# Ballistic Coefficients vs Drag Coefficients

• Feeb

#### Feeb

So, I'm currently writing a mathematical analysis of a bullet with a muzzle velocity of 790 m/s. I have found that the standard equation for drag force...

Fd = 1/2 * ρ * v2 * Cd * A​

does not work because the drag coefficient for a bullet (.295) does not account for supersonic speeds. What I want to know is, could I substitute the ballistic coefficient into the problem in order to get the value for drag force? If not, what would be the proper way to calculate for the drag force on the bullet, assuming I know every variable besides the correct coefficient of drag? Also what is the difference between the two coefficients?

This is an article discussing how the BC is derived:

http://en.wikipedia.org/wiki/Ballistic_coefficient

In general, Cd is not a constant for all speeds. It's not clear where you obtained the value for your bullet nor for which speeds it might be valid.

In particular, when the drag coefficient for projectiles is plotted versus velocity, the value of Cd is constant in the subsonic speed regime until trans-sonic velocities are reached. The values of Cd then take a wild swing, going down initially and then rising as the projectile passes Mach 1 and then starts a curved decline after reaching a maximum value just after Mach 1, but Cd never returns to a constant value like it was when subsonic.

The following sites show plots of Cd versus velocity to illustrate this situation:

http://www.shootingsoftware.com/coefficients.htm