AR Sponsor
Posted: 6/25/2016 5:40:10 PM EDT
|
The AR-15 Accuracy and Precision Series
Index Post #02 - The Essentials of an Accurate AR-15 Post #03 - Accuracy versus Precision Post #04 - A Primer on the Mean Radius Post #05 - AR-15 Bench-Rest Methodology Post #06 - The Texas Sharpshooter Post #07 - The Internet Commando’s Nephew Post #08 - The Trouble with 3-Shot Groups (abridged version) Post #09 - An Accuracy Comparison of Three Different Barrel/Ammunition Combinations Post #10 - Why Not 20-Shot Groups? Post #11 - Observations On The Points of Impact Of Statistically Significan Shot Groups Sizes Post #12 - Reproducibility Post #13 - Rate of Fire Comparison For Accuracy Testing With a 24" Krieger Barrel Post #14 - “Match Grade” Post #15 - Maximum Shot Radius and Covering Circle post #16 - A Note on AR-15 Barrel Break-In Post #17 - Random Quotes on the Passing Scene Post #18 - to be continued . . . ... |
|
#02
The Essentials of an Accurate AR-15 
Without making this overly complicated, you need three basic components for a semi-automatic AR-15 to produce its best mechanical accuracy (technically, precision): a match-grade barrel, a quality free-float handguard and match-grade ammunition, preferably hand-loads tuned for your barrel. (The free-float handguard doesn’t add to the accuracy of the barrel per se, it simply prevents any outside influence from detracting from the accuracy of the barrel.) Anything after that will not immensely improve the mechanical accuracy of the semi-automatic AR-15, but several things can help you, the shooter, shoot to the level of the intrinsic accuracy of your semi-automatic AR-15. 
While there are certainly gifted individuals among us that can do amazing things with iron sights, most of us will benefit from using a quality, high-power scope to achieve the highest level of accuracy/precision from an AR-15. In order to hit the exact same spot on the target every time, you have to be able to see that you are holding on the exact same spot every time. It’s also important for the scope to be mounted at the proper height and at the correct eye-relief for the particular scope. One of the most common errors I see with scopes mounted on AR-15s is the scope not being mounted far enough forward for its eye-relief. In order to maintain that exact hold on the target throughout the trigger pull, it helps not to be fighting with a heavy, gritty, stock trigger. There are a variety of aftermarket triggers now on the market for both standard size trigger pins and the larger Colt trigger pins. Personal preference will definitely play a role in trigger selection. Among the two-stage triggers, I’ve found the Geissele triggers to be the smoothest, lightest, most consistent and most reliable. For single-stage triggers, it’s hard to beat the JP Enterprise Fire Control System. Keep in mind that the JP trigger does require fitting. Following the scope and trigger selection, some shooters will find that items like aftermarket grips and stocks will help them achieve a better “fit” with their AR-15. (Shooters don’t all come in the exact same size and shape.) Once you’ve put your accurate rig together, you have to find a match-grade factory load that your barrel “likes” or better yet, develop a match-grade handload for it. A semi-automatic AR-15 is not going to shoot to the same level as a precision bolt-gun, but today’s precision AR-15s are capable of a level of accuracy/precision that is truly outstanding for a semi-automatic rifle. The 10-shot group pictured below was fired from one of my Krieger barreled semi-automatic AR-15s from a distance of 100 yards. I used Sierra 55 grain BlitzKings that were hand-loaded on a Dillon XL-650 progressive press. The group has an extreme spread of 0.474”. 
…. |
|
#03
Accuracy versus Precision Pictures, a thousand words, yada, yada, yada. (The aim-point for all examples below is the "X".) Low level of precision and low level of accuracy . . . 
High level of precision and low level of accuracy . . . 
Low level of precision and high level of accuracy . . . 
High level of precision and high level of accuracy . . . 
Even when using factory loaded ammunition, today's semi-automatic AR-15s can be very accurate and precise. The 10-shot group pictured below was fired from a semi-automatic AR-15 at a distance of 100 yards. 
..... |
|
#04
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. 
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. 
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. 
Over-laying the targets of at least three, 10-shot groups fired in a row and determining the mean radius of the composite group gives us a statistically powerful tool for evaluating the radial dispersion of a rifle/ammunition combination. 
The table below will give you an idea of the relationship between the mean radius and extreme spread for 10-shot groups. 
.... Here are some interesting quotes pertaining to the mean radius from old issues of American Rifleman: “Mean radius is the mean distance of bullet impacts from center of the test group. It is used in government ammunition acceptance because it takes account of every shot and comes close to maximizing the test information. While there is no exact relationship between this measure and the simpler and more convenient group diameter, the 10-shot group diameter averages slightly over 3 times the mean radius.” "These examples illustrate the sensitiveness of the extreme spread to number of shots in the group. Indeed, as the table indicates, the measures made to only the outside shots of the group, e.g. the extreme spread, are very sensitive to number of shots, while the measures made to all the shots, e.g. the mean radius are far less so. It may be added that the latter measures are also less variable in their representation of the group; they are more efficient. This explains why the target testing of U.S. military rifle ammunition is by mean radius." ... |
|
#05
AR-15 Bench-Rest Methodology Most of the accuracy (technically, precision) evaluations obtained for this series of articles were conducted using my AR-15 bench-rest set-up. The shooting set-up will be described in detail below. As many of the significant variables as was practicable were controlled for. Typically, shooting is conducted from a concrete bench-rest from a distance of 100 yards (confirmed with a laser rangefinder.) The barrels used in the evaluations are free-floated. The free-float handguard of the rifle rests in a Sinclair Windage Benchrest with the aid of a forend adaptor, while the stock of the rifle rests in a Protektor bunny-ear rear bag. Sighting is typically accomplished via a Leupold VAR-X III set at a magnification of 25X and adjusted to be parallax-free at 100 yards. A mirage shield is attached to the objective-bell of the scope. Wind conditions on the shooting range are continuously monitored using a Wind Probe. The set-up is very similar to that pictured below. 
The Wind Probe. 
Atmospheric conditions on the range are monitored and recorded using a Kestrel 4000 Pocket Weather Tracker. 
This bench-rest methodology has enabled me to obtain some excellent results using a semi-automatic AR-15. 
... |
|
#06
The Texas Sharpshooter (Second Cousin of the Internet Commando) Envious of all the attention his cousin, the Internet Commando, receives at the local tavern, as well as on the popular firearms forums on the Internet, our antagonist decides it is time for him to make his mark in the world. He decides he needs to perform some feat of marksmanship that surpasses even the accomplishments of his cousin, the Internet Commando. But what can he possibly do that the Internet Commando hasn’t already done? Our antagonist recalls the tales of the Internet Commando. He remembers his cousin boasting of shooting sub-minute of angle groups using XM193. How could he possibly top that? Then, it dawns on him. The Internet Commando was using his sights when he fired those sub-minute of angle groups with XM193. “Anyone can shoot a small group using their sights,” he thinks to himself. “It would take real skill to shoot a good group without using the sights, say . . . as in shooting from the hip!” Seeing his destiny laid out before him, our antagonist sets up his target at 25 yards and proceeds to fire on the target shooting from the hip. As our antagonist walks towards his target to examine his results he begins to grin from ear to ear. “Wait until my cousin sees this,” he actually speaks aloud. That night at the local tavern our antagonist shows his target (pictured below) to those who have been hanging on every word that his cousin, the Internet Commando has been saying. The people are absolutely astonished that our antagonist was able shoot such an amazing group firing from the hip at 25 yards. Bewildered by the incredible skill demonstrated by our antagonist, the Internet Commando tells his cousin, “You’re quite the sharpshooter Tex!” 
