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Good recommendation.


.22WRF,

No such function as you are looking for was ever derrived, AFAIK, because the drag function is different for every bullet shape. Also because the huge swings in drag in the transonic velocity range make it difficult to devise one. As close as it comes is recognition that in the sub-sonic range the drag function is proportional to the square of velocity times a form factor for the bullet. That's also true above about Mach 5. But inbetween, as soon as a bullet is going fast enough that some portion of the air moving over it reaches the speed of sound there is a huge jump in drag way beyond the v� proportionality as energy starts to go into shock wave formation. That extra drag drops off at still higher velocities until it is diminished to near insignificance as it approaches Mach 5 (the fastest bullets seldom fly above Mach 4). So the standard way of handling the shock wave drag is to calculate the v� drag for all velocities, then multiply it by the what is called the drag coefficient, which is a correction factor function of velocity that is 1.0 at subsonic velocities, then climbs as the transonic range is entered, peaking at about the speed of sound then falling off in a vaguely 1/v proportional relationship until its significance is diminished.

Ballistics software uses several strategies to arrive at drag. Mostly the ballistic coefficient is used with tabular data for the drag coefficient taken from real measurements of fired projectiles, so this is curve fitting rather than calculation from first principles. The BC scales the bullet's behavior to that of a standard projectile weighing 1 lb and have 1" diameter (sectional density of 1.0) and a particular shape whose drag is being modeled.

The first of those was what is now called the G1 projectile, which was fired literally for years and thousands of times at different velocities over 19th century electromechanical chronographs until how much time it took to traverse every yard was known for a wide range of velocities. The Army Ballistic Research Lab ran the data on other shapes for the military using more modern equipment and completed that work and was shut down near the end of the 60's, IIRC. McCoy's book goes into this in more detail, though it's been awhile since I worked my way through it. Be aware that the book was published just after Robert McCoy passed away and before he could edit the proofs, apparently, as there are a number of errors in it. Don Miller and some of his other students have an errata list and corrections available on line for free.