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I thought that deploying flaps will increase both the drag and lift, thus increasing L/D ratio? But do they increase proportionately? And how exactly does that correlate with the increase/decrease of the minimum drag speed (VimD)? So I'm left with four different possibilities:

  1. increase VimD and increase (L/D)max
  2. increase VimD and reduce (L/D)max
  3. reduce VimD and increase (L/D)max
  4. reduce VimD and reduce (L/D)max
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  • $\begingroup$ The first notch of flaps mainly increases lift, the last notch mainly increases drag. $\endgroup$
    – Jim
    May 8 at 6:21
  • $\begingroup$ I see. But the rate at which the drag increases is much higher than the rate of increase of lift thus decreasing (L/D)max? $\endgroup$ May 8 at 9:42
  • $\begingroup$ How are you defining “minimum drag speed”? The speed at which drag is minimum is zero- always. $\endgroup$
    – Jim
    May 8 at 13:29
  • $\begingroup$ @SpeedBird789 -- thought "flight dynamics" was an appropriate tag; to add it I had to pick another tag to delete. Feel free to roll back/ undo if you prefer the tags the way they were. I know on ASE we seem to have reached the conclusion that its ok to have tags give information that's not included in the actual question so if you really want to constrain the question to General Aviation, feel free to undo or revise my tag edit. $\endgroup$ May 8 at 17:52

2 Answers 2

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Lowering flaps generally reduces L/D max and reduces L/D max speed

It really depends how you want to design your plane, but usually you want to have maximum excess power at your climbing speed$^1$. This is where your plane is "clean" with its highest L/D ratio. Or, one could design for max L/D at cruising speed, especially if they were blessed with excess power (jets) and wanted to save fuel.$^4$

But landing is generally slower, so you add flaps to increase lift, but L/D will be generally lower$^2$.

From your questions here, a better understanding can be had with the $Lift$ $Equation$:

Lift = Air Density × Wing Area × Coefficient × Velocity$^2$

Coefficient is a combination of airfoil type and AoA. Dropping flap changes the airfoil type, increasing the lift coefficient. So L/D max will be slower$^3$. Greater deflection of flaps generally increases drag, lowering L/D but allowing a slower, steeper approach (bush pilots love this).

These are some guidelines, but further refinements can be made in discussion of a specific aircraft type.

$^1$ for best climbing performance
$^2$ dropping flaps creates more drag producing surfaces such as sharp corners. Lift increases (for a given speed) but drag increases at a proportionally greater rate, giving a lower L/D.
$^3$ very high L/D ratios can be had with heavily cambered wings, but these are slower, making wind direction (groundspeed) more of an issue.
$^4$ longer runways and no speed limits at lower altitudes could make this a reality (not likely)

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  • $\begingroup$ Just a nitpick: Dropping flaps increases lift very briefly, but mainly lowers angle of attack and increases the maximum possible lift coefficient. Since lift should equal weight, lift will stay constant over the long term. $\endgroup$ May 8 at 14:25
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    $\begingroup$ @PeterKämpf I would posit that lowering flap (increasing coefficient) allows lower AoA (as measured along the fuselage) at the same airspeed or lower airspeed at a given AoA . Interesting here, that all things being equal, the drag increase slows the aircraft down when flaps are deployed, forcing us either to add power of increase glide angle to keep our safer AoA. $\endgroup$ May 8 at 18:16
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I thought that deploying flaps will increase both the drag and lift, thus increasing L/D ratio

The lift coefficient increases, but the lift force does not, at least over the long run. The lift force in steady-state horizontal flight must equal weight. In a moderate climb or glide lift still must be almost equal to weight-- the actual formula is lift = weight * cosine (climb or glide angle).

But do they increase proportionately?

No they do not. For the vast majority of (or perhaps all) airfoils used in actual aircraft, deploying the flaps (even slightly) decreases the maximum value of the ratio of ((lift coefficient) / (drag coefficient)), which is also the ratio of ((Lift force) / (Drag force)), which (in the case of an unpowered glider with zero thrust) is also the glide ratio.

And how exactly does that correlate with the increase/decrease of the minimum drag speed (VimD)?

The speed for minimum Drag force (which is not the speed for minimum drag coefficient, but which is also the speed where the least Thrust is required to maintain constant altitude, or to maintain any given glide or climb angle) occurs at the speed for the maximum ratio of ((Lift force) / (Drag force)), which is also the speed for the maximum ratio of ((lift coefficient) / (drag coefficient)). Deploying flaps is somewhat like decreasing the weight of the aircraft-- due to the increased lift coefficient, the entire curve of L/D (or Cl/Cd) versus airspeed gets shifted to the left (toward lower airspeeds), as well as distorted in other ways (to reflect the decrease in max L/D or Cl/Cd), and thus the speed for the max L/D (or Cl/Cd) ratio, which is also the speed for minimum Drag force, occurs at a lower airspeed with flaps down than with flaps up.

The answer to your question is therefore option "4".

If you intended to ask about the minimum drag coefficient-- that would always correspond to high-speed flight, at a low angle-of-attack, with the flaps up. Lowering the flaps would increase the drag coefficient at any given airspeed or airspeed or angle-of-attack, at least if we are talking about flight well above the max L/D speed.

Related ASE answers--

Is the maximum lift-drag ratio found at minimum drag? (see several answers) -- establishes that minimum Drag force occurs at the angle of attack (and logically also the flap setting) for max L/D

Can we show through simple geometry rather than formulae or graphs that the best glide ratio occurs at the maximum ratio of Lift to Drag? -- same conclusion, but geared toward gliding flight -- "Also note that the geometry of the triangle is such that the maximum Lift to Drag ratio also coincides with the minimum Drag value..."

What determines the best glide speed? -- similar

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