As per the video from Smithsonian channel
BA flight 38's captain retracted the flaps of the Boeing 777 by 5 degrees to extend glide, to travel further. Why?
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Some answers presume that raising flaps reduces lift.
That is wrong.*
All it does is to increase angle of attack, until the change in flap setting is so severe that the airplane stalls. Only then will the airplane lose lift. With a smaller flap setting, the pitch trim changes and the airplane pitches up a little to keep lift constant. If the (auto)pilot does not correct the pitch trim for the new flap setting, the airplane will settle at a new, higher speed. Here, however, we can be sure that the autopilot kept speed constant (it only disengaged at 150 ft, and then the copilot took over. He certainly did not dive to pick up speed at this altitude!).
Raising the flaps does, however, reduce drag. See below for the A320; with a B777 the result will not be all too different.
A320 polar with 3 different flap settings (picture source)
Assume the airplane flies at a lift coefficient of 1.2 with flaps at 35°. Raising them to the next setting of 22.5° will move the operating point horizontally forward to the 22.5°-polar curve. Here the airplane flies at the same lift, but a smaller drag coefficient.
Retracting the flaps completely will not allow it to stay at this lift coefficient because the baseline polar stops below a lift coefficient of 0.9. The airplane will stall and needs to accelerate to keep flying. Only then will the airplane have to pick up speed.
I remember two occasions where that happened to me and raising the flaps saved my butt:
* Since this statement raises blood pressure in others, let me explain. I only posted here after one answer after the next repeated this meme. Now some authors have edited and improved their answer. Would that had happened without clear words? Judge for yourself.
Now to the issue of lift loss: When the flaps move up (slowly), the lift force decreases just a tiny bit. The aircraft starts to sink, which immediately raises the angle of attack and puts an end to any further lift loss. Liftforce is immediately restored to its old value. That is why I simplified this process and said there is no lift loss, because there effectively isn't.
Next, the change in pitching moments from flap movement lets the aircraft pitch down unless pilot or autopilot retrim for the new flap setting. This is a much slower process because it involves a rotation of the airplane and its lengthwise acceleration.
It is all about airspeed. Flaps increase both lift and drag. At any given airspeed an increase in flap extension will increase the amount of drag being created. To maintain that given airspeed, the airplane’s glide path angle must be increased. The greater the glide path angle, the more altitude is lost over a given distance. Under a certain power level, the drag increase caused by the flaps make it impossible to maintain the necessary airspeed to keep the force of lift high enough to maintain flight without increasing the descent angle.
Retracting flaps will cause an immediate drop in lift and a gradual corresponding increase in airspeed. Given enough altitude, the increased range due to the shallower glide path of the aircraft can more than make up for the altitude loss caused by the loss of lift.
How does retracting flaps help extend the glide of an aircraft?
Because the ratio of the lift coefficient to the drag coefficient dictates the glide ratio that may be achieved at any given angle-of-attack or at any given airspeed.
In fact, in still air, the glide ratio is exactly the same as the ratio of lift coefficient to drag coefficient.
(With a headwind, the glide ratio becomes lower than than the Cl/Cd ratio, and with a tailwind, the glide ratio becomes higher than the Cl/Cd ratio.)
Extended flaps increase the lift coefficient at any given angle-of-attack, which helps the glide ratio at that angle-of-attack, but extended flaps also increase the drag coefficient at any given angle-of-attack, which hurts the glide ratio at that angle-of-attack.1 The latter effect generally "wins", so the best possible glide ratio is generally achieved with flaps up. But read on for a more nuanced view--
If the airspeed is free to vary as needed to optimize the glide ratio, then we can say that only one flap setting-- typically fully retracted-- will yield the maximum ratio of lift coefficient to drag coefficient. Of course, if we are slower than the best-glide airspeed for that configuration, we'll suffer an extra altitude loss as we accelerate to that airspeed, but for a long glide it will be worth it in the long run, as noted in another answer.
(While we are accelerating, we are not in a steady-state condition, and it's no longer true that the glide ratio through the airmass is exactly equal to the ratio of Cl/Cd. It is worse, as we convert some of our altitude into airspeed. If the remaining distance to glide is rather short, it may not be worth it to to allow the aircraft to accelerate very much, at least in the case of a large heavy aircraft.)
