Could compressed air launch a missile that large, or would it require a propellant charge?
Short answerCompressed air is a plausible option. Electromagnetic launch is another possibility, provided the missile can survive the acceleration.
NotesCompressed air is suggested as a feasible launch method because it already launches much larger ballistic missiles. Electromagnetic launch is another possibility, provided the missile can withstand the initial acceleration. A proposed railgun or coilgun launch at Mach 3 or Mach 4, followed by a sustaining rocket motor, is offered as a route to much greater range, conditional on surviving those high acceleration loads. Protected turret-like missile launchers had also been considered before arm launchers and vertical-launch systems became established. Protection motivated those earlier turret proposals.