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I have been working on fixing up a beautiful old mauser sporter, 1909, ss match barrel, 30-06. My results at the range have been OK for a hunting gun but I have a feeling this gun will do alot better. I have noticed that my dispersal is almost all along one axis, about 30 degrees off horizontal. Lot's of real tight groups, then a flier will open it up to 1.5, but fliers is always on that line. If I subtract that axis, the gun consistently shoots .5, which my gut tells me this gun will do.
What is the standard gap for barrel float? I kept it tight because the fit is so nice, I didn't want an unsightly gap. A folded dollar is snug in the crack but will slide with some light resistance.
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If your barrel is floated, it seems your load is not quite there. Almost sounds like it wants a tad more powder or a seating depth adjustment. Try +/- .010" - .020" seating depth change?
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I sometimes have this very same problem to a slightly lesser degree. My fix? practice. I've found that when I have a flyer low and right it is my trigger pull or a flinch, low and left and it was my hold or breathing. Not sure if that's what it is for you or not, but practice has sure helped close my groups up. After that I would probably try waiting a good 2-3 minutes between shots to let the barrel come back to the same temperature. When my barrel warms up it can wander a bit.