Help with drag coefficient calculated from ballistic coefficient

[programador]

I want to make a video game about snipers and I would like it to have proper bullet physics, not something very accurate, but with "credible" bullet physics. So I need to implement a simple trajectory solver.

I thought of taking into account just the gravity and turbulent air drag. The equations for the air drag according to Wikipedia are:
F = 1/2*ρ*v²*Cd*A, where Cd is the drag coefficient (0.47 for a sphere), so given a Cd value (or function of the velocity) I can already estimate the trajectory.
On the internet, these Cd values for bullets are not available, one can find just the "ballistic coefficients" --BC-- of some bullets if we search a bit. The thing is that I need a standardized formula to obtain the Cd values to determine the actual trajectories, most websites explain these concepts in a non "scientific way" and rather suggest to use some free tools to get the bullet drops. On wikipedia I find the formulas to be very ambiguous for what seem to be several BC definitions (BC-physics, BC-projectile and BC-smallarms).

What I understand so far is that the drag coefficient varies with the Mach number (in this case v/340 in the SI units) and bullet manufacturers give a BC value using the G-model as the reference (how? what is the formula linking both things). I was lucky enough to find the G1 drag coefficient table that is mentioned everywhere but not shown. What I need now is how to use this table, the given BCs values and of course the mass and velocities to estimate a bullet's trajectory.

 

[jrmichler]

Did you search exterior ballistics? The Hornady hit has a good discussion, and the Wikipedia hit has a nice chart of drag vs Mach number.

Since you only want "good enough to be credible", you could use published information for bullet velocity at various ranges to find a drag coefficient. Use the air drag equation you listed, and adjust the Cd until the calculated velocity matches the published velocity at the various ranges. Then solve for bullet drop. The errors from assuming constant Cd will be relatively small, so the results should be good enough to be credible. You will need to find a separate Cd for each bullet at its muzzle velocity.

 

[programador]

Did you search exterior ballistics? The Hornady hit has a good discussion, and the Wikipedia hit has a nice chart of drag vs Mach number.

Since you only want "good enough to be credible", you could use published information for bullet velocity at various ranges to find a drag coefficient. Use the air drag equation you listed, and adjust the Cd until the calculated velocity matches the published velocity at the various ranges. Then solve for bullet drop. The errors from assuming constant Cd will be relatively small, so the results should be good enough to be credible. You will need to find a separate Cd for each bullet at its muzzle velocity.

That's what I have been doing, using a constant Cd, but as you can see from the figure you are referring, the Cd varies dramatically as a function of the Mach number in the range shown. So approximating the trajectory with a constant value doesn't seem right, specially with high velocity rifle projectiles.
Okay, I said "credible", but I think it takes almost zero additional effort to use a lookup table for the Cd parameter to improve the accuracy.
I have the feeling that it might be like this Cd(M) = G1(M)/BC, where G1 is the table I linked or the figure you referred, from

The deceleration due to drag that a projectile with mass m, velocity v, and diameter d will experience is proportional to 1/BC, 1/m, v² and d².

(it doesn't give an actual formula, just a wordy explanation of the term OMG)

 

[PhysicsSharpshooter]

You had a good intuition for the relation between Cd and BC. However, this link explains the real relation between these two variables:
https://sites.google.com/site/techn...rag-coefficients-of-bullets-arrows-and-spears
I'm a gamer myself, and very much into simulators. I'd like to know the name of your game!