Ballistic Coefficients vs Drag Coefficients

In summary, the standard equation for drag force, Fd = 1/2 * ρ * v2 * Cd * A, does not work for supersonic speeds due to the variability of the drag coefficient, Cd. In order to properly calculate for the drag force on a bullet, the ballistic coefficient (BC) can be used instead, which takes into account the changing Cd at supersonic speeds. The BC is derived from a number of factors, including the shape and weight of the bullet, and is a more accurate measure of the bullet's aerodynamic performance. Cd is not a constant for all speeds and can vary greatly at supersonic speeds, as seen in plots of Cd versus velocity.
  • #1
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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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  • #2
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.
 
  • #3
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
 

1. What is the difference between ballistic coefficients and drag coefficients?

Ballistic coefficient (BC) is a measure of a bullet's ability to maintain its velocity and trajectory over long distances, while drag coefficient (CD) is a measure of the air resistance that affects the bullet's flight. In simple terms, BC measures how streamlined a bullet is, while CD measures how much air resistance it experiences.

2. How do ballistic coefficients and drag coefficients affect bullet performance?

A higher BC means the bullet will retain its velocity better and thus have a flatter trajectory, making it more accurate and able to travel further. A lower CD means the bullet will experience less air resistance and maintain its velocity for longer, resulting in a longer effective range and greater impact force.

3. What factors can influence the values of ballistic coefficients and drag coefficients?

The shape and design of the bullet, its weight, velocity, and the atmospheric conditions (such as air density) can all affect the values of BC and CD. Additionally, the surface roughness of the bullet can also play a role in determining its drag coefficient.

4. How are ballistic coefficients and drag coefficients measured?

Ballistic coefficients are typically determined through experiments and calculations based on the bullet's weight, shape, and other factors. Drag coefficients are also determined through experiments, where the bullet is fired through a chronograph to measure its velocity and then compared to the expected velocity based on its BC and other factors.

5. Is there a relationship between ballistic coefficients and drag coefficients?

Yes, there is a direct relationship between the two. A higher BC generally means a lower CD, as a more streamlined bullet will experience less air resistance. However, other factors such as bullet weight and velocity can also have an impact on the values of BC and CD.

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