Ammunition accuracy measurements and acceptance standards

Good day, gentlemen
I’m looking for info on small arms ammunition accuracy measurements and acceptance standards

basically, what criteria is used to accept a batch of ammo for service? While looking at the Northrop Grumman / Lake City pamphlet I found numerous inconsistencies in listing accuracy of various round even in the same caliber (i.e. 5.56) as shown below:




Can someone please explain those differencies, and what is accepted standard procedure for ammo accuracy measurements and acceptanse (i.e. number of strings of shots, round count in each string, procedures of processing averages etc).

Similar info on non-US data and procedures also is most welcome

The M193 represents the old military system, in use for about a century:
Shoot a group of 10 shots and measure the coordinates of each impact.
From this, calculate the mean point of impact (MPI).
From the MPI, measure the radial distance of each of the shots.
Take the sum of the radii and divide by 10: this is the mean radius.

In typical acceptance tests, 9 shot groups were used and the average mean radius taken. In special cases, 180 shots (18 groups) were used. From a statistical point of view, mean radius is an excellent measure of dispersion, its quality comparable to standard deviation.

Adoption of M855 and M856 brought the change to compute the standard deviation in place of mean radius. It is computed for vertical and horizontal dispersion separately. At the same time, the procedure was changes from 9 groups of 10 shots to 3 groups of 30 shots. So the total of 90 shots was kept.
“Standard deviation”, a little complicated to describe, is used in engineering worldwide. You can look it up in any textbook or ask an engineer or a math teacher.
I would not be surprised if Dvoryaninov describes the above process in detail.

For the Western readers: In Russia, 20 shots are fired and the mean point of impact determined as above. Then the radial distance of each shot is measured as above.
Counting from inside out, the radii of the 10th and 11th impact are added and divided by 2. This is called R50 and used as the acceptance criterion. 3 groups are fired, meaning 60 shots.
This R50 figure can often be found on ammunition flyers from former Eastern Bloc manufacturers.

Caveat: The above is based on publicly available documents. Changes may have taken place.


I am not sure that there is much of an agreement among the various military services as to what a good “accuracy” standard is for small arms ammunition. I know for sure that the U. S. Navy operates on entirely different accuracy test procedures for small arms ammunition than the U. S. Army does, and to me it makes more sense. Their method is to fire five-10 shot groups from each of two test barrels, and determine the average extreme spread (ES) of the 10 shot groups (i.e., the average ES of five groups) at 300 yards from each barrel. Their standard is an average ES not exceeding 3.5" from each test barrel, with no single group exceeding 4.5" The firing is conducted on an enclosed indoor range which eliminates wind effects.

I have developed and performed computerized statistical simulation modeling and have concluded that relying on the average ES of at least five 10-shot groups is very efficient in providing a high degree of statistical confidence, which I define as the standard deviation of the average ES of five-10 shot groups being within 5% of the mean ES of a very large (actually infinite) number of 10-shot groups. I am not much of a believer in most of the other methods, and there are lots of them

For those who want to delve more deeply into the topic, I’d recommend a paper entitled “Statistical Measures of Accuracy for Riflemen and Missile Engineers” by Frank E. Grubbs, Ph.D. (1991). You can probably find it on the internet. It is extremely math-heavy. If you can’t find it, please contact me and I can probably send it as a PDF eMail attachment to you.

Thank you for your response. In some cases, like 7.62 mm M852, the Army also used Extreme Spread. I did not add more details because I had the feeling that my description already was too much on the technical side. The lack of any questions by readers shows that my feeling was right.

Your results are another proof of what most shooters overlook: A large number of shots is needed -you mention at least 50- to get a reliable answer.

By the way, the GRUBBS booklet can indeed be found on the Internet. The version with a date of the preface from 1991 or later should be used, not the 1964 version. Readers beware, if the above posts are too technical, that booklet is not for you.

