Theories, Myths, and Fables of Accuracy

A Key to Improved 22 Long Rifle Accuracy Discovered

This story starts over a decade ago, when I read that measuring the rim thickness of 22 long rifle bullets would improve accuracy. I also learned at this time that some of the bench rest shooters were experimenting with weighing their bullets to improve accuracy. Being of solid Norwegian and German descent, you can’t tell me anything. Furthermore, even if you have proof, I will still go out and prove it to myself. So starts the last ten years of research that has finally yielded the first key to improved accuracy for 22-caliber long rifle ammunition. This theory, applied from center-fire experience, reduced group diameters by 35 percent (0.200 inches) with a target grade test rifle at 50 meters.

Not only did I decide to sort ammunition by rim thickness for accuracy testing, I also measured the rim concentricity, bullet weight, bullet diameter, case diameter, length to ogive, velocity, and bullet concentricity. In the tables of data that I collected, the more expensive ammunition has a much smaller range of variance for these measured aspects when compared to less expensive ammunition.

My initial testing was from hard sandbag rests at an indoor facility with a 1413 Anschutz equipped with a 20x Unertl scope. I originally shot 5 round groups, and the testing grew to include seventeen brands of ammunition. The first tests that I conducted were for rim thickness, bullet weight, and bullet concentricity. I already had a nice powder scale to weigh bullets, and there were at least three different models of rim thickness measuring tools on the market. However, no one was offering a reliable tool to measure the bullet concentricity of 22 long rifle bullets. Therefore, I had to build my own 22-caliber bullet concentricity gauge with my Unimat DB200 lathe/milling machine.

VIEW ORIGINAL CONCENTRICITY GAUGE

The data from the 1994 tests for rim thickness and shell weight sorting was inconclusive. The last test conducted at this range was for bullet concentricity. Bullet concentricity, also called run-out, is the relationship of the bullet axis to the case axis as illustrated in Figure 1. Finally, a test that actually had some consistency in the data. The data was not perfect because of my errors in technique. However, I had enough to convince myself to continue testing.

Figure 1;

Part of my inconsistent results from the first tests, Bullet Concentricity

were due to my beginning incompetence of how to

conduct a shooting test and then how to interpret the

test results. A decade later, now I believe that some

of these other factors can and do influence accuracy.

However, the results are small and masked in the bullet axis

data by other dispersion factors (errors) that have

a greater influence on measured accuracy. For

those of us who don’t have access to the six degrees

of freedom trajectory code, it may be important to case axis

identify the priority of accuracy influencing errors.

We then can reduce or eliminate those errors that

have a large influence on dispersion, and therefore

conduct tests with diminished masking errors.

My conclusion from the 1994 results was simple, I needed better facilities to conduct tests and collect data. Then a good friend of mine, Dr. Dan Durben, came through with a gift from heaven, permission to use the Olympic Training Center’s indoor shooting range. The Center’s indoor range is a 50 meter facility with electric target changers, and most importantly to me, a bench rail test vise. The bench rail vise at the OTC is the style that mounts a rifle in the stock and my 1413 Anschutz was again used for testing.

Once again the rim thickness sorting did not produce statistical results. Additionally, the bullet weight measurements did not produce any reliable data. However, Eley 10x shot two consecutive tests that strongly supported the bullet concentricity theory. Figure 2 contains the measured results of these two bullet concentricity tests. These tests were shot with 10 round groups. Because of the multiple tests I had prepared for, the bullet concentricity tests were fired with bullets that all had the same 0.041” rim thickness.

Figure 2: Bullet Concentricity Test**, Group Diameters-inches, OTC, 50 Meters.

Bullet Concentricity	Loose*	.000	.001	.002	.003
Eley 10x, Lot EEL98, series 1	.360	.350	.510	.570
Eley 10x, Lot EEL98, series 2	.400	.390	.450	.570
Average of the two series	.380	.370	.480	.570

*Loose = bullet that is physically seated loose in the case.

VIEW ACTUAL TARGETS FROM SERIES 1

VIEW ACTUAL TARGETS FROM SERIES 2

I tested ten brands of ammunition in these 1995 experiments at the Olympic Training Center. This lot number of Eley 10x shot the smallest groups when firing the baseline trial. I am convinced that this particular lot of Eley 10x produced the above groups because it was the best harmonically balanced with my 1413 Anschutz. However, I have no evidence to prove this statement. Another important conclusion that this testing session revealed was, only the best ammunition is worthy of testing at 50 meters or longer. Less expensive brands of ammunition seem to have too many accuracy limiting errors, probably due to the economics of component cost, and the speed of manufacturing used to reduce unit expenses.

