding it. Jadias (talk) 05:06, 26 May 2009 (UTC)[reply]
This should be re-added, along with mention that flaps extended above certain airspeeds can cause structural damage/failure. 64.148.241.133 (talk) 21:19, 12 September 2009 (UTC)[reply]

Flap deployment and pitch attitude

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The author says, useful side effect of flap deployment is a decrease in aircraft pitch angle resulting from the increase in angle of attack relative to the fuselage. This allows the pilot to lower the nose for better ground visibility. Have I misread this because whenever I have deployed flaps on base leg, the nose has pitched markedly UP and I have to trim forward to rebalance the aircraft before turning onto final? Maybe it should be rewritten that flap deployment allows the pilot to trim the nose down more for the same amount of lift, thus increasing his visibility. —Preceding unsigned comment added by Percussim (talkcontribs) 16:49, 19 September 2009

Hi Percussim. You have identified some shortcomings in the article so I have made some amendments. Hopefully they improve the article.
The article is referring to the steady-state situation following deployment of flaps, and you are referring to the transient effects. As wing flaps are extending or retracting the pitching moment is changing. As wing flaps are extended on a high wing aircraft the increase in downwash onto the horizontal stabilizer is predominant and the aircraft pitches nose-up, requiring the pilot to push on the elevator control or trim nose-down. Conversely, as wing flaps are extended on a low-wing aircraft the increase in pitching moment coefficient is predominant and the aircraft pitches nose-down, requiring the pilot to pull on the elevator control or trim nose-up.
Regardless of whether the aircraft pitched nose-up or nose-down, when the aircraft is restored to the trimmed condition after extending flaps the wing will have a lower angle of attack because of the greater camber of the wing with flaps extended. Consequently, in a conventional aircraft, after flaps are extended for approach and landing the pilot has a better view of the ground ahead because of the lower angle of attack. Conversely, in an aircraft with leading-edge slats or Krueger flaps the effect appears to be reversed because leading-edge devices allow a much greater angle of attack than is possible without these leading-edge devices. Aircraft with a clean leading-edge approach to land with a generally nose-down attitude providing a good view of the ground ahead, but aircraft with leading-edge devices extended approach to land with a generally nose-up attitude.
Delta-wing aircraft such as Concorde, the Fairey Delta 2 and the Mirage are a third case. They can achieve very high geometric angles of attack without stalling and without the aid of leading-edge devices so they approach to land in a very nose-up attitude with resultant poor view of the ground ahead. In the cases of Concorde and the Fairey Delta 2 it was so accentuated that the aircraft were equipped with drooping noses. Dolphin51 (talk) 12:03, 20 September 2009 (UTC)[reply]

Flaps VS Slats

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Guys, there is a difference between a flap and a slat, the flap can usually be found at the trailing edge of the wing, whilst the slat is usually located at the leading edge of the wing. Most civilian airliners (except for the supersonic Concorde, including the smaller STOL, or bush type will have both, whereas in military aviation the presense of both or one of either does not usually indicates the role for which the aircraft was designed for. An example being the conventional wing strike fighter F/A-18 Hornet, it has slats as well as modified version of flaps, known as flaperons. Compare that to a delta wing Mirage III, the latter has no flaps and the lack of a horizontal stabilizer, or bettern know as tailplane, meant that flaps cannot be used, resulting in a long takeoff run and a high landing speed for the type. So to set the record straight, stop using flaps to pass off as leading edge slats. Please reword if you ever come across such errors in any aircraft article pages because it is extremely misleading. Thank you~! --Dave1185 (talk) 10:36, 12 October 2009 (UTC)[reply]

