Averaging Banded Ballistic Coefficients For Dummies

This article is exclusively for my Patreon Patrons and will never be published for consumption by the general public.

Isn’t is always this way. You ask someone for detailed information and it comes back entirely more detailed than you wanted meaning you’re either confused or annoyed or both. Bullet companies tend to provide G1 ballistic coefficient data as a single value. That value is averaged for the anticipated launch velocity of the bullet across its supersonic range in many cases but some like varmint bullets may be calculated/advertised based on their anticipated usage. This is done because G1 BC’s take velocity into account so as velocity changes, so does your effective BC.

So you might find an advertised BC from a light flat base varmint bullet is only accurate really to about 400yrds and then observed drops start to depart from calculated drops. Why? Well most varmint hunting is done inside 400yrds. They’re small targets. Nobody shoots them at 1000yrds and expects to hit them there.

Similarly, bullets optimized for long range target or battle applications will have the manufacturers design intent baked into their advertised BC. Ahhh, but not all bullet companies do this. Some are a great deal more pedantic than the average bear and that only serves to confuse us and make people do things wrong.

Who’s this pedantic? Well Sierra for one. They only advertise BC’s in bands. Hornady has also jumped on the getting it right bandwagon and has started publishing BC’s in bands (though they do theirs in Mach values which is as helpful as tits on a nun for most people). Many other companies do it too but the two above are the ones most of us give a crud about. Very few ballistics calculators allow for banded BC’s though so it can be a pain to deal with. Often I’ll just take the middle and low velocity values and average them directly and call that done.

One thing to note, BallisticXLR is about to incorporate banded BC’s as a feature because what we discuss below has some definite flaws to it and they show up across the board. This is one of the gotchas with G1 model ballistics. When you take this averaging too far you’re making more error. It’s a good way to reach about 85% or so of your max supersonic range with good data from about mid-range to impact. Short range calculations will likely be compromised in such a way that you end up shooting high.

Want the easy way? It really is easy and it’s nothing but a little add/multiply/subtract math against simple pairs of values which are easy as pie to identify. Here’s how. You should have your inputs put in with the highest advertised BC for the bullet you’re using. We’re going to correct the values for that and then update your inputs table but we need some info out of the gate. Start by opening up the Secondary Functions tab of BallisticXLR and looking at the remaining velocity and time of flight columns.

Secondary Functions table in BallisticXLR

Secondary Functions table in BallisticXLR

Here comes the math. Keep up. So you see in the image above the remaining velocity and time of flight columns. Good. That’s where we’re getting our data for the math part.

The way I calculate averaged BC’s is to take the percentage of total time of supersonic flight that a bullet is capable of within each velocity regime and then dividing that number by the total time of supersonic flight to get a percentage of total time of flight which is inside each velocity band. I do that for each velocity regime/band and then multiply the results by the stated BC for the velocity regime and then sum the results to get a properly averaged BC. So, let’s set up some example data.

Example BC Data: BC .585 at > 2600fps, .520 at < 2600fps, .480 <1800fps for a .264 cal 140gn bullet (Note: I pulled those BC numbers from my ass. This is an example after all.) You might note that I treat the values a little approximately. Well, we’re approximating a BC when we average several to get one so honestly we’re not really hurting anything. The differences between being insanely obsessive and being a very tiny bit loose with the numbers is going to land final BC differences in the +/- .00x range. It’s not going to be enough to cause any negative effect that the rifle being operated by a human won’t mask.

Other Ballistics Details: scope height 2 inches, MV 2800, calibre .264, bullet weight .140gn, twist 1 twist in 8 inches, barometer 29.92inHg, zero range 100yrds, temp 59F. This is as generic as things come right?

Ok, on to the math part.

In this case, there was 1.47 seconds of flight to 1000yrds (I cut it off there for the purposes of this example) composed of .11 seconds of flight over 2600fps (rounded) which peters out by 100yrds, and ~.82 seconds below 2600 but above 1800 and .54 seconds below 1800. Max range at supersonic is 1300yrds.

So the math was:
Divide time of flight in band by total supersonic time of flight
.11 / 1.47 = .074
.82 / 1.47 = .54
.54 / 1.47 = .369

Multiply results from above by state BC in appropriate band
.074 * .585 = .043
.285 * .520 = .289
.369 * .480 = .177

Sum results from last step to yield correctly calculated BC.
.043 + .289 + .177 = .509 to 1000yrds

You see, the BC that we calculate out is good only to a given distance. The .585  BC was good to 100yrds right? .520 was only good between 100yrds and  the .520 value is only good between 100yrds and 900yrds. Directly averaging the two would cause problems all over the place if taken much further. Let’s see how.

So the averaged BC in this case is .509 to calculate correctly for 1000yrds. I’d drop in .520 or .530 so it’s easier to remember later (round numbers) and so it’s not biasing so hard to the long end. With a 6.5mm bullet at that speed and with its ballistics it could do an easy 1300yrds supersonic. So let’s let’s see what happens if we do it for the full 1300 this time.

First, find total time of flight with max BC. In this case it’s 2.16 seconds.

So the math was:
Divide time of flight in band by total supersonic time of flight
.11 / 2.16 = .051
.82 / 2.16 = .378
.88 / 2.16 = .407

Multiply results from above by state BC in appropriate band
.051 * .585 = .0297
.378 * .520 = .1968
.407 * .480 = .1955

Sum results from last step to yield correctly calculated BC.
.0297 + .1968 + .1955 = .422 to 1300yrds

Once we do that and plug that number into the calculator though we see a MASSIVE reduction in supersonic range and it’s clearly wrong (see below). A bullet with that high of a BC and MV is known to get to 1300 in the densest air. That means, the process shown above has limitations.

Secondary Functions Table From BallisticXLR Showing Max Range Reduction From Taking BC Averaging Too Far.

So how do you deal with this? Well, honestly a lot of it is a combination of experience, intuition and going out and burning ammo to get observed data. This is why it’s important enough to have banded BC capability in your ballistics calculator that I’m adding it into BallisticXLR and BallisticPRS in an upcoming version.

Advertisements
%d bloggers like this: