Bestfold

Bestfold

Paper planes designed by simulation, each folded by hand from a single sheet of A4 paper.

Folding the sheet…
Figure 1. The current best design. Drag to rotate.

Bestfold D-1

How to fold it Watch it fly

Flight simulation

Both planes are thrown with the same speed and angle and simulated live in your browser. Pick one of the 16 test throws or set your own.

Force per stripStalledWeightLift loading
Figure 2. The planes are drawn five times their real size. Grid squares are 1 m.

A design is scored on the average of its worst 8 throws out of these 16, which vary the throw, the folding and the drag model. Every design gets the same 16 throws.

Wind tunnel

The plane is held still in a stream of air. The smoke moves with the air as the simulator computes it, including the swirl around each vortex panel. You can see the air pushed down behind the wing and the vortices trailing from the tips. Past the stall, the flow over the wing breaks up.

Slower airFaster airForce per strip
Figure 3. True size. Drag to look around.

The search

Best designMedian across plane types
Figure 4. Best design at the selected point in the search.

How to fold it

Every measurement comes from the geometry the simulator flew. You need one sheet of A4 and a ruler.

Figure 5. Front of the sheet light, back blue. The dashed red line is the next crease.

    Step diagrams

    The folded shape at the start of each step, with the crease to make in red, drawn to the same scale.

    Contribute

    You can help the search by leaving this page open. Your browser runs its own copy of the optimiser in the background and sends any improvement to a shared board. The server re-runs the simulation for every submitted design before it is listed.

    Connecting…

    This browseridle

    It runs while this tab is open, and you can stop it at any time. Results count for the mission selected above.

    #Found byScoreChecked
    No shared designs yet.

    Method

    Folding. Planes are only folded. Nothing is cut, taped or glued, so the folds themselves have to hold the layers together. In the model, the sheet is a set of polygons. Each fold reflects the layers on one side of a crease and restacks them. Some folds move only the top layers, which is how locks are made. A design is rejected if a fold would tear the paper, if more than eight layers meet at a crease, or if a large flap is left free to open in flight.

    Mass. Mass, balance point and inertia are computed from every folded layer of 80 g/m² paper.

    Aerodynamics. A vortex-lattice model on the wings, keel and winglets, with corrections for sharp paper edges (lost suction, and vortex lift on swept edges), skin friction, drag from thick folded edges, and stall. It is checked against wind-tunnel data for flat plates and sharp delta wings and against a measured A4 dart.

    Flight. A six-degree-of-freedom simulation in 4 ms steps, including the air the plane has to push aside. Creases act as springs, so the wings rise under load. An energy check stops any flight that gains energy.

    Trim and launch. The elevator angle and the launch angle are worked out for each plane, the way you would adjust and throw a real one.

    Search. The optimiser keeps the best plane of each type (sheet orientation, sequence of folds, winglets) and improves each with CMA-ES, spending more time on the promising types.

    Details, limitations and references are in the source repository.

    Figure 6. Lift-to-drag ratio against body angle of attack at 6 m/s. The peak is roughly the distance travelled forward for each metre of height lost in a steady glide.