column By: Staff | February, 21

There is a common belief among rifle shooters that smaller velocity variation equals smaller groups. This belief has been repeated so many times that now it is assumed as fact. When shooters share groups from their fine-shooting black powder cartridge rifle (BPCR) they will add, “And the velocity standard deviation is in single digits.” Generally, shooters like numbers such as scores, groups in inches, and velocity variation. As a result of my professional training, I probably like numbers more than most people. We all like to use numbers to quantify the quality, or lack of, just about everything. For example: golf scores and handicaps, time to run 40 yards or drag race a quarter mile. We have even gone so far as to rank football quarterbacks with a number. The passer rating for NFL quarterbacks ranges from 0 to 158.3. If everything worked out according to the numbers when two teams meet, the team with the highest quarterback rating wins. Similar to chronograph readings, it does not work out that way. The lowest velocity spread does not always equal the smallest group.

About 20 years ago, I was shooting with some friends in Raton, New Mexico. One of our group had a very nice three-screen chronograph. Of course, we all wanted to shoot our pet load across the chronograph and see how well it would perform. One fellow in our group had a Sharps chambered in .45-70 that he was very proud of and, unfortunately, his velocity spread was much lower than my .38-50 Remington Hepburn load. He announced to the group that his load was therefore much more accurate than mine. Challenge accepted. At one time, there was a large round gong on the Raton silhouette 500-meter line. It was proposed that we each shoot a 10-shot group on the gong and determine which load was indeed more accurate. After firing and measuring the groups, my .38-50 group was much smaller than his .45-70. Being fascinated by such things, I kept trying to understand how that could have been the outcome. The other shooter and I were of fairly equal ability and the shooting conditions were good. As I recall, it was not one or two shots that spoiled his group, it was just large overall. At the time, I thought if the velocity spread was smaller the group had to be tighter. I became mildly obsessed with velocity variation and velocity standard deviation.

Like many shooters, I receive multiple shooting magazines in my mailbox. Whenever any accuracy and velocity spread information was presented in an article, I would pour over the values to determine if there was any correlation between small velocity spread and small groups. On an anecdotal basis, my review found that, as often as not, the smallest groups in the presented tests did not have the lowest velocity spreads.

The data presented within the articles were normally comparing six, five-shot groups. I realized that one of the problems with this analysis is the sample size was too small. For a statistical theory to be applied, a test should have a sample size of 30 or greater. Meaning, only when we have greater than 30 groups can we reasonably determine if there is indeed a correlation between velocity spread and accuracy. That is a lot of shooting and reloading for a BPCR. If you have read *Shooting Buffalo Rifles of the Old West* by Mike Venturino, you would find that Mike shot 79, five-shot groups at 100 yards and measured the size and velocity spread of the groups. This book is a wealth of information and a joy to read. I highly recommend it. Mike was kind enough to permit me to use the data presented in his book for statistical analysis. I don’t intend to do a deep dive into statistics, but just enough to prove my point.

What we have is 79 data points with cartridges ranging from the .40-70 BN Sharps to the .50-90 Sharps. Black powder and lubricated lead bullets were used for shooting each five-shot group. Of course, due to the different cartridges, many rifles were used for the test. Using many rifles in the test is a good thing as it creates more variability within the data set. If we desire to develop a correlation between a dependent variable, (group size) and an independent variable, (velocity spread) data variability helps us identify a relationship.

Plotting the group size and associated velocity spread resulted in the following scatter graph, Table 1. There is also an equation for the fitted line. What the equation tells us is that an increase of 10 feet per second in velocity variation results in a group size increase of 0.45 inch. So, there is a relationship between velocity spread and group size for this data set. However, there is more to the story. Look at the graph and you will see the data does not perfectly follow the fitted line.

There is also an R2 value for the equation. This is pronounced “R squared” and is also known as the coefficient of determination. The R2 for this data is 0.111. The basic interpretation is that only 11.1 percent of the change in group size is explained by the variance in the velocity spread. Conversely, it means that about 89 percent of the variation in group size is explained by something other than velocity spread. Think about all the variables that could impact accuracy: bullet lube, powder charge, bullet fit to the barrel, a weak hammer spring, broken firing pin, and perhaps the buttstock is loose. We have now identified some of the things that make our rifles more or less accurate. I am not saying that chronograph readings don’t add to our quest for finding the most accurate match load. Chronographs just don’t have as big an impact as we might believe. In the case of this data set, they help us explain 11.1 percent of the change in group size.

