This new and original Paper Airplane Launcher design is called a Sine-bow because it operates like a cross-bow and each unloaded bow shape is a sine wave. The thickness of the bows are not constant, and have been engineered to distribute stress when loaded.
With the Sine-box I have been able to launch a variety of paper airplanes, with the accuracy and distance of an average human thrower!

YouTube video: https://youtu.be/mOcpIyeAw1A

The required filament type, for this design, is PETG, because it is stronger and more flexible than PLA. PETG also sticks better to the printer bed (than PLA) and therefore does not need a brim.
No rubber bands are required. The Sine-bow is a very compliant structure.
However, do Not leave the launcher in the cocked position for a long period of time (i.e. more than a few minutes). The plastic will creep and take a new set, reducing the effectiveness of the launcher.
It is designed to print on a small 3d filament printer (minimum of 180x180 mm bed). Depending on your printer and your settings, the Sine-bow can be printed in under 2 hours. I have had many successful prints using 0.35 mm layer thickness.
A small amount of assembly is required.
This design requires two printed parts; 1) the main Sine-bow and 2) the trigger.
The Sine-bow needs a 5mm diameter tube (aluminum, brass, steel- something stiff and smooth), 300 mm long
The tube is the slide for the bow and keeps the bow stable.
Attach trigger to Sine-bow with two #4 diameter x ½ inch length min. screws.
Preferably button head (countersunk should work) plastic or wood screws.

The Sine-bow was designed in OpenSCAD, which is a free code-based CAD program. The Sine-bow code is included with the Thingiverse files, so one can see how it is designed, and modify it if you want. The analysis part of the code is not included, as that is not ready for general release to the public.
However, you can still modify the design if you are adventurous. Enjoy.