If the airspeed is constrained to be well below some value that is below the optimimum value for getting the flattest possible glide, then we can still say that only one flap setting will give the maximum ratio of lift coefficient to drag coefficient at the present airspeed, giving the maximum glide ratio that is possible at that airspeed. Typically the optimal flap setting in such a case would have the flaps only slightly extended.
As a comment by another contributor suggested, see Section 15.2.3 of the excellent "See How It Flies" website for a rather dramatic example of retracting flaps to extend the glide, even though the initial airspeed was quite slow and the aircraft needed to speed up a lot to reach the optimal gliding speed for the clean configuration. Of course, some of the dynamics involved in attempting to execute a similar series of maneuvers in a very large, heavy aircraft would have been significantly different-- especially the altitude penalty associated with accelerating to the best glide airspeed for the "clean" configuration.
As another answer has pointed out, it is not always necessary to accelerate to a higher airspeed to realize some improvement in glide ratio by making some reduction in the flap setting. Remember, raising the flaps reduces the lift coefficient associated with any given angle-of-attack. If we raise the flaps but also increase the angle-of-attack as needed to hold the airspeed constant, the lift coefficient stays essentially the same.2 Whether the glide ratio will be improved or degraded by raising the flaps without changing the airspeed, depends on whether the aircraft has a higher drag coefficient in the clean configuration at the higher angle-of-attack or in the "dirty" configuration at the lower angle-of-attack. In other words, whether or not the ratio of Cl/Cd for that given airspeed is increased or decreased by raising the flaps while increasing the angle-of-attack. In other words, whether or not the drag coefficient for that given airspeed is decreased or increased by raising the flaps while increasing the angle-of-attack. Unless the aircraft is hanging on the edge of a stall, any time a substantial amount of flaps have been deployed, some amount of reduction in the flap setting will generally (safely) provide some improvement in the glide ratio, even if the airspeed is not increased.3 So depending on the specific situation at hand, including the whether the aircraft is large or small, and the distance remaining to be covered in the glide, the best strategy for a pilot needing to extend his gliding range may range from a modest reduction in flaps with little or no increase in airspeed, to a larger retraction in flaps along with a modest increase in airspeed, to fully "cleaning up" the wing while allowing the aircraft to accelerate all the way to the best-glide-ratio airspeed for the "clean" configuration. Each successive "escalation" in strategy gives up more altitude to accelerate the aircraft, but eventually brings the aircraft to a flatter glide angle.
Of course, we get "the best of all possible worlds" if the aircraft has a substantial amount of flaps deployed, but is already travelling at an airspeed that is well above the speed for the best glide ratio for that configuration. This was likely the case in the video attached to the question. Now we can retract the flaps as needed to give the best possible glide ratio for the current airspeed, without sacricing any extra altitude to accelerate. Once we've reached this point, if the distance remaining to glide is far enough, then additional steps along the "chain of escalation" described above may be warranted, to get the aircraft into an even cleaner configuration at a still higher airspeed. Obviously, in the case in the video, the remaining distance to glide was too short (i.e. the aircraft's altitude was too low) to make it worthwhile to dive to accelerate to the best-glide airspeed for a clean or nearly-clean configuration, even if landing in such a configuration were somehow feasible.
