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In general aviation aircraft such as Diamond star DA-40, flaps to take-off are used until 500ft AGL and speed before retracting flaps is Vy (best ROC speed)-67kts and after retracting flaps is 80kts.

Why can't we use take-off flaps until cruise altitude such as 6000ft MSL and maintain 67kts and climb sooner?

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    $\begingroup$ Related: Why do flaps retract? $\endgroup$
    – ymb1
    Sep 13 at 14:15
  • $\begingroup$ BTW, I checked the DA40's manual. Make sure you're checking the rate of climb at the same weight. Both tables don't start at the same weight so they've had me confused as well. $\endgroup$
    – ymb1
    Sep 13 at 14:16
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    $\begingroup$ This is a good question. I find the current answers not completely compelling, since they don't address whether it's generally better to climb as quickly as possible or to pick up airspeed and climb more slowly but with better ground and air speed. Constant factors, such as engine cooling prop pitch, and transient factors, such as winds aloft, enter into play. $\endgroup$ Sep 13 at 15:38
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    $\begingroup$ Who says you can't? You can climb all the way to cruise at Vx if you really want to... ;) $\endgroup$ Sep 13 at 19:43
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The image below from this answer shows characteristics of airfoils with flaps.

As you rightfully concluded, lift ($C_{L_{max}}$) goes up with the deployment of flaps, but the drag also goes up and even quicker than the lift. Increasing lift is good, but if it comes at the cost of more drag, it will require more thrust (therefore fuel) to maintain this higher lift.

Thus, the value we should maximize is the ratio of lift and drag. The ratio of the two $\frac{L}{D}_{@C_{L_{max}}}$ is also shown below, and it shows that the basic airfoil performs better than those with flaps.

enter image description here

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    $\begingroup$ +1 for mentioning L/D. Lift remains roughly constant (at constant weight), but if L/D is lower with flaps, the same amount of lift comes with more drag. $\endgroup$
    – Bianfable
    Sep 13 at 9:23
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    $\begingroup$ This is pretty much all there is to it. Flaps are simply a way to get initial height quickly, but sacrifising fuel doing so. Without flaps you would eventually get to your destination quicker and with less fuel, but you would take a risk taking off, and while we're at it, landing too. $\endgroup$
    – Jpe61
    Sep 13 at 17:23
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    $\begingroup$ @Jpe61 your comment is partially incorrect. The DA40 climbs faster with flaps down, so it is in fact more efficient if we are only concerning fuel burned vs. altitude. See aviation.stackexchange.com/a/89213/20394 for the numbers from the DA40's POH. $\endgroup$ Sep 13 at 19:45
  • $\begingroup$ Oh, I stand corrected in that sense. However, it climbs faster, but does it advance as fast as in clean config? Which configuration would produce a sort of an inverted brachistocrone? $\endgroup$
    – Jpe61
    Sep 13 at 19:51
  • $\begingroup$ @Jpe61 That's a great question! A real-world answer is really hard and can probably only be found through dynamic programming. If we assume a constant wind field as we climb, then we might be able to find a closed-form synthesis. If we assume a calm day, then an evaluation could be done by looking at the glide ratio: in one minute the flapped DA40 travels 912' less but climbs 110' more. The glide ratio is around 10:1, so that means it could glide 1100' extra. I take this to mean that in energy terms, it is marginally more efficient to climb at the slower air speed in still air. $\endgroup$ Sep 13 at 20:34
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This is a good question, and I don't feel the other answers get at the essential part which is:

Is it optimal to climb with the flaps deployed?

As with any optimal question, the answer relies on what it is we wish to optimize. It's worth examining two goal states:

  1. To climb to altitude as quickly and efficiently as possible. For instance:
    • the winds aloft are so good that the pilot wants to minimize the time spent down low
    • the pilot would like altitude for aerobatics
    • the pilot would like to do high altitude testing
  2. To go from point A to point B while employing best safety practices all while reasonably minimizing time and/or fuel costs.

Why use the flaps in the first place?

In general, getting off the ground and clearing any obstacles while remaining close to the airport is generally considered best practice, even if it means burning a little more gas. Depending on a number of design choices, the climb angle with flaps can be much improved, which means that obstacle clearance is better and in the event of a takeoff emergency the plane has a lot more runway in front of it, or it's not so far from the airport.

The advantages of taking off with flaps down:

  • Wheels leave the ground at a lower airspeed, eliminating rolling resistance. (It's surprising how much drag comes from those tires, esp. in grass and soft fields.)
  • Climb angle is better
    • From the DA40 manual, pgs. 5-14 and 5-16, STP climb rate with flaps is 9.7deg (1160fpm @ 67kts) and without is 7.8deg (1050fpm @ 76kts).
  • Climb rate might be better

So what are the disadvantages?

Increased drag at higher airspeeds

As @ROIMaison shows in this answer, for a Clark Y airfoil the L/D ratio with flaps deployed isn't even remotely close to the normal airfoil. At higher airspeeds this loss of efficiency is acutely felt.

Of course, the DA40 has a much more advanced airfoil and so the spread might be much closer together. Diamond's airfoils come from gliders, and gliders use flaps in low-speed flight in order to turn more quickly. As you might imagine, gliders are optimized for efficiency, so it's fair to reason that the flapped L/D ratio for DA40's airfoil is potentially much better than the venerable Clark Y's.

In case the link between drag and climb rate is not immediately obvious, the more drag there is the less surplus energy is available to increase the plane's potential energy, i.e. to climb.

Engine cooling

The engine cowling is designed to provide appropriate cooling at relatively high airspeeds. There's a certain thermal inertia which protects the engine for a minute or so, but after that temperatures start reaching critical points. It's important to nose over and pick up airspeed in order to improve cooling.

