Calculating a Ballistic Coefficient (BC) from two velocities

[jr-c1]

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?

 

[jrmichler]

I found this page: https://www.sellier-bellot.cz/en/products/ballistic-coefficient-calculation/. Translating into metric, and entering into their equation, I got BC = 0.412. Their equation looks the same as yours, except they use a constant that includes air density. Look at both equations, then look at the units in each. Look for a unit inconsistency.

 

[jr-c1]

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!