# Does the Prandtl flying wing have a lower maximum speed than other designs?

Does the design of the wing with its "twist" near the wingtips necessarily limit the maximum speed of an aircraft utilising that technology?

Also, with the leading edge profile/attack angle varying along the length of the wing, does this generate any unusual strain requiring complex engineering to accommodate?

( I am a novice here-as I am sure you can guess but a very determined one and I am going to build a Micro Turbine-powered(hopefully!) Prandtl-type wing for myself this year, I may need to consult the many experts here on a regular basis.)

Please try to minimise any mathematical equations in your answers since I’m a bit rusty on my math.

• Mar 9, 2020 at 8:46
• "Please try to minimise any mathematical equations in your answers" trying to understand aerodynamics without math is like trying to drive a nail without a hammer, possible, but prone to errors and head injury. Mar 9, 2020 at 8:47
• @gregor kropotkin if it is high speed performance you are after G loads will neccesitate a lower aspect design, rather than the graceful Prantyl wing. A twist in a swept wing is generally beneficial. Proverse yaw can cleverly be created by lowering a leading edge, rather than raising a trailing edge as with standard ailerons. On the opposite side, raising the leading edge creates less drag, and you get a roll and yaw in the same direction. Spoilers on the inside wing are employed in a similar manner. Mar 9, 2020 at 18:58

Maximum speed is correlated with wing loading. A high wing loading shifts all speeds up. A flying wing will always have a lower wing loading in comparison to a conventional design when payload, range and landing speed of both are identical. So you will start at a disadvantage.

Due to the high lever arm of the conventional tail, the conventional configuration can use high-lift devices (or highly cambered airfoils) for a much higher maximum lift coefficient than what is possible in regular low-pitching-moment airfoils. This allows to keep the wing small for the same landing speed. Unfortunately, the flying wing is restricted to those low camber or even reflex airfoils because its surfaces for creating a pitch balance have a small lever arm and, consequently, a poor moment-to-lift ratio.

The design of the Prandtl wing leads to a bit of downforce at the tips when in normal flight in order to lower the wing's root bending moment. But only a bit. Sweep places this downforce in the aft region of the wing so the inner, more forward region has to create all the lift for carrying its own weight, the payload and, of course, compensate for that downforce, too. Since the low wing bending moment will allow for a light wing, the total lift requirement is rather low, too, but still encumbered by the aforementioned loads.

Now to the maximum speed: A flying wing will allow for very low drag coefficients. There are no intersections between parts and no tailboom which adds friction drag, so for a given wing loading a flying wing will allow to reach high speeds with limited power. However, the lower wing area of the conventional design with the same landing speed has less wetted area and so can easily accommodate that tailboom drag. Once the details like part intersections are well designed, the conventional design should come out ahead.

What you need to watch out at high speed is flutter: That wide, light, swept wing will start to flutter much earlier (at lower speeds) than the rigid, strong, small, straight conventional wing. With sweepback you will encounter a speciality of flying wings, a coupling between the short period mode and the wing bending eigenfrequency. Since the short period mode frequency goes up with speed and the bending eigenfrequency is constant over speed, flying fast will bring both together and require a stiff wing in order to shift that point up. Don't forget that pitch damping of flying wings is an order of magnitude lower than that of conventional designs, so the short period mode will show up in a Prandtl wing if you go fast enough.

• Horten gliders. Oct 27, 2020 at 12:46
• "The idea of a Prandtl wing is to create a bit of downforce at the tips" Is that right? Prandtl's original analysis described a bell-shaped curve with positive lift approaching zero towards the tips. Yes the airfoil there has negative incidence, but is cambered enough to actually produce a small lift-and-thrust component. Oct 28, 2020 at 11:10
• @GuyInchbald: Prandtl's lift distribution was for the maximum bending moment; regular flight would be at a much lower lift and angle of attack. With the low lift near the tips, this reduced angle of attack means a downforce there in level flight. Oct 28, 2020 at 11:23
• @PeterKämpf OK, thank you. I guess something like "The design of the Prandtl wing leads to a bit of downforce at the tips when in normal flight" would be clearer to me. Oct 28, 2020 at 11:35

Your question has been at issue ever since the early pioneer days of flight. British pioneer J.W. Dunne discovered the principle around 1905-6 and developed a tailless swept monoplane with drooped and washed-out wingtips. He used their negative lift to provide lateral as well as longitudinal stability. He patented it in 1909 (UK pat. 08118), got it flying as the D.7 in 1911, and lectured the Aeronautical Society on its aerodynamics in 1913 ("The Theory of the Dunne Aeroplane"). His rivals and the military bureaucracy were all convinced that those wing tips must be horribly inefficient, despite its evident firecracker performance and the reports of the serving officers who encountered it. They became so persuasive that at one time poor Dunne even began to believe them himself. So I am intrigued to see this hoary old debate rising from its coffin yet again after more than a century has gone by.

