Bullseye Questions and Answers - Handgun Accuracy

by mikemyers 11/3/2017, 6:04 am

Bullseye Q & A
By: Dave Salyer

Question:
Although I haven’t recently received a specific question on the factors contributing to handgun accuracy, I decided to write about a method for calculating or closely approximating the combined effects of the various factors that keep all shots from going through the same hole in the target. There is always lots of discussion about the subject when shooters get together.

Answer:
About eight years ago (December 27, 1996) I developed a theoretical method for calculating the combined effects of any number of factors that can affect shot group sizes. The calculation is based on a fairly standard statistical formula for showing the combined effects of more than one variable.

I will try to illustrate this by dealing with the capabilities of some of the hardware used in shooting as well as the soft tissue inside of the hard head of us pistol shooters. When speaking about offhand pistol shooting the human capability variable is almost always the largest contributor to errors.

For purposes of illustration I will leave the effect of wind blowing on the shooter and his bullets in flight out. Also, I will assume the sights to be perfectly zeroed with the center of all groups of shots. My examples will assume we are talking about government model 45 ACP’s with the standard 5-inch barrel. I will also assume we are talking about only slow fire at 50 yards in this writing.

Any variability that can be measured can be combined mathematically using the method that will follow. Some of these variables are: the ammo grouping capability, measured by testing it through a fixed barrel known to be of excellent quality. The gun barrel’s grouping capability measured by a barrel tester such as the one designed by Nathan Wade, of Pelzer, SC. The overall pistol’s capability can be measured by shooting 30 - shot groups from that pistol mounted in a machine rest such as the well-known Ransom Rest.

The shooter’s holding capability is the most elusive to measure. However, I am convinced it can be done if great care is taken and the shooter can be totally honest with himself. Keep in mind that this capability is different from time to time based on all the human factors. On a given day you can closely approximate your capability to “hold” the gun if your pistol is fitted with any of the commonly available red - dot “scopes”. Just take your position and stance at the 50 - yard line and aim (without shooting) at the standard NRA target. Hold the gun about 20 seconds as steady as you can with the dot wobbling about the center of the target. Make a mental note of the outer edge of your wobble area by comparing it with the edge of the black bullseye or the scoring rings outside the black. For example, if your wobble area (arc of movement) is about the size of the 7-ring you can measure that with a ruler.

To illustrate the principle of combined shot grouping capability, I will assume the following has been measured by testing as described above:

* the ammo is good for 2” groups ... Call that... GA
* the pistol is fitted well enough to give 3” groups... Call that... GP
* the shooter can hold a 9” circle (just over 8-ring) ... Call that... GS

We will use the following statistical formula to combine these group spreads:

ES² = GA² + GP² + GS²

or,

ES = SQRT (GA ² + GP ² + GS ²)

…where ES is the extreme spread expected when the other capabilities are combined.

ES = SQRT (2 ² + 3 ² + 9 ²)
ES = SQRT (94)
ES = 9.7”

Let’s try a second example assuming the pistol and ammo capability is perfect with no spread of the group, and the shooter still has a holding capability of a 9-inch circle. The total extreme spread would be the square root of 81, or 9”. Note that the difference in these two examples is only 7 tenths of an inch!

Let’s try another example using a typical out-of-the-box government model:

From the Ransom rest we find that the gun and ammo we test gives a 30 shot group of 9” at 50 yards.

The same shooter can still hold a 9” diameter arc of movement.

ES = SQRT (9 ² + 9 ² ) or SQRT (162) or 12.7”

Since our imaginary shooter has good trigger control and he won’t jerk or heel any shots, we can assume all of his hits cluster about the center of his wobble circle in accordance with the “bell curve” for standard normal distribution. If I simulate his hits this way graphically on a target it will show that his 30 shots of slow fire will yield a most likely score of 288 for the accurized 45, a 281 for the out-of-the-box pistol, and the imaginary perfect pistol/ammo combination would yield a theoretical score of 291.

My personal testing using a barrel and bullet testing rig along with a Ransom machine rest has verified to my satisfaction that the above theory is compatible with actual results. When I have a good day at the range and don’t jerk and heel I can verify the theory by hand, also.

Good equipment and ammunition are still vital because they give us a slight mechanical advantage along with the confidence needed to cause us to put forth our very best effort. Many categories, classes, matches and national championships are won by only one point and sometimes by a few “exes”.

Originally printed in the Virginia sport shooting association’s news magazine “The Bullet”

(Re-formatted by Mike Myers - if there are any text errors, it's probably my fault.)