Leap forward through the next eight years of raising four kids and studying anything I could find concerning rifle accuracy. Contained within this stack of books I found the physics law responsible for how bullet concentricity effects dispersion. The challenge now was to take my meager evidence to someone with the facilities capable of proving the theory true in 22 caliber long rifle ammunition, and then convince them to help me conduct a final controlled test. This theory is not new to the firearms industry and its effect has long been battled in the design of modern target rifles and ammunition. To my knowledge, no one has ever researched this theory in 22-caliber long rifle ammunition with low ballistic coefficient lead bullets at subsonic speeds.

I am lucky enough to live in the Black Hills of South Dakota. This area is very firearms industry rich, and one of those companies is H-S Precision. H-S Precision is known for building very accurate rifles, pistols, and barrels utilized by the public, law enforcement, and the military. They are also the originators of the aluminum chassis bedding block composite synthetic stock. In addition, they manufacture ballistic test barrels and equipment for all of the firearms industry. It was only natural that I chose H-S Precision to present my evidence to, a company renowned for its’ pursuit of accuracy. It took a little finesse and a lot of luck, but I scored a meeting with Tom Houghton Jr., President of H-S Precision. I presented my data and evidence to Tom and he agreed to help me finish testing. It took over a year to get in the tunnel because of their busy schedules and commitments. However, it was worth the wait to access this quality of equipment.

In preparation for these tests, I had learned to only use the best ammunition available on the market. My prototype 22 rimfire bullet concentricity gauge measures the axial relationship of the bullet to the case. In reality, this measurement is the statistical variance of bullet seating during the manufacturing process. Figure 3 shows the percentage yields of the bullet concentricity measurements for the test ammunition. I also added some extra brands of ammunition, just for reference.

Figure 3: Bullet Concentricity as percentage by brand.

Brand	Loose	.000	.001	.002	.003	.004	.005	.006	.007	.008
Eley 10x, 1995 lot	14 %	17 %	53 %	13 %	3 %	**
Eley 10x	3 %	16%	69 %	12 %	1%
Eley Ultimate EPS	15 %	5 %	32 %	35 %	11 %	2 %	**
Lapua Dominator	4 %	6 %	39 %	45 %	6 %
Lapua Midas M	1 %	5 %	37 %	44 %	12 %	1 %
Eley Club Xtra	2 %	8 %	22 %	34 %	23 %	7 %	2 %	1 %	1 %
Federal Ultra	4 %	8 %	20 %	41 %	12 %	11 %	3 %
Winchester Mk III	0 %	3 %	18 %	27 %	20 %	15 %	8 %	5 %	2 %	2 %

** = less than 1 percent of the measured ammunition.

Loose Þ bullets that are physically seated loose in the case.

On to the 2004 shooting tests at H-S Precision. The shooting tests were conducted in one of H-S Precision’s climate controlled shooting tunnels. H-S Precision supplied a new 22-caliber ballistic test barrel that is 2 inches in diameter, and 22 inches long. The barrel was mounted in a machine vise and bolted to the concrete floor. Every round was chronographed to detect any large variance in velocity, which may influence groups. The ballistic test barrel was cleaned between every brand of ammunition and seasoned with four rounds of ammunition at the start of each brand. All individual test groups were fired with 20 rounds. Some of the brands were fired in progression of the bullet concentricity and some in regression, to minimize the effect of barrel fouling in the data. Additionally, two of the four brands of ammunition were fired with mixed lot numbers, this was by accident not design. From the results of the 1995 shooting test, I had calculated that for every 0.1 degree in base angle, there is 0.15 inch dispersion at 100 yards. This calculated slope is what I would be looking for in the new charted data.

We suffered a couple of nights of setbacks due to mechanical problems. But Tom was great and had them fixed in short order. After 10 years of trials and research I have to admit that sleep was short, very short. Finally, the third night at H-S Precision we are shooting. However, the targets are not very good. There seemed to be a trend, but it is not straight line like expected or predicted. Arriving home that night disgusted, I pulled out my dial caliper and started to measure groups anyway. Then some math, and plotting of the data. The average slope of the dispersion line on the graph is at the expected angle, but it is way too high. This told me that it is working, but it’s not. It is now 2:00 a.m., I have hardly slept in three days, and I have to be at work at 6:00 a.m. Good night.

