Can we build an air start rocket, and tube launch it with the VERA??? What a spectacle for one of the big Rocketry events.
With VERA? No, for reasons that range from engineering (her barrel only elevates a few degrees) to finances (who's gonna pay for it?) to legalities (read: liability). That said, an air start of a gun launched rocket is totally doable.
Long, long ago,
I did it myself. Granted, my attempt was very crude and done on the cheap, but I proved what I wanted to prove.
I'm also aware of another guy who did it with a roughly 40 mm x 1000 mm rocket but my google fu appears to be weak at the moment and I can not find him.
However, something tells me that you're on the lookout for something a bit more spectacular. I suspect a (vertically mounted) VERA clone is a bit out of your logistics and/or price regime so putting on my thinking cap for a moment....
You'll want to go with a hybrid design. Pure pneumatics on a large scale simply become too cumbersome, in my opinion. Plus, they're absolutely limited to Mach 1. I mean, if you're gonna build it, why not shoot for supersonic?
Throwing some numbers around...
6" bore x 20' long barrel. Large enough to be useful. Small enough to be affordable and easy to transport (yes, "affordable" and "easy" are relative terms).
8" x 72" combustion chamber.
3" burst disk.
That'll launch a 25 pound projectile to just over 500 ft/s and give you a clean air start at well over 1000 feet AGL.
And it'll be pretty loud.
edit: On the other hand... If you've a fair chunk of change... As VERA demonstrates, much can be done.