Ballistic Coefficients vs Drag Coefficients

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SUMMARY

The discussion focuses on the relationship between ballistic coefficients (BC) and drag coefficients (Cd) in the context of calculating drag force for a bullet with a muzzle velocity of 790 m/s. It is established that the standard drag force equation, Fd = 1/2 * ρ * v² * Cd * A, is inadequate for supersonic speeds due to the variability of Cd. The drag coefficient is not constant across different speeds, particularly transitioning from subsonic to supersonic velocities, where it experiences significant fluctuations. The discussion emphasizes the need to understand the specific conditions under which the drag coefficient is valid for accurate calculations.

PREREQUISITES
  • Understanding of drag force equations in fluid dynamics
  • Knowledge of ballistic coefficients and their derivation
  • Familiarity with supersonic and subsonic flight dynamics
  • Ability to interpret velocity vs. drag coefficient graphs
NEXT STEPS
  • Research how to calculate drag force using variable drag coefficients
  • Study the effects of Mach number on drag coefficients in projectiles
  • Explore ballistic coefficient calculations and their applications in ballistics
  • Examine experimental data on drag coefficients for various bullet types
USEFUL FOR

Ballistic engineers, firearms enthusiasts, and researchers in projectile dynamics will benefit from this discussion, particularly those interested in accurate drag force calculations for bullets at varying velocities.

Feeb
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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?
 
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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

https://sites.google.com/site/techn...rag-coefficients-of-bullets-arrows-and-spears
 

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