Josh's Marksmanship Blog

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Vertical Dispersion Experiment

Introduction

This is an experiment in modeling several ballistic curves. The genesis of this idea was in reading the recent issue of Rifle Firepower magazine – one of my favorites amongst the general tripe one can find in the bookstore. An article appeared in which the author attempted to reconstruct the record-setting sniper shot recorded in 2009, in which a British sniper achieved two hits at 2,707 yards. The article treated a number of the key elements, particularly equipment concerns when holding an incredible 200MOA above the target. Other factors, such as the environmental variables, were also treated at length.

But one key issue was not addressed, which stood out to me. As if there aren’t enough variables already in long-range shooting, I was interested in how significant the variability in performance of ammunition might affect the ability to successfully group hits on a man-sized target at that awesome range. It was my hypothesis that the inherent vertical dispersion of your grouping will increase non-linearly as range increases, which makes it more difficult to actually achieve small groups. Let’s get into the details…

Variable Ammunition Affects Group Size

Ammunition is not perfect. We like to talk about muzzle velocity as if it’s the same every time for a certain load, but there are various factors that introduce variance. Many handloaders study the quality of their loads by evaluating the standard deviation (SD) and extreme spread (ES) for their loads. If you can get your SDs and ESs lower, the increased consistency will improve groups. Since faster rounds typically hit higher on the target, this introduces a minimum vertical dispersion for your groups. Here’s a little chart I made to demonstrate how this effect works at range:

Graph showing extreme spread impact at long range

This graph shows several data sets. Starting with data for a 178gr Hornady Amax bullet at 2,675, I ran numbers through JBM Ballistic’s trajectory calculator for several simulated extreme spreads. By taking the high and low drop figures for each simulated load variance, I calculated the total vertical dispersion that results from these changes in velocity. E.g., the “ES 30fps” line shows the vertical difference between the 178gr Amax at 2,660 and 2,690 feet per second.

What you can see is that the variance in muzzle velocity has a non-linear effect. The spread has an essentially negligible impact on the vertical dispersion at less than about 400 yards (unless you’re a benchrest shooter, perhaps). But, by the time you reach 1,200 yards, the difference is quite substantial. If you are cursed with ammunition that varies by 50fps from round to round, you won’t (typically) be able to get a group smaller than 2.5MOA – at 1,200 yards, this is 31 inches! No matter how good your technique, you will need better ammunition before you can reliably hit a silhouette target.

Note that you could interpret the above chart as curves for the SD (standard deviation) instead of the ES (extreme spread) – in which case, you can just expect that about 2/3s of your rounds fit within the stated vertical dispersion, and you will get some fliers every once in awhile.

Real World Numbers

Sniper Central prepared an excellent 308 match load analysis that gives us a good sense for what this will look like in the real world. According to their testing, quality match loads vary in SD from 9.26 to 33.05 feet per second. The extreme spreads (which will encompass statistically aberrant fliers) go as high as 91fps!

Conclusions

I offer several conclusions:

  • If you’re shooting under 300 yards or so, you really don’t have to care about the variance in velocity of your loads, unless you’re trying for groups less than a quarter minute.

  • Confirmed hits at extreme ranges really do put the shooter’s equipment to the test.

  • Stephen Hunter’s book, I, Sniper features “perfect geometric shot placement” as a plot device. I found this part of the book very hard to believe, particularly due to the influence of velocity variance in ammunition impacting POI.

  • The variance of your ammunition’s muzzle velocity is a bigger concern the longer the range.