In the American Civil War, infantry soldiers fought with rifled muskets, reasonably accurate projectile-launching weapons used to wound or kill enemy soldiers. However, in order to hit the chosen target, soldiers need to choose a correct firing angle. The primary question this study answers is at certain distances, what is the likeliness that the mean soldier can choose a correct firing angle.
Basic Assumptions:
- A male human is roughly 70.2 inches tall (5 feet 10.2 inches) and has a head that is 10 inches in height.
- A rifleman fires from about the height of his chin (as he compresses his body before firing).
- The target is an infinitely long and 70.2 inches in height, so as to isolate the vertical angle of firing.
- The bullet is an accelerating reference frame (according to Einstein’s Theory of General Relativity), thus the projectile can be assumed to travel in a straight line instead of an arc influenced by gravity.
- The chosen image supplies the firing angles of rifles chosen at random (that each angle is randomly chosen and independent of the others is a stretch, but I will make do all the same).
- The GIMP Measure Tool can approximate the firing angles (again, a stretch, but I will make do).
Based off simple trigonometry, the angle of error that still hits the target can be approximated.
Table of yards and degrees of error:
Variance of Firing Angle of Reenactors:
The GIMP Measure Tool was used to approximate the firing angles of each musket to the right of the smoke. Unfortunately, the Measure Tool does not indicate a positive or negative slope, and thus negative and positive values were randomly assigned to the angles. It should be understood that this may exaggerate the variance in firing angles. Running a 99% confidence interval with 13 degrees of freedom indicates that the mean firing angle is 99% likely to occur between -4.60 degrees and 2.51 degrees. Thus, it is likely that the mean infantryman will aim his rifle within 7.11 vertical degrees of the needed value to hit the target.
Chance of Correct Angle:
The chance of the mean rifleman will choose the appropriate angle to hit the target can be approximated by the needed angle divided by 7.11 degrees (the mean variance of the firing angle).
This formula suggests that a rifleman has the following probabilities of firing at the correct angle at the given distances:
10 yards – 100%
50 yards – 31.3%
100 yards – 15.7%
160 yards – 9.80%
Conclusion:
The average Civil War infantryman would be lucky to hit a target in battle conditions. At the estimated average engagement range of 100 yards (Paddy Griffith), a soldier could be expected to aim correctly only 15.7% of the time. Under battle conditions, it is not only likely for this percentage to decrease, but other factors, such as fouling of the barrel and smoke, would likely contribute to a very small chance of hitting a chosen target. Outside of 160 yards, chances of hitting a target would be very slim.
It should be noted here that this study is merely an overview of the chances of hitting a target, and it should be verified by other sources or studies which do significantly more research to determine those chances. In addition, sharpshooters with sights are not accounted for, and their accuracy should not be inferred from any equations or data derived.