What we are skirting around is explored and tested in Bryan Litz's latest volume (III) of Modern Advancements in Long Range Shooting, and resulted in his so called TOP (Theory of Precision) Gun Theory. He takes a bunch of data across many rifles and shots on barrel motion with high speed cameras, and also group size. He then explores a variety of models (mathematical equations) that involve momentum, energy, and weight of the rifle and bullet, and how well they fit the experimental data. His conclusion is the following equation:
Precision = 0.005*(KE/W_r)+0.039
Precision = 5 shot group average at 100yds in MOA
KE = Kinetic energy of bullet at the muzzle in ft-lbs
W_r = Weight of the rifle in lbs
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Conservation of momentum did predict barrel motion well. However, barrel motion did not correlate well with precision.
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