A Boeing 737 showing the leading-edge (Krueger) flap inboard of each engine nacelle, and slats outboard.
I agree there are flaps, slats, and even slots, and they are all different. There is such a thing as a leading-edge flap. To the best of my knowledge the only leading-edge flaps in production at present are Krueger flaps. Wikipedia even has an article on the subject. A slat always forms a slot, but a leading-edge flap does not.
The Boeing 737 has leading edge slats outboard of the engines, and Krueger flaps inboard of the engines. The leading-edge (Krueger) flaps are clearly visible in this image, particularly when the image is expanded to full size
A useful generic term is leading-edge devices. Dolphin51 (talk) 12:05, 12 October 2009 (UTC)[reply]
  • I'd rather that Krueger flaps be used instead of leading edge flaps, because to my knowledge Krueger flaps was developed for use on the leading edge and the naming convention should remain so even though it is located there. Slats or slots are usually longer than flaps, right? Since Krueger flaps are short span, thus they are flaps. Let's keep things simple, shall we? --Dave1185 (talk) 16:28, 12 October 2009 (UTC)[reply]
I have no objection to use of the term Krueger flaps where that is the term applied by the airplane manufacturer. If we ever find a leading-edge device that is not a slat, and not a Krueger flap, we can search for the name given to it by its manufacturer.
I disagree that the difference between a leading-edge slat and a Krueger has anything to do with its length. When a slat is extended it creates a slot and the combination is aimed at boundary layer control - air accelerates through the slot, sweeps away the boundary layer and replaces it with a fresh boundary layer that remains attached to the wing surface for a greater proportion of the chord. In contrast, a Krueger flap does not create a slot - in the photograph above we can see that the space behind the Krueger is an ironmonger's delight with a torque tube and lots of scissor-mechanisms and hinges. There is no high-speed flow of air between the wing structure and the Krueger. A Krueger works partly by increasing the effective radius of the leading edge of the wing, and partly by increasing the camber of the airfoil.
I recall there was an airplane type with full-span Krueger flaps, but I don't know what type. Perhaps it was the Convair 880 or 990. Dolphin51 (talk) 22:09, 12 October 2009 (UTC)[reply]

Junkers flaps

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I seem to remember hearing about "Junkers flaps" being used on some ultralights, probably the Apollo Fox is one. They seem to be separate from the wing permanently. Is anyone able to document them? Jan olieslagers (talk) 19:43, 7 February 2011 (UTC)[reply]

Gratitude to NiD.29 for serving me to full satisfaction! Jan olieslagers (talk) 19:16, 18 October 2011 (UTC)[reply]
My pleasure - I was amazed I found a reference. NiD.29 (talk) 04:08, 19 October 2011 (UTC)[reply]

Pretty pictures spoil article at present

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The many images on the right mean that the reader cannot see the body of the text without scrolling down. The article is therefore not user-friendly. --TraceyR (talk) 05:45, 27 May 2011 (UTC)[reply]

Right. So you think the article World War II would be much improved if you could read all of it without scrolling down? --BjKa (talk) 12:03, 12 April 2017 (UTC)[reply]

Fluidics

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The section has been copied from the page it links to word for word - and doesn't make any sense on either. Fluidics appears to be a means of using hydraulic pressure to control components (complete with logic gates) but its application to aviation seems problematic, and the claims (particularly about being faster or more efficient) made for it seem absurd since earlier on the fluidics page, it suggested in was several orders of magnitude slower than electronic systems, and was being phased out in the only application anyone has found for it - namely automatic transmissions. Sounds to me like some badly done corporate advertising rather than a legitimate addition to the flaps page - especially since no other mechanisms used to move flaps are discussed (though perhaps they could be?) Does someone have an explanation that isn't complete gibberish?NiD.29 (talk) 03:34, 18 October 2011 (UTC)[reply]

Flaps for takeoff

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Author says Since flaps increase drag as well as lift, using flaps on takeoff in a general aviation aircraft will reduce acceleration, and thus increase the length of the ground roll, delaying the point at which the aircraft is able to leave the ground, and reducing its climb rate afterwards. Typically flaps would only be used for a short field or soft field

I think something is wrong here. If they delay the point at which the aircraft is able to leave ground then why it would be used for short runways? — Preceding unsigned comment added by Afdsdgse (talkcontribs) 22:41, 13 November 2011 (UTC)[reply]