Ultimately, the wingtips combine two functions, as the tail stabilizer split in half and stuck on the ends of the wings, and as vortex-reducing winglets. Compared to a conventional layout they lack the drag of a tail fin and have one less set of tip vortices when the horizontal stabilizer has work to do. Moreover they allow the wing structure to be lightened, Prandtl's key discovery when he re-examined them in the 1930s. Does all this counter the disadvantages of a larger than normal span and a stabilizer moved further forward where it is less effective? Should the evidence of the D.7 be taken at face value or does it really hold the plane back? Its proponents publish analyses which say yes, its critics raise snags which say no.

We may recall Convair's F-102, F-106 and B-58, all of which featured tailless wings with progressive conical washout after the manner of Dunne (though independently rediscovered) and were renowned supersonic "hot ships". The conical droop did add some drag but not a lot. What penalties would an alternative solution to the problems it solved have brought? Would that have made the planes faster or slower?

Frankly, the world has no better idea in 2020 than it did in 1911.

• Very well written answer. The world does have a better idea indeed 2020 in airliner design (actually when they built the DC-3). Study polars and see how Lift/Drag ratio suffers in cruise when wing is not at optimal AOA. This is why the variable AOA wing Dunne so brilliantly conceived at the dawn of aviation was superseded by movable slats. And deltas do have additional drag penalties of their own. However, some washout in a model or even a recreational aircraft where fuel efficiency is not critical is a great idea. Mar 10, 2020 at 12:50
• Uh - conical camber is no washout. Not at all! It uses camber on a supersonic airplane (albeit with a subsonic leading edge) to eke out a bit of suction with a forward tilt. And Dunne was not alone - Igo Etrich and Franz Wels flew a glider with a similar stabilisation technique as early as 1907. Mar 10, 2020 at 15:23
• These comments are excellent examples of how the nay-sayers have updated their criticisms over the years, just as the advocates have refined their case. But there was a sharp contrast between the "seagull" aerodynamics of the Dunne and the "zanonia" or "crow" aerodynamics of Page and Weiss. Oh, and if you visit RAF Cosford you can check out the B.Ae EAP, a supersonic delta with washout that postdates the Convair designs by several decades. Mar 10, 2020 at 19:10

Twisting the wing tips to a lower angle of attack helps create an "elliptical" lift distribution, which reduces stress loads on the wing the farthest away from the wing root.

However, if one ever watches the take-off roll of the Rutan Voyager, one can see the dangers of this design combined with a tricycle landing gear. In this (extreme) case, the wing twist caused the wing tips to have a negative angle of attack, causing the wing tips to bend downward and scrape the ground until the nose was lifted.

It is here that retractable slats are most beautiful. At higher angles of attack, dropping slats increases the "twist" of the wing, greatly improving stall characteristics. At lower angles of attack, such as in cruising, they can be retracted to reduce drag.

The Voyager was an extreme case where a slightly longer nose strut may have helped.

For an R/C model powered by a microturbine, or electric motor, some twist or "downwash" on the wingtips will be very helpful. You may find slower flying this wing with less power, or even gliding it, to be more enjoyable.

At higher speeds, all potential sources of wing loading, including G forces and flutter, need be carefully evaluated for safety.

• As an aside, I've seen first-hand evidence of down-lifting wingtips in my own flying. When cruising at high airspeed, the lower side wires of a hang glider can actually be slack. Although the net lift contribution of each wing obviously has to be upward, if we view the wings as hinged at their roots, the net torque contributed by each wing about this hingeline can actually act in the downward direction. A solid wing strut would experience a compressive load in this situation; in the hang glider case the download is borne by the upper side wires, running from the wings up to the kingpost. Mar 9, 2020 at 1:10
• For added clarity re the above comment, bear in mind that many hang glider wings are highly tapered (essentially a modified delta shape). Most of the lifting area is concentrated well inboard, but the small amount of lifting area (or at high speed/ low angle-of-attack, downlifting area) that is located near the wingtip can contribute lots torque by virtue of acting at a long moment-arm, as measured to the aircraft centerline ("keel tube"). Mar 9, 2020 at 1:21
• "Twisting the wing tips to a lower angle of attack helps create an "elliptical" lift distribution, which reduces stress loads on the wing the farthest away from the wing root." You're misunderstanding OP, they are talking about the twisted flying wing, like in this question Mar 9, 2020 at 8:45
• @AEhere supports Monica There are certainly many ways to design a wing. "Twist or washout" will reduce the lift coefficient of that section of the wing, giving a stronger rectangular wing an "elliptical" lift distribution. And by the way, are not all wings designed to fly? You can attach a tail and fuselage if you'd like, and get something like ... a DC-3!. Thanks for your comment. Mar 9, 2020 at 14:07
• Robert, the idea of a Prandtl wing is to not use an elliptical distribution. The outer, rear wing actually creates a downforce, like the bell lift distribution of the Horten flying wings. Sorry, no upvote this time. Mar 10, 2020 at 16:24