Acceptable mean radius..

[2ac]

I've been working up an MK262 load and am wondering if a mean radius of .6 is considered acceptable. I'm using TAC and Nosler to get a bit over 2700fps..
This is nowhere near my target load. It's just for shooting steel, things that might need shot, etc..

[Molon]

First off, simply stating a mean radius of "X.X" inches means nothing. You need to associate the mean radius with a distance and the number of shots in the group to give it meaning.

Here's a little reference material to help you in your quest.




“MATCH GRADE”


Unlike caliber .30 and caliber 7.62mm ammunition, there has never been a National Match standard for caliber 5.56mm/.223 Remington ammunition.

In 1965, the caliber 7.62mm Match ammunition was standardized as M118 . The 1965 lot of 7.62mm M118 National Match ammunition had an acceptance testing mean radius of 1.9” for 10-shot groups fired at 600 yards. At that time, this was the smallest acceptance mean radius ever achieved for National Match ammunition since records were kept, starting in the year 1919. Naturally, the ammunition was tested from machine-rested, bolt-actioned test barrels. The composite target pictured below shows the twenty-seven, 10-shot acceptance groups (that’s 270 rounds!) of the 1965, M118 National Match ammunition fired from the test barrels at 600 yards. The small circle has a diameter of 6” and the large circle has a diameter of 12”.





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From American Rifleman, September 1965






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From American Rifleman, August 1962.





Everything else being equal, (which of course, it seldom is) a mean radius of 1.9” at 600 yards would have a mathematical equivalent of 0.32” at 100 yards. Now, 100 yards is not 600 yards, but then, a semi-automatic AR-15 is not a machine-rested, bolt-actioned test barrel either. For this reason, I like to use the mean radius of 0.32” for 10-shot groups fired at 100 yards as the benchmark for match-grade ammunition, when fired from a semi-automatic AR-15. I personally prefer that my match-grade hand-loads have a mean radius “in the twos,” i.e. a mean radius of 0.2x”. My best hand-loads fired from a semi-automatic AR-15 at 100 yards have had mean radii “in the ones,” i.e. a mean radius 0.1x”.




Range Report: Black Hills MK262 Mod 1


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The 77 grain MK262 ammunition produced by Black Hills Ammunition has been referred to as the most accurate mass-produced 5.56mm ammunition that has ever been type-classified and issued by the US Army. Since its inception, genuine MK262 has been manufactured solely by Black Hills Ammunition. For years, MK262 was only available to the civilian population as “seconds,” but more recently Black Hills has made first-run production lots available on the commercial market. It is the first-run version of MK262 Mod 1 that I tested for this report.

MK262 Mod 1 is loaded in WCC 5.56mm brass and uses a cannelured version of the 77 grain Sierra MatchKing. The round is charged with a proprietary ball powder.



The 77 grain MK262 Mod 1 projectile compared to the M193 projectile.

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MK262 powder. (The squares of the red grid measure 1/10 of an inch.)

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The specification for accuracy testing of MK262 calls for multiple 10-shot groups to be fired; which is exactly what I like to do for a range report. An accuracy (technically, precision) evaluation of the first-run MK262 Mod 1 ammunition was performed following my usual protocol. This accuracy evaluation used statistically significant shot-group sizes and every single shot in a fired group was included in the measurements. There was absolutely no use of any Group Reduction Techniques (e.g. fliers, target movement, Butterfly Shots).

The shooting set-up will be described in detail below. As many of the significant variables as was practicable were controlled for. Also, a control group was fired from the test-rifle used in the evaluation using match-grade, hand-loaded ammunition; in order to demonstrate the capability of the barrel. Pictures of shot-groups are posted for documentation.

All shooting was conducted from a concrete bench-rest from a distance of 100 yards (confirmed with a laser rangefinder.) The barrel used in the evaluation was free-floated. The free-float handguards of the rifle rested in a Sinclair Windage Benchrest, while the stock of the rifle rested in a Protektor bunny-ear rear bag. Sighting was accomplished via a Leupold VARI-X III set at 25X magnification and adjusted to be parallax-free at 100 yards. A mirage shade was attached to the objective-bell of the scope. Wind conditions on the shooting range were continuously monitored using a Wind Probe. The set-up was very similar to that pictured below.



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The Wind Probe.

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The test vehicle for this evaluation was one of my semi-automatic precision AR-15s with a 20” stainless-steel Lothar Walther barrel. The barrel has a 223 Wylde chamber with a 1:8” twist.

Prior to firing the MK262 ammunition, I fired a 10-shot control group using match-grade hand-loads topped with the Sierra 77 grain MatchKing. That group had an extreme spread of 0.69”.



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Next, three 10-shot groups of the MK262 Mod 1 were fired in a row with the resulting extreme spreads (from smallest to largest):

0.96”
1.12”
1.21”

for a 10-shot group average extreme spread of 1.10”. The three 10-shot groups were over-layed on each other using RSI Shooting Lab to form a 30-shot composite group. The mean radius for the 30-shot composite group was 0.33”. For those of you who might not be familiar with the mean radius, I’ve posted some information about it below.