Thanks for drawing our attention to that statement. I have removed the offending sentences. They were technically incorrect, and not attributed to any source. Dolphin (t) 06:49, 14 November 2011 (UTC)[reply]
The speed at which the aircraft will fly is lower, but it may take more time to reach that speed because of the extra drag. The change in distance depends on the specific aircraft, as will the amount of flap the manufacturer would recommend for takeoff. If it lacks power - such as a loaded Cessna 172, the amount of flap deflection suggested for takeoff will be very small, and more proficient pilots have been known to accelerate without flaps, then lower them when they have reached the flaps down flying speed.
Had they used full flaps all the way, the extra drag would reduce acceleration so that it would take longer to reach even the lower speed now needed. On aircraft with more power, more flap deflection is possible, always balancing the additional drag with the reduction in acceleration.
Presumably this section needs to be rewritten to make it clearer. NiD.29 (talk) 05:54, 14 November 2011 (UTC)[reply]
@NiD: You have written that flaps cause extra drag and this reduces the acceleration prior to takeoff. This statement is incorrect. Partial-span flaps significantly increase lift-induced drag because they disrupt the spanwise lift distribution on the wing. During the takeoff ground roll the lift generated by the wing is zero, or very small, so induced drag is insignificant. Proficient pilots know that an aircraft should be completely in the takeoff configuration prior to setting power and releasing the brakes for takeoff. It would be very poor airmanship to rely on some adjustment, such as extending flaps, during the takeoff run. If a pilot is concerned that his weight is so heavy, or his runway so short, that he is tempted to set takeoff flap as he approaches lift-off speed he is not proficient. He should be doing something constructive about the problem, such as reducing his weight or using a different aircraft. Dolphin (t) 06:58, 14 November 2011 (UTC)[reply]
Both partial and full span flaps increase frontal area and hence drag even if no lift is generated - but lift is still generated even if it isn't enough for flight - try stopping on a wet runway with full flaps on and you'll find enough lift to reduce traction well below flying speed. Plain flaps and split flaps work by forcing the air under the wing down - Newtonian physics (not by distrupting spanwise flows - if they did that they would reduce the amount of lift, not increase it) - but it comes at a price - far more drag is generated this way than would be by Bernoulian lift, hence it would reduce acceleration. Perhaps you should try this in a flight simulator to see what I mean - MS Flight Sim models the physics well.
A different aircraft is rarely an option, and reducing weight may not always be possible either - one works with what one has. The technique is used by bush pilots who don't always have the luxury of a straight and level runway of known length. It isn't something your average airline pilot, or spamcan driver needs to know - hence my comment about skill.NiD.29 (talk) 12:58, 14 November 2011 (UTC)[reply]
I agree that the wing and flaps contribute to frontal area. It is meaningful to say these things increase the drag coefficient. Drag varies with the square of the airspeed so drag is insignificant during the early stage of the takeoff run. Leaving flap retracted during this early stage of the takeoff run and then extending it later, in the belief that it shortens the takeoff run, is naive in the extreme. I don't doubt that some pilots have tried it but I do doubt that it actually achieved the desired effect. To determine whether a change of configuration or engine or propeller causes a change in performance requires very careful measurement and usually multiple tests, just like any scientific experiment. Bush pilots don't have this luxury so they wouldn't know whether their strategy had any effect.
I seriously doubt that a reliable published source could ever be found for this flap-setting strategy so it has no place in Wikipedia and there is little point in discussing it much further. Dolphin (t) 21:42, 14 November 2011 (UTC)[reply]
It may be hard to pose general rules in this area, because likely there are vast differences between various types of aeroplane. But both from ground class and from experience I can confirm that on most aircraft, flaps are used on take-off, mostly partially, but in some cases even to full deflection, in order to reduce the take-off distance aka roll. I can only suppose the increase in lift and reduced stall speed make up for the (indeed unavoidable) increase in drag. Jan olieslagers (talk) 17:57, 14 November 2011 (UTC)[reply]
@Jan: You are supposing correctly. Wing flaps reduce stalling speed and this allows lift-off and climb-out at a lower airspeed, and hence they reduce the takeoff distance. During the ground roll and initial takeoff (still in ground-effect) the contribution to drag from the wing flaps is small. However, wing flaps cause a significant contribution to drag during the climb-out and this explains why there is a limit to the amount of flap used during takeoff, and why pilots retract wing flaps as soon as they achieve the necessary airspeed. Dolphin (t) 22:34, 14 November 2011 (UTC)[reply]
Digging through various POH's (http://www.micro-tools.net/pdf/Cessna/) the consensus is that flaps trade runway distance for climb rate - using flaps reduces ground roll slightly (10% less ground roll for C172/C150 if a maximum of 10 degrees of flap are used, and if takeoff isn't hot or high) but it reduces the climb rate, as the aircraft leaves the ground before sufficient speed has been reached for the aircraft to be able to make its best rate of climb and has to accelerate post-takeoff and while also climbing to that speed. Normal C172 takeoff recommends not using any flaps on takeoff unless the ground is rough or soft. A PPRuNe discussion suggests this holds true for large airliners as well - the sole difference there being more flap may be used, although even then full flap is rarely used as that reduces climb to below safe margins. In either case if there are obstacles flap use should be minimized. Some multi-engines aircraft may be able to leave the ground while using flaps on takeoff (such as the Beech Baron) before safe single engine speed has been reached and so discourage the use of flaps for takeoff entirely.NiD.29 (talk) 05:34, 15 November 2011 (UTC)[reply]

