I'm afraid this will require some explanation. I'm sorry, this will be a long read but I hope it's an interesting conundrum. If anyone reading this isn't familiar with NASA's PRANDTL wing research, Al Bowers' main paper is here: https://ntrs.nasa.gov/citations/20160003578

As a brief summary, Bowers and his team surmise that a Bell-Shaped Lift Distribution (BSLD) rather than the ubiquitous elliptical one, combined with very pronounced wing twist, can produce 'proverse yaw' which they explain as a portion of the outer wing producing a lift vector tilted forward. They then design a series of gliders based on this theory which are flying wings, with no vertical stabiliser. These gliders are tested, and it is found that they can in fact execute coordinated turns without a rudder or other independent yaw control surface.

Then, in answering this question: Why isn't the bell distribution used? Peter Kämpf's excellent answer suggested that in fact at most angles of attack (I.E. except near stall) the BSLD is actually producing negative lift at the tips, which seemed to agree with the stall analysis done of the design: https://ntrs.nasa.gov/citations/20180006832 in tandem with another paper outlining the model validation tests: https://ntrs.nasa.gov/citations/20210014683 this perfectly well explains the proverse yaw and controllability without any controversy.

That seemed to be that, however, keen to examine the wing further, particularly in the assertion by Bowers and his team that the flying wing would yaw out of a slip angle back into the prevailing wind direction, which I still do not understand, I did some CFD. I downloaded a CAD model from the internet which was shared by the team, stitched it, stuck it into simscale with no slip angle, and no adjustment to angle of attack from the CAD file, and did a few quick check runs to see if it all worked nicely. It did, but the results seem to me pretty startling... my question is, looking at the CFD below, what on earth is going on?! The simulation can be found here in case you wish to interrogate it yourself: https://www.simscale.com/projects/vh23138/prandtl-d_incomp-/ it's an incompressible simulation with potential flow initialisation at 13.7m/s flight velocity (45ft/s as per above papers).

  1. CAD file tip geometry: this is the CAD file in Fusion 360, the wingtip foil is symmetrical, and at an AoA of around -2.2 to the flow axis CAD file in Fusion 360, the wingtip foil is symmetrical, and at an AoA of around -2.2 to the flow axis

  2. SimScale wake: There is clearly upwash along the outboard region of the wing,SimScale Downwash distribution

  3. SimScale pressure slices: a) slice taken just above the port wingtip, location shown in second image, pressure slice location of slice relative to wing b) slice taken just below the port wingtip, location shown in second image pressure slice location

  4. SimScale wingtip pressure distribution: this is a slice taken as a cross-section through the wingtip airfoil, showing a sort of chord wise pressure distribution as far outboard on the starboard wing as I could get without there being virtually no airfoil there, the location is shown in the second image (sorry, it's hard to see the wing wireframe). enter image description here enter image description here

So my question: 1. shows symmetrical airfoil at -AoA, 2. shows upwash at that foil, 3. appears to show modest lift production, or at least, a marked lack of clear downforce. Which leads to the question: How?! currently the best I can assume is this a 3D aerodynamic effect produced by the flow field around the whole wing, but that isn't an answer...


1 Answer 1


Having done some more thinking and a little more investigation of the flow around the wingtips in SimScale, I think I have a theory which explains the observations. The important thing to note is the angle of attack experienced by the wingtip is not the same as the relative angle of a given tip airfoil to the horizontal. Examining again the CFD, this can be clearly seen using streamlines, which appear to be close to the same angle of attack as the wingtip, and so the wingtips could conceivably be at a slightly positive incidence (see below, Red line is added on afterwards, showing chord line of top airfoil) enter image description here

Now the question has become 'Why is the airflow experiencing such pronounced upwash before the tips?' and this I think can be explained in a pretty standard way: the wing has a 24 degree sweep angle, and it is known that swept wings experience a pronounced reduction in downwash toward the tips, which can sometimes become an upwash, due to the influence of the inboard (and more forward) portion of the wing's trailing vorticity.

This is however, only a working theory, and I have no real way of testing it without redesigning the PRANDTL-3 wing with varying sweep angles and observing wingtip flow behaviour. Any answers with more concrete explanations would be welcome...

  • $\begingroup$ This isn't really an answer and should be appended to your question with an edit. $\endgroup$
    – Pilothead
    Jan 30 at 17:49
  • $\begingroup$ I agree that it isn’t using a hugely rigorous evidence base to answer the question, I’m just looking at relative airflow angles, but the question is not hugely rigorous. This ‘answer’ is in no way clarifying, adding to or correcting the question, it is attempting to posit an explanation. As a result, I felt it wouldn’t be an appropriate addition to the question since it attempts to answer it $\endgroup$ Feb 3 at 23:04

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