Determining the Correct Group Center

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By Pierre van der Walt

 

While one can often get away with a rough estimate of the actual of a fired on a target and adjust accordingly relying somewhat on trial-and-error, there are instances such as open sight adjustment, when the exact statistically center of the has to be determined. That center of the 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.)

 

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.

 pic-group-centre-target-small

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.