More flap types

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Just came across a mention of the Cosandey flap - it is used on the rear airfoil of a tandem wing aircraft such as the flying flea and deflects up (acting much as an elevator) seemingly allowing a higher angle of attack than normal for a "parachute descent", but I can't find any good paper refs for this - can anyone help?NiD.29 (talk) 05:04, 8 January 2012 (UTC)[reply]

Found another previously unknown flap - the Arado travelling flap - can't find any info on it either but it looks suspiciously like a Fowler flap.99.246.44.77 (talk) 05:36, 30 January 2012 (UTC)[reply]

Also found a reference to a Multhopp-Klappe (landing flap/diving brake) used by the experimental Focke-Wulf Fw 191.NiD.29 (talk) 06:08, 1 February 2012 (UTC)[reply]

Effect of flaps on climb rate and climb angle

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In recent times, the lead paragraph in the article stated that extending flaps increases the climb rate. Recently, User:A merch amended the sentence so it said that extending flaps increases the climb angle - see the diff. User:NiD.29 reverted A merch's edit, adding an Edit Summary saying that flaps reduce the angle so that obstacle clearance at the runway end becomes an issue - see the diff. It is a worthy topic of debate as to what effect extending flaps has on climb rate and climb angle. This is the place for that debate.

I have done some copy editing to clean up the lead section of this article - see the diff. In doing so I erased any mention of what effect flaps have on climb rate or climb angle. When we have determined a position the result can be incorporated into the lead section. Dolphin (t) 01:07, 28 May 2012 (UTC)[reply]

The effect as written was from the Cessna POI, backed up up by the POI's of several other types - I thought there was a reference listed for it.
In any case refer to:
Cessna 172 POH May 1981 edition on page 4-15 @ http://www.scribd.com/doc/30246646/cessna-172p-1982-poh
  • "using 10 degrees wing flaps reduces ground roll and total distance over an obstacle by approximately 10%"
ie: you are 10% closer to the obstacle because you have a 10% reduced rate of climb - you just get to do it at a slower speed
In the 182Q POH it is even clearer also on page 4-15 @ http://www.flight.org/blog/download/manuals/C182-POH.pdf
  • "If an obstruction ahead requires a steep climb angle, a best angle of climb speed should be used with flaps up and maximum power."
In other words - if you have to get out of Meteor Crater, flaps won't help! (for bonus points see if you can spot the Cessna who thought otherwise).NiD.29 (talk) 03:07, 28 May 2012 (UTC)[reply]
Thanks NiD. When you made your edit to Flap (aircraft) you restored the comment that extending flaps increases the climb rate. Do you want to make a comment, or supply a source, about flaps increasing the climb rate? Dolphin (t) 05:17, 28 May 2012 (UTC)[reply]
Confusion abounds - I was undoing the climb angle because I remembered it was definitely wrong, but it appears climb rate was as well.
What you get for using flaps is the ability to get into the air at a lower speed and a reduced stalling speed. Forget about climb.
From the "Normal Checklist Diamond DA 20-C1" @ http://www.sealandair.ca/images/checklist_DA20C1.pdf
  • Vx (Best angle of climb) flaps down 57 knots indicated air speed
  • Vx (Best angle of climb) flaps up 60 kts
  • Vy (Best rate of climb) flaps down 68 kts
  • Vy (Best rate of climb) flaps up 75 kts
The extra 3 and 7 kias are going to make a difference on the number of feet per minute the aircraft is climbing so safe to say, the angle and the rate are both reduced when flaps are used in a climb. YMMV on other types but a modern, reasonably well designed light plane like the Diamond won't be far from the norm (though other types of flaps could make a difference). The Cessna manuals don't explicity mention rate, only angle.
According to PPRUNE Vx & Vy (industry standard notation for these two numbers which should be included) are rarely used on large commercial aircraft because they aren't needed - fuel burn limits the rate of climb rather than any limits imposed by the airframe and engines and so are largely irrelevant.NiD.29 (talk) 06:54, 28 May 2012 (UTC)[reply]

Intro

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The intro reads terribly:

Flaps are hinged surfaces mounted on the trailing edges of the wings of a fixed-wing aircraft to reduce the speed at which an aircraft can be safely flown [...]

