By Pierre van der Walt
While one can often get away with a rough estimate of the actual center of a fired group on a target and adjust accordingly relying somewhat on trial-and-error, there are instances such as open sight adjustment, when the exact statistically correct center of the group has to be determined. That center of the group is not in the middle of the bullet holes the furthest apart horizontally and vertically.
When you really need to be accurate you obviously have to start with a fouling shot not aimed at the target reference. Once the barrel has been fouled, you then fire your group, but it has to consist of at least 5 shots for moderate statistical validity. A 3-shot group is useless for this purpose. Once the group has been fired you draw a vertical line (AA in our example) through the left-most bullet hole if the group is on the left of the target, or through the right-most bullet hole if the group is to the right of the aiming point. Also draw a horizontal line through the bottom bullet hole if the group is above the aiming point, or through the top hole if it is below the aiming point. (BB in our example.)
Determining Horizontal Center
| Step 1 | Total the Deviations from the AA Reference Line | |||
| Shot 1 | = | 0.000” | (0,00mm) | |
| Shot 2 | = | 1.044” | (26,5mm) | |
| Shot 3 | = | 1.119” | (28,4mm) | |
| Shot 4 | = | 0.747” | (18,8mm) | |
| Shot 5 | = | 1.284” | (32,6mm) | |
| TOTAL | = | 4.194” | (106,3mm) | |
| Step 2 | Divide the Total for an Average Deviation | |||
| 4.194” | ÷ | 5 shots | = 0.8388” | |
| 106,3mm | ÷ | 5 shots | = 21,36mm | |
| Step 3 | Mark the Center Line | |||
| Draw a Vertical Line XH 0.8388” to the right of line AA. That constitutes the statistical horizontal group center. | ||||
| Step 4 | Measure Correction | |||
| Measure distance between XH and the aiming point to determine correction required. In our example it is 0.863” (21,9mm) indicated by the horizontal green arrow. | ||||
| Determining Vertical Center | ||||
| Step 5 | Total the Deviations from the BB Reference Line | |||
| Shot 1 | = | 0.836” | ( 21,2mm) | |
| Shot 2 | = | 1.867” | ( 47,4mm) | |
| Shot 3 | = | 0.000” | ( 00,0mm) | |
| Shot 4 | = | 1.492” | ( 37,9mm) | |
| Shot 5 | = | 1.192” | (30,3mm) | |
| TOTAL | = | 5,387” | (136,8mm) | |
| Step 6 | Divide the Total for an Average Deviation | |||
| 5.387” | ÷ | 5 shots | = 1.0774” | |
| 136,8mm | ÷ | 5 shots | = 27,4mm | |
| Step 7 | Mark the Center Line | |||
| Draw a Horizontal Line XV1.0774” above line BB. That constitutes the statistical vertical group center | ||||
| Step 8 | Measure Correction | |||
| Measure distance between XV and the aiming point to determine downward correction required. In our example it is 1.5934” (40,5mm) indicated by the vertical green arrow. | ||||
| Answer | X Marks the Spot | |||
| The intersection point (X) is the actual center of this group. One can now adjust very precisely and save on ammo and time. | ||||
This method is particularly important when intending to drift open sights. The formula for open sight drifting is provided in the article: Open Sight Adjustment & Formula.
