How do you maximize lift while keeping span as short as possible?

Question

This weekend I saw the Fly Baby at the Smithsonian Air & Space Museum at the Washington Dulles Airport, and it was at some point the smallest airplane (since surpassed by the Bumble Bee II, if I understand correctly). To be able to carry a pilot and lift the plane off the ground in the first place, but still be the smallest airplane, you are mostly limited by wingspan, or more generally, the total width of the airplane.

For the purpose of this question I would like to assume a given airfoil and to exclude modifications to the airfoil itself, i.e. any mechanism that increases lift in pure 2D flow, e.g. camber, slats, flaps, active blowing of the upper surface etc. I would like to limit the scope to the "3D planform" of the wing(s) - e.g. aspect ratio, sweep, depth, winglets/end plates/..., box wings, number of wings etc. The airplane needs to have a fuselage that holds the pilot and an engine. Otherwise the configuration can be whatever it needs to be. If the configuration for maximizing lift depends on the choice of airfoil, then just assume a suitable airfoil.

Both record-holding planes are biplanes, with the Bumble Bee having a relatively large horizontal stabilizer. It also has endplates on the wingtips, reducing lift loss due to the tip vortex.

How can one maximize the lift for a given width?

(I could list all of the ways that come to mind and ask whether and how much they help, but then I'd have "more than one question" and I'm not sure that would be suitable for this format)

Edit: Further clarification: I am asking about maximizing the coefficient of lift of the entire airplane, not about lift itself (which could be maximized by flying faster, to a certain extent). Also, I would like the answer to be valid for low flying speeds (incompressible flow).

Answer 1

The Chance Vought V-173 "flying pancake" was designed to provide low speed flight with very low aspect ratio wings. In fact, the entire body is a wing and the twin propellers are arranged to blow their slip stream over that body. It could very nearly hover, so the lift coefficient is extremely high.

With modern flight control computers the vestigial horizontal tail could be incorporated into the rear fuselage as is done with flying wings. You can see that this has already been done with the center part of the tail. If you were concerned about the width of the props, they could be moved inboard and wing twist altered.

Answer 2

The only significant option you have within the parameters given is to increase the chord. And this has no maximum unless the plane also has a maximum length. but then you increase effective wing area by vertically stacking more wings, again like cord theoretically infinite unless you have a height restriction.

Wingtip devices are effective but rather binary in nature, either you use them or don't, their isn't any real scaling involved other than matching the general size of the wing. They also add weight, which is why they are popular for long haul where fuel is a large fraction of payload but not short haul where the added weight causes more fuel burn than the aerodynamic savings. Many many variables, maybe too many to fully account for with current engineering tools and knowledge, at least for a question like what is "best".

By the way the bumble bee was a terribly unstable short range racing plane. The Bee Gee was the short wing speed record and racing airplane. It was designed to get lift from speed and minimize high speed drag without regard to low speed effectiveness.The Bee Gee was the short wing speed record and racing airplane.

Answer 3

... camber, slats, flaps, blowing of the surfaces

Unfortunately, they are some of the best ways of increasing Coefficient of Lift, far better than trying multiple wings, as seen with the Fiesler Fi 156 Storch.

Deep camber, undercamber, increasing chord (and, proportionally, thickness) are helpful in particular, as are endplates. Another wing or two can be added. Weight should be reduced as much as possible with safe structural strength requirements in mind.

But now you have a very draggy, slow aircraft with limited range, unless you can retract these devices and speed up a little.

Lift is proportional to V$^2$

If you have even more power, and the option to go supersonic, a short single wing like this or a lifting body with no wing at all like this one would suffice.

It really depends on your fuel budget and available thrust. Cost conscious subsonic airliners use retractable lifting devices, and even slower speeds are required only because of airspeed limits, runway length, and the quality of the landing gear (especially tires).