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If a hypothetical aircraft, which is a tailless straight flying-wing with no fuselage, has the following characteristics:

  • moderate forward sweep
  • an aspect ratio = 9
  • a dihedral angle of 3 degrees
  • a slight tapering of 5 degrees on each edge
  • wing twist (10 degrees of total incidence difference between centreline and wing tip)
  • positively cambered airfoil at centreline, slightly less at the root, minimally positive camber at the inboard section, symmetrical outboard section, negative camber from there towards the wing tips
  • thickness 10% at the tips, 15% at the root and 20% at the centerline
  • a low wing loading, i.e. 50 kg/m2
  • slightly forward CG

And if the required stability in yaw (proverse yaw) is considered to be ensured through sufficient wing twist and symmetrical airfoil/negative camber at the tips,

what kind of airfoil characteristics - or even better - what specific airfoil examples (or at least, a specific airfoil category) would provide both low induced drag and ample lift ability at low speeds of 50KT, but still have low resistance at higher speeds i.e. at 200 KT?

Specifically, how much camber and reflex camber change (in ratio to symmetrical) should be sought for each of the different segments of the wing centreline, root, outboard section and wingtip?

Or, would it be sufficient if the whole planform has an identitical airfoil shape (scaled for chord length due to taper)?

What would be the Centre of Pressure positions (in chord percentage) of such a wing at slow flight or in high-speed cruise?

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I know it may be a fairly wide question with a myriad of possible answers but I would be grateful to see some examples, so I can have some notion on what the camber/reflex camber for these wing characteristics should be, and to better understand via examples.

Thanks

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  • $\begingroup$ You should get this book: marskeaircraft.com/new-book-the-wing-%26-i Marske uses reflexed airfoils with modest FORWARD sweep and a large center rudder and is probably the most successful designer of flying wing gliders, $\endgroup$ – John K Dec 14 '20 at 4:46
  • $\begingroup$ Thanks for the comment - I was considering forward sweep as I saw some examples similar to what you posted - regarding the rudder, it seems like a solid way to ensure the handling is sufficient yet the numerous examples of proverse yaw by wing washout / tip negative camber etc. are intriguing - I would very much like to know if the reduction in drag by eliminating the rudder would be perhaps not such a big benefit because of additional drag due to the negative (or less lift) load at the tips by using a high wing twist difference $\endgroup$ – ivanantuns Dec 14 '20 at 18:51
  • $\begingroup$ The main benefit of forward sweep is elimination of spanwise flow problems endemic to aft swept wings. The Marske FWs have impeccable stall behaviour bc the inboard elevator is incapable of achieving stall AOA.Also check out Rol Klingberg's youtube channel. Here is one vid where he talks about spin issues with swept flying wings due to tip stall youtube.com/…. He is designing a swept flying wing ultralight glider and has a unique one-way tip rudder system (he calls "auto yaw") that greatly enhances yaw stability. $\endgroup$ – John K Dec 14 '20 at 19:50
  • $\begingroup$ I saw the klingberg wing on youtube a couple of weeks ago, and the video of his glider in the 80s, i will this video now. The forward sweep is very interesting but i need to understand better the negative aspects from it, other than bending moments; as i read, it seems that fwd swept wings need upward wing twist at the tips $\endgroup$ – ivanantuns Dec 15 '20 at 15:14
  • $\begingroup$ I don't think the Marske wings use wash-in which would tend to promote tip stall which promotes spins. Marske exploits a phenomenon where the initial flow separation at the TE renders the wing root elevator ineffective before the stall deepens, which prevents any part of the wing from being brought fully to stall AOA. The story of the Genesis is quite interesting because Marske's partners more or less forced him to add a small horizontal surface at the top of the fin. He insisted it was totally unnecessary but added it when the partners threatened to kibosh the program if he didn't give in. $\endgroup$ – John K Dec 15 '20 at 18:10
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For a wing to be stable in its own right, its aerodynamic centre must remain static with changes in angle of attack. The usual approach is to sweep the wing and wash-out the outer section. Because your wing is unswept, you have only two choices in creating a stable aerofoil:

  • A symmetrical aerofoil, i.e. with zero camber.
  • A cambered aerofoil with reflex camber towards the trailing edge.

