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Is there an obvious, ideal lift distribution for human-powered aircraft?
Elliptic or Bell (unloaded tips) distribution?

For this who will tell the Bell distribution, I have a counter-question ready, why don't put wires to wingtips to reduce bending moment at root and use elliptic distribution?

So what is the purpose of any Bell distribution, if the wing is designed correctly?

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    $\begingroup$ You're probably focusing on the wrong issues. At least one of the record teams let various team members try pedaling it when they were done with the aircraft. It quickly broke as the result of a very minor oops - these things are so delicate, and require such ideal conditions that getting a pro cyclist to complement all the infrastructure and ground support crew is the easy part. Anyway, notice that they're basically glider wings, in some cases having as much in common with model aircraft construction as traditional airplanes. $\endgroup$ – Chris Stratton Jan 21 at 19:34
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The essential feature of a human-powered aircraft is to maximise aerodynamic efficiency, which is to say to minimise drag for a given amount of lift. This is what the bell curve achieves. The elliptical distribution minimises drag for a given span, which says nothing about the lift available. The bell curve also gives you a lighter structure for a given amount of lift. Yes you can brace an elliptical wing for reduced weight, but you can brace a bell wing for an even greater reduction.

Also, the ideal distribution will depend on things like how tightly you want to turn. The inner wing will tend to stall, the outer wing to drag backwards (adverse yaw). Jonathan Bowers at NASA has shown that achieving the bell distribution through significant washout can create negative tip drag and proverse yaw. UK pioneer JW Dunne published as much in 1913. Washout also greatly reduces the problems of tip stalling and Dunne's biplanes proved wholly unstallable.

No doubt computer simulations could help refine the exact optimisation of washout, airfoil variation and span loading for the flight regime envisaged, as they did for Bowers' PRANDTL-D research drones, but it is not going to be far from the classic bell distribution.

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All modern HPAs (Human Powered Aircraft) use a bracing wire, so the theory which yields the bell distribution as the optimum cannot be applied directly since it applies to cantilever wings. The best you can do is to use a semi-bell for the part of the wing outboard of the bracing wire attachment point and use an almost constant lift load over span inboard of this point (still with its maximum at the wing root, though).

If you care about ground handling, roll speed and the maximum bank angle in low level flight, you might want to reduce span a bit in order to keep all three up. The last meter of wingspan in case of the ideal bell distribution doesn't save much drag anymore but leaving it out will make hangaring and maneuvering easier.

Note that you can save more induced drag by picking a lower height over ground than by optimizing wing shape. In the end, you need to consider what the HPA is meant to achieve.

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what is main reason why this is very hard to achieve

Human powered flight generally? The most basic reason would be insufficient power-to-weight ratio.

In order to hold an airplaine aloft, you have to accelerate air downwards. For any given total weight of flying vehicle, the product of added vertical speed and volume of air per second which is given this acceleration kick is something you can not change. Only choice is either accelerating small amount of air to high speed or big amount to lower speed.

But energy/power you need to put into accelerating this airmass increases with square of added velocity (while provided lift depends on velocity only linearly). So it is always much more efficient to be pushing down big volume of air by only little (compare to induced drag of airfoil).

Theoretically, this energy necessary for staying aloft could be arbitrary low, jast take a sufficiently big amount of air and push it downwards only a little.

Well, not exactly. Important question is where are you getting the air to accelerate from. And here starts all practical problems.

You can either increase wingspan, so aircraft ploughs through more air at same airspeed, or you can increase airspeed. First comes with penalty in mass (so you need even more lift and many related issues), second results in increase in "common" parasitic drag -- power necessary increases with third power of speed -- so there is relatively hard celing (you can not expect being able to pedal big airplane much faster than your common bike regardless of any lift being generated or not, can you?).

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  • $\begingroup$ Not sure that any of this addresses the specific question in the OP (at least in its current, re- re-edited form). The quoted question ("why is this hard...") no longer appears in the post. $\endgroup$ – Ralph J Jan 23 at 20:49
  • $\begingroup$ Yes, the question was re-edited many times, and I happened to see a one where formulation sounded like looking for general explanation why human powered flight could not work with much lower power levels than previous attempts. True, that the answer does not fit current wording. I can remove it if you believe it is the best thing to do. A comment or clarification from @EBV821 would be nice too. $\endgroup$ – Martin Jan 24 at 0:06
  • $\begingroup$ @EBV821 please keep the discussion polite without personal invective. It is really unclear what are you actually asking. When I wrote my answer, the question was worded in line with wanting average person to be able to flight by its own power (so, roughly, power lower by factor 5 compared to realized flights). This seems rather0 unfeasible from general rough estimates already regardless technical details (of course, an analysis can go much deeper than my answer). Or maybe you know all this already and looking only for some minuscule optimization through lift distribution? $\endgroup$ – Martin Jan 24 at 15:04
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    $\begingroup$ This popped up in review as low quality post. In view of the change history of the question, I will not recommend deletion; the answer is valuable in the context of the question in its state when the answer was written. @Martin, if you could update the question and add a section that answers the question in its current state, that would be best. Of course you can also choose to delete your answer. $\endgroup$ – DeltaLima Jan 26 at 10:43

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