In terms of accuracy, the critical kiss-off is that last part of your barrel that touches the bullet.
Once in a while you'll hear knowledgeable shooters claim that their rifles shot comparatively better groups at 200 and 300 yards than at 100 yards. This clearly doesn't wash because we understand "minute of angle," don't we? The natural progression is that a one-inch group at 100 yards will disperse to a two-inch group at 300 yards and so forth. Ignoring wind and aiming errors as distance increases, this is the best-case scenario, right?
With a rounded sporting crown, the easiest way to examine the blast marks for concentricity is to paint the crown with typewriter white-out, then fire about three rounds. What you want to see is concentric, consistent blast marks at the rifling grooves where the hot gases escape as the bullet exits.
Surprisingly, the phenomenon of better groups at 200 yards than can be obtained at 100 yards does occasionally occur. It would be really rare for the groups to be smaller, but if you shoot a one-inch group at 100 yards and a 1 1/2-inch group at 200 yards, you have beaten the MOA and your 200-yard group is comparatively smaller. This does happen, and as unlikely as it seems, it isn't that rare. Especially when you consider that relatively few of us shoot groups at longer distances.
How can this be? The most likely answer is a muzzle crown that is slightly irregular. As the bullet exits the muzzle, the burning gas exits considerably faster. Most nitrocellulose propellants