This is a very good explanation of the Physics, and how to shrink Group sizes at Long Range.... Long Range Shooting: Barrel Vibration & Accuracy | The Arms Guide
Your assuming that load velocity has a standard deviation of 0, or using it as a constant. Any velocity difference will effect either dogma. Standard Deviation & Load Development – North American Arms
Great Article! Taking it even further, It has also been found that "Tuning Harmonics" is even better at improving accuracy. Back in the 50's Winchester discovered that tensioning the barrel with a really heavy and dense hard wood stock would actually attenuate the harmonics of the Barrel during the entire firing cycle that the bullet was still in the barrel, thus mitigating POI shift and much of the fluctuation went away. Further, The Winchester Olympic Match Rifles of 1953 had an adjustable tensioning system to actually allow them to be tuned to the ammo being used. I have one of the first 300 Mod 52 Winchester Match rifles Made in that year FOR the U.S. Olympic Rifle team members, And I can attest to that rifles unbelievable accuracy! Fast forward to the mid 90's and A few enterprising folks started making what amounted to a rubber doughnut that slid down over the barrel and could be adjusted to dampen a barrels harmonics, effectively cutting group sizes by almost 1/3 or better. We saw another improvement in the Military when equipping long rifles with Suppressors, turns out that the alloys being used and the size and weight all contributed to increasing accuracy, Aluminum being a relatively neutral alloy and some what dead, is a pretty effective material for tuning harmonics. Combined into a tuned suppressor that had effective sound control as well as just the right amount of mass and bearing surface on the barrel it's self, accuracy was improved by quite a bit! The Big Ass Magnum .338 Laupua really came to the fore front thanks to the application of several of these tuning techniques, and is why the worlds absolute distance record was made, and still held with this caliber!
Here is one of the longest standing accuracy records: Mac McMillan’s Legendary .009″ Group — Lookee Here « Daily Bulletin The shooter & rifle name may be familiar?
Don't forget to click on the new record. Best Group Ever: Michael Stinnett’s .0077″ Five-Shot Group « Daily Bulletin Note the tuner! McMillan didn't have one.
Just another Note, here: When Dan Wesson introduced his patented Revolvers with the interchangeable Barrels, that were tensioned at both ends, by the Frame threading on one end, and the Barrel Shroud on the other, Pistol Accuracys increased by a significant amount.... Those were the "Rage" in the Pistolerro Crowd, and still are... I bought a Pistol PAC for AlaskaChick, in Stainless, .357 Magnum... which she still shoots to this day... It is a much better shooter, than ANY comparable Pistol, S&W ever built...
Boy do I sure wish I still had my Dan Wesson stainless .44 mag, MAN that was one sweet shootin iron! I got a pretty good deal on it, carried it as a back up on deployments, then traded it for a super sweet Python .357, I made out ok, but I think it was a mistake letting that big .44 go!
One very nice Bonus, the Dan Wesson Revolvers, have..... If you happen to Assassinate one of your Prime Enemies, with one, you can chuck the Barrel & Shroud, into a very deep Lake, or Ocean, mount one of the other Barrels & Should, and NO BALLISTIC Match, Possible..... My Opinion, YMMV.....
Interesting to note that, in blacksmithing many add a chain around the anvil and or a magnet , to reduce the ring that occurs when it is struck. Normally anvils are mounted on a tree round/biscuit something relatively soft. Perhaps if the anvil were bedded in lead or aluminum, the same thing might occur.
That sort of reminds me of Mike Ventureo, the gun writer. He was at a BPCR match and did every well. Some idiot goes "That's all the better you can shoot? Why with MY rifle and MY ammo I can cut that in half!! Blab, blah, etc., etc." Mike finally got POed and pulls out a $100 bill, slaps it down and goes "PROVE IT! That is yours if you can out shoot my target!" "well... er.... ah... that is... um... I don't... um... my rifle.... er... um... no ammo with me.... well... that is... I, um..." Every/any idiot can do anything until someone slaps down a $100 bill and goes PROVE IT! Unfortunately the crowd I hang out with is more likely to pull out an ONE dollar bill, so when I win it hardly seems worth it.