Calculating ballistics coefficient from two velocities

In long range rifle shooting, knowing your true ballistics coefficient is very useful. You might get a ballistics coefficient listed on your ammunition, but depending on your range that ballistics coefficient might not be accurate. I have two velocity readings at 0 range and (let’s say) 100m. How can I calculate the ballistics coefficient for that shot?

I have been looking at this thread to solve ballistics coefficient (BC) with two velocity readings:
https://www.physicsforums.com/threa...t-bc-from-two-velocities.958802/#post-7069285
The author gives this formula to calculate BC,

BC = (AirDensity * Distance) / ( SQRT(Velocity0) - SQRT(Velocity100))
but in the variables, he provides a "air resistance" value and not "air density". I am aware these can't be used interchangeably and cannot find a clear answer on the internet.

Values given by author:
Air Resistance = 0.0052834
Distance = 100 meters
Velocity0 = 914.4 mps
Velocity100 = 838 mps @ 100 meters
BC = .451

Can someone help me out?

Your new thread leans on a five year old one that at least explains what BC stands for: a Ballistic coefficient.

This is a physics forum, and it would be nice to know what this is about.
Please post a complete problem statement, list and explain known variables (include units),
list all relevant equations you need and post your work.

And convert variables to a consistent set of units, preferably SI.

The arms trader reference no longer explains the relevant equation used in the old thread (##{\bf BC} = {\rho d\over \sqrt v_0-\sqrt v_1} \qquad (1)## ).
(##\rho## is air density, ##d## is distance -- we must guess there are two velocity measurements, ##v_0## and ##v_1##, with a distance ##d## between them)

Regrettable, since the dimension of this ballistic coefficient should be [mass]/[distance]² and that's not the dimension on the righthand side of ##(1)##.

We can ask @jrmichler if he/she can recall

jrmichler said:

Translating into metric, and entering into their equation

about translation and equation...


[edit] Ah, you added some context. Thanks

##\ ##

For what its worth and as I understand it from [1], the BC for a particular bullet varies as a function of speed since the drag coefficient varies with speed with a profile that is somewhat dependent on the shape, as shown below (also from [1]).


I also understand that the BC profile for most long range ammunition match well with a scaled G7 bullet (bottom curve) rather than the G1 (upper curve) and if that is also the case for your bullet you may be able to establish a BC speed profile from that. However, I am not aware of the exact data set for the G7 drag profile and [1] is also written using imperial units making it difficult to compare with your data. If you "just" need the BC data I would suggest that you use a ballistic calculator that is able to base its calculations on the proper bullet shape or (constant) form factor relative to a standard bullet (like G7). If you need theoretical insight I suggest you read [1] or similar.

[1] Applied Ballistics For Long-Range Shooting 2nd Edition, Bryan Litz, 2011.

Later: I missed this problem was listed as homework so the input above may not be very useful in that context.

According to https://en.wikipedia.org/wiki/Balli...h,and hence, different ballistic coefficients and my algebra,
##BC=\frac{\rho s}{2(\ln(v_0)-\ln(v_1))}##