Bjorn’s Corner: Aircraft drag reduction, Part 11

By Bjorn Fehrm

January 05, 2018, ©. Leeham Co: In the last Corner we described a dominant drag component affecting the Wright Brothers’ Flyer, Form drag. The many wires and braces on the Flyer created separations and a high Form drag was the result.

At the time, Langley and others thought friction drag could be neglected. Now we describe how it was discovered one couldn’t and how it gradually made its way to the top of the drag contributors.

Figure 1. The Supermarine Spitfire with its elliptical lift distribution wing. Source: Google images.

Friction drag

When the Wright’s did their first flights at Kitty Hawk in North Carolina, a young Professor at the Technical University of Hannover (Germany), Ludwig Prandtl, was studying how friction affected the flow of a fluid when it passed over a surface.

At the third International Mathematics Congress in Heidelberg, the year after (1904), the 29 years old Prandtl presented his theory of what happened when a fluid with a viscosity (a sticky fluid) flowed over a surface. He presented the first boundary layer theory.

Prandtl said; “there is a thin layer on top of a surface where the fluid stream goes from zero velocity due to friction against the surface, and then flows faster and faster until it flows with full free stream velocity at the edge of the boundary layer” (Figure 2).

Figure 2. The boundary layer of an aircraft’s wing. Source: Prandtl’s boundary layer by John D. Anderson.

The standing still of the air in direct contact with the surface was because of the air’s stickiness (viscosity) causing friction against the surface thus slowing the air to a stand-still. As the air came further from the surface the friction would slow the air less, until it kept its full speed a few millimetres out from the surface. The quickly changing speed layers causes shear stresses between the layers, which are the source of Friction drag.

Prandtl also postulated “what is happening in this layer will affect the whole fluid stream over the object”. In fact, he predicted there would be situations where the boundary layer would separate from the airfoil and the smooth flow would break down. This was the first explanation on what happens at a wing’s stall, more of below.

Boundary layer research

The proceedings from the 1904 conference, with Prandtl’s paper, were distributed in 1905. The presented theory was the trigger for aerodynamic boundary layer research and measurements over the next 50 years.

After the presentation in Heidelberg, Prandtl was made the Director of the prestigious Institute for Technical Physics at the University of Göttingen. Prandtl and his Göttingen Institute (which he elevated to world fame) would dominate the world of aerodynamics for the next 40 years.

He and his students researched a number of subjects and developed theories and calculation methods, not only for friction and the boundary layer effects, but also for wing lift and the physics behind induced drag.

A famous result of Prandtl’s theory of induced drag and how a wing should be designed to minimize it, was his elliptical lift distribution theory. To minimize induced drag for a given span, a wing should be designed to have an elliptical lift distribution.

Reginald Mitchell, the Supermarine Spitfire designer, used Prandtl’s friction and induced drag theories when he designed the high-performance Spitfire wing, Figure 1. The smoothly shaped wing had a form to create a true elliptical lift distribution. While beautiful and efficient, it wasn’t easy to produce.

Flow separation and stall

Prandtl in his 1904 theory predicted the mechanism behind the stall of an aircraft’s wing.

Subsequent detailed research by Prandtl’s team at Göttingen showed what happens at boundary layer separation and stall, Figure 3.

Figure 3. The separation of the wing’s boundary layer causes wing stall. Source: Prandtl’s boundary layer by John D. Anderson.

When air has passed the crest of a wing profile, the way to the trailing edge is flow against gradually higher pressure (the lowest pressure point is at the profile’s crest). When the wing is given increased incidence against the air (increased alfa angle) to create more lift, the adverse pressure gradient increases.

This increasing pressure causes the boundary layer to slow down. It can then no longer force its way against the higher pressure. It doesn’t want to flow back, instead, it flows beyond the back-pressure air, it separates from the surface. The boundary layer from the bottom surface of the wing is the blue trail at the trailing edge. Between the two separated boundary layers is the turbulent wake, destroying the lift of the wing and causing high Form drag.

In the next Corner, we will describe more about the research into the boundary layer and the effects of skin friction drag.

28 Comments on “Bjorn’s Corner: Aircraft drag reduction, Part 11

  1. Pradtl began his first tenure at the TH Hannover in 1901/2

    Also noteworthy is that he worked in an (partly preexisting) environment of abstract theoretical research. Riemann and others had developed the “abstract math language” to work with that basket of research topics.
    IMU numeric CFD analysis held so high by some is overvalued. Theoretical understanding is often much more conducive to making progress and good design decisions. The “Elliptical wing” was a theoretical derivation of insights.

  2. Being born at the end of WW2 the aircraft I saw we from that war. Nothing quite like the beauty of the Spitfire wing (and the lovely crackle of the Merlin engine!)

    • The Merlin no doubt makes a lovely sound, but I think I prefer the slightly more menacing sound of the Griffon in a Spitfire; there’s more power there, and it’s even more visceral. That is of course unless there’s two Merlins, in a Mosquito.

