Hyperloop-like spacelaunch

The use of compressed air instead of a rocket engine as stage 1 (acceleration to a speed of about 4km / s). Preliminary calculations show the technical feasibility of the idea (see file "Notes & explanations"). A key element: a high-speed air valve ( www.ista-pneumatics.ru https://www.youtube.com/watch?v=ri0FUGmcJqo ) Now there are more questions than answers.