Marxman, the idea of using the sound recording is indeed interesting.
The principle is that being the sound speed through the air known (with due corrections for the meteorological conditions, i.e. temperature, humidity, altitude, pressure) you can easily estimate the average bullet velocity. This would be obtained by using the time lapse between the shot and the reception of the sound of the bullet that banged on the target. You will then subtract the time needed for the sound to travel between the target and the sound recorder placed besides the rifle. The residual time is the one employed by the bullet to travel from the muzzle to the target, which may be converted to a velocity value by taking into account the distance between the two points.
However, this gives you only an average velocity and no information on the BC, the MV, or even the trajectory. In order to measure these variables you need other measurements, that may be in part confirmed by the mentioned time lapse.
In this regard, I used the velocity data I generated thanks to the Chrony in order to
estimate the drag coefficients (at muzzle velocity) for the two copper bullets, Barnes VOR-TTSX and Federal TC. This was obtained using the following formulas:
BC = SD/I
i = CB/CG
where
SD = sectional density
i = form factor
CB = drag coefficient of the bullet
CG = drag coefficient of the G1 model bullet
In order to obtain CG I used the calculator available at
http://www.jbmballistics.com/cgi-bin/jbmgf-5.1.cgi where I entered the BC I derived from my velocity recordings, as well as the MV I measured with my Chrony.
Here are the input data and the results for Federal TC:
BC = 0.455
MV = 2,770 ft/s
CG = 0.541
CB = 0.322
…and Barnes VOR-TTSX
BC = 0.380
MV = 2,615 ft/s
CG = 0.553
CB = 0.394
As you can see, the VOR-TTSX bullet has drag coefficient (CB) approximately 22% greater than the TC. Unfortunately, I don’t have all the needed sizes of the two bullets to explain this difference. But I tried anyway, with some approximation. What it came out is that two key factors seem to play a significant role:
-
the boattail shape: the TC as a slightly narrower base (~0.65 mm) compared to the VOR-TTSX (~0.7 mm);
-
the bullet's nose length which is slightly longer in the TC (~1.8 mm) compared to its kin (1.75 mm).
I was able to confirm this hypothesis by entering the data I had in another JBM other calculator, i.e.
http://www.jbmballistics.com/cgi-bin/jbmdrag-5.1.cgi
That’s all for now!