Propeller inefficiency at slower speeds[*]

For a fixed-pitch cruise prop, efficiency suffers quite significantly at lower airspeeds. Speeding up will gain some extra propeller and engine performance.

[*] Note that this doesn't apply to constant-speed props.

Conclusion

With the above in mind, we can see that the best practices of getting up off the ground quickly, with plenty of runway to spare, and with enhanced obstacle clearance is a Good Thing (TM). These goals are largely met by 500', so this is an opportunity to reevaluate our optimal process. Do we still want to climb, or do we want to go somewhere as well?

Unfortunately, I don't have any basic sense of whether it's generally optimal to continue to climb with the flaps deployed. It might even depend on the particular plane model whether absolute climb rate is better with flaps up or down. If the climb rate is worse with the flaps down, then the answer is clearly to get them up as soon as practical.

Supposing climb rate is better with flaps deployed, the situation doesn't really become clear. If the winds aloft are favorable, then getting to altitude quickly is valuable. But more valuable than proper engine cooling? Hmmm...

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  • $\begingroup$ You say "advantages of taking off with flaps down: [...] Climb angle is better". Is that something special for the DA40? For example, in a B737 the exact opposite is the case and you actually want lower flaps when obstacle clearance is limiting. $\endgroup$
    – Bianfable
    Sep 13 at 17:17
  • $\begingroup$ @Bianfable in the video at 3m02s I see the image you're referring to. The short answer is I really don't know. The T/O flaps for the DA40 are 20 degrees, which is somewhat close to the 737's 25 degrees. But IIRC, turbines are very ineffective at slow speeds, so it's also possible the 737 looses a ton of efficiency if it flies slowly. Check out aviation.stackexchange.com/questions/49946/… to see why a turbojet could wind up lifting earlier but losing climb angle. $\endgroup$ Sep 13 at 17:56
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    $\begingroup$ Thanks for including the numbers from the manual. It could be that the opposite is only true for jets. OTOH, the 737 limitations are based on the OEI (one engine inoperative) climb performance, where the relevant numbers here are for normal climb with both engines. $\endgroup$
    – Bianfable
    Sep 13 at 18:20
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Because it would not be efficient. Flaps increase drag (and lift), so you would burn more fuel climbing to cruise altitude with flaps extended compared to if if you retract them.

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    $\begingroup$ This is incorrect in the case of the DA40 (and any other plane where the climb rate is higher with flaps deployed). At full throttle, its climb rate is higher with flaps in T/O position, so it will use take less time and less fuel to get to the target altitude. See aviation.stackexchange.com/a/89213/20394 for the performance numbers from the DA40's POH. $\endgroup$ Sep 13 at 19:41
  • $\begingroup$ Regardless of the data in the manual, you'd have to redefine the word 'flap' to get a better climb rate with flaps down. Flaps will increase camber, means worse L/D, means more drag, means less excess thrust, means less climb rate. That's physics. The rest is conjecture. If they don't do that they are not Flaps $\endgroup$
    – Radu094
    Sep 16 at 5:18
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Most people fly in order to get somewhere, so cruise climb is used as it covers more ground while getting to altitude.

Here is the DA40 airspeed table that would have been nice to include in your question. Depending on weight, cruise climb speed is 6-9kt higher than takeoff climb speed. If your objective was just to gain altitude, as for local observation, you could use takeoff flaps if you wanted. In some aircraft you have to keep an eye on engine temps if you fly slowly at high power.

enter image description here

A better illustration is in transport aircraft where the speed difference is much higher. Here is the BaE146 takeoff sequence. There are speed limitations for deployed flaps, so retraction is structurally required as speed increases. Staying under a 135kt limit for takeoff wastes a lot of time when 220kt cruise climb is available and 250kt is the target.

enter image description here

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    $\begingroup$ Worth pointing out that for some aircraft, apparently not the DA-40, full or near-full flaps aren't optimal even for max ft/min rate-of-climb. As others have mentioned, the DA-40 has flaps with good aerodynamics so the L/D ratio stays somewhat efficient, but on other aircraft the L/D ratio can be much worse with flaps out. $\endgroup$ Sep 14 at 7:59
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Flaps give you more lift, but also more drag. The drag means that your horizontal speed is lower.

The usual phases of flight where low speed is an advantage are:

  1. When taking off from a runway. You don't want to run out of runway and you want to end wheel drag as soon as possible.

  2. When trying to clear obstacles. You want as much time to gain altitude before you get to them.

  3. When at low altitudes. You don't want to get too far away from the airport when your gliding range is low.

  4. When near landing. You need to drop altitude but also keep your speed down.

  5. When landing. You want to get as slow as possible before you touch the ground.

Flaps make the lift/drag trade-off worse for you. That's only sensible when the drag is a good thing or the extra lift is absolutely necessary.

Once the drag becomes a loss rather than a benefit and you have enough lift without flaps, the logic of flaps stops applying. You want the most efficient wing configuration with as little drag as possible for the lift generated. That's the configuration your wing was built for.

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Flaps provides extra lift at lower airspeeds but for the cost of huge drag.

At some point the drag stops the plane acceleration and it cannot climb any faster.

Note that the airlines want as fast transport from Gate A(XYZ) to Gate B(HKL). Airports want as short runways as possible. Government wants as small noise-loaded areas as possible.

Short runway limits the take-off/landing speeds significantly so the wing setup must provide lift at low airspeeds even at the cost of drag.

The government demands as fast climbing as possible and from some altitudes the noise is spread so wide the ultimate climb rate is not mandatory and airlines are free to optimize for the most crucial parameter - cost.

Here the drag is the adversary so flaps are retracted. Plane can fly faster for smaller thrust needed and the thrust reserves can be used for nose-up climb as well.

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