Orbital Railgun

[Fr1ki]

Hey all

I joined just so that I can ask a couple of questions as I can't seem to find what I am looking for in my textbooks.
I am a 3rd year Chemical Engineering student and I am doing this for extra credit in the subject : Momentum, Heat and Mass transfer.

I am designing an orbital railgun simulator in MS Excel.
I have already completed a simulator for the railgun and only need help with the ballistics of the projectile.

Here is what I have so far :
Station orbits at around 2000km above sea level
Model for air density as function of altitude
Projectile shape

What I need :
a drag coefficient formula dependent on projectile shape ; a formula that returns different results for a bullet shape and a cylinder
the flow regime ; laminar, turbulent, or Stokes regime

I will be using Navier-Stokes to model the ballistics.
In the end, what I require is the velocity at which it strikes the earth ( terminal velocity most likely, but not sure because of variable air density )

Thank you for your time

[Fr1ki]

Hey again

I have overcome the final velocity issue. I want it to be 1% the speed of light.
The problem now, is to work out the velocity at which the projectile leaves the barrel.
Does NavierStokes take into account the initail velocity? I am still new to this subject and have yet to come across such a problem or example.

What I have :
Final Velocity ( +- 300 000 m/s )
Projectile Shape ( spear like )
Projectile weight ( 20kg )
Air density model
Total distance ( 2000 km )
Railgun simulator

What i need :
Exit velocity needed of the projectile from the barrel to achieve 1% SoL at ground zero.

Thank you again