It is not so much the number of shots which is important, but the number of shot pairs. The number of shot pairs in a single group is (n(n-1))/2, i.e, for a 5-shot group, the number of shot pairs is (5 x 4)/2 = 10. For a 10 shot group it is (10 x 9)/2 = 45 shot pairs. My analysis model indicates that for high statistical reliability, a minimum total of around 225 shot pairs are required (which is five 10-shot groups (5 x 45)). The same could be said about firing a single group of 22 shots: (22 x 21)/2 = 231 shot pairs. However, I feel it is much better to have more than one group in the average ES, and five 10-shot groups is indicated to be the practical optimum. Statistical reliability can be improved by firing more shots and more groups, but that also takes more time and requires more ammunition. Consider that the same logic applied to five-shot groups indicates that firing at least 22 groups (110 rounds fired) would be required to get the same level of statistical reliability in the average ES, i.e. (22x 21)/2 = 231 shot pairs as firing five 10-shot groups (50 rounds fired). There are some additional very interesting ramifications discovered in my analysis model, but I won’t get into them.

BTW, the Navy has provided me with some results of their testing on the Mk 262 Mod 1 5.56 round, including actual test targets, for comparison with my model.

Please corect me if I’m wrong, but isn’t ES conceptually similar to R100 (actually, ES = 2 x R100)?

So, basically, using average R100 for, say, several 20-shot strtings is a fairy accurate estimate for “infinite length” string?

Other measure widely used in Russia is R50 (radii of best 50% hits), which is also measured across several 20-round strings of fire, either from a test barrel or from a weapon being tested.

From a statistical view these are indeed very similar, but not the same.
Extreme spread is the largest distance between 2 shot holes, independent of the center of the group. That makes it so attractive, because ist extremey easy to measure.
R100 requires first to obtain the mean point of impact and only after that to measure the shot hole with the largest radial distance.

Both have in common that only extreme impacts are used for determining the dispersion. The statistical information provided by all the other shot holes of the group is ignored. In Russian literature you will find that no fixed relation between R100 and R50 is given, because of the exposure of R100 to random effects of the extreme shot. Dvorjaninov, for example, on p. 430 of vol. 4 shows a relation of R100 being 2.2 to 3.9 times R50. A comparable variation applies to extreme spread, according to the statistical simulations of 3 million normally distributed “shots”.
While several simulations of different populations of 3 million shots showed extremely small variations of mean values (4th decimal digit), the smallest and largest encountered extreme spread varied a lot. I assume the same would apply to R100, which I did not simulate.

Assuming R100 is the radius of a group of an infinite number of shots, it is possible to estimate it from the average extreme spreads of smaller groups, and my statistical model predicts it. I prefer to call it the diameter of the circle of maximum dispersion (CMD). I won’t go into the details, but the relationship of the average ES of at least five 10-shot groups to the ES of a group consisting of an an infinite number of shots is approximately 1.3. For example, if the average 10-shot group has an ES of 1", then the CMD would have a diameter of approximately 1.3". For an average of 5-shot groups, it is approximately 1.6. For 20-shot groups, it is approximately 1.15. For groups of 100 or more shots, the ES approaches the CMD, within 5%. Of course, the radii of the CMD would be half that. Note that my model assumes that large groups are approximately circular, and it is my experience that they are.

It seems to me we are using different defiitions of R100. My understanding of the normal distribution is that, mathematically, an infinite large numer of shots would have an infinite large dispersion.

Be that as it may, let me come back to the R50 and R100 as used in Russia. Measurements from a simulation of 150000 groups of twenty shots each (3 million shots) show the average R100 is 2.27 times larger than R50. But the real problem is the variation between them: the smallest is 1.16 times larger than the R50 of the same group and the biggest 6.50 times.
This means, there is in my view no useful relation between real ammunition dispersion and the R100 result, because this measure of dispersion varies by a factor around 6 for shot groups from the same (simulated) ammunition lot.
R100 is not alone in this regard. Extreme spread or the old method of adding vertical and horizontal spread have the same shortcoming of only using extreme shot locations and ignoring the rest of the group.