analysis

Shot Point Accuracy Analysis – Coming Soon!

Several years in the making and the stars have finally aligned. Bison Armory will be releasing the alpha version of Shot Point, our camera based accuracy analysis system. Unlike any other system on earth, Shot Point calculations are based on the work of David Bookstaber at www.ballistipedia.com and our own proprietary analysis.

In addition to correct calculations of mean radius, we include 90% confidence intervals for the results so you can see in real time how meaningful the data is regarding true accuracy of your rifle. And unlike anyone else we do this for extreme spread as well. Based on the nature of your group we can determine the expected 3 and 5 shot extreme spread as well as a 90% confidence interval around this value. The point being – you can’t fool yourself into believing your results are more accurate than they really are – a huge problem in accuracy analysis until now.

You can read more about accuracy analysis on an old blog post here:

MOA, Sub MOA, and Accuracy Indicators

Super simple to set up and easy to use. We provide everything but a tripod and Windows 11 laptop or tablet (or Mac running Parallels or similar Windows virtualization software). Simply mount the camera, point it at the target, plug it into the computer, and fire up the program. Works from 25 to 200 yards, though we find 50 to 100 yards is best for most weapons in order to analyze accuracy with minimal effects from wind. Extremely accurate rifles, such as F-Class and Benchrest benefit from 200 yard analysis so the target doesn’t get shot out – Shot Point has to see the holes to analyze them!

Future releases will have a Benchrest mode where up to 20 or even 30 individual targets can be engaged on the single sheet of paper that you print yourself at home. In this way the shooter can take up to 30 independent shots and have them combined into a single composite group for analysis. The data is all saved in csv format so you can recall, plot, and analyze offline later.

And you NEVER lose your data – if something goes wrong you can start over and just pick the bullet holes on paper and Shot Point will re-analyze the target. Several groups can be shot on a single target – just move your windage and elevation around a couple MOA to engage a clean are of the paper and fire away. Shot Point is also highly adept at picking out overlapping bullet holes in the paper and figuring out where the bullet center was located.

That image is from an old session – we have a NRA Highpower Match mode that was giving the scores above which was not applicable in analysis mode. This image demonstrates three groups shot on the same target and the relative analysis for the third group (in green). You can see on the left the zero-correction for the group, extreme spread analysis (The 9 shot group has an ES of 0.87 MOA), the mean radius of 0.32 MOA, and the 90% confidence intervals around these estimates.

We’re still working on the GUI and will be fixing some simple bugs soon. If you are interested in obtaining the system, the cost is planned to be $400 including the camera, 500mm f8 lens with tripod adapter, SB-C cable, and the software application. Early adopters will get free software updates for life. We have been testing and will eventually add a laser based dry-fire option that works out to 100 yards at the rifle range so you can see how well you perform without recoil and without using up expensive ammo. A great training aid for beginners and experts alike.

Case Volume and Loading for Long Range Precision: Part 1 The Basics

All long range competitive shooters agree that ammunition must be accurate at short range in order to be accurate at long range. They also know that this is a necessary condition, but not a sufficient one. In addition, the ammunition should have very low variation in muzzle velocity and the bullets should have a good ballistic coefficient.

Many factors influence muzzle velocity, and variation in these factors will lead commensurate variation in muzzle velocity. These include:

  • Powder charge
  • Case neck tension
  • Case mouth uniformity
  • Flash hole uniformity
  • Primer consistency
  • Bullet weight
  • Bullet seating depth
  • Case volume
  • Recoil technique (strange but true – a topic for another post)

Each of these factors has a limit to which we can minimize variation, and at some point the effort to decrease variation leads to diminishing returns. In this article I will consider ammunition that is between reasonably and superbly controlled for most of the factors in the list and both how and how much controlling additionally for case volume can result in improved variation in muzzle velocity.

Suppose Case Volume was the Only Factor

The simplest place to start is with ammunition that is perfect in every way except for variation in case volume. Quickload and experiment have both shown that for many typical cartridges, powders, bullets, etc., muzzle velocity varies with case volume at a rate of approximately 20 fps to 30 fps per grain of H2O as a measure of case capacity. From here I will use “grains” in place of “grains H2O”, the “H2O” being implied.

Consider ammunition from a simulated population of 500 284 Win cases in which the volume of the cases is normally distributed about a mean of 69.1 grains with a standard deviation of 0.175 grains. I got the mean and SD used here from real world measurement of 100 cases. Assuming that a case with 69.1 grains capacity produces 2800 fps muzzle velocity for a 180 grain Berger Hybrid, and a 20 fps per grain volume variation, a randomly generated population is shown in the following graph:

Most of the muzzle velocities are centered around 2800 fps as expected and we see a high an extreme spread of about 20 fps, which is not surprising since the population of cases has an extreme spread of case volumes that is about 1 grain.

So what does this mean in practice? How will this otherwise perfect lot of ammunition shoot, all else being perfect? Using a typical G1 drag model for the Berger 180 Hybrid we get the following vertical distribution on paper from 600 to 1000 yards down range:

And again with vertical dispersion measured in minutes of angle instead of inches:

I prefer looking at the plot that shows POI vertical variation in minutes because it is easier to relate to score in high power rifle competition. At 200 yards the vertical variation is very small at just over +/- 0.1 minutes. I don’t know many people outside short range bench rest who would lose too much sleep over that. At 600 yards we’re approaching +/- 0.5 minutes, now that’s something. In Service rifle that can cost you an X or a point, and in F-Class we are definitely talking points to lose for a shot that would otherwise be near the inside edge of scoring a 10, and at 600 yards these days, X-count often separates winners and losers.

For those of us who shoot long range matches, which are typically from 800 to 1000 yards and shot on an LR or LR-F target, you can see that we’re talking serious points to lose with the vertical spread approaching +/- 1 moa.

Adding Measurement Error

We cannot measure case capacity perfectly. How much does measurement error influence our results so far? With the Bison Armory Case Capacity Gauge, I have performed some experiments to determine measurement error and a normal distribution with zero mean and standard deviation of 0.025 grains fits the data. Adding random measurement error to the muzzle velocity vs case capacity shown earlier, in which we keep the muzzle velocity where it was for the perfect case and only vary the measurement due to error we get the following:

I think it is clear from this figure that case capacity measurement error is not a significant factor. If case volume was the only contributor to muzzle velocity variation, and we can measure case capacity as accurately as indicated in the figure, then it would be a simple thing to produce a batch of ammunition for a match that had minimal velocity spread.

Of course it’s not so simple. In the next post I’ll add muzzle velocity variation from all other sources and we’ll see how that complicates matters, and also how to make the best use of case capacity measurements to decrease muzzle velocity dispersion.

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