Explain On-the-Fly Ballistic Coefficient Changes

I've chronographed 4 different weight Sierra 30 caliber match bullets getting 100 yard zeros recording environmental conditions. Metallic sights were used as their angular LOS adjustments are easy to calculate exact windage and elevation values per click.

Zeros at 300, 600, 800 and 1000 yards on another range in different conditions calculated with Sierra Infinity software were within a half MOA of what was actually needed.
 
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Swifty Morgan said:
The other day, I was shooting with a pro doing my spotting. The ballistic coefficient on my ammo box was 0.462. After a few shots, he told me to change it to 0.420 in my ballistic calculator.

How did he know to do that?
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Here's what Sierra says for their 30 caliber 168 grain HPMK G1 BC:

.462 @ 2600 fps and above
.447 between 2600 and 2100 fps
.424 between 2100 and 1600 fps
.405 @ 1600 fps and below

https://www.sierrabullets.com/product/30-caliber-7-62mm-168-gr-hpbt-match/
 
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Box BC's are the G1 BC at a typical muzzle velocity for the bullet. G1 BC's usually decline with velocity, though you see a few bullet shapes where it can go up. and the 168 has some of that behavior.

I put an Excel plot together to show the drag coefficients for the G1, G7, and 168-grain SMK. You can see the shape of the G7 is much closer to that of the 168-grain SMK than the G1 is.

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A ballistic coefficient is chosen to scale a bullet's drag to match that of a reference projectile as closely as it can. Here, your eye quickly tells you that if you apply the right scale factor to the 168 SMK drag curve to cause it to match either of the other curves at Mach 4, it's not going to match as well at Mach 1. Less obvious, without a magnifying glass is that matching them at Mach 2 won't have them matching at Mach 1.5, either. This is what multiple velocity range BC's are intended to improve upon (actually, you want multiple Mach number ranges, but there is an assumption you are shooting in a standard atmosphere). You can also find the best average BC for any particular range, which is what the coach was doing here.

Here, in a standard atmosphere, for a 168-grain SMK fired at 2605 fps (2550 fps at 78 feet from the muzzle, the military test barrel spec for M852) with its velocities after different yardages from the firing line determined by the drag function the BRL measured for this particular bullet, are the best G1 BC's for the first 600 yard increments of range. (Note that this bullet has a dynamic instability (attempts to overcorrect) starting at about 1400 fps and below, and so it can start to tumble at about 700 yards when fired from a 10" twist).

Sierra 168-grain SMK. 2605 fps MV in ICAO standard atmosphere (Mach 1 - 1116.8 fps)

0-100 yd .42704
0-200 yd .42659
0-300 yd .42775
0-400 yd .42788
0-500 yd .42694
0-600 yd .42443

100 fps slower:
Sierra 168-grain SMK. 2505 fps MV in ICAO standard atmosphere (Mach 1 - 1116.8 fps)

0-100 yd .42582
0-200 yd .42776
0-300 yd .42808
0-400 yd .42747
0-500 yd .42609
0-600 yd .42209
 
Box BC's are the G1 BC at a typical muzzle velocity for the bullet. G1 BC's usually decline with velocity, though you see a few bullet shapes where it can go up. and the 168 has some of that behavior.

I put an Excel plot together to show the drag coefficients for the G1, G7, and 168-grain SMK. You can see the shape of the G7 is much closer to that of the 168-grain SMK than the G1 is.



A ballistic coefficient is chosen to scale a bullet's drag to match that of a reference projectile as closely as it can. Here, your eye quickly tells you that if you apply the right scale factor to the 168 SMK drag curve to cause it to match either of the other curves at Mach 4, it's not going to match as well at Mach 1. Less obvious, without a magnifying glass is that matching them at Mach 2 won't have them matching at Mach 1.5, either. This is what multiple velocity range BC's are intended to improve upon (actually, you want multiple Mach number ranges, but there is an assumption you are shooting in a standard atmosphere). You can also find the best average BC for any particular range, which is what the coach was doing here.

Here, in a standard atmosphere, for a 168-grain SMK fired at 2605 fps (2550 fps at 78 feet from the muzzle, the military test barrel spec for M852) with its velocities after different yardages from the firing line determined by the drag function the BRL measured for this particular bullet, are the best G1 BC's for the first 600 yard increments of range. (Note that this bullet has a dynamic instability (attempts to overcorrect) starting at about 1400 fps and below, and so it can start to tumble at about 700 yards when fired from a 10" twist).

Sierra 168-grain SMK. 2605 fps MV in ICAO standard atmosphere (Mach 1 - 1116.8 fps)

0-100 yd .42704
0-200 yd .42659
0-300 yd .42775
0-400 yd .42788
0-500 yd .42694
0-600 yd .42443

100 fps slower:
Sierra 168-grain SMK. 2505 fps MV in ICAO standard atmosphere (Mach 1 - 1116.8 fps)

0-100 yd .42582
0-200 yd .42776
0-300 yd .42808
0-400 yd .42747
0-500 yd .42609
0-600 yd .42209
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Your numbers are fascinating to me; the first thing that jumps out to me is that the BC's is "dynamically adjusting" up and down--which to me suggests it is not a linear function of strictly of velocity/range. Are these based on actual recorded velocity/range numbers?

I have read of "optimal spin stabilization" required of bullets to reach a certain range--like a 300 win mag large bullet needing a minimum of two to three hundred yards to achieve optimal spin stability/accuracy. I have never understood how a projectile without control surfaces achieves that--I even wrote Bryan Litz once asking him about that and how exactly that happens (admittedly I'm a nobody amateur compared to the likes of him, but he does cite that in his literature) but unfortunately never heard back from him.
 
How did he know to do that?
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Years of experience and based on where your shots were impacting he made an educated guess as to how much to change the BC in your calculations.

As said BC changes with velocity. The .462 on the box is based on a specific expected MV. And as range increases velocity drops and BC changes. Every bullet maker uses a different method to calculate their bullets BC. All are accurate the way they shot them, but if you're velocity is vastly different, or if you're shooting at a different range than they tested the actual BC in your gun will be different.
 
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