My wife is a competitive American Rimfire Association (ARA) shooter. I'm the pit crew and chief roadie.
Tuning is fundamental to success in rimfire competition and we are blessed with a seemingly endless supply of "tools" (mid-barrel tuners, end-barrel tuners, deresonators, slides, etc.) to help achieve that elusive perfect state of tune.
The theory is simple, we want the bullet to exist the barrel as the muzzle is moving upward. In this happy state faster moving bullets exit earlier than slower moving bullets. Since the barrel is moving upward, the slower moving bullets exit at a launch angle that is steeper than the launch angle of the faster moving bullets.
This state of bliss is known as positive compensation and helps minimize the vertical dispersion that would result if both the faster moving bullet and the slower moving bullet existed the muzzle at the same launch angle.
While the tuning process can be modeled, the only practical way to tune a given rifle is through very tedious and often frustrating trial and error.
But, for those inquiring minds that wish to dive a little deeper into the subject, Varmint Al has a very technical webpage on the subject - complete with FEA - enjoy:
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JackHughs