1-- Note that a description of what happens to the lift coefficient and lift force as we retract the flaps while holding the airspeed rather than the angle-of-attack constant would be quite different-- see next footnote. In actual practice a pilot would rarely have any reason to try to hold the angle-of-attack constant while retracting the flaps. In actual practice he (or the autopilot) will generally hold the airspeed constant, or allow to only change smoothly and gradually (but see the "See How It Flies" anecdote for a dramatic exception!) But it is still helpful to understand that extended flaps do increase both the lift coefficient and the drag coefficient that are obtained at any given angle-of-attack. Note also that while in many aircraft, retracting the flaps decreases the trimmed lift coefficient, meaning that the aircraft tends to come to equilibrium at a higher airspeed if the pilot (or autopilot) makes no pitch control inputs to compensate, it is true that in some aircraft, retracting the flaps actually increases the trimmed lift coefficient, meaning that the aircraft actually tends to come to equilibrium at a lower airspeed if the pilot (or autopilot) makes no pitch control inputs to compensate. The latter can only happen if retracting the flaps changes the balance of pitch torques on the aircraft in a way that significantly increases the trim angle-of-attack. The issue of the effect of flap retraction on the trimmed lift coefficient is fundamentally different from the issue of the effect of flap retraction on the lift coefficient at any given angle-of-attack. If the pilot is hand-flying the aircraft to maintain a given airspeed, or the autopilot is maintaining a given airspeed, then the effect of flap retraction on the trimmed lift coefficient is irrelevant. At any rate, in the particular case at hand, there's no reason to assume that the angle-of-attack was held constant as the flaps were retracted, so nothing in this answer is intended to suggest that the actual achieved lift coefficient was reduced as the flaps were retracted. From the behavior of the aircraft we can see that the lift coefficient must have stayed nearly constant, meaning that the angle-of-attack must have been increased as the flaps were retracted.
2-- Technically speaking, if we change the flap setting and vary the angle-of-attack as needed to hold the airspeed constant, while not changing thrust, the lift coefficient doesn't stay exactly constant. If the glide angle is increased, then the lift vector and lift coefficient have also been very slightly increased, and if the glide angle is decreased, then the lift vector and lift coefficient have also been very slightly decreased, due to the relationships covered in the first link below. But it's a good first approximation to say that the lift coefficient and lift force stay constant for all practical purposes, as we vary the flap setting while also varying the angle-of-attack as needed to hold the airspeed constant.
3-- In fact, the diagram attached to the related answer How does retracting flaps help extend the glide of an aircraft? suggests that there is NO airspeed where retracting the flaps to a lower setting while adjusting angle-of-attack as needed to hold airspeed constant would not decrease the drag coefficient and improve the glide ratio, except for cases were that would take wing to an "off the chart" part of the graph, which presumably indicates a stall. (Example: retracting the flaps from 25 degrees to 0 degrees while flying at a lift coefficient of 1.2 would take the wing "off the end" of the 0-degree flap curve.) In other words, none of the curves cross. Perhaps this would not be true if a curve representing, say, 10 degrees flap deployment were included-- it seems likely that there is some airspeed well below the best L/D airspeed for the clean wing, but above the stall speed for the clean wing, where a lower drag coefficient and a better glide ratio is achieved with some small amount of flaps deployed than with the clean wing.
Here are some other related questions and answers on ASE:
(Q) Best Glide with Flaps T/O in DA20-A1 (see all answers)
(Q) Do negative flaps increase glide ratio? (see all answers)
The short answer is: flaps increase lift, but they increase drag more than they increase lift. So it's better to retract them and dive to gain airspeed, then pull up to a shallower dive to maintain that speed or trim the aircraft to higher angle of attack, until your wings produce enough lift.
EDIT: In the BA 38 case, the flaps were not completely retracted, just raised from 30 to 25 degrees. And they did not dive, as Peter said. I don't know why this was done, but some aircraft do fly better at lower speed, with flaps slightly down, than at high speed with flaps up
Flap position affects more than just flaps. It's tied to everything from slats to landing gear warnings. Airplanes have a reduced drag position used in a go-around or missed approach.
Retracting flaps fully may not be possible due to time and loss of systems. Retracting flaps beyond the initial setting will typically also retract slats or leading edge devices, which can have a significant impact on stalling speed.
On modern aircraft with electronic displays, minimum speeds will be evident by indications that appear on the airspeed tape. On older analog aircraft, we put little plastic "bugs" around the airspeed indicator to provide the relevant speeds for retraction.
If the aircraft is flying at a speed faster than the minimum sink speed or "best glide" or "driftdown" speed, then it will need to be slowed to a speed allowed by the aircraft configuration, without getting too slow.
In most large aircraft, raising the landing gear (to reduce drag) actually increases drag during retraction, due to movement of the gear doors. Moving flaps the only other option, is limited by altitude, airspeed, weight, etc.
If an engine fails on final aproach, typically a flap retraction to the go-around setting is in order, but not much else.