As a second data point, I found some 6.5x47 data on YouTube where five-shot groups were fired with 10 different powder charges, and the velocity variation was presented with group size. This test was presented to demonstrate that low velocity spreads resulted in smaller group sizes. I could not resist. I followed the same methodology as presented for the BPCR groups and obtained an R2 of 0.0089, which is extremely low. Not surprisingly, the equation was found to not be statistically significant, which means for the 10 groups measured there was no valid correlation between velocity variation and group size.

I do have one housekeeping issue. If you are wondering, yes, I did run an ANOVA table on the black powder data, and both variables, (velocity spread and group size), and they were found to be statistically significant variables for this data. It is possible to fit equations to data that are not statistically significant. Meaning there really is not a relationship even though you have an equation, such as the 6.5x47 data. Enough statistics.

I know what the next discussion item will be: “Wait a minute, although the velocity variation explains only 11 percent of the change in groups size if there is too much velocity variation, then the vertical spread of the group at an extended distance will be enormous.”

For that reason, I need a chronograph to find the load with the least velocity spread so that I will not have high and low shots at long range. Yes, this is partially true. I have seen the tables shooters develop showing how much higher or lower the bullet impact will be with 10 or 20 feet per second variation in velocity. To a certain extent, this is theoretically correct. However, we have to make one large assumption. That assumption is the muzzle of the barrel is in the same position every time the bullet exits the barrel.

Unfortunately, this is not the case. All barrels vibrate. This vibration occurs while the bullet travels down the barrel and continues after the bullet exits. As an example, “the Springfield rifle, with standard military ammunition, has an angular movement of the muzzle due to vibration equal to more than 40 feet at 1,000 yards.” This type of movement of the rifle barrel makes 10 or 20 feet per second velocity variation seem small in comparison. Harold Vaughn’s book, *Rifle Accuracy Facts* is an extremely interesting book for those that enjoy empirical information on what truly impacts a rifle’s accuracy. If you happen to have the book and you open to chapter four (Barrel Vibration), the opening sentence reads, “Barrel vibration is one of the largest contributors to rifle inaccuracy.” Certainly, this also applies to black powder cartridge rifles as well.

There are five proposed barrel vibration modes, with Mode 3 being the one accepted by Vaughn. I have used Excel to present a sketch that mimics the barrel vibration in Mode 3. Vaughn used accelerometer measurements near the muzzle of his rifle to validate the Mode 3 vibration. The rifle action is defined as the supporting end and the barrel is a cantilever beam. You can see a similar vibration by whipping your favorite fishing rod, the nodes as presented in Table 2 will become apparent.

There are simple methods we can use to detect and track our barrel vibration and use it to our advantage. If we do this, we can minimize long-range vertical dispersion and increase the accuracy of our black powder match loads. It is possible to adjust our velocity so our bullets exit the muzzle at either the top of the vibration or at the bottom of the vibration, (Figure 2 shows the barrel at the top of the vibration path). The reason we want to be at either end of the vibration is the muzzle must stop momentarily before it can reverse direction. It does not stop for long but it does stop. In the end, adapting to barrel vibration will result in smaller group sizes than fiddling with the chronograph. Increased accuracy and precision is our goal and many components impact this. We have seen that velocity variation has an impact, but is less than we might believe. Now I have shown that barrel vibration also has an impact. However, I would like to save the discussion related to tuning loads to deal with barrel vibration for a future installment.

**References:**

1. *Lyman Reloading Handbook, 1970, 45th Edition*.

2. Venturino, Mike 2002, *Shooting Buffalo Rifles of the Old West*. MLV Enterprises, Livingston, Montana.

3. Vaughn, Harold 1998, *Rifle Accuracy Facts, Precision Shooting Inc. Manchester, Connecticut*.

4. T. J. Napier – Munn 2014, *Statistical Methods for Mineral Engineers*, Julius Kruttschnitt Mineral Research Centre, Queensland, Australia.