      My personal, ultimate engine is the Bristol Centaurus out of a Sea Fury. It’s quite an engine, and like the big American rotaries (which are also deeply impressive) the last of the piston breed. I was impressed by the idea of overcoming the large frontal area (which had previously made large rotaries pretty draggy) by making the airflow through and among the pistons more of a streamlined pathway. I gather the Centaurus got a tiny bit of thrust that way too.

      Sorry for the thread drift. I know that Merlins were made in large numbers, but the supply of flyable examples must be diminishing. Does anyone know the world situation? Can the existing ones be maintained ad-infinitum, or could we make new one?

  3. It has some altitude influence as the Spitfire mainly got superior at higher altitudes with its wing and the Sir Stanley Hooker 2 stage compressor design fed RR Merlin 60.
    For the lower altitude Reno unlimited races the warbirds normally get modified with clipped wings to reduce drag. “Critical Mass, for example, has 38.5 in. removed from each wing, giving it a 32-ft wingspan and Dago Red has about 30 in. cut off each wing, taking the wingspan from 37 ft down to 32 ft”

  4. Does anybody know why thickened trailing edges (MD11) and parabolic dihedral (787) improve drag?

    Also, why are the trailing edges of flap boats on modern airliners (A330) so blunt? You’d think they’d be tapered to the same point as the trailing edge of the wing, but not at all!

    • parabolic dihedral: Is that intentional?
      I thought this to be fallout from choosing a slim profile and building straight ( easy to produce ) beams.
      ( Airbus seems to more go for an unloaded gulled shape that “straightens out” under aero loads. rather pronounced :A380)

      blunt ended flap fairings : same pressure on both sides diminished laminar flow. straight cut off ( see why plug nozzles work.)

      • The A380 wing is gull shaped in order to get clearance for the inboard engines, not for some minuscule aerodynamic benefit. It is because the wing root is thick (thicker than the distance from the lower floor to the fuselage bottom) and the lower floor has to sit low to accommodate the upper floor. Long spindly gear is a good thing to avoid if at all possible.

    • Hi Chris,

      With any aft body used for the purpose of streamlining (tail cone, wing trailing edge, or flap canoe fairings, etc.) determining how sharp a point or edge to use involves trading off various factors such as; form drag, skin friction drag, weight, off-design conditions (due to angle of attack or yaw) and manufacturability just to name a few. I don’t think there is ever a case where a designer will want to streamline a fairing to such a degree that it requires a perfectly sharp point.

      Even if one ignores all the factors except drag alone, the minimum drag solution would still not be streamlining to a perfectly sharp point. As the point gets sharper the form drag decreases because the tip area decreases. However, the skin friction drag increases because of the additional surface area required to bring the body to a sharper point. Bodies with shallower cone angles will have blunter points to minimize drag. Now, if other factors such as weight or manufacturability come into play, the best solution will likely be even blunter.

      The canoe fairings that cover flap mechanisms need to have low drag in the cruise configuration, but also minimize interference when flaps are deployed.

      As for dihedral, it is there to provide roll stability, not to improve drag. Increasing dihedral will actually increase the induced drag for an aircraft if everything else is equal. This is because the lift force from a wing with nonzero dihedral is angled in toward the fuselage. This horizontal component of the lift force is unusable for carrying weight, so a wing with dihedral must generate more lift to compensate (i.e. at higher angle of attack). Generating more lift means generating more induced drag.

      • Correction
        The example I used to illustrate that bodies will never be streamlined to a sharp point is only good for moderate Reynolds numbers where the boundary layers are larger but the flow can still separate on the length scale of the body.

        At the high Reynolds numbers, where commercial aircraft operate, the flow near tail ends of streamlined bodies is often already separated and turbulent. Thus, streamlining to a sharp point is pointless (hardy har har).

  5. Professor Ludwig Prandtl is one of the three “founding fathers” of modern fluid mechanics. G. I. Taylor from Britain and Theodore von Karman of the US (originally from Germany and actually a doctoral student of Prandtl) are the other two. All three are giants in their own right, but I regard Prandtl as the greatest of the three, mainly because of his boundary layer theory. His paper on it was in an obscure German journal and was not noticed widely initially, but it opened up a whole new way of looking at such processes and there are now literally tens of thousands of technical papers dealing with boundary layers, including atmospheric and oceanic ones. Many of Prandtl’s students and junior colleagues also made significant contributions. One of them was Adolf Busemann, the founding father of swept wings, which have made high speed flight possible.

    GI, as he was fondly known to his students, excelled in theoretical approaches (for example to turbulence) and combining them with simple but elegant experiments. Karman is well-known for explaining the failure of Tacoma Narrows suspension bridge, which was caused by torsional resonance of the bridge to the Karman vortex street generated by high winds. He ended up competing with Prandtl, racing to discover the so-called logarithmic law for the velocity in a turbulent boundary layer. The constant in that law is named after him. However, Prandtl has a number named after him, the so-called Prandtl number, and of course, the boundary layer theory is frequently referred to as Prandtl’s boundary layer theory. At the end of the Second World War, Karman was part of a team sent to Germany to interrogate German scientists and he was able to sit in Prandtl’s chair in Gottingen and interview Prandtl on his group’s activities during the war. Karman also headed Jet Propulsion Laboratory at CalTech, which is now famous for its activities related to space.