While the above fable is fictitious, it is based based on a real target that I fired from an AR-15. I actually fired that group pictured above from 25 yards while shooting from the hip. For those of you that haven’t already figured out how I was able to perform such a feat, here are the little details that Texas Sharpshooters fail to mention. I actually fired 30 shots from the hip at the “target” which was a blank piece of paper measuring 36” X 24” (kind of like the broad side of a barn). I then found 3 shots that formed a cluster and “drew” the bulls-eye around the shots. Those 3 shots occurred randomly. Not from any outstanding shooting skills of mine, nor from any outstanding qualities of the rifle or ammunition I was using, but purely by chance. (The actual extreme spread of the 30-shot group was 31”; that's 2 feet, seven inches.) The fallacy of the Texas Sharpshooter is based on the fact that clusters of data can occur randomly or by chance (the clustering illusion). “In making statistical observations, results will not be distributed with total uniformity but will naturally be sparser in some areas and denser in others, purely by chance.”* Human beings tend to want to discern patterns in random clusters where none actually exist. We try to assign significance where there isn’t any. In the case of the Texas Sharpshooter “information that has no relationship is interpreted or manipulated until it appears to have meaning.”* More specifically, “although the shots were random, the Texas Sharpshooter makes it appear as though he has performed a highly non-random act. In normal target practice, the bulls-eye defines a region of significance, and there's a low probability of hitting it by firing at random. However, when the region of significance is determined after the event has occurred, any outcome at all can be made to appear spectacular.”* If you had not known that the Texas Sharpshooter had drawn the bulls-eye after the shots were fired, you would “falsely assume he's an excellent marksman by reasoning from effect (bullet holes in the bulls-eye) to cause (he fired the bullets).”* The fatal flaw is “assigning significance to the outcome of a random event after it has occurred.”* The danger is in “jumping to a conclusion that a random cluster is a causal pattern.”* The Texas Sharpshooter “takes a random cluster, and by drawing a bulls-eye onto it makes it appear to be causally determined.”* Here is a pic of the target before the bulls-eye was drawn on it, shown with a yardstick on the left border. 
Here is the target in negative. 
Lastly, the target in negative with the random cluster (actually two random clusters) highlighted. 
*Sentences in quotation marks are from multiple unknown authors. …. Two schools of thought pertaining to the Texas Sharpshooter: “We are Texas Sharpshooter.” The Borg Collective model. 
“There can be only one!” The Highlander construct. 
.... |
|
#07
The Internet Commando’s Nephew The scene opens with Billy rushing into his house to tell his mother of his accomplishments while at the shooting range with his uncle that afternoon. Billy: Guess what, Mom! I can shoot sub-MOA groups all day long with my chrome-lined, NATO chambered AR-15 using XM193 ammunition. I’m a real Internet Commando now! Mother: Billy, how many shots were in those groups? Billy: Aw, gee Mom. They were only 3-shot groups, but all the other kids are shooting 3-shot groups. Mother: And if all the other kids jumped off a bridge, would you do that too? Billy: No, Mom Mother: Billy, you know that 3-shot groups aren’t good for you. What have your father and I told you about 3-shot groups? Billy: 3-shot groups don’t mean jack-shit? Mother: That’s right, Billy. So how many of those 3-shot groups of yours were actually sub-MOA.? Billy: Well . . . only two. Mother: And how many groups did you actually fire? Billy: Five. Mother: Billy . . .? Billy: Ok, it was ten groups. You happy now? Mother: So you fired ten, 3-shot groups and CHERRY- PICKED two groups to brag about? Your father and I raised you better than this, Billy. Billy: Sorry, Mom. Mother: Sorry doesn’t cut it, young man. I’m going to have a long talk with your uncle and you’re no longer allowed to log-on to glock-gab.com. That site is rotting your brain. Billy: But Mom! Mother: No buts, Billy. And the only reason that I haven’t grounded you is because you haven’t used the “F” word. Billy: You mean f . . . l . . . Mother: Watch it, Billy. Billy: Flier! (Billy turns and runs to his bedroom as fast as he can.) Mother: That’s it! You’re grounded, and just wait until your father gets home! This is all because of that uncle of yours!” After Billy finished his week of being grounded, his parents decided to supervise an experiment at the shooting range with him to reinforce the folly of using 3-shot groups to evaluate the accuracy of an AR-15 rifle/ammunition combination. Shooting from a bench-rest at a distance of 100 yards using his father’s Krieger barreled, semi-automatic AR-15 (Billy’s actually a pretty good shot for his age) and using his father’s hand-loads topped with Hornady 55 grain FMJ projectiles, they had Billy shoot thirty shots in a row (each round was single-loaded) on thirty different targets; one shot per target (all while monitoring the wind conditions on the range using a Wind Probe). (Prior to Billy shooting his thirty shots, Billy’s father fired a sub-MOA 10-shot control group from the same rifle.) They then collected their targets and headed home to continue the experiment. Once at home, they entered each of the thirty individual targets into the computer using the software program RSI Shootng Lab. Next, they used the software program to form ten, 3-shot groups from the thirty individual shots. (The first 3-shot group was formed from shots 1-3, the second 3-shot group was formed form shots 4-6 and so on.) The results are pictured below. (The point-of-aim for the groups shown below is the double white circle.) 
The ten, 3-shot groups. 
Billy’s parents pointed out to him that the 3-shot groups had wide variations in their extreme spreads from shot-group to shot-group. The extreme spread of the largest group (group number 8) was five times as large as the smallest group (group number 2). They also pointed out the centers of the various 3-shot groups varied quite a bit in their location from the point-of-aim. For example, all three shots from group number 3 where higher than the point-of-aim, while all three shots from group number 4 where lower than the point-of-aim. Also, the center of group number 3 was to the left of the point-of-aim, while the center of group number 4 was to the right of the point-of-aim. (If Billy’s uncle had fired those ten, 3-shot groups, he would have cherry-picked group number 2 and group number 5 to represent the accuracy/precision of his AR-15 rifle and ammunition and pretended that the other eight groups didn’t exist.) Next, Billy’s parents had him form three, 10-shot groups from the thirty individual shots using the software program. (The first 10-shot group was formed from shots 1-10, the second 10-shot group was formed from shots 11-20 and the third 10-shot group was formed from shots 21-30.) The results are pictured below. 
Upon seeing the 10-shot groups pictured above, Billy immediately noticed how much smaller the variations in extreme spreads were from shot-group to shot-group. In fact, the extreme spread of the largest 10-shot group (group number 3) was only 1.5 times as large as the extreme spread of the smallest 10-shot group (group number 1). Billy even pointed out to his parents that the centers of the three 10-shot groups were all located very similarly from the point-of-aim. “That’s my boy,” cheered Billy’s mother. Billy’s father proudly remarked to Billy, “So now you see why 10-shot groups give us a much better picture of the actual radial dispersion of the shots fired from a rifle/ammunition combination.” Billy’s father went on to explain, “And if we over-lay three 10-shot groups that were fired in a row on each other and use the mean radius of the 30-shot composite group that is formed, we get a very good indication of the radial dispersion produced by a rifle/ammunition combination.” 
