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.