A Black Powder Cartridge

Reloading dies come from the factory with a case neck expander. The diameter of these expanders can vary, especially with calibers such as .40-65 WCF, .38-50 Remington Hepburn, or .45 Colt. Normally, I use aftermarket expanders since the standard ones supplied are not always appropriate for the bullet diameter. These are either too large or more frequently, too small. Completing some limited neck tension testing in the distant past, I always felt that the expander should be the same diameter as the bullet. This was anecdotal evidence, at best, since the sample size for the prior test was far too small to provide any statistical validity. Being on a revived pursuit for black-powder cartridge accuracy, I decided to retest neck tension in detail to determine if there was any measurable impact on accuracy.

TEST PLAN

The plan was to use four different expander diameters to test for any accuracy difference between the resulting neck tension. Expander diameters used were .373, .375, .376 and .377 inch. Gauge pins were modified and used as expanders. These were rounded and tapered on one end and held in a bullet puller to effect expansion.

Gauge pins can be purchased relatively cheaply. The selected pins were Z plus. These pins are approximately three ten-thousands of an inch over the stated diameter. As a point of reference, the final case inside diameter was consistently .001 inch less than the pin expander diameter. If an expander with the same diameter as the bullet is used to expand the case, it will spring back enough to hold the bullet firmly. The final inside diameters tested were: .372, .374, .375 and .376 inch. The 20:1 (Pb:Sn) 367-grain Money bullet was used for all the tests and has a base diameter of .376 inches. All case neck inside diameters were double-checked with gauge pins before loading. For clarity, the final neck tension for the four tests was four, two, one and zero thousandths of an inch. This is based upon the final expanded inside dimension of the case and the outside dimension of the Money bullet basebands.

A total of 35 cartridges, plus foulers, were loaded for each neck tension, resulting in a total of 140 rounds for the planned test. The hypothesis for the test was there will be no difference in accuracy between the four different neck tensions. To avoid shooting the four tests under dissimilar conditions, I decided to shoot the four different neck tensions as a series of five-shot groups. Rather than basing the analysis on group size, which would only represent the two worst shots, I decided to use a variation of the mean radius method for the analysis. Five-shot group sizes are included in the analysis section for interest. Julian Hatcher in Hatchers Notebook and JS and Pat Wolf in Loading Cartridges for the Original .45-70 Springfield Rifle and Carbine both present a good description of the mean radius method.

To obtain the mean radius of a five-shot group, measure the heights of all shots above a horizontal line drawn through the lowest shot. Averaging these measurements will give the center of the group above the horizontal line. In the same manner, measure the horizontal distance from a vertical line drawn through the furthest left shot. Averaging these measurements will locate the center of the group from the vertical line. Where the vertical and horizontal averages cross is the group center. The distance from the group center is measured for each shot. These measurements are normally averaged to arrive at the mean radius. I input the horizontal and vertical data into an Excel document. Rather than measuring the distance from each shot to the center of the group, I calculated the values. However, this could be done with a No. 2 pencil and a ruler.

Using the mean radius method, I end up with one value for each group of five shots. I did calculate the distance from the group center to each shot as prescribed in the mean radius method, but I did not average the five shots radius distance. Using this methodology allows for the inclusion of the variation from each shot in the analysis, which resulted in 35 data points for each expander diameter, rather than seven data points (seven, five-shot groups). From a statistical view, any sample size less than 30 is considered a small sample. This is the rationale for 35 shots for each expander diameter. As part of the testing program, I planned to complete an analysis to determine if there was any statistically significant accuracy difference between the four expander diameters.

Since the test required 140 shots, I couldn’t complete the test in one shooting session. Sessions were limited to 40 shots, which were two, five-shot groups for each of the four expanders per visit to the range. The shooting order of the tests was varied. Range sessions were conducted on carefully selected days with near-perfect conditions. All shooting was from 200 yards, prone, over cross sticks. Two wet patches between shots controlled fouling. After every 20 shots, (four, five-shot tests, one for each expander diameter), I ran two extra wet patches and allowed the barrel to cool. Before starting the next 20-shot series, I fired two fouling shots. Using a ground scope, I observed where each shot landed. Since I was shooting two, five-shot groups on a Schützen target, I did this to ensure the groups were separate and discrete. During the shooting, I did have one occasion when one shot overlapped into the prior group. This was picked up with the ground scope and easily accounted for.

