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

  • 1
    $\begingroup$ 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
    Commented Apr 29, 2020 at 8:18
  • 2
    $\begingroup$ 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
    Commented Apr 29, 2020 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
    Commented Apr 29, 2020 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. $\endgroup$ Commented Apr 29, 2020 at 13:00
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    $\begingroup$ It is misleading and incorrect to presume that a negative AOA at the tip will result in upward lift and forward thrust. I understand how the vortice could be reduced, but the net lift vector will in that section will be downward, not forward and up. Because if you could generate "induced thrust" in the way it is shown in the diagram on the right, why wouldn't you design a wing with the camber on the bottom to take full advantage of this? (or camber on the top, but negative AOA?!) It defies common sense... $\endgroup$ Commented Jul 23, 2021 at 16:47

2 Answers 2


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 in practice need a separate elevator, fore or aft, to apply the significant trim changes as payloads vary for operational reasons. 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.

Also, if a significant fuselage is added to increase payload volume, this is likely to extend forward of the wing and need a compensating vertical fin, despite the inherent stability in the turn of the Prandtl wing through proverse yaw. 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 and a century before Bowers flew the Prandtl-D). 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
    Commented Apr 29, 2020 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. $\endgroup$ Commented Apr 29, 2020 at 13:54
  • $\begingroup$ Any better now? $\endgroup$ Commented Apr 29, 2020 at 13:56
  • $\begingroup$ @ROTOR It depends. On some designs it can be constantly negatively loaded. In other designs it is less loaded. It also depends on the bell curve. Using Horten bell distribution the wing tips are usually negatively loaded. Using Prandtl bell distribution the wing tips can often be neutrally loaded or even positively loaded. Partly this is caused by the Horten brothers' misinterpretation of what makes the bell-shaped curve stable for flying wings and they didn't fully trust Prandtl's results so made the tips negatively loaded for safety margin. $\endgroup$
    – slebetman
    Commented Jul 23, 2021 at 4:53

… and how today aeronauticals engineers dont understand at all "bell spanload concept"

This is another case of NASA marketing overselling their achievements. The engineers of the past understood the concept fully well. Note that even Ludwig Prandtl himself wrote in the article "Über Tragflügel kleinsten induzierten Widerstandes"

Die Abbildung zeigt, daß die in letzter Zeit bevorzugten spitzendigen Flügel von unserem Standpunkt aus den Vorzug verdienen, vor denen mit annähernd rechteckigem Umriß, daß es dabei aber im einzelnen auf den Grad der Zuspitzung nicht allzusehr ankommt.


The illustration shows that from our point of view, the recently preferred pointed wings deserve preference over those with an almost rectangular outline, but that the degree of tapering is not too important.

Interpretation: The engineers were already designing wings with something like a bell or near triangular lift distribution. And they continued to do so until recently. Witness the article "The aerodynamic design of the A350 XWB-900 high lift system" by Henning Strüber, where he writes on the first page:

The highly tapered inboard loaded wing is optimized for aerodynamic cruise efficiency and low structural weight.

"inboard loaded" is just another term for a bell-like lift distribution over span. Again, high taper has been used to reduce the root bending moment. And you can rest assured that engineers will continue to design such wings in the future, NASA marketing notwithstanding.

Next, the number of 20 to 30% in savings by leaving off the tail is higher than the tail drag contribution of most designs, so there is less to save to begin with. But tailless designs need much larger wings to create the same lift since part of the wing is needed for stability. Tailless designs cannot use powerful flaps, and only by using large flaps can airliners cover the speed range that makes them so efficient. Al Bowers should know this. The claim of 60% of drag reduction is only possible if one particular operating point of a very poor design is compared to an ideal tailless design. Overall efficiency will be poorer than that of conventional designs.


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