Billy then asked his parents, “Should I try to explain this stuff to Uncle?” His father replied, “You can try . . .” .... The shot-groups depicted in the above fable are from my actual targets obtained during live-fire testing. .... |
|
#08
The Trouble With 3-Shot Groups (The Distant Prequel to The Trouble With Tribbles) As our story begins, we find our Hero sitting down at the shooting bench on the 100 yard line at his local range. Our Hero is a real Internet Commando. He has watched the movie Heat 87 times, is registered on all of the important Internet firearms forums, knows the difference between a "clip” and a "magazine” and attends every local gun show without fail. His latest acquisition from the local gun show is a 16” barreled Frankengun that originally belonged to a Delta Force operator who was at the Battle of Mogadishu. (He could tell you the name of the operator, but then he’d have to k……well, you know.) The seller at the gun show let our Hero in on another secret too. Eugene Stoner himself helped the Delta operator assemble this particular AR-15. Our hero settles into position on the bench and fires his first 3-shot group. (He only fires 3-shot groups because everyone from the Internet knows that you only have to fire 3-shot groups to test the accuracy of your rifle and ammunition.) His first group forms a nice little triangle at the bottom of the 10-ring. Our Hero just knew this was going to be a good day. After all, he was using that XM193 ammunition. A former SEAL who was selling beef jerky at the gun show had told our Hero that the SEALs used ammo just like XM193 in Viet Nam and that a single shot in the buttocks from this ammo would "blow your head clean off!” At the cease fire our Hero checks his first target. (Our Hero’s targets are NRA High Power type targets reduced for 100 yards. The X-ring measures 1.5” and the 10-ring measures 3.5”). Much to his satisfaction, his first group measures 1.16”, almost minute of angle! Now most Internet Commando wannabees would have stopped right there and gone home and spent the next 3 hours posting threads on the internet about their great accomplishment, but not our Hero. He makes the decision….to fire a second group! group one 
Our Hero has read reports of other Internet Commandos who have been able to achieve sub-minute of angle groups using XM193. After all, this ammo uses "Full Metal Jacket” bullets and is made to "Mil-spec.” Our Hero carefully watches the bench-rest shooter three lanes down (who monitors the wind conditions on the range using a Wind Probe) and only fires immediately after the bench-rester does. He does this for three shots and then checks his target at the next cease fire. Our Hero measures this target three times just to be sure. The group measures 0.93”! Hooah, a sub-minute of angle group! Our Hero is now one of the few, the proud, the real Internet Commandos who can claim to shoot sub-minute of angle groups using XM193! group two 
There’s just one little problem with that second group our Hero fired. It is centered in a different location on the target than the first one. The second group is centered 0.12” above the center of the target and the first group is centered 1.44” below the center of the target. Hmmm… Well our Hero is a real Internet Commando so he can’t let details bother him. After all, sub-minute of angle is sub-minute of angle! As our Hero starts to pack up his targets, something in the back of his mind starts to nag at him. He recalls the reports of the other Internet Commandos. They didn’t just shoot sub-minute of angle groups with XM193; they did it "all day long.” Well, not wishing to be looked down upon by the other Internet Commandos our Hero decides to shoot one more 3-shoot group. After all, if his carbine and ammo could shoot two, sub-minute of angle groups, they could surely do it "all day long.” So, our Hero settles back into position and again taking his cue from the bench-rester fires a third 3-shot group. Upon retrieving his third target and measuring the group our Hero can not believe his eyes. The group measures 2.5”! How can this be possible? He was using XM193 and not just any XM193. It was the fabled LOT #3, the most accurate and hard to come by of all the lots, yet this third group was larger than the first two groups combined! Hmmm… Our Hero wonders how he can ever show his avatar on an Internet forum again after firing such a group with XM193. group three 
Then, slowly our Hero starts to recall a word he has heard mentioned many times before on his favorite Internet forum. It starts with the letter F. Hmm . . .F . . .Fl . . . Flyer! That’s it, flyer! That low shot down at seven o’clock on the target is a flyer! It’s not the fault of the gun or the ammo, it’s a flyer. It's caused by user error, the loose nut behind the stock, the wind, the sun or any other excuse that can be dreamt of in your philosophy, but not the rifle or ammo. The flyer is something to be discounted as if it never happened. (Why be concerned with reality when you are an Internet Commando?) Since that shot is discounted, why not discount that whole group as if it never happened? (After all, isn’t that what an Internet Commando does?) Our Hero decides to discount the entire group and throws the target in the trash. He makes a solemn vow to never mention this group to anyone. After all, he is a real Internet Commando. Upon returning home our Hero makes all the usual posts on the Internet about his sub-minute of angle groups using XM193. True to his solemn vow, he makes no mention of his 2.5” group. At no time does he mention that these groups were 3-shot groups. Nor does he make any mention of the fact that the groups were centered in different locations on the target. Our Hero ends his day wondering if his grandson, or great-grandson or even great great-grandson will remember the accomplishments of the real Internet Commandos or if their contributions to the shooting world will eventually be lost in time? He even wonders what his progeny might someday be named, James or possibly Tiberius? Hmmm… Dedicated to DK-Prof for his shining example of "truth in accuracy reporting" in these two threads: How Accurate is XM193? Apparently, I suck at shooting. .... While the fable above is obviously fiction, the examples of targets shown are based on a real target of a 10-shot group fired from 100 yards using XM193. When all of the 3-shot groups from above are overlayed on a single target you see a much truer example of the limitations of the rifle and ammo. The gap made by the so-called “flyer” is filled in by the other seven shots of the whole group. You can see that when the first 3-shot group (which is centered 1.5” below the second 3-shot group) is displayed with the second 3-shot group you are actually seeing a much better indication of the total dispersion of the rifle and ammo combination. Most people fail to mention that their 3-shot groups are impacting at different locations on the target. This is why 10-shot groups are a much better indicator of a the radial dispersion of a rifle/ammunition combination. 
the real target 
Rick Jamison, the author of the Precision Reloading column in Shooting Times magazine approaches accuracy testing in a scientific manner. He uses a machine rest for testing and fires 10-shot groups. Here are his own words on the subject from one of his articles: "There are stories of a single bullet that for no explained reason flies out of what might have been a tight cluster. This often occurs with a three-shot string and many times with a five-shot string. If you're lucky enough to fire a group without a flier, you can end up with a very tight group. However, usually what happens if another five or seven shots are fired to complete a 10-shot string, other bullets fill in the space between the main group and the flier to make a reasonably rounded group. Ten shots are a more reliable indicator when it comes to predicting what a load is likely to do in the future. The problem with 10-shot groups is that when you report them, everyone thinks you aren't shooting very well or that the ammunition is not good because the group sizes are so much larger than three- or five-shot groups. Also, when we're firing three- or five-shot groups with a flier, it is only natural to assume that it was caused by a flinch or “pulling” the shot. Therefore, since the flier was our own fault, the tendency is to eliminate it from any reporting of group size." machine rest 
.... Here’s another example demonstrating that 3-shot groups do not provide a valid indicator of the radial dispersion of a rifle/ammunition combination. The test vehicle for this demonstration was a one of my AR-15s that has a free-floated Colt HBAR and is wearing a Leupold 3.5-10X40 LR/T. 
Prior to beginning this demonstration, I fired a 10-shot control group at a distance of 50 yards using a hand-load topped with the Sierra 77 grain MatchKing. The target used is an NRA High Power type target reduced for 50 yards. The X-ring measures 0.75" and the 10-ring measures 1.75". The 10-shot control group had an extreme spread of 0.493”. 
Next, I fired a couple of 3-shot groups from 50 yards using Federal XM193 ammunition. (Shooting was conducted at an indoor range, so wind was not a variable in this case.) The two targets are pictured below. 
The center of the first 3-shot group was located approximately ¼ MOA high and ½ MOA to the right of the center of the target, which was the point-of-aim. However, the center of the second 3-shot group was located approximately 1.5 MOA low and ½ MOA to the left of the center of the target. The centers of just these two, 3-shot groups are almost 2 MOA apart in elevation. The centers of the individual 3-shot groups are indicated below by the blue crosses. 
I actually fired a total of ten, 3-shot groups in a row with the XM193 ammunition for a total of thirty shots. Thirty occurrences of something that is being studied is what the statistics types like to refer to as a "large sample." Using the RSI Shooting Lab software program I was able to overlay all ten of the 3-shot groups on each other for a 30-shot composite group. 