    Just a bit of interesting history!

    • Interesting, do you know why there were never a series of big wind tunnels built at Douglas in Santa Monica? In those days it must be very hard to design a good aircraft without spending huge amounts of time in the wind tunnels trying out model after model and have them refined for another set of runs. Boeing had theirs and Douglas really needed one after the first DC-8’s and DC-9’s were produced.

  6. Are we not missing two other vital elements for a stall.

    1. The flat wing on the underside becomes a huge drag force.

    2. The aircraft is attempting to climb and the hp is not remotely close enough (most aircraft) to overcome that pull of gravity.
    A component of that has to be prop stall as well.

    I always felt these things did not exist by themselves in a vacuum (pun intended)

    • No, Bjorn mentioned both the lost lift and high drag associated with a stalled wing.
      “Between the two separated boundary layers is the turbulent wake, destroying the lift of the wing and causing high Form drag.”

      1. The destroyed lift and greatly increased drag of a wing is almost exclusively caused by the changed flow field above the wing. The flow field below the wing remains virtually unchanged, thus has very little to do with it. Imagine a wing at a high angle of attack that is just below the critical angle. Both the top and bottom boundary layers remain attached so the wing is not stalled and is generating a lot of lift with relatively little drag (more than at low angles of attack, however). Now, increase the the angle of attack just a little bit so that it is beyond the critical angle. The top boundary layer separates because the adverse pressure gradient (increasing) along the top surface is too great, but the bottom boundary layer remains attached because the pressure gradient is much less adverse. The change in flow field above the wing is huge while the flow field below the wing remains almost the same except for differences due to a slight change in angle. The lost lift and huge drag increase are caused by what happens above the wing, not below it.

      2. The aircraft does not need to climb in order to stall. Stalls can happen during level flight at low speeds and high angles of attack.

  7. Karman was born in Budapest (not Germany) and graduated from university there. The Lisunov Li-2 (Soviet version of DC-3) on which Goldtimer Foundation still offers pleasure flights from the grass airfield of Budaors on the outskirts of Budapest is named in his honour.

    • He studied engineering at the city’s Royal Joseph Technical University, known today as Budapest University of Technology and Economics. After graduating in 1902 he moved to the German Empire and joined Ludwig Prandtl at the University of Göttingen, where he received his doctorate in 1908. He taught at Göttingen for four years. In 1912 he accepted a position as director of the Aeronautical Institute at RWTH Aachen, one of the leading German universities.
      Adolf Busemann:
      The next year he was given the position of aeronautical research scientist at the Max-Planck Institute where he joined the famed team led by Ludwig Prandtl, including Theodore von Kármán, Max Munk and Jakob Ackeret. In 1930 he was promoted to professor at Georg-August University of Göttingen.

      Küchemann, Johanna Weber, ..

      There existed a strong research nexus around Prandtl.
      IMU there was another center of excellence in the UK around.

      • Yes. So many illustrious scientists Prandtl and Gottingen produced! That is why he is a giant in my opinion. I have a black and white photo of him on my office wall. There was a strong group around GI in UK (Cambridge University, if my memory is correct) as well, but not as big as in Gottingen. GK Bachelor was one of them. In any case, a whole lot of findings in aerodynamics, aircraft engines, rocketry etc. occurred BEFORE 1945, with major contributions from groups like Prandtl’s. Nostalgia!

    • Thanks for that clarification. I forgot to mention he was a Hungarian by birth.

      • Hungary is the only european country to use ‘eastern name order’ like China Japan, Korea etc where the surname is written first. So in Hungary its Kármán Tódor.
        I dont know where the von came from ?

        • ‘Von’ is like the French ‘de’. It denotes an aristocratic background (or at least pretensions to having come from an aristocratic ancestry. One such example is Dominic de Villepin, former prime minister of France.

          The Dutch ‘van’ (as in Ludwig van Beethoven) is different. Beethoven apparently once tried to pass himself of as being of noble birth in an Austrian court, relying on confusion between ‘van’ and the German ‘von’ and uncertainty as to whether his ‘van’ implied nobility or not.

          They all literally mean ‘of’.

    • We will come to this when we discuss induced drag. Many think winglets affect the wingtip vortices and have some secret sauce effect on these. They have not. They are simply an extension of the wing to tune the lift distribution for a wider, (close to) elliptical pressure distribution. The wider distribution, the less induced drag. You can achieve the distribution you want with span or span+winglet.

      If you are not span constrained, a winglet is a complication you don’t need. Flutter factors might entice you to do a raked tip. But a normal tip works as well.

      Winglets on bizjets are a must, however, otherwise, the guy who is hauled thinks he’s bought an old-fashioned aircraft for his millions.

      • Thanks Bjorn.

        See the wingspan is 35.9 (surface area?) and MTOW 79T, same as A320. Guess they will look at winglets for higher MTOW or stretched model/s?

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