LOADING DETAILS

All shooting was completed using a CPA Stevens 44½ chambered in .38-50 Remington Hepburn. The rifle has a Green Mountain 12-twist barrel with nominal barrel dimensions of .376 bore and .367 groove. Hornady brass was used for the testing. The brass was fireformed from new Hornady .30-40 Krag brass using a small charge of pistol powder and Cream of Wheat filler capped with a wax wad. After forming, all cases were subsequently fired with black powder to ensure full expansion. The cases were then trimmed to 2.250 inches, sized, cleaned, annealed, flared and expanded to the appropriate diameter. The Hornady brass was found to be 13 grains heavier than my normal Winchester brass. This resulted in 2.5 grains less powder capacity. Based upon a brass density of 8.73 g/cc and the bulk density of black powder (1.72 – 1.8 g/cc) the lost capacity is equivalent to .19 grains of black powder per grain of brass. The neck thickness after fireforming was extremely uniform and the Hornady brass is of very high quality. I obtained far better brass by this fireforming method than I have in the past using a series of four expanders to open the case neck.

A 367-grain Money bullet cast from my 20:1 (Pb: Sn) alloy was used for all the tests. Each cartridge was loaded with a charge of 57 grains of 2Fg Swiss with a CCI Large Pistol primer and a .090-inch HDPE over powder wad. Before seating the bullet, all powder charges were compressed .190 inch. The overall cartridge length was 3.340 inches which is .030 inches proud of being fully seated in the chamber. Due to the taper of the bullet, the cartridges can be fully seated with strong thumb pressure, alternatively, the Stevens action upon closing easily seats the cartridges.

All cartridges were kept in separate containers based on the expander diameter used and were color coded with a felt-tip marker. The test targets were also labeled with the expander diameter, large enough to be read with the spotting scope from 200 yards to ensure keeping the correct cartridges on the correct target.

The rifle and bullet combination has been a very reliable performer in the past, so it was selected for this extensive test. All shooting was done with an MVA six-power scope with DZ mounts.

ANALYSIS

After all of the shooting, I ended up with a data set containing 35 measurements from the center of each group for each expander diameter. My hypothesis was there will be no difference in accuracy by using the four different expanders, .373, .375, .376 and .377 inch (null hypothesis). Completing an Analysis Of Variance (ANOVA), it can be stated with greater than 99 percent confidence, that there is a difference in accuracy between the four tests, Table I presents a summary of the results.

It is very apparent the .377 test demonstrated some very nice results with an average distance of .96 inch from the center of the group with a variance of .30. This leads us to believe that the .377 test is statistically different from the other tests. By removing the values for the .377 expander from the data set and rerunning the ANOVA, it was found there was no statistically significant difference between the .373, .375 and .376 tests. The three tests’ radius average ranged from 1.40 to 1.73 inches. Based upon the finding of no statistical difference between those three tests I can conclude the .377 expander gave the most accurate results for these test conditions.¹ The same analysis was completed using the vertical measurements to find if one of the expanders gave less vertical dispersion than the others. Again, the .377 expander resulted in a significantly smaller vertical with greater than 99 percent confidence, Table II presents the results.

Out of curiosity, the two widest shots for all of the five-shot groups for each expander size were measured to the nearest 1⁄16 inch using a wood ruler. The average of the seven, five-shot groups were 4, 41⁄16, 39⁄16, and 211⁄16 inches for the .377, .375, .376 and .377 expanders respectively. One might state, that based upon the five-shot group average, it is very evident that the .377 expander is much better. Yes, in this case, that appears to be correct. But it does not always work out that way and the statistical analysis allows us to interpret the results confidently. As Elmer Keith was fond of saying, “That proves it beyond the shadow of a doubt.”

CONCLUSIONS

Using the .377 expander with the .376 Money bullet resulted in minimal bullet tension and yet, still required a reloading press to seat the bullets. Immediately after seating, a small percentage of the bullets could be spun using finger pressure. The following day, no bullets could be spun without significant finger pressure. I assume the brass relaxed? During reloading, I was concerned about this minimal tension and felt the perceived inconsistency would not result in great accuracy. It turns out it was the most consistently accurate.

I am not certain why the very light neck tension works so well in my rifle. Perhaps greater neck tension reduces the diameter of the lead bullet or distorts the bullet? Maybe the light neck tension holds the bullet just enough to keep it properly aligned with the rifle chamber? Not knowing the exact mechanism for the accuracy improvement was not as important to me as the outcome.

I am very pleased with the test results and analysis. It is certainly easier to fire one or two, five-shot groups and draw some conclusions. However, if the test is not repeatable, or better yet, statistically significant, it is anecdotal at best; an anecdotal test usually with cognitive bias.

REFERENCES
¹ T.J. Napier-Munn pg.157

T.J. Napier – Munn, Statistical Methods for Mineral Engineers – How to design Experiments and Analyse Data. Julius Kruttschnitt Mineral Research Centre, Queensland, Australia, 2014

Hatcher, Julian S., Hatchers Notebook, Firearms Classic Library, Published for the National Rifle Association, Odysseus Editions, Inc, 1996
J.S. and Pat Wolf, Loading Cartridges for the Original .45-70 Springfield Rifle and Carbine, 2nd Edition, Published by Wolf’s Western Traders, Sheridan, Wyoming, 1996