You should study the work the EMSL group, a loosely knit network of aerospace ENGINEERS did 20 years ago during the Star Wars/SDI salad days. They had it ALL worked out : nose cone angle of no less than 8 degrees, lithium pore nose(or cast-in Li beads)for ablation losses in the troposphere and thru the tropopause, min weight of 10 kg(max of 1500 kg).
Exit angles anywhere from 15 deg elevation to 90 deg(small on-board rocket to give side thrust once in orbit). Payload : mostly WATER(cryogenically frozen = super HARD). Water for drinking, hydroponics, steam engines, solar flare shields, hydrolysis for H2/O2 fuel cells....
They tested out all the components that would go into an EMSL projectile at up to 150,000 gees, only failure was a delicate clock. They looked at railguns, homopolar generators, ultracapacitors(the ones available then)but the BEST idea was the quenched superconducting ring-cannon.
So, these EXPERTS had it ALL figured out, even back then. Then the VESTED INTERESTS boys at NASA said : Uh OH, there goes our $20,000/# to LEO MONEY that we make on the shuttle with horribly inefficient rockets....So EMSL got quietly forgotten about.
The love of MONEY is the root of all evil. Google ElectroMagnetic Space Launch, LEARN, then get back to us, better educated...
And so all those EXPERTS went off and designed a 500 mpg carburetor, and those bastard oil companies.....