Screwing up

The model rocket body is a thin, solid plastic, gradually tapering helix about a foot and a half long with a hollow egg shaped nose cone at its widest end.

The missile’s launcher is a hollow tube with a relatively heavy flywheel near its top that can be depressed, (or joyful if the occasion warrants), about eight to ten inches down into the tube on strong spring loaded sliders.
The corkscrew is loaded into the top of the tube and twisted slightly until small splines on its side align with slots in the flywheel but do not slide all the way through the flywheel's center. The flywheel is depressed causing bumps on its inner surface to raise, these keep the corkscrew from disengaging from the flywheel.
A spring-return pull cord on the launch tube's side is pulled repeatedly until the flywheel is rotating as fast as you can make it go. (deluxe models may have gear boxes for greater speed).
When the launch button is pressed the fly wheel is jerked violently towards the end of the tube on its sliders while releasing the extrusions which hold the corkscrew to it. It stops its upward movement just as suddenly.
The unfettered rocket then screws itself into the sky until the resistance of its forward momentum is no longer enough to hold the egg shaped nose cone from releasing the parachute that lets you do the whole thing over again, without having to buy a new rocket engine.