What formulas should I use to calculate drag for a supersonic bullet?

[darkdave3000]

I'm a computer scientist currently developing projectile simulators. My software will factor in drag coefficients of various shaped projectiles as well as gravity, air pressures, air density and temperatures at various heights. I am familiar with the drag formula but it's only useful up to Mach 0.8. Please help me understand what additional formulas I must use for speeds beyond Mach 0.8 in the thought experiment below:

Assuming that a bullet is a perfect sphere like a musket ball fired out of a hypothetically long barrel tank type caliber musket with 100mm caliber with enough energy to send the ball to supersonic speeds at say mach 1.5 and the ball is a sphere: drag coefficient of 0.47.

Assuming the ball leaves the barrel at mach 1.8 at an angle of 45 degrees, the ball will continue to slow down from supersonic to sub-sonic speeds.

What formula should I use to calculate drag while the ball is still in supersonic speeds?
What formula should I use to calculate drag while the ball slows to trans-sonic speeds?(mach 0.8-1.4)
I'm assuming that once it slows down to mach 0.8 I can use the normal drag formula that factors in drag coefficient.

 

[jedishrfu]

What you're asking for is a quick course in engineering ballistics. We can't help much here with that.

I would suggest finding a good book on the subject and do some self learning.

Here's one such resource:

http://www.swri.org/4org/d18/engdyn/survmech/home.htm

Others might be found via Google searches.

 

[berkeman]

And with jedi's helpful post, this thread is done.