I will agree that no two barrels are exactly alike and the way they perform will confound any predictions that they "always do that".
I wanted to see just how repeatable greased bullets are on target. This is a practice, very popular around WW1 because the bullet jackets of the era fouled something awful and it took nasty chemicals to remove cupronickel fouling. I know the Austrialians were still greasing their 303 British rounds in the 1940's, and the Swiss were still greasing their service rifle ammunition until the 1970's.
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I either greased this first shot like this
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or this
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This is the rifle, not a target rifle, but a first year production M70
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First shot at 300 yards, clean and oiled barrel, greased bullets, using zero's established at a previous range session.
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The rest of the ten shot string
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I always clean my barrels between matches, if the period between matches is days. I have shot tens of thousands of rounds in NRA competition, occasionally the match would have to start at the 600 yard line, for range maintenance reasons, and I got to see that hardly used match barrels would print their first shot in the X ring. I did not get to place the first shot at 600 yards with a well used barrel, but at 200 yards, bullets from a high mileage barrel would walk until the barrel was fouled. That was around two to three rounds, might be more if I shot really worn barrels.
I have seen point of impact on my smallbore prone rifles walk as the bore fouled. I will throw 2 shots into the berm and all is good after that.
And I has seen the first shot from a clean and oiled target pistol print way away from the pistol zero with a fouled barrel. Around shot three the barrel is shooting to its previous zero.
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I would like to try more cold bore greased shots at long distance to see if constant bore lubrication produces repeatable zero's. Generally I want to try something different each trip so I probably won't get around to it.
One real problem with all non mechanical rest shooting, is that my position on the rifle or pistol first shot is always going to be different as I settle in! I see that time and again during practice, or, during my sighters in small bore prone. I will shoot enough sighters to make sure I and the rifle, are sufficiently fouled.