Really, flaps are put on airplanes to reduce the safe speed it can be flown at?

I came here wanting to get an overview of the purpose of flaps, to see whether it matched my guess. I guessed that they allow some control over where thrust goes, either into speed or lift. During takeoff/landing, you might want more lift as you are moving slowly, but while at cruising speed you will get plenty of "natural" lift without the flaps down. I take it they're also used as brakes to slow down more quickly. This kind of general overview is what the introduction should provide. Not "lowering stall speed and increasing drag". 67.198.70.66 (talk) 05:55, 19 June 2013 (UTC)[reply]

The introduction looks satisfactory to me. Flaps are installed on many aircraft because, when deployed, they lower the stalling speed. However, when deployed, they also increase the drag coefficient and that is usually not a good thing. Extra drag during the landing approach is beneficial but extra drag is definitely not a good thing during take-off. Consequently, pilots select a small amount of flap for take-off, and full flap for landing.
You have suggested that flaps allow some control over where thrust goes, either into speed or lift. That is not an accurate assessment of the purpose or effect of flaps. Dolphin (t) 07:37, 19 June 2013 (UTC)[reply]
It is difficult to define the purpose in terms sufficiently generic, because the practical use varies with the individual type of plane. For just one example, on mine full flaps are applied on take-off as well as on final. My own wording would go towards "modifying the wing's speed/lift/drag parameters away from the standard cruise behaviour, to better match the particular requirements of landing and/or take/off". HTH, Jan olieslagers (talk) 16:11, 19 June 2013 (UTC)[reply]

blown flaps

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Greetings NiD.29, The quoted source doesn't say the blown flap was a British invention nor that first flight tests were in Germany.

It quotes a British test report dated May 1939 (ie before the war) and a German test report dated 1938. It doesn't say when the tests were actually done, nor who invented the blown flap or when.

It says German flight tests were done during the war but it doesn't claim they were the first although they may well have been. It just doesn't mention any others. The report was written in 1955 and I don't suppose the author would have known about tests in the Soviet Union, for example, if there had indeed been any. Best regardsPieter1963 (talk) 23:39, 12 January 2016 (UTC)[reply]

Degrees

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I've often seen flap settings measured in degrees of deployment. The article also talks about "10° of flaps" for takeoff in a Cessna 172S. The definition of this number should be explained in the article. I could for example imagine a ruler laid against the flap, measured against the chord of the original wing profile, or the changed chord measured against a ground surface, or many other ways. So which one is it? --BjKa (talk) 12:10, 12 April 2017 (UTC)[reply]

Any measurement you can imagine that isn't relative to the airframe would be pointless because the whole aircraft can be retrimmed to other angles other than by the flap - the 10° is relative to the aircraft itself, and is the same whether you choose to use the aircraft's datum line or the camber of the wing, or any other pair of points unless there is a serious structural problem. The flap has rotated 10°, period. - NiD.29 (talk) 14:22, 12 April 2017 (UTC)[reply]
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Title of article should be "Flaps (aeronautics)"

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That's the preferred usage in the article. Autodidact1 (talk) 07:10, 23 June 2020 (UTC)[reply]

That would be incorrect per Wikipedia's policy on article titles. - BilCat (talk) 07:19, 23 June 2020 (UTC)[reply]
Oops, forgot to cite the policy:

Use the singular form: Article titles are generally singular in form, e.g. Horse, not Horses. Exceptions include nouns that are always in a plural form in English (e.g. scissors or trousers) and the names of classes of objects (e.g. Arabic numerals or Bantu languages). For more guidance, see WP:Naming conventions (plurals).

BilCat (talk) 08:21, 23 June 2020 (UTC)[reply]

Drag of split flaps

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There's an interesting discussion from DarkAero about different types of flap designs.[1] At 8:56, he's talking about Cd of a split flap and argues that it's not as bad as commonly believed. RoySmith (talk) 23:53, 19 February 2024 (UTC)[reply]

References

  1. ^ "The biggest myth about split flaps - YouTube". youtube.com. Retrieved 19 February 2024.