Mach 7, huh? That's almost 8,000 feet per second. A=v^2/r Let's say you build one of things out of unobtanium, and it's 400 feet across, for a radius of 200 feet. That's 320,000 ft/sec^2, or 10,000 g's. Has there ever been a rocket that could stand 10,000 g's sideways? Or even 1,000? Is there a form of unobtainium that also works as rocket fuel? That this proposal hasn't been laughed out of every venue it's been mentioned at is an indictment of how physics is taught (or not taught) in the USA.
On the other hand, if you had something useful that could stand 100 g's (almost conceivable) maybe you could make a straight track somewhere, 2 miles long, that could obtain that speed with less trouble. You'd need the right mountain, I suppose. that still leaves a few problems, though. Even if it released at 15,000 feet, max q would still be, unless I've messed it up using internet calculators, on the order of 47,000 lbs/ft^2! That's as opposed to maybe 735 lbs for a Falcon 9, which would be something like 10 miles up and a bit over Mach 2. I'm sure there will be thermal issues, too, although I suppose if you made much of your vehicle out of uranium, that would be refractory enough. So it might be a valid way to deliver fissile material to orbit. I'm not sure anything short of large scale interplanetary exploration a la the Orion Project would need that much. And there just MIGHT be PR problems. I suppose if you were leaving the solar system, you could keep it all secret somehow until just after you left.
https://www.digitaldutch.com/atmoscalc/
http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/compressible/index.html
https://www.flyingmag.com/has-anybo...ring a typical Falcon 9,or so into the flight.