This 30-shot composite group gives us a much better picture of the radial dispersion of the rifle/ammunition combination (and in this case particularly the ammunition) than 3-shot groups by themselves do. These 30 shots also give us give us a much better indication of where the center of the points-of-impact are. .... The ten, 3-shot groups that were fired in a row for the above demonstration measured (from smallest to largest): 0.40” 0.57” 0.64” 0.74” 0.80” 0.85” 1.03” 1.13” 1.19” 1.54” The variation between the smallest and largest group above is 74%! In addition to firing the ten, 3-shot groups listed above, I also fired three, 10-shot groups in a row from 50 yards for another thirty rounds of XM193. The groups measured (from smallest to largest): 1.24” 1.46” 1.97” The variation between the smallest and largest of these three groups is only 37%. Using the same total number of rounds in a set, but firing one set using ten, 3-shot groups and the other using three, 10-shot groups shows that the group to group variation of the 10-shot groups is far less than that of the 3-shot groups, half as much in this case. This shows again that 10-shot groups are a more consistent indicator of the radial dispersion of a rifle/ammunition combination or as Rick Jamison stated, “Ten shots are a more reliable indicator when it comes to predicting what a load is likely to do in the future.” Here is another quote about 3-shot groups from another Precision Reloading article by Rick Jamison. “Some shooters may have two or three three-shot groups to prove the load is really accurate. It really takes more shooting than that to make a judgment on a load’s accuracy potential. Three shots forming a tight cluster is nice to look at, but it is little more than an accident. Shooting three-shot groups to see how everything is working is essentially a waste of time and components.” .... Before I can continue with The Trouble With 3-Shot Groups, I need to define the concept of “mean radius” (also called average group radius.) 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.
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.
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.
Over-laying the targets of at least three, 10-shot groups fired in a row and determining the mean radius of the composite group gives us a statistically powerful tool for evaluating the radial dispersion of a rifle/ammunition combination.
The table below will give you an idea of the relationship between the mean radius and extreme spread for 10-shot groups.
Here are some interesting quotes pertaining to the mean radius from old issues of American Rifleman: “Mean radius is the mean distance of bullet impacts from center of the test group. It is used in government ammunition acceptance because it takes account of every shot and comes close to maximizing the test information. While there is no exact relationship between this measure and the simpler and more convenient group diameter, the 10-shot group diameter averages slightly over 3 times the mean radius.” "These examples illustrate the sensitiveness of the extreme spread to number of shots in the group. Indeed, as the table indicates, the measures made to only the outside shots of the group, e.g. the extreme spread, are very sensitive to number of shots, while the measures made to all the shots, e.g. the mean radius are far less so. It may be added that the latter measures are also less variable in their representation of the group; they are more efficient. This explains why the target testing of U.S. military rifle ammunition is by mean radius." .... As explained previously, the mean radius method of measuring groups gives us information about each shot in the group, not just the two worst shots of the group as is the case when measuring the extreme spread. The following comparisons will be made using the mean radius of the different groups. Besides doing a 30-shot composite group formed from the ten, 3-shot groups fired in a row with XM193 as shown above, I also compiled a 30-shot composite group formed from the three, 10-shot groups fired in row. Here they are, side by side for comparison. 
The 30-shot composite group formed from the ten, 3-shot groups has a mean radius of 0.45” (indicated by the inner blue circle.) The 30-shot composite group formed from the three,10-shot groups has a mean radius of 0.42” (also indicated by the inner blue circle.) Finally, I compiled a 60-shot composite group formed from all of the above groups. 
The mean radius of the 60-shot composite group is 0.44”. This sixty-shot composite group gives us a fairly definitive idea of what we can expect from the rifle/ammunition combination in question when fired from 50 yards. Just as importantly, this demonstrates that the thirty-shot composite groups come quite close to the same results as the 60-shot composite group; differing by only a couple one-hundredths of an inch in mean radius from the 60-shot composite group. .... Since the mean radius method of measuring groups gives us a better picture of what is occuring with all the shots in the group, we can use the mean radius measurements to get more accurate comparisons between groups. The mean radii of the ten, 3-shot groups from above are as follows (from smallest to largest): 0.17” 0.23” 0.25” 0.30” 0.32” 0.32” 0.46” 0.50” 0.50” 0.69” The 3-shot groups have a variation of 75% from smallest to largest! The mean radii of the three, ten-shot groups from above measure (from smallest to largest): 0.34” 0.39” 0.50” The mean radii of the 10-shot groups only have a group to group variation of 32%, less than half that of the 3-shot groups. Once again this shows the vastly improved consistency of 10-shot groups compared to 3-shot groups. If you recall from the above post, the sixty-shot composite group had a mean radius of .44”. Look at how much closer the mean radii of the individual 10-shot groups come to the mean radius of the sixty-shot composite group than the mean radii of the 3-shot groups do. The mean radius of the 30-shot composite group formed from over-laying the three 10-shot groups on each other is even closer. Consistency and a high degree of predictability are what make the use of 10-shot groups (particularly three,10-shot groups fired in a row) far superior to 3-shot groups in evaluating the precision of our rifles and ammunition! .... Here is a final demonstration that further illustrates and reinforces all the concepts previously presented. Using one of my AR-15s that has a free-floated Colt HBAR, I fired five, 10-shot groups from 100 yards using a hand-load topped with 55 grain FMJ bullets. The five 10-shot groups were over-layed on each other to produce a 50-round composite group with a mean radius of 0.70”. The average extreme spread for all five groups was 2.30”. 
I then proceeded to fire another 50 rounds of the same hand-load in 3-shot groups, for a total of sixteen, 3-shot groups (with an extra 2-shot group at the end.) Several of the groups were sub-MOA. group #06: 0.66” group #12: 0.92” group #13: 0.59” group #15: 0.41” group #16: 0.63” However, several other groups had extreme spreads of well over 2”. group #02: 2.53” group #07: 2.89” group #08: 2.39” group #09: 2.86” group #11: 2.47” Those who espouse the use of 3-shot groups for evaluating the radial dispersion of a rifle/ammunition combination like to point to the smallest 3-shot groups for their accuracy claims and then pretend that all those large 3-shot groups don’t exist. The average extreme spread for all sixteen of the 3-shot groups was 1.72”. Also, the statistical centers of many of the groups, (both large and small) were located at different locations on the target. Pictured below is the first 3-shot group of the 55 grain FMJ load and beneath that the first three, 3-shot groups over-layed on each other. 
As we continue to sequentially over-lay the 3-shot groups on each, the pieces of the puzzle begin to fill in the gaps giving us a more complete view of the entire picture. 
Finally, when all of the 50 rounds fired in 3-shot groups have been over-layed on each other, we have a composite group that is remarkably similar in radial dispersion to the 50 round composite group formed from the five 10-shot groups. 
Here’s the only target from the above shooting session that the Internet Commando would have posted. 