The next day at work it hit me, there is an error in the machine vise. That is a logical conclusion of why the group diameters have all shifted up the graph, from their expected smaller diameters. Well, now I had a fun job. I had to go to Tom that night and explain my mathematical evidence shows a problem existed in his expensive test equipment. At least he didn’t throw me out. We went down stairs, and after some investigation of the machine vise, we found the left front floor bolt was loose because the expansion nut in the concrete had pulled out. Could that really be the error of this 250-pound monster, shooting a 22? We fixed the floor mounts and began to shoot again. From the first little bug hole that night, targets poured out of the machine vise just about exactly as they were predicted. That single loose floor bolt was the problem, and almost ended ten years of work. Figure 4 shows the measured results of these shooting tests.

Figure 4: Bullet Concentricity Shooting Tests*, H-S Precision, Machine Vise, 2004

==== 20 round Group Diameters in inches ====

Bullet Concentricity	Loose	.000	.001	.002	.003	.004
Eley Club Xtra **		.330	.280	.390	.340	.350
Eley 10x W2B066		.240	.270	.275
Lapua Midas M		.230	.280	.295	.315
Eley 10x EEL98	.290	.250	.270	.320
Eley Ultimate EPS	.310	.240	.300	.380	.380
Average ( 80 rounds )	.300	.240	.280	.318	.348

** Eley Club Xtra not included in the average group diameters or statistics.

VIEW THE ACTUAL TARGETS FIRED IN THESE TESTS

Eley 10X Lot W2B066

Lapua Midas M

Eley 10X Lot EEL98

Eley Ultimate EPS

Eley Club Xtra Lot FN1447

Figure 4A: Statistics of Bullet Concentricity Shooting Test, H-S Precision, 2004.

Bullet Concentricity	.000	.001	.002	.003
Mean	.240	.280	.318	.348
Standard Deviation	.008	.014	.045	.046
Confidence	99 %	98 %	98 %	95 %
Confidence Test	.240±.002	.280±.004	.318±.011	.348±.014

For those who are not familiar with a Confidence test, the proper way to read this is;

This rifle has a 99 percent chance to shoot .000 B.C. bullets in a .240” diameter ± .002”. (Diameter from .238” to .242”). Everyone should be able to substitute the other three confidence tests into this statement. I don’t think you really need any more evidence, the bullet concentricity theory is true with match grade 22 caliber long rifle bullets.

Following is a chart of the shooting test data for bullet concentricity measurements. There is a color key at the bottom of the chart. The four brands of ammunition all have their own color code seen in the key. The average of the four brands included in the 2004 tests at H-S Precision is shown in heavy black. The heavy brown line at the bottom of the chart is the expected dispersion calculated from the testing at the Olympic Training Center. These two equal dispersion slopes provide confirmation of the data between the two independent tests. The reason the shooting test groups do not go to zero is because of the other remaining errors in the machine vise. A discussion of how multiple accuracy influencing errors effects group diameters follows later in this article.

There are blanks in the shooting tests because the yield of bullet concentricity’s from the 1,000 rounds purchased for a brand was not enough to complete a 20 round test. One disparity in the tests is how the loose bullets reacted. In the Anschutz test, they shot most like the bullets with no run-out. In the ballistic barrel, the loose bullets shot more like the bullets with .001” run-out. I have evidence that loose bullets perform this well because they “self align” with the bore axis in match grade chambers to some extent. The logical conclusion is that they will shoot more like the no run-out bullets in other match grade rifles. I included Eley Club Xtra in this test for confirmation of my earlier conclusion. Once again the conclusion of the test; cheap ammo is still cheap ammo.

I am surprised about the statistical evidence we were able to produce. There are a number of errors that could have influenced the results. First, my homemade bullet concentricity gauge was manufactured on a Unimat with over a .0005 inch error in it. Second, I am only human, I could have misread the swing on the gauge needle, or simply dropped the bullet into the wrong box after measuring. These are some of the possible errors that probably did creep into the numbers somewhere. I am sure there are more.

I mentioned earlier that there are physics laws responsible for the bullet concentricity dispersion. This law of physics states that pressure can only act perpendicular to a surface. Upon exit from the barrel, the base of the bullet is still under high pressure, (5,000-15,000 psi ±). In this region of transitional ballistics, if the base of the bullet is angular to the bore axis, the bullet is influenced on a new dispersion at an angle perpendicular to the base of the bullet. Figure 5 is a pictorial representation of this event. The amount of dispersion is a result of three factors; angle of the base, pressure on the base, and time of pressure acting on the base. Resources that I studied suggest that this dispersion occurs in about the first eight calibers from the muzzle. Originally I thought that long barreled 22 caliber rimfire rifles probably have one of the lowest dispersions because the powder is burned in about 16 inches of the barrel. The muzzle blast pressure would therefore be substantially reduced before exit in a long barrel. However, from my experimental results, the calculations show that the dispersion of 22 rimfire bullets is fifty percent greater than high-power cartridges per degree of base angle. Time might be my error, possibly the deep hollow base of match grade bullets is more efficient at transferring the muzzle blast energy to the low mass bullet.

