An examination of the 737 airliner wing profile and that of a blue whale leads to the question of whether the high Reynolds number subsonic cruising airfoil and the low speed, high AOA airfoil are compatible.

Supercritical airfoils are designed for efficient cruising flight, relying on bottom lift and minimizing acceleration of air over the top to avoid creating drag producing transsonic shock waves.

The blue whale is designed to cruise efficiently over thousands of miles, through a viscous, non-compressible fluid (water). Their shape includes a rounded, sloping lower fore and a flatter top, very similar to a supercritical airfoil! Applying thrust to this shape would provide "lift" simply by directing water "down" (or pushing the whale "up").

Reynolds Number = Velocity×Chord/Kinematic Viscosity

Reynolds Number 20th century Type VII U Boat (submarine): speed: 4 meters/second chord length: 70 meters. Kinematic viscosity (sea water): 1.04 × 10e-6

      4 × 70/1.04 × 10e-6 = 269 million

Reynolds number Blue Whale: speed: 5 meters/second, chord length: 30 meters Kinematic viscosity (sea water): 1.04 × 10e-6

      5 × 30/1.04 × 10e-6  = 144 million

Reynolds number Supercritical Airfoil (approximate): speed 300 meters/second, Chord length: 4 meters Kinematic Viscosity (air): 1.46 × 10e-5

    300 × 4/1.46 × 10e-5 =     82 million

Reynolds Number Cessna 172 Airfoil : speed 30 meters/second Chord length: 2 meters Kinematic Viscosity (air): 1.46 × 10e-5

   30 × 2/1.46 × 10e-5 =         4 million

Reynolds Number Albatross (bird) airfoil: speed 10 meters/second Chord length: 0.2 meters Kinematic Viscosity (air): 1.46 × 10e-5

  10 x 0.2/1.46 x 10e-5 =        140,000

We can see the supercritical wing is more in the range of the blue whale!

When pitched up to a higher AOA, this shape would be a very poor wing in the classic Bernoulli sense, as the significantly contributing top lift would be lost at a lower AOA than a top rounded airfoil, behaving much more like a flat plate (see polars).

There are accounts of airline pilots extending their slats at higher speeds for better performance (and getting into trouble for doing so).

So, for modern designers, would it not be important to consider a more robust low speed system that could be left on (in varying degrees) at higher speeds (V maximum flaps and slats extended airspeed) to help avoid stalling?

This could create a wider safety margin for the climb-out and landing phases of flight. Hard earned efficiency gains in cruising flight (from the supercritical wing) would be kept, when they are fully retracted, but only at safe speed and AOA conditions (for example, above 10,000 feet or at cruising flight level).

  • 1
    $\begingroup$ I think whales benefit a lot from their size, alas buoyancy is negligible in heavier-than-air flight. Apart from that distraction (whales don't stall), it's a good question. $\endgroup$
    – ymb1
    Sep 27 '19 at 15:42
  • $\begingroup$ Blue whales and their like, minke and sei, are amoung the fastest of the whales. They could not be caught by sailing ships. If only buoyant, they would be fully symmetrical (like blimps). Look again at their profile, and please give me a Reynolds number of a 35 meter blue whale swimming through water at 20 knots. My guess is they are both bouyant and partially lifting (like some modern airships) $\endgroup$ Sep 27 '19 at 16:00
  • $\begingroup$ If that's the case, how do they deal with their lousy aspect ratio? It can be a good question for Physics.SE or Biology.SE. Their shape is so (and they flap up/down not left/right like fish) because of their mammalian vertebral column. IMO the question will be better if we forget about whales here. $\endgroup$
    – ymb1
    Sep 27 '19 at 16:08
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    $\begingroup$ I think the whole "whales" thing is clouding your question and will get people off-topic. Whales use other "lift devices" than just the fins (like air in the lungs) so I don't think you can do an apples-for-apples comparison here on the other lift devices. Plus whales don't travel at trans-sonic speeds, even if they are fast. $\endgroup$
    – Ron Beyer
    Sep 27 '19 at 16:10
  • $\begingroup$ @ymb1 The underbelly fairing of the Pilatus PC-24 in another question got me thinking. $\endgroup$ Sep 27 '19 at 16:38

The short answer, whales aside, is yes. Such wings, called "supercritical" because the critical Mach# is elevated, tend to suffer from leading edge stall that makes the aircraft's natural stall behaviour dangerous. These airplanes typically require stick pushers (as @Peter Kampf mentions in this answer, the 737, even the later ones that got redesigned wings, doesn't really have a "pure" supercritical wing and I believe that's why they don't require stick pushers).

The Challenger business jets and the CRJ line of Regionals all have supercritical wing profiles. The profile promotes a pre-stall flow separation and immediate reattachment at the LE, called a Laminar Bubble, which would form at some AOA prior to stall.

Laminar Bubble sketch

This had an effect similar to having a stall strip or ice shape, with the bubble forming a trip wire so to speak. It causes the wing to stall at the leading edge instead of advancing from the trailing edge, which meant the entire wing just let go all at once with no buffet or other warning, with a tendency to progress right into a deep stall. The Challengers and RJs have stick pushers because of this; they must never be allowed to stall naturally, because it is probably going to be unrecoverable. Bombardier did a lot of testing with various aerodynamic band-aids like vortex generators and vortilons and such, and they didn't help.

The CRJs larger than the 200 have LE slats and are just about unstallable slats out, but they also have the same LE stall slats retracted and still require stick pushers. Flying with slats extended at high speed is out of the question. The drag they produce is massive, as you discover when you first land one after flying a hard leading edge CRJ200. Incorporating a fixed slot in the leading edge could be done but they are pretty draggy and would negate the benefit you're trying for in the first place, and I'm sure there are other mach related issues with a fixed slot.

  • $\begingroup$ Good explanation. The other side of the story is the wing sweep for these types of aircraft, which contributes to pitch up post stall. $\endgroup$
    – JZYL
    Sep 27 '19 at 17:36
  • $\begingroup$ Thks. I have a chum who's experienced a natural stall on a CRJ200, when extruded LE sealant (the a/c was released before it had fully cured) tripped the flow on one wing PRIOR to pusher when he was doing the shaker/pusher test. The shaker started going then suddenly it kind of quarter snap rolled. I think what saved them was instead of going into a spin or deep stall it just fell away while knife edge and ended up in a dive. $\endgroup$
    – John K
    Sep 27 '19 at 17:44
  • $\begingroup$ @John K certainly would keep the supercritical at cruise. It may be helpful to be able to extend slats at a higher airspeed than currently available to give a pilot more safety margin while manuvering, retracting them for cruise under safer conditions. $\endgroup$ Sep 28 '19 at 2:49
  • $\begingroup$ @RobertDiGiovanni that's just not really a problem on an airliner. As it is you usually have slats out to the initial setting not that much below 200 kt on an arrival (on the RJ's the first slat/flap extension you do passing below 190kt). For maneuvering at high G however, the F-86 had automatic slats for exactly that purpose. $\endgroup$
    – John K
    Sep 28 '19 at 3:07

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