Remember, all the data for the above examples were obtained during live-fire testing from my bench-rest set-up, not from computed generated models that fail to demonstrate a correlation with actual real-world data. .... Institutions and organizations that buy enormous amounts of ammunition and weapons are far more interested in facts, than sales hype and propaganda and most of them demand that accuracy/precision testing be conducted using 10-shot groups. This includes the Federal Bureau of Investigation, Crane Naval Surface Warfare Center, the US Army Marksmanship Unit and the US military’s acceptance testing of both 5.56mm ammunition and weapons. On the other hand, businesses that use 3-shot groups for making their accuracy claims are usually trying to sell something. .... At the 1992 Barcelona Olympics, USA Shooting Team members Launi Meili and Robert Foth won the gold and silver medals in the three-position rifle events. The Olympians used the new Federal Gold Medal ammunition to aid them in obtaining their victories. This was the first time in more than 30 years that an American won an Olympic medal in one of the small bore shooting events while using American-made ammunition. It’s interesting to note that pertaining to the accuracy/precision development and multifaceted testing of the Federal ammunition that helped the US Olympians win gold and silver medals in Barcelona, Federal’s Director of Product Engineering, Dave Longren, had this to say: 'The standard test string was three 10-shot groups, with the most attention paid to the 30-shot composite. "When you’re working at this level, the traditional five 5-shot group test simply doesn’t give you statistically valid results.”'* * Hunnicutt, Robert. “Ammo Good as Gold.” American Rifleman Nov. 1992: 32-33, 72-73. Print. ..... "We all use math every day. To predict weather, to tell time, to handle money -- math is more than formulas and equations; it's logic, it's rationality. It's using your mind to solve the greatest mysteries we know." Charlie Eppes from NUMB3RS
. . . and it helps us evaluate and improve our rifle-craft. Molon |
|
#09
An Accuracy Comparison of Three Different Barrel/Ammunition Combinations For this article, I compared the accuracy (technically, precision) of three different barrel/ammunition combinations. The three different AR-15 barrel/ammunition combinations tested are as follows:
The same 20” Lothar Walther barrel was used to test the two different GECO loads. This stainless-steel barrel has a 223 Wylde chamber and a 1:8” twist. 
The 16” Colt HBAR used to fire the Wolf 62 grain FMJ ammunition is chrome-lined and has a 5.56mm NATO chamber with a 1:9” twist. This is the same barrel found on the Colt 6721. 
All of the shooting for this article was conducted using my AR-15 bench-rest set-up. The shooting set-up will be described in detail below. As many of the significant variables as was practicable were controlled for. Shooting was conducted from a concrete bench-rest from a distance of 100 yards (confirmed with a laser rangefinder.) The barrels used in the evaluations are free-floated. The free-float handguard of the rifle rests in a Sinclair Windage Benchrest with the aid of a forend adaptor, while the stock of the rifle rests in a Protektor bunny-ear rear bag. The same AR-15 lower was used to test all three of the different barrel/ammunition combinations. The lower houses a Geissele Hi-Speed National Match trigger. Sighting is accomplished via a Leupold VAR-X III set at a magnification of 25X and adjusted to be parallax-free at 100 yards. A mirage shield is attached to the objective-bell of the scope. Wind conditions on the shooting range are continuously monitored using a Wind Probe. The set-up is very similar to that pictured below. 
The Wind Probe.
Atmospheric conditions on the range are monitored and recorded using a Kestrel 4000 Pocket Weather Tracker.
Prior to shooting the factory loaded ammunition, control groups were fired using match-grade hand-loads. The radial dispersion of the control groups was significantly smaller than that of the factory loaded ammunition. ... 
A 3-shot group of the GECO 223 Remington 55 grain FMJ Target ammunition was fired from the Lothar Walther barrel at a distance of 100 yards. This group had an extreme spread of 0.47” 
... 
A 3-shot group of the GECO 5.56x45mm 55 grain FMJ ammunition was fired from the Lothar Walther barrel at a distance of 100 yards. This group had an extreme spread of 0.46” 
... 
A 3-shot group of the steel-cased, bi-metal jacketed, Wolf Performance 62 grain FMJ ammunition was fired from the Colt 16” HBAR (6721) barrel at a distance of 100 yards. This group had an extreme spread of 0.47” 
Looking at the 3-shot groups above, you might be misled into believing that the precision of the three different barrel/ammunition combinations is virtually identical. However, according to ballistipedia.com, the use of 3-shot groups for evaluating precision “is statistically almost meaningless.” http://ballistipedia.com/index.php?title=Describing_Precision Now, if instead of using “statistically almost meaningless” 3-shot groups, we follow the practice of the US Army Marksmanship Unit for evaluating the precision of AR-15 barrel/ammunition combinations and shoot three consecutive 10-shot groups, a much different picture emerges when comparing the precision of the three different barrel/ammunition combinations being evaluated; particularly if we over-lay the three 10-shot groups on each other to form a 30-shot composite group and use the more statistically powerful mean radius to compare the radial dispersion of the three different barrel/ammunition combinations. Three 10-shot groups of the GECO 223 Remington 55 grain FMJ Target ammunition fired in a row from a distance of 100 yards from the Lothar Walther barrel produced the following extreme spreads: 1.71” 1.06” 1.52” for a 10-shot group average extreme spread of 1.43”. 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 0.47”. Three 10-shot groups of the GECO 5.56x45mm 55 grain FMJ ammunition fired in a row from a distance of 100 yards from the Lothar Walther barrel produced the following extreme spreads: 2.55” 2.09” 2.19” for a 10-shot group average extreme spread of 2.28”. 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 0.79”. Three 10-shot groups of the Wolf 62 grain FMJ ammunition fired in a row from a distance of 100 yards from the Colt 6721 barrel produced the following extreme spread: 4.23” 4.29” 3.68” for a 10-shot group average extreme spread of 4.07”. 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 groups was 1.22”. The 30-shot composite groups . . . 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The 10-shot control group fired from the Lother Walther barrel for the GECO 223 Remington 55 grain FMJ Target ammunition test . . . 
The 10-shot control group fired from the Lothar Walther barrel for the GECO 5.56x45mm 55 grain FMJ ammunition test . . . 
The 10-shot control group fired from the Colt 6721 barrel for the Wolf Performance 62 grain FMJ ammunition testing had an extreme spread of 0.89”. .... |
|
#10
Why Not 20-Shot Groups? Inevitably, there will be someone who, after reading The Trouble With 3-Shot Groups, will snidely comment, “Why not 20-shot groups?”, “Why not 30-shot groups?”, for evaluating the radial dispersion of a rifle/ammunition combination. Here’s “why not.” The group pictured below was fired from one of my precision at AR-15s at a distance of 100 yards. It’s a 20-shot group. 
Even though there are 20 shots in the above group, I can only distinguish the outlines of 12 bullet holes. The other 8 shots went through the ragged hole in the center of the group. So, while I fired an additional 10 shots more for this group, I only gained an additional 2 shots worth of data and lost 8 shots worth of data. This is highly inefficient. The disparity between the number of shots fired and the number of shots “captured” is even greater with 30-shot groups. .... |
|
#11
Observations on the Points of Impact of Statistically Significant Shot-Group Sizes The Set-up For this ballistic exercise I used a semi-automatic AR-15 with a 20” stainless steel Lothar-Walther barrel. This barrel has a 223 Wylde chamber with a 1:8” twist rate. This Lothar-Walther barreled AR-15 has produced 10-shot groups with extreme spreads measuring in the “sixes” (0.6xx inches) when fired from the bench at a distance of 100 yards using match-grade hand-loads. Prior to the beginning of this exercise, this barrel had approximately 2,040 rounds fired through it. 
The ammunition used for this exercise was factory loaded Black Hills red-box 223 Remington ammunition seated with the 69 grain Sierra MatchKing with a cannelure. Since I had been testing other ammunition with the Lothar-Walther barreled AR-15 prior to the beginning of this exercise, as well as throughout this exercise, I fired three “seasoning rounds” of the Black Hills 69 grain Sierra MatchKing ammunition to condition the bore of the Lothar-Walther barrel with the powder used in this factory load. This process was repeated immediately prior to shooting each of the groups evaluated for this exercise. 
All of the shooting for this ballistic exercise was conducted from a concrete bench-rest at a distance of 100 yards (confirmed with a laser rangefinder.) The Lothar-Walther barrel used in this exercise was free-floated in a LaRue Tactical railed free-float handguard. The free-float handguard of the AR-15 rested in a Sinclair Windage Benchrest (with the aid of a Sinclair forend bench-rest adaptor) 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 shield 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. 
The Wind Probe.
