In this video AL Bowers (former NASA chief scientis) talk how bell spanload solution can reduce OVERALL DRAG by 60%(11% reduction in total aircraft drag due to spanload, elimination of the tail results in another 20-30% efficiency gain, and then 15.4% improvement in propulsive efficiency, the total efficiency increase is on the order of 60%) and how today aeronauticals engineers dont understand at all "bell spanload concept".

So are we using "wrong" spanload solution(eliptical or all versions of eliptical) all these years?

sources : NASA link

on bell spanload(right wing) resultant force is tilted forward, that cause thrust at wingtip. Eliptical spanload(left wing) has drag at wingtip.

often people think,that wingtip produce download(negative lift),this is not true, wingtip produce lift all the time you can see from graph lift dont go below zero line.
enter image description here enter image description here

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    $\begingroup$ I don't know how representative the images are, but the integrated lift on the left side is substantially larger than on the right side. It makes sense that you have less induced drag if there is less lift. $\endgroup$ – ROIMaison Apr 29 '20 at 8:18
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    $\begingroup$ the answer to such questions is almost always a resounding NO when it comes to engineering problems. There might be room for improvement on existing principles, but that doesn't mean those principles aren't sound if they've been shown to work and work well for a century or more. $\endgroup$ – jwenting Apr 29 '20 at 9:33
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    $\begingroup$ what are you trying to optmize for? did the people that came up with the elliptical distribution optmize for the same? did you use the same boundary conditions/constraints? $\endgroup$ – Federico Apr 29 '20 at 9:50
  • $\begingroup$ These are low speed soaring bird designs, yes, they all work well but produce too much drag at higher speeds. I would question "tail elimination" claims, as loss of stability would greatly increase drag (pitch and yaw oscillations) and hinder low speed control. Birds kept theirs. $\endgroup$ – Robert DiGiovanni Apr 29 '20 at 13:00
  • $\begingroup$ The excellent diagrams alone should leave this open. Note how leading edge slats also help with a bit of thrust, but can be retracted for higher speed flight, where there can be too much lift. $\endgroup$ – Robert DiGiovanni Apr 29 '20 at 14:55

The elliptical and bell curves give optimal solutions to different problems. Obtaining the most efficient wing for a given span leads to the elliptical distribution, whereas the most efficient wing for a given load is given by the bell distribution. For a given central load, the bell or Prandtl wing will have longer span but a lighter structure and reduced tip losses.

For a swept wing the Prandtl type is inherently stable, so there is no immediate need for a tail stabilizer. However practical considerations include CG range, and this is the tailless type's big weakness: unless it is sharply swept, as in a typical supersonic delta, it will need a separate elevator, fore or aft, to apply the large trim changes necessary. For a straight wing an airfoil with reflex camber to give a static center of pressure will also make it stable. But such airfoils are relatively inefficient and wing area must be increased. All this reduces the practical advantage of the Prandtl wing well below its theoretical value.

Roll inertia will also be affected by the increased span, which can impact highly manoeuvrable or very large aircraft.

One way of looking at the Prandtl wing is to see the tip section as a vortex-reducing winglet, which just happens to be blended in. I recall the Airbus A380 chief designer saying that it makes little difference in practice whether the winglet section is horizontal or vertical.

Having said all that, I am a fan of the Prandtl wing (which is really the Dunne-Prandtl wing, as J W Dunne discovered it empirically and flew it as the D.7 twenty years before Prandtl did the maths). Now that NASA have rediscovered it, I would expect it and its design principles to find some modest wider application in the future, with or without a tail. For example in long-endurance electric drones with fixed CG and minimal maneuvring needs.

  • $\begingroup$ wingtips at bell spanload are never negatively-loaded,they always produce small lift,look at lift distribution at my diagram,if wingtips have negative litf than lift will goes below zero line... $\endgroup$ – ROTOR Apr 29 '20 at 13:38
  • $\begingroup$ Ah, OK, Figure 4 in Bowers' original paper appears to show it, but on checking I see that it is relative to the elliptical loading and not absolute. I'll edit my answer accordingly. Thanks. $\endgroup$ – Guy Inchbald Apr 29 '20 at 13:54
  • $\begingroup$ Any better now? $\endgroup$ – Guy Inchbald Apr 29 '20 at 13:56

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