The first of these has poor low-speed characteristics and has really only seen use on aerobatic and early supersonic types.

The reflex type offers better low-speed characteristics, thanks to its positively cambered leading edge. RAF 34 provides a good example; it was developed in the 1920s when RAF 33, with even greater reflex, was found to have high drag. RAF 34 had much better performance above 200 kt and was used on several tailless types (usually swept and washed-out as well) such as the Westland Pterodactyls. It would be a good starting-point for your search.

But be aware that your tapered "plank" wing will have abysmal handling characteristics and a vicious, unrecoverable stall. Washout can help a little here, and the CG position will depend on this, as well of course as on your chosen aerofoil. Maybe using it as a hang-glider might be tenable, as the pendulum stability will mask the worst handling issues, but I would not want to take it up in case it stalled!

Addendum

Some remarks have touched on the NASA Prandtl-D experiments led by Albion Bowers, which owe much to Prandtl's "bell-shaped" lift distribution and Reimar Horten's exploitation of it in his flying wings. Prandtl's analysis applied principally to the straight wing and was not concerned with stability or yaw. By contrast the Horten/NASA implementation is applied exclusively to tailless swept flying wings, where stability and proverse yaw in the turn are essential to docile handling. In this latter context, many subtle variations of aerofoil across the span have been tried over the years. JW Dunne anticipated it all, and more, intuitively back in the pioneer era - the Science Museum archive contains boxfuls of his research models - but he was no mathematician. The precise relationships between the various design features and resultant flying characteristics still remain somewhat clouded and contentious, and Dunne's work studiously ignored, so some aspects of the original question here remain unanswerable. But one thing everybody I have mentioned has agreed on; if you do not sweep your wing then you are making life much harder for yourself.

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  • $\begingroup$ Thanks for the answer- can you comment on how would forward sweep with RAF34 affect the AC? What about plank wing as I mentioned, but with RAF34 and a sizeable central rudder (as commented above by John K on the Marske glider)? can you please comment also on this airfoil: airfoiltools.com/airfoil/details?airfoil=prandtl-d-root-ns ; it is the Prandtl-wing by Al Bowers, with proverse yaw. However, that aircraft has prominent sweep; there is this example: youtu.be/UsopLXgzpeM ; a version of the Prandtl-wing, no sweep, fairly delta-shaped with leading edge taper. $\endgroup$ – ivanantuns Dec 14 '20 at 18:30
  • $\begingroup$ Also, in an answer on a question regarding wing twist (aviation.stackexchange.com/a/24470/53529) user Peter Kampf stated that forward swept wings can do away with twist by airfoil camber / having negative camber at the tips (if I understood correctly). Please let me know thoughts on this (I will edit question accordingly) $\endgroup$ – ivanantuns Dec 14 '20 at 18:47
  • $\begingroup$ First query: A central fin on an unswept wing is useless, while the control surface acts more like an aileron than a rudder. Bowers' aerofoil and its AoA both vary significantly across his wing, the root is just one extreme. Unlike RAF 34 it was designed solely as the root of a swept wing. If you are chasing proverse yaw, then wing sweep plus washout plus tip anhedral (as per the Dunne D.7 monoplane en.wikipedia.org/wiki/Dunne_D.7 ) and Frise ailerons are your friends. Delta is equivalent to tapered and swept, see the Lippisch Deltas en.wikipedia.org/wiki/RRG_Delta_I. $\endgroup$ – Guy Inchbald Dec 14 '20 at 18:57
  • $\begingroup$ Second query: I did not see forward sweep mentioned by Peter Kampf, perhaps I missed it; anyway, the forward swept wing needs upwards twist at the tips not downwards. Also, there are two kinds of twist, aerodynamic and physical. He seems to be talking of the aerodynamic type, which is a lot more subtle. $\endgroup$ – Guy Inchbald Dec 14 '20 at 19:01
  • $\begingroup$ Perhaps I misunderstood when I read it, he wrote: “a positively swept wing can go away without twist if the airfoil is changed along the span from positive camber at the root to negative camber at the tip”. $\endgroup$ – ivanantuns Dec 14 '20 at 19:16

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