MEAN RADIUS
The mean radius is the method of measurement of the dispersion of shot-groups used by the US Military for accuracy testing of ammunition. It provides a more useful analysis of the consistency of ammunition and rifle accuracy.
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.
http://home.comcast.net/~gocartmozar...example_02.jpg
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).”
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 using the group from the above target. 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.
http://home.comcast.net/~gocartmozart/group1_graph.jpg
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”.)
http://home.comcast.net/~gocartmozar...01_resized.jpg
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.
http://home.comcast.net/~gocartmozar...02_resized.jpg
Next, find the left-most shot of the group and draw a vertical line through the center of that shot.
http://home.comcast.net/~gocartmozar...03_resized.jpg
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).
http://home.comcast.net/~gocartmozar...05_resized.jpg
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).
http://home.comcast.net/~gocartmozar...06_resized.jpg
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!
http://home.comcast.net/~gocartmozar...08_resized.jpg
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”.
http://home.comcast.net/~gocartmozar...09_resized.jpg
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).
http://home.comcast.net/~gocartmozar...10_resized.jpg
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.
http://home.comcast.net/~gocartmozar...11_resized.jpg
