Calculating a Ballistic Coefficient (BC) from two velocities

In summary, the conversation was about calculating a Ballistic Coefficient (BC) using two velocities and a known distance. The formula for BC is (AirDensity * Distance) / ( SQRT(Velocity0) - SQRT(Velocity1)) and in the given example, the BC was found to be 0.0329. However, this result did not match with the vendor's published BC (.415) or two online BC calculators (.455 and .422). After some discussion and research, it was found that the air density needs to be factored in and the correct formula was BC = 0.412. The conversation also discussed the use of different units, such as using meters instead of yards, and the final calculated
  • #1
jr-c1
3
0
I have been attempting to calculate a Ballistic Coefficient (BC) from two velocities of a known distance using the formula:

BC = (AirDensity * Distance) / ( SQRT(Velocity0) - SQRT(Velocity1))​

for example

AirDensity = 0.0751265 lb/ft³
Distance = 100 yards
Velocity0 = 3000 fps
Velocity1 = 2772 fps
BC = 0.0329​

In this example, I have compared this result with the vendor's published BC (.415) and two online BC calculators (.455 and .422) and I'm considerable off.

As I understand it, air density needs to be factored in.

Can someone help with the correct formula?
 
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  • #3
I see my first problem was thinking the 0.0052834 constant had to be converted to use either the ICAO or Metro standard atmosphere used by the manufacturers, which led me to use Air Density and Air Resistance constants interchangeably. Thanks for straightening this out for me.

After going back and revisiting the calculations using metric values and appropriate speed at 100 meters vs 100 yards:

Air Resistance = 0.0052834
Distance = 100 meters
Velocity0 = 914.4 mps (3000 fps)
Velocity100 = 838 mps @ 100 meters (vs 2772 fps at 100 yards)
BC = .451

@jrmichler, your the BEST!
 

Related to Calculating a Ballistic Coefficient (BC) from two velocities

What is a ballistic coefficient (BC)?

A ballistic coefficient (BC) is a measure of a bullet or projectile's ability to overcome air resistance in flight. It is a dimensionless number that is calculated by comparing the projectile's performance to that of a standard projectile, typically a sphere or a G1 shape.

Why is calculating a BC important?

Calculating a BC is important because it allows us to predict the trajectory of a bullet or projectile more accurately. This information is crucial for long-range shooting and can also help with determining the optimal bullet for a specific firearm.

How do you calculate a BC from two velocities?

The most common method for calculating a BC from two velocities is the velocity-ratio method. This involves measuring the muzzle velocity (V1) and downrange velocity (V2) of a bullet or projectile, and then using the following formula: BC = (V1/V2)^2. This calculation assumes that the drag coefficient remains constant throughout the flight.

What are some limitations of calculating a BC from two velocities?

There are a few limitations to calculating a BC from two velocities. Firstly, this method assumes that the drag coefficient remains constant, which may not always be the case. Additionally, it does not take into account other factors that may affect a bullet's trajectory, such as wind, temperature, and altitude. It also relies on accurate and precise measurements of the velocities, which may not always be possible.

Are there other methods for calculating a BC?

Yes, there are other methods for calculating a BC, such as the drop method and the chronograph method. The drop method involves measuring the drop of the bullet at a known distance and using that information to calculate the BC. The chronograph method involves using a chronograph to measure the time it takes for a bullet to travel between two known distances, and then using that information to calculate the BC. However, all methods have their limitations and may not provide the most accurate results.

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