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"Slow, heavy, clean" are the three major conditions generating stronger wing vortices. It's very clear how "slow and heavy" aircraft create stronger vortices, but why a "clean" configuration generates stronger wake turbulence is less clear.

I did some digging on this, and found some people saying "use of the flaps reduces the AoA and thus leads to weaker wake turbulence" and others claiming "use of flaps moves the center of lift toward the root of the wing and that leads to less lift around the tip of the wings and thus less wingtip turbulence.

Which explanation is correct?

Edit) I checked the answer given here What is the relationship between angle of attack and wake turbulence?, but I'm not really sure "not really" is the right answer to this. The AIM (Aeronautical Informational Manual) is very clear about this, designating "clear" (along with "heavy," and "slow") as one of the three factors that increase wake turbulence.

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  • $\begingroup$ Any valid explanation should also deal with conservation of momentum and energy. To generate the same amount of lift while accelerating the air less requires either accelerating more of it (that is affecting it to bigger height above and below the wing) or accelerating it more uniformly (that is changing the lift distribution closer to elliptical). $\endgroup$ – Jan Hudec Feb 27 '17 at 18:05
  • $\begingroup$ @lemoncider do you have a source for the 'slow, heavy, clean'-statement? As can be seen from the duplicate, another individual also found the same statement, so I believe some source is providing wrong information. $\endgroup$ – ROIMaison Feb 28 '17 at 9:00
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    $\begingroup$ What if the AIM is wrong? It would not be the first time that a meme goes unchecked. Gear and flaps have a very minor effect on wake turbulence. $\endgroup$ – Peter Kämpf Mar 1 '17 at 22:39
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    $\begingroup$ @ROIMaison Yes I have. Click on this link: faa.gov/air_traffic/publications/media/aim.pdf. In 7-3-3 (p.519), the manual says: "The greatest vortex strength occurs when the generating aircraft is HEAVY, CLEAN, and SLOW. " $\endgroup$ – lemonincider Mar 4 '17 at 10:37
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I would actually assume the opposite to be true.

Let us assume the vortex intensity and the induced drag are directly correlated. The induced drag coefficient can be expressed as:

$c_{Di}=\frac{c_L^2}{\pi\cdot AR \cdot e}$

  • $c_L$: Lift coefficient
  • $AR$: Wing aspect ratio
  • $e$: The so-called Oswald factor, a number which equals one for elliptic lift distributions. It decreases for distributions that deviate from the elliptic one.

Most wing designs aim to achieve an elliptic-like lift distribution in order to minimise induced drag in clean configuration.

As flaps, spoilers, air-breaks and so on are deployed the lift distribution will deviate substantially from the elliptic one (see diagram), hence reducing the $e$ factor and increasing the induced drag. If the first assumption still holds, an increase in induced drag will have been caused by an increase in vortex intensity.

Lift distribution for different flap configurations

Additionally, significantly higher lift coefficients can be achieved with deployed high-lift devices, which also contribute to increase vortex intensity.

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  • $\begingroup$ This might be true if the lift coefficients with and without flaps are compared at the same AoA, but the thing is the AoA needed for takeoff and landing changes when flaps are deloyed or retracted in actual flight. For example, we would need higher AoA for landing without use of any flpas, but with flaps the AoA needed for the same lift is lower than that. Personally, I think the key is here, but I'm not sure. $\endgroup$ – lemonincider Mar 4 '17 at 10:52
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    $\begingroup$ @lemonincider, note that the formula does not contain any $\alpha$ term, only $C_L$, so what is compared is the same $C_L$ That depends on $\alpha$, but we don't care about the actual values of that, only values of $C_L$. $\endgroup$ – Jan Hudec Mar 5 '17 at 22:22
  • $\begingroup$ @lemonincider, also the values of $\alpha$ are somewhat arbitrary here—the flaps increase the incidence of both the chord line (connects leading and trailing edge and the trailing edge moves down) and the zero-lift line (by even more, because camber increases). $\endgroup$ – Jan Hudec Mar 5 '17 at 22:26
  • $\begingroup$ @JanHudec Thank you for correcting me. So should I conclude the writers of the AIM are simply wrong? As far as I know this theory has been around for quite a long time and it's difficult to believe the AIM got this wrong. $\endgroup$ – lemonincider Mar 5 '17 at 23:41
  • $\begingroup$ @lemonincider, I am inclined to think that yes, it's wrong. After all it would not be the first widespread misconception about aerodynamics. $\endgroup$ – Jan Hudec Mar 6 '17 at 17:50
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What causes wing vortices? When the wing produces lift, there is higher air pressure underneath it, and lower air pressure on top of it. At the wing tip the high pressure air flips over to the low pressure air, and this creates the rotational element of the vortex, as described in this article. The more lift is generated at the wing tip, the stronger the vortex will be.

Aerodynamic lift is a product of lift coefficient, air density, air speed, and wing area. For subsonic speeds: L = $C_L$ * ½ * ϼ * $V^2$ * A. Only the factor ½ in this equation is a true constant! We have one equation with five variables, so lets have a look at what varies when.

Contrary to our first instinct, wing area is not a constant. Modern aircraft have Fowler flaps at the trailing edge, which are extended outwards and increase the wing area, as well as changing the curve of the wing which increases lift coefficient at a given AoA. So there is the first part of our answer: with deflected flaps we have more wing area to produce a given amount of lift, therefore lower required air pressures, therefore less air flippings at the wing tip :).

The second part of our answer also has to do with flaps. Elliptical lift distribution is only possible when the wing tip has zero AoA, a situation designed to occur in cruise. A clean wing configuration is designed for the cruise condition, where there is lots of airspeed to generate lift and we want to keep induced drag to a minimum. This same clean wing is very ill suited to produce the same amount of lift at the lowest possible landing speed.

CL is a function of angle of attack and of wing shape. The answer with the graph of CL shows CL at constant alpha as a function of flap deflection. A graph of CL at constant flap deflection as a function of alpha would show relatively more lift generated near the wing tip, and that is where the wing vortices are generated. Flaps are located more inboard, meaning that when deflected, a greater portion of the lifting force is generated away from the wing tip.

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I've seen both of those reasons used to explain this, and probably they both contribute to it, but in my CPL training I was taught the reason is that a non-clean aircraft (and remember that this includes landing gear, spoilers, slats, etc.) causes airflow to be disturbed which reduces vortex generation. The statement is always made referring to 'clean', not 'flaps retracted'.

The question came up also on Quora, and two answers came back, one with the reasoning I gave, and another using the increased AoA concept.

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I am not sure that everything is so simple and obvious regarding flaps and gear.

Actually with flaps we have at least four points for vortices generation: on wing tips and on flaps outer edges, and they can mix with each other. FAA/EASA answer seems based upon the following NASA research, and takes into account combining wing tips vortices with flaps/gear vortices, and faster weakening of total vortex strength. I suppose that it really makes sense: aircraft in clean configuration generates "traditional" rather well-studied vortices, while aircraft in landing configuration generates much more complicated interfered turbulent flows. It is very hard to say which one is stronger and more dangerous.

Very interesting thread about the subject can be found on PPRuNe, with nice pictures of totally confused situations when vortex from the left wing is dissipating, while the right one remains stable and narrow.

And here is one more research about wake turbulence with interesting results.

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