The Groups No changes were made to the elevation or windage settings on the scope throughout the entire course of this exercise and the exact same point of aim was used when shooting each group. After firing the three “seasoning rounds” of the Black Hills 69 grain Sierra MatchKing ammunition, I settled-in and fired a 20-round group of the aforementioned ammunition. The group is pictured below. The center of the 20-round shot-group is located in the lower-right quadrant of the two inch circle on the target. After shooting this group, I continued testing other ammunition from the same Lothar-Walther barreled AR-15. 
A little later that day, I fired a second 20-shot group of the Black Hills 69 grain Sierra MatchKing ammunition from the Lothar-Walther barreled AR-15. The second group is pictured below.
As you can see, the center of the second 20-shot group showed no significant shift whatsoever in its location on the target as compared to the first 20-shot group. The next image shows the first and second 20-shot groups over-layed on each other using Adobe Photoshop with the blending opacity set at 50%; further illustrating that the centers of the two 20-shot groups showed no significant shift in their locations on the targets compared to each other. 
On an additional trip to the shooting range, I repeated this entire ballistic exercise just as described above. The findings were the same; the centers of two 20-shot groups fired from the Lothar-Walther barreled AR-15 using the same lot of Black Hills 69 grain Sierra MatchKing ammunition showed no significant shift in their locations on the targets compared to each other. Nor did the centers of these third and fourth 20-shot groups show any significant shift in their locations on the targets as compared to the first and second 20-shot groups fired in the previous ballistic exercise. The graphic below shows all four of the 20-shot groups over-layed on each other (forming an 80-shot composite group) illustrating that the centers of all four of the 20-shot groups showed no significant shift in their locations on the targets compared to each other. Of those 80 shots in the composite group, 95% of them are contained in a covering-circle that has a diameter of 0.97 MOA. All of the 80 shots in the composite group are contained in an area-of-dispersion (bounding rectangle) that measures 1.07 MOA wide by 1.08 MOA high. 
…. |
|
#12
Reproducibility
The hallmark of a sound test methodology is being able to repeat a test and arrive at the same conclusion. Below are two different demonstrations that were conducted using my AR-15 bench-rest methodology that will confirm the reproducibility of this set-up. For the first demonstration, I conducted two accuracy evaluations of the most accurate lot of IMI M193 that I've come across, from my bench-rest set-up using a semi-automatic AR-15. Even though this is the most accurate lot of IMI M193 that I’ve tested, this M193 clone using 55 grain FMJ bullets will still show a much greater variation in radial dispersion from shot-group to shot-group than match-grade ammunition. 
I conducted an accuracy (technically, precision) evaluation of the IMI M193 ammunition 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 at 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 (with the aide of a forend bench-rest adapter), 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. 
The Wind Probe.
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 IMI M193 ammunition, I fired a 10-shot control group using a hand-load topped with the Sierra 55 grain BlitzKing. That group had an extreme spread of 0.83”. 
Four 10-shot groups of the IMI M193 ammunition were fired in a row with the resulting extreme spreads: 2.73” 1.76” 1.74” 2.03” for a 10-shot group average extreme spread of 2.07”. The four 10-shot groups were over-layed on each other using RSI Shooting Lab to form a 40-shot composite group. The mean radius for the 40-shot composite group was 0.62”. Next, I repeated the test just as described above. These four 10-shot groups fired in a row produced extreme spreads of: 2.64” 1.25” 2.43” 2.00” for a 10-shot group average extreme spread of 2.08”. These four 10-shot groups were over-layed on each other using RSI Shooting Lab to form a 40-shot composite group. The mean radius for this 40-shot composite group was 0.66”. I over-layed all eight of the 10-shot groups on each other using RSI Shooting Lab to form an 80-shot composite group. The 80-shot composite group had a mean radius of 0.64” That the mean radii for the two, 30-shot composite groups only vary by 2/100ths of an inch from the 80-shot composite groups strongly reinforces the reproducibility of my AR-15 bench-rest methodology. The smallest 10-shot group . . . 
….. The second demonstration of the reproducibility of my AR-15 bench-rest methodology involves the accuracy evaluation of a 16” Noveske N4 barrel. 
The Noveske 16” N4 Light barrel is a cold hammer forged barrel. It has a mid-length gas system, “M4” feed-ramps and a chrome-lined chamber and bore. The barrel has a 5.56mm NATO chamber and a 1:7” twist and has been high-pressure/magnetic particle tested; as the barrel stamp indicates. Contrary to erroneous Internet reports, the N4 barrel does not have polygonal rifling. 
The accuracy (technically precision) of this Noveske barrel was conducted using my AR-15 bench-rest methodology just as described for the previous demonstration. For this evaluation, I used one of my standard match-grade hand-loads topped with Sierra 55 grain BlitzKings. When fired from my Krieger barreled AR-15s, this load has produced ½ MOA 10-shot groups at 100 yards. 
Three, 10-shot groups were fired in a row from the Noveske 16” N4 Light barrel from a distance of 100 yards with the resulting extreme spreads: 1.29” 1.18” 1.31” for a 10-shot group average extreme spread of 1.26”. 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 of the 30-shot composite group was 0.37”. After firing the above three groups, I fired an additional five, 10-shot groups in a row for a total of eight, 10-shot groups fired in a row. The average extreme spread for all eight of the 10-shot groups was 1.24”. I over-layed all eight of the 10-shot groups on each other using RSI Shooting Lab to form an 80-shot composite group. The mean radius for the 80-shot composite group was 0.39”. That the mean radius of the 30-shot composite group formed from the first three consecutively fired 10-shot groups only varies by 2/100ths of an inch from the mean radius of the 80-shot composite group strongly reinforces the reproducibility of my AR-15 bench-rest methodology. The smallest 10-shot group . . . 
.... 
.... |
|
#13
Rate of Fire Comparison
For Accuracy Testing With a 24" Krieger Barrel For this accuracy (technically, precision) test , I compared the results of firing three consecutive 10-shot groups with each successive shot fired in a casual, steady manner, to that of firing thirty, 1-shot “groups” (by 1-shot groups, I mean that I fired one single shot on each of thirty different targets) in a row with a 1.5 minute cooling period in between each shot. As with my usual method, testing was conducted from a concrete bench-rest at a distance of 100 yards. The test vehicle was one of my precision AR-15s with a 24" Krieger barrel. The handguard of the rifle rested in a Sinclair Windage Benchrest and the buttstock rested in a Protektor bunny-ear bag. For sighting, I used a Leupold Competition scope (45X magnification) with a mirage shade attached. The scope was adjusted to be parallax-free at 100 yards. Wind conditions were monitored using a Wind Probe. The ambient temperature during testing was a balmy 72 degrees F. Just prior to the beginning of this test, I fired off a 10-shot control group from 100 yards using handloaded 55 grain Sierra BlitzKings that had an extreme spread of 0.74”.
The Wind Probe. 
