Nevermind the sonic boom... Would two turbojets pass the airport noise restrictions? And would turbojets this small even get this thing off the ground
Taking your points in reverse order - proposed takeoff (per the patent) is with
both turbojet and rocket power. But that obviously makes your first point more relevant - what kind of noise does two turbojets PLUS a high-thrust rocket make? Probably not Space-Shuttle volume - but could be similar.
Probably depends on the weight that has to be moved. This thing has a payload estimate of just 2-3 tonnes (20 pax), but a BIG tank of slurried H2.
Some other tech points that have been missed:
1) Emissions -
everything is H2/O2-powered, so zero carbon or sulphur emissions. Just water, and some loose H2 (which is what 99.99999% of the universe is made of anyway.) Nitrides or ammonia - probably some from the turbojets when burning hydrogen with atmosphere (a non-chemist's guess), but that is only in the subsonic phases. On-board electric is either batteries or H2O2 fuel cells.
2) At Mach 4.5 horizontal cruise, the shock cone is twice as narrow (11-15°) as with, say, Concorde (30°). So it doesn't sweep the ground until twice as far away (even without the doubling of cruise altitude). If it's quieter than, say, the shunting of railroad freight cars I hear all the time (from 2 miles away they still sound like explosions in a boiler-factory), and which are apparently legal, and far more common....?
Economics? Hey, the 1% of the 1% probably doesn't care if it costs $200,000. The real question is how often, in the era of smartphones and skype and such, they really need to make a transglobal round-trip in one day (and how comfortable they are on rollercoasters!)?
I won't get into the patent "politics" - except to say I don't disagree with most of what already has been said.