Figure 5: How an angular bullet base at muzzle exit effects accuracy.

BARREL

BORE LINE

PRESSURE PLANE

NEW BULLET TRAJECTORY

MUZZLE BLAST

Pistol bullets exit with almost maximum muzzle blast pressure and will therefore suffer greater dispersion per angle of base. Magnum rifle cartridges will also show a greater dispersion because of their increased muzzle blast pressure. As a footnote, bullet concentricity is not the only reason that a bullet can be angular to the bore. Bullet design, throat asymmetry, case neck concentricity, chamber and case dimensional differences, and bore to chamber axial alignment, could all cause or enhance this dispersion. In modern target rifle and target ammunition all of these manufacturing errors usually have been addressed, but not in sporting rifles or ammunition that are mass-produced.

It may help some to understand how multiple error dispersions in a rifle effect the total group size. The total dispersion in a system is equal to the square root of the sum of the squares of the individual error sources, Total Error = Ö A² + B² + C² + D² + E² ..…. As an example, if we have a system that has 6 error sources, each of ½ inch dispersion, the total dispersion is not 3 inches. The correct dispersion answer is 1.225 inches. So, if we fix one of the ½ inch dispersion errors, group size is not reduced by ½ inch, we only reduced our group size by 0.1 inch. A graphical picture of this progression of the total amount of dispersion is shown in Figure 6. As you study this chart, keep in mind that in a real ballistic system, errors of dispersion are not of equal value. You may remember my earlier comment about the priority of accuracy influencing errors in a ballistic system. It is possible that you could be testing for an error of small influence, and another error with a larger influence on dispersion could completely mask your results when shooting test groups with a minimum number of rounds.

Figure 6: Group Diameter Dispersion in a rifle with six equal error sources of ½ inch.

1.22 “
	1.12 “
			1.00 “
				0.87 “
					0.71 “
						0.50 “
1 error	2 errors	3 errors	4 errors		5 errors	6 errors

We can use this Root Mean Square Formula to calculate the individual dispersion contribution of the bullet concentricity measurement. From the OTC test, we can assume the bullets with .002” run-out is total dispersion, and the bullets with .000” run-out are the remaining unresolved errors. With simple substitution into the Root Mean Square Formula; .570 = Ö .370² + X². We can calculate the individual dispersion contribution of .002” bullet concentricity is 0.434 inches at fifty meters. From this calculation you can easily see that bullet concentricity is a significant contributor to dispersion. However, this is probably not a true calculation in relation to the bullet concentricity measurement. First, I have evidence that there is chamber straightening occurring in match grade rifles, therefore the calculated dispersion contribution should be larger. Second, bullet concentricity is not the only reason you can have an angular bullet base at muzzle exit. Third, this calculation is only for bullets with .002” run-out, and in the samples measured there were bullets with up to .005” run-out in the match grade ammunition.

One last important discussion about bullet concentricity and its effect on you. Please refer to Figure 2, the original test at the Olympic Training Center. From this test we can formulate that for every .001” error in bullet run-out, dispersion increases 0.1 inch at 50 meters. (Every .001” B.C. = 0.1” @ 50 meters) Now if we refer to Figure 3, you can see that 1-2 percent of match grade ammunition measures .004” bullet run-out. Theoretically, these .004 bullets would shoot a .770 inch group, and could be solid 9’s even with a perfect hold in this rifle. (.370” base + .400” dispersion = .770”). Be aware that this is not straight-line correlation. First, these bullets can strike anywhere in the .770” diameter and mathematically 33 percent will score a 9. Second, because sometimes the bore line could be left, and the dispersion goes right. This 1 bullet out of ±200 might just shed some light on a few of you that just knew that shot was an X in the sights. It’s happened to me, and that is exactly what got me in this mess.

Keep in mind that the rifle, test barrel, and ammunition used in these tests all have their own personalities, (remaining unresolved errors). My out of the box 1413 Anschutz showed a 35 percent reduction of group size (-0.200 inch) with Eley 10x. However, group size did not go to zero, that means there is more personality in my Anschutz. What is important to remember is the relationship of the reduction of group diameter by the bullet concentricity theory, and the number and magnitude of remaining errors in a ballistic system also influence group diameter. In plain language; firearms with fewer and smaller remaining errors, will have a greater percentage reduction of group diameter after correcting one of those errors.

Copyright 2004

Lester L. Nielson

www.nielsonbrothersarms.com