Would adding a slat and a slotted flap increase the of a multi element foil to 6.5?

I understand, as a general rule, the max $C_L$ for a classic NACA airfoil is as follows:

  • Base: 1.5
  • Slat: + 0.7
  • Slotted flap: + 1.3
  • Total $C_L$: 3.5

But with a Selig multi-element foil, the starting max $C_L$ is around 4.5.

Would adding a slat and flap to a Selig airfoil, with a 20° deflection of the main foil, increase the $C_{L_{max}}$ to anything close to 6.5? Assume a Reynolds number in the 600-900k range.

Here is a pic of the foil:

Selig high lift multi element foil

  • $\begingroup$ An examination of soaring (eagle/vulture) bird wing tips may yield a design potential, especially if a lot of excess power is available. Draggy, yes, but lift they will. $\endgroup$ Jul 23, 2019 at 12:17

1 Answer 1


The theoretical maximum lift of a cylinder is 4π. At that point the forward and rear stagnation points coalesce on the bottom of the cylinder. Practical solutions use rotating cylinders (Flettner rotor) but will not reach this theoretical limit.

This should illustrate that 6.5 is not outright impossible but the distance between a cylinder and an airfoil is quite large, so this theoretical limit does not apply to airfoils.

Adding a slat and a slotted flap to a regular airfoil will bring you at most to a c$_{l_{max}}$ of 2.8. Now you want to add them to a multi-element foil. Would that be several slats and flaps in sequence? Practical solutions use a single slat and a multi-slotted flap where the deflection angle of the single flap elements increases along the flow path of the air. A typical example would be the airfoil of the Boeing 727 which had a triple slotted flap which could reach a two-dimensional c$_{l_{max}}$ of 4.2 with 60° deflection and rearward movement of the flaps which increased the effective wing area. Note that wing sweep and ailerons reduced the practical maximum lift coefficient of the full aircraft to 3.0 (see plot below, taken from A. M. O. Smith's excellent article High-Lift Aerodynamics).

enter image description here

With modern CFD this could be improved a bit, but then the preference of aircraft builders has been to reduce the number of flap elements while losing only a little of lift.

Another practical limit is the maximum Mach number in the suction peak of all the airfoil elements. Once this reaches 1.58, no lift growth could be observed in experiments. This translates to a maximum for the product of Mach squared and pressure coefficient of -1.0. In other words: You need to fly very slowly in order to achieve high values of c$_{l_{max}}$.

The only practical design I know which reached that magic limit of 6.5 given as the c$_{l_{max}}$ of its wing airfoil is the Antonov An-70. Here this number is valid for the inner wing which is immersed in the prop wash of the mighty Aerosila SV-27 propellers, driven by the 13,240 hp Progress D-27 turboprop engines. By using the flight speed and clean wing chord for the reference parameters, this looks to me a bit like cheating. But the achieved lift is real!


Now that you show the Selig airfoil, it should be obvious that it is a point design for maximum lift and no practical applicability in real aircraft. Neither will it allow a thick spar nor low drag at lower lift coefficients. Adding a slat will help little, because the limiting part is the pressure rise on the main airfoil. The accelerating flow up to a chord of about 20% is meant to increase the area in the c$_p$-plot and the pressure rise aft of this point is a Stratford distribution which maximizes pressure gain without separation. Reduce pressure in the suction peak only a bit and the flow will separate, and lift collapses.

  • $\begingroup$ A cylinder is the shape of theoretically highest lift? Goodness, that's a surprise. I'm guessing its drag is astronomical too, given planes don't have cylindrical wings? $\endgroup$
    – Dannie
    Jul 22, 2019 at 12:07
  • $\begingroup$ @Dannie a rotating cylinder. See: en.wikipedia.org/wiki/Magnus_effect If you are interested in what a cylinder has to do with airfoils, look up the Zhukovski transformation. $\endgroup$ Jul 22, 2019 at 12:11
  • $\begingroup$ @Peter Kampf re max cl of 2.8. As you can see, a multi element foil can have a much higher cL max than a single element foil. I'm sure a slatted and slotted multi element foil could be modelled in java foil, if one had the time... $\endgroup$
    – Fred
    Jul 27, 2019 at 16:50
  • $\begingroup$ @Dannie: This is only valid in the theoretical realm of irrotational and friction-less flow. In the real world it can be approximated by a Flettner rotor but practical airfoils do not make use of that effect. $\endgroup$ Aug 5, 2019 at 21:32
  • $\begingroup$ In my account, it suggests offering a bounty for this question. What is a bounty? $\endgroup$
    – Fred
    Aug 14, 2019 at 14:57

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