The smallest 10-shot group.

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The 30-shot composite group.

https://app.box.com/shared/static/oql8zrpvdaefx6zc5s5xcxtpcugcd0bg.jpg

[Molon]

A PRIMER ON THE MEAN RADIUS

The Mean radius is a method of measurement of the dispersion of shot-groups that takes into account every shot in the group. It provides a more useful analysis of the consistency of ammunition and firearms (accuracy/precision) than the commonly used method of extreme spread.

The typical method used to measure a group consists of measuring the distance between the centers of the two most outlying shots of a group. This would be the “extreme spread” of the group. We are essentially measuring the distance between the two worst shots of a group. Take a look at the two targets below.




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Most people would intuitively conclude that the second target shown is the “better” group. Measuring the two groups using the extreme spread method, we find that both groups measure 2.1”. Once again with the typical method of measuring groups we are measuring the distance between the two worst shots of the group. This method tells us nothing about the other eight shots in the group. So how can we quantitatively show that the second group is better than the first? (Yes, we could score the groups using “X-ring” count, but this does not give us any differential information about all those shots in the X-ring.) This is were the mean radius method comes in. It will give us that extra information we need to better analyze our groups, rifles and ammuntion. If I just reported the measurements of the two groups above using the extreme spread meathod, without a picture, you would assume that the two groups were very much the same. Using the mean radius method shows that the second group is much more consistent. It has a mean radius of 0.43” compared to 0.78” for the first group.

Mean radius as defined in Hatcher's Notebook “is the average distance of all the shots from the center of the group. It is usually about one third the group diameter (extreme spread)” for 10-shot groups.

To obtain the mean radius of a shot group, measure the heights of all shots above an arbitrarily chosen horizontal line. Average these measurements. The result is the height of the center of the group above the chosen line. Then in the same way get the horizontal distance of the center from some vertical line, such as for instance, the left edge of the target. These two measurements will locate the group center.

Now measure the distance of each shot from this center. The average of these measures is the mean radius.

Once you get the hang of measuring groups using the mean radius it becomes very simple to do. While being very simple to do, it is also very time consuming. Modern software programs such as RSI Shooting Lab make determining the mean radius a snap.

The picture below is a screen snapshot from RSI Shooting Lab. The red cross is the center of the group (a little high and right of the aiming point). The long red line shows the two shots forming the extreme spread or group size. The yellow line from the red cross to one of the shots is a radius. Measure all the radii and take the average to obtain the mean radius.




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Mean Radius Demonstration

Let’s say you fired a 5-shot group from 100 yards and the resulting target looks like this. (The X-ring measures 1.5” and the 10-ring measures 3.5”.)




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The extreme spread of the group measures 2.83”, but we want to find the mean radius (or average group radius.) In order to find the mean radius we must first find the center of the group. By “eye-balling” the target most people would see that the group is centered to the left of the “X-ring” and probably a little high, but we need to find the exact location of the center of the group.

Locating the Center of the Group

The first step in finding the center of the group is to find the lowest shot of the group and draw a horizontal line through the center of that shot.




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Next, find the left-most shot of the group and draw a vertical line through the center of that shot.




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Now measure the distance from the horizontal line to the other four shots of the group that are above that line. Add those numbers together and divide by the total number of shots in the group (5).




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2.50” + 1.03” + 2.01” + 1.30” = 6.84”

Divide by 5 to get 1.37”. This number is the elevation component of the center of the group.

Next we need to find the windage component of the center of the group. From the vertical line, measure the distance to the other four shots of the group that are to the right of the line. Add those numbers together and again divide by the total number of shots in the group (5).




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1.76” + 2.54” + 0.45” + 1.19” = 5.94”

Divide by 5 to get 1.19” This is the windage component of the center of the group.

Finding the windage and elevation components of the center of the group is the most difficult part of this process. Once that is done the rest of the process is a piece of cake.

Using the windage and elevation components, locate the position on the target that is 1.37” (elevation component) above the horizontal line and 1.19” (windage component) to the right of the vertical line. This location is the center of the group!




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Determining the Mean Radius

Now that we have located the position of the center of the group, the first step in determining the mean radius is to measure the distance from the center of the group to the center of one of the shots. This line is a single “radius”.




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Now measure the distance from the center of the group to the center of each of the rest of the shots in the group. Add the measurements of all the radii together and then divide by the total number of shots in the group (5).




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0.85” + 1.35” + 1.38” + 0.84” + 1.61” = 6.03”

Divide by 5 to get 1.21”. This is the mean radius (or average group radius) of the group!

Using the mean radius measurement to scribe a circle around the center of the group gives you a graphic representation of the mean radius. This shows the average accuracy of all the shots in the group. This demonstrates why the mean radius is much more useful than the extreme spread in evaluating the accuracy of our rifles and ammunition.




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The table below will give you an idea of the relationship between the mean radius and extreme spread for 10-shot groups.




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