Testing was conducted using hand-loaded Hornady 55 grain FMJ bullets. The thirty, 1-shot groups were fired first. In order to mitigate possible effects of barrel heat on the points of impact of the 1-shot groups (and therefore the overall mean radius of the 30-shot composite group that would later be formed from the thirty individual shots) I allowed the barrel to cool between each individual shot. The barrel was allowed to cool for approximately 1.5 minutes between each shot. The barrel remained only slightly warm to the touch during the firing of all thirty 1-shot groups. I was able to wrap my hand around the barrel and hold it before each new shot was fired without the slightest bit of discomfort. Also, to mitigate possible effects of the so-called “heat soak” effect (the cartridge “soaking” heat from hot chamber walls while sitting in the chamber) on the points of impact of the individual shots, I single-loaded each shot just before firing it and left the bolt locked open after each shot to allow the chamber to cool. The thirty, 1-shot groups were overlayed on each other using RSI Shooting Lab to form a 30-shot composite group that had a mean radius of 0.46”. The three consecutively fired 10-shot groups were fired following the 1-shot groups. I fired at a casual, steady pace, but no intentional time was allotted between each shot for the barrel to cool nor was any time allowed for the chamber to cool. Each round was immediately single-loaded into the chamber after firing the previous shot. The three 10-shot groups were also over-layed on each other using RSI Shooting Lab. The mean radius for that 30-shot composite group was 0.42”. Next, I measured (by hand) the individual radius of each shot from the statistical center of the 30-shot composite group formed from the 1-shot groups. I repeated the same procedure with the 30-shot composite group formed from the three 10-shot groups. These measurements gave me two sets of data for further comparison, with each set containing 30 data points on the accuracy/precision level of the two different methods of firing a total of 30 shots; that is the three 10-shot groups fired at a steady pace versus the thirty 1-shot groups fired with time for the barrel to cool between each shot. Lastly, I ran a statistical analysis comparing the two data sets obtained in the manner described above using an unpaired, two-tailed t-test. The results of the t-test showed that there was no “statistically significant” difference in the mean radii (and thus the accuracy/precision) of the two 30-shot composite groups. ... I'm Range Dog and I approve this test. 
.... |
|
#14
“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, heavy 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”. 
From American Rifleman, September 1965 
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, heavy test barrel either. For those reasons, I like to use the mean radius of 0.32” for three 10-shot groups fired in a row (30-shot composite group) at 100 yards as the benchmark for 5.56mm/223 Remington match-grade ammunition, when fired from a semi-automatic AR-15. The pic below demonstrates jut how far the AR-15 and its ammunition have come since their introduction. On the left side of the pic is a 30-shot composite group obtained from over-laying three 10-shot groups that were fired in a row off my bench-rest set-up from an AR-15 with a free-floated 20” Colt M16A1 barrel (chrome-lined, 5.56mm chamber, 1:12” twist) using IMI M193 ammunition. The 30-shot composite group has a mean radius of 1.09”. The 30-shot composite group pictured on the right was obtained from over-laying three 10-shot groups that were fired in a row off my bench-rest set-up from an AR-15 with a free-floated 20” Lothar-Walther barrel (stainless steel, 223 Wylde chamber, 1:8” twist) using factory loaded Barnes Precision Match 5.56mm 85 grain OTM ammunition (magazine length). That 30-shot composite group has a mean radius of 0.22”. 
…. |
|
#15
Maximum Shot Radius and Covering Circle The maximum shot radius “is the distance from a group's statistical center to the center of the most distant hole.” It is basically your worst shot in the group, the one farthest from the center of the group. Using the maximum shot radius measurement to scribe a circle around the center of impact of the group will give you a diameter (twice the maximum shot radius) that all the shots of your group will fit in. In the example below, the maximum shot radius = 1.61”. Using this measurement to scribe a circle around the center of the group gives you a circle with a diameter of 3.22” in which all the shots of the group fit in. The circle scribed by the maximum shot radius is the covering circle. 
In the RSI Shooting Lab analysis the maximum shot radius is represented by the outer blue circle. For example this 10-shot group of Hornady 5.56 TAP ammunition has a maximum shot radius of 0.65”. Therefore all the shots from the group will fit in a 1.3” covering circle. Keep in mind this is not the same thing as the extreme spread, as the extreme spread for this group is only 1.16”. (The X-ring on the actual target below measures 1.5”.) 
.... |
|
#16
A Note on AR-15 Barrel Break-In Even an expensive, single-point cut-rifling stainless-steel Krieger barrel that has been chambered and hand-lapped by Krieger can benefit from a judicious break-in. The first bore-scope pic below is from the leade of one of my brand-new Krieger AR-15 barrels (that was purchased directly from Krieger and that was chambered and hand-lapped by Krieger) prior to firing. As you can see in the pic, there are still tooling marks on the lands in the leade running perpendicular to the bore direction. The barrel won't shoot to its potential until those tool marks have been removed. 
The next bore-scope pic shows the same barrel after I conducted a short break-in procedure. The tooling marks on the lands in the leade are completely gone. 
And here’s what an AR-15 barrel that has been properly broken-in can do . . . 
.... |
|
#17
Random Quotes on the Passing Scene from the experts at ballistipedia.com . . . http://ballistipedia.com/index.php?title=Describing_Precision From the above link: •Extreme spread of a 3-shot group, usually at 100 yards. This is statistically almost meaningless, especially when there is no reference to how many 3-shot groups were sampled. •The US Army Marksmanship Unit at Ft. Benning, GA uses a minimum of 3 consecutive 10-shot groups fired with the rifle in a machine rest when testing service rifles. •Armed forces also often explicitly uses the more statistically powerful Mean Radius and Circular Error Probable measures. •An extended practical, and amusing, critique of the 3-shot group is archived here. The hot-link above takes you to a thread on AR15.com: http://www.ar15.com/mobile/topic.html?b=3&f=118&t=279218 That thread is entitled: The Trouble With 3-Shot Groups By Molon While you’re on ballistipedia.com, check out the references page: http://ballistipedia.com/index.php?title=References From the references page: Molon, 2006, The Trouble With 3-Shot Groups Through an extended forum thread, Molon offers intuitive explanations and illustrations of the problems with Extreme Spread samples. We have not been able to identify the real person behind that now-inactive user account. If anyone knows please contact us so we can give well-deserved credit! .... ..... The Crane Naval Surface Warfare Center is involved in developing special munitions and weapons for our warfighters. At Crane, they’re not interested in sales hype and propaganda; they’re only interested in facts. They’re not driven by profit margin; their goal is developing the best tools to help our Special Operating Forces accomplish their missions. When it comes to evaluating the accuracy of ammunition, what is the number of shots per group that Crane requires? Why, 10 shots per group, of course! 
.... “To establish facts, repetitious tests must be performed to ascertain that the results can be obtained at will. If 3 separate 10-shot targets are first fired to establish a value, and then another 30-shot test fired using the changed powder, etc., and an improvement noted, then it can be said with some assurance that an improvement has been made.” American Rifleman July 1958 .... I love this quote from the book Black Magic: For accuracy usage, the 55 grain FMJ is an evil bullet... Under sufficient magnification, it wouldn't surprise me a bit to find a small “666” tattooed into its shiny little ogival head. Abandon all hope, ye who seek tiny groups here! ..... Here is some additional information on U.S. M193 from a 1988 back-issue of Rifle magazine. The accuracy requirement from a test fixture calls for a maximum of a two-inch mean radius at 200 yards from ten 10-shot groups (which equates to approximately three MOA). .... Here is a quote by John Feamster from a chapter in Precision Shooting, Reloading Guide. “The US Army Marksmanship Unit at Ft. Benning, GA uses a minimum of 3 consecutive 10-shot groups fired with the rifle in a machine rest when testing service rifles.” .... One of the interesting things about the TV show NUMB3RS is that the episodes are based on real mathematical and statistical concepts. The show even mentioned the Texas Sharpshooter fallacy in episode #309: “Waste Not.” ... The LAT specification for the accuracy of MK262 Mod1 calls for a total of ten, 10-shot groups groups to be fired from test barrels; five 10-shot groups are fired from each of two different test barrels. ... 
.... |
|
Quoted:
The free-float handguard of the rifle rests in a Sinclair Windage Benchrest with the aid of a forend adaptor, ... Something in this picture finally clicked with me... Can you elaborate on that rest? It looks like the free float handguard is essentially "locked" to the front rest. Is that true? |
|
Quoted:
Something in this picture finally clicked with me... Can you elaborate on that rest? It looks like the free float handguard is essentially "locked" to the front rest. Is that true? It is not "locked" into the front rest.  The forend adapter allows the rifle to "ride" the the bags without the picatinny rail snagging on the front bag.
