I first posted this on Thingiverse on 1/23/2022. A couple of copies were posted here as original work (without attribution) and were taken down, so I've decided to also post my original design here.

Print using 0.4mm line width and no supports. You may need to sand the launch tube smooth (and this inside of the rocket, too, if you have a round file) to eliminate any friction. You want a close, but relatively friction-free fit.

Watch it go:

CAUTION- HIGH SPEED PROJECTILE: Do not shoot yourself in the face, anyone else in the face, or anywhere else, for that matter.

Notes on scaling: If you want to scale this up, you need to scale the rocket and plunger by slightly different amounts from the launcher to maintain tight clearances. You can use the following formulas:

LS = desired launcher scale factor (say 1.5)
RS = rocket scale factor
PS = plunger scale factor

PS = 1.01444 x LS - 0.01444
RS = 0.95633 x LS + 0.04367

Or, just use one of these sets of percentage scalings:
Launcher scale: 125%, Plunger scale: 125.4%, Rocket scale: 123.9%
Launcher scale: 150%, Plunger scale: 150.7%, Rocket scale: 147.8%
Launcher scale: 200%, Plunger scale: 201.4%, Rocket scale: 195.6%
Launcher scale: 250%, Plunger scale: 252.2%, Rocket scale: 243.4%
Launcher scale: 300%, Plunger scale: 302.9%, Rocket scale: 291.3%