学习笔记----Mean radius

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转帖， https://www.ar15.com/forums/t_3_16/512887_.html&page=1

MEAN RADIUS

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.



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. 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.



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”.)



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.



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



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).



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).



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!



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”.



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).



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.



The table below will give you an idea of the relationship between the mean radius and extreme spread.

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手工计算mean radius还是太繁琐了，好在现在有免费app可以使用，推荐 http://www.qiangyou.org/bbs/forum.php?mod=viewthread&tid=14575&extra=page%3D1 这个帖子里的app，iphone版叫sub moa。

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mean radius多用在比较严谨的场合，比如M24狙击步枪的精度要求

Accuracy: According to MIL-R-71126(AR), the M24 shall achieve the accuracy results stated below when using M118 Special Ball and fired from a Government approved machine rest. The average mean radius, calculated using 5 targets of 10 shots each, shall be less than or equal to the following values:[1]

200 yards (183 m): 2.6 inches (1.242 MOA)
200 metres (219 yd): 2.8 inches (1.223 MOA)
300 yards (274 m): 3.8 inches (1.146 MOA)

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那么来上喜闻乐见的靶纸和心得体会

现在打10发组为主了，主要是省子弹。打5X5最少要25发，打10发组的话，就算开始用5发10发热身的话也才20发就搞定了。而且1x10的参考价值至少应该在3x5以上。



这次明显不如上次，一开始先打了一组5发还凑合的，



第一发飞了，之后的4发很紧凑。看来新手还是要保持打实弹之前先用snap cap热身的好习惯，两块多一发的实弹糊里糊涂打飞了挺可惜的。

但是马上就发现肩膀很疼，flinch得厉害，后来的一个组简直没法要，完全压不住。注意力全部都集中在克服flinch上了，呼吸和扳机控制糊里糊涂。回家照镜子一看肩膀上锁骨末端青了一大块。卧姿和坐姿的抵肩位置不一样，坐姿打几十发都没感觉的。

还有这把枪打到这个时候已经差不多60发没清理了，是目前为止最长间隔的一次。

但是虽然不如上次的10发组精，却比上次的组准。10发组的光用最大散布的数值来衡量的话有点浪费。还有用mean radius计算的话flyer对精度的负面影响会比较小。