See my new and improved paper airplane launcher design here: https://www.thingiverse.com/thing:6841245
The new version was uploaded on November 21, 2024.

A new version of the model was uploaded on April 7, 2024, to make the trigger work when printing with PLA.

April 30, 2024: The (9) rings are to keep the beams spaced apart when the launcher is ready to shoot. The rings are joined to the beam on one side and free on the other. If there is filament connecting the rings on the free side, it needs to be cut before using.

Video of project: https://youtu.be/54cBfEDvcXs
The End Game of FTC CENTERSTAGE season contained a drone (paper airplane) challenge (see game video at time 4:45: https://youtu.be/6e-5Uo1dRic?si=IAk4fGD14f4Ds6jY) . It was fiendishly hard because it required a precise paper airplane flight. During the season we made hundreds of tests with different airplanes, rubber bands, rubber band tensions, angle of launch and other small features.

During the season the Mark Rober’s World’s Smallest Nerf Gun video came out and we wondered if a similar process could be applied to a paper airplane? (https://youtu.be/9c2NqlUWZfo?si=hDiZxToKSbAoWZpr).

The answer is Yes! Even though we didn’t use this during the season, here is a one-piece 3D printed paper airplane launcher.

It just flexes. No rubber bands required. No assembly required. It can be printed on a small 3d filament printer (180x180 mm bed), such as a Prusa MINI, and in a relatively short (2 hour 22 minute) print time (with the Input Shaper feature, which reduces the time).

Included in the video is an easy-to-fold airplane, made from half a sheet of letter paper, that flies straight and consistent, and will go about 4.5 meters (much further than needed for CENTERSTAGE).

The launcher was designed using OpenSCAD (https://openscad.org/) and specifically designed for PETG filament, which has more flexibility and higher strength, than PLA, making for a better flexible (compliant) design.

For this design, when latched:
Force to pull launcher to trigger for PETG is 19.2 Newtons, for PLA is 22 N.
PLA has greater potential energy (35 N-mm) than PETG (30.4 N-mm).
PETG has greater margin to failure than PLA.

Assuming:
Modulus of Elasticity (NEWTONS PER mm^2), PLA = 2344
Modulus of Elasticity (NEWTONS PER mm^2), PETG = 2068