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

Question

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.

Answer 1

Short answer: Yes.

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.

Answer 2

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.

Answer 3

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.