... |
|
Thanks. The new picture clarified it perfectly. It does look more easily centered in your rest with this adapter. And that makes me think about how sloppy my inexpensive front bag is with most forends, let alone rails. And my rest is a Lyman elevating rest with a Caldwell front rest bag, so it's not like I've spent a bunch on it, but still... |
|
Quoted:
Thanks. The new picture clarified it perfectly. It does look more easily centered in your rest with this adapter. And that makes me think about how sloppy my inexpensive front bag is with most forends, let alone rails. And my rest is a Lyman elevating rest with a Caldwell front rest bag, so it's not like I've spent a bunch on it, but still... Quoted:
Thanks. The new picture clarified it perfectly. It does look more easily centered in your rest with this adapter. And that makes me think about how sloppy my inexpensive front bag is with most forends, let alone rails. And my rest is a Lyman elevating rest with a Caldwell front rest bag, so it's not like I've spent a bunch on it, but still... Da nada. 
... |
|
Quoted:
Thanks. The new picture clarified it perfectly. It does look more easily centered in your rest with this adapter. And that makes me think about how sloppy my inexpensive front bag is with most forends, let alone rails. And my rest is a Lyman elevating rest with a Caldwell front rest bag, so it's not like I've spent a bunch on it, but still... Quoted:
Thanks. The new picture clarified it perfectly. It does look more easily centered in your rest with this adapter. And that makes me think about how sloppy my inexpensive front bag is with most forends, let alone rails. And my rest is a Lyman elevating rest with a Caldwell front rest bag, so it's not like I've spent a bunch on it, but still... There's a lot more to shooting a gun off a bench than just "clamping it in the rest." |
|
Quoted:
There's a lot more to shooting a gun off a bench than just "clamping it in the rest." Quoted:
Quoted:
Thanks. The new picture clarified it perfectly. It does look more easily centered in your rest with this adapter. And that makes me think about how sloppy my inexpensive front bag is with most forends, let alone rails. And my rest is a Lyman elevating rest with a Caldwell front rest bag, so it's not like I've spent a bunch on it, but still... There's a lot more to shooting a gun off a bench than just "clamping it in the rest." Yeah, I get that. I was just trying to make sense of what I was seeing. Sure, my cheap setup isn't in the same class as Molon's, but I learn a lot from just asking simple questions. Looking at Molon's picture made me curious. And from this I've learned that I probably need at least a better front bag - one that fits the forend of my rifle better. |
|
Quoted:
Quoted:
Thanks. The new picture clarified it perfectly. Here's another view . . . https://app.box.com/shared/static/s6ry2po4pl.jpg .... So the rail adapter just lets the forend fit in the front bag. Nice picture! |
|
Quoted:
So the rail adapter just lets the forend fit in the front bag. Nice picture! Quoted:
Quoted:
Quoted:
Thanks. The new picture clarified it perfectly. Here's another view . . . https://app.box.com/shared/static/s6ry2po4pl.jpg .... So the rail adapter just lets the forend fit in the front bag. Nice picture! 3" rail and 3" bag. |
|
Quoted:
#05 My AR-15 Bench-Rest Methodology Most of the accuracy (technically, precision) evaluations obtained for this series of articles were conducted using my AR-15 bench-rest set-up. The shooting set-up will be described in detail below. As many of the significant variables as was practicable were controlled for. Typically, shooting is conducted from a concrete bench-rest from a distance of 100 yards (confirmed with a laser rangefinder.) The barrels used in the evaluations are free-floated. The free-float handguard of the rifle rests in a Sinclair Windage Benchrest with the aid of a forend adaptor, while the stock of the rifle rests in a Protektor bunny-ear rear bag. Sighting is typically accomplished via a Leupold VAR-X III set at a magnification of 25X and adjusted to be parallax-free at 100 yards. A mirage shield is attached to the objective-bell of the scope. Wind conditions on the shooting range are continuously monitored using a Wind Probe. The set-up is very similar to that pictured below. https://app.box.com/shared/static/xo4duzdgtp.jpg https://app.box.com/shared/static/7o9zt9idk7889mmzlcbkjaqe16r5mz8h.jpg The Wind Probe. http://www.box.net/shared/static/lkg47ptc04.jpg Atmospheric conditions on the range are monitored and recorded using a Kestrel 4000 Pocket Weather Tracker. https://app.box.com/shared/static/rwruh372al3yh9kafscx370ewe74e6el.jpg This bench-rest methodology has enabled me to obtain some excellent results using a semi-automatic AR-15. https://app.box.com/shared/static/caq50zgmm8fnbwnmq1uydfa759pjrs52.jpg ... Can you share more about this. I have the same rest and rear bag. Edit: I should have read the responses first. Is than an arms bipod mount hooked to a piece of wood? |
|
Quoted:
Can you share more about this. I have the same rest and rear bag. Edit: I should have read the responses first. Is than an arms bipod mount hooked to a piece of wood? Quoted:
Quoted:
#05 My AR-15 Bench-Rest Methodology Most of the accuracy (technically, precision) evaluations obtained for this series of articles were conducted using my AR-15 bench-rest set-up. The shooting set-up will be described in detail below. As many of the significant variables as was practicable were controlled for. Typically, shooting is conducted from a concrete bench-rest from a distance of 100 yards (confirmed with a laser rangefinder.) The barrels used in the evaluations are free-floated. The free-float handguard of the rifle rests in a Sinclair Windage Benchrest with the aid of a forend adaptor, while the stock of the rifle rests in a Protektor bunny-ear rear bag. Sighting is typically accomplished via a Leupold VAR-X III set at a magnification of 25X and adjusted to be parallax-free at 100 yards. A mirage shield is attached to the objective-bell of the scope. Wind conditions on the shooting range are continuously monitored using a Wind Probe. The set-up is very similar to that pictured below. https://app.box.com/shared/static/xo4duzdgtp.jpg https://app.box.com/shared/static/7o9zt9idk7889mmzlcbkjaqe16r5mz8h.jpg The Wind Probe. http://www.box.net/shared/static/lkg47ptc04.jpg Atmospheric conditions on the range are monitored and recorded using a Kestrel 4000 Pocket Weather Tracker. https://app.box.com/shared/static/rwruh372al3yh9kafscx370ewe74e6el.jpg This bench-rest methodology has enabled me to obtain some excellent results using a semi-automatic AR-15. https://app.box.com/shared/static/caq50zgmm8fnbwnmq1uydfa759pjrs52.jpg ... Can you share more about this. I have the same rest and rear bag. Edit: I should have read the responses first. Is than an arms bipod mount hooked to a piece of wood? It's a piece of ultra high molecular weight (UHMW) polyethylene with teflon impregnated tape over it. . |
|
All these threads have me drooling to build a sub 0.5 MOA AR.
I was looking at barrels at CLE, and heavy wall uppers at Precisions Firearms and so on. A few questions: I'm willing to spring for a Kreiger or Bartlein barrel, but what are the recommend twist and length for lighter bullets. Where are the best places to get them? Do flash hiders / muzzle brakes make a measurable difference in group size? Or should I stick with a bench rest style crown? Part of me would like to have it threaded so I could try my 5.56 supressor on it, but it is not worth it if it causes a measurable difference. Does the lower matter at all? Is a billet set more or less important than a heavy wall upper with anybody's lower? Thanks! |
| ditto on curiosity about flash hiders or brakes. I've read that the best ones are those that vent gas symmetrically around the muzzle, so A1 flash hider is better than A2, but it's also got to be concentric with the bore, so a cheap surplus or knock-off A1 might not be the best either |
|
Quoted:
Do flash hiders / muzzle brakes make a measurable difference in group size? Or should I stick with a bench rest style crown? There are at least half a dozen variables involved with turning down the muzzle of the barrel, threading it and installing a muzzle device. Which system has the higher probability of producing more consistent precision; the one with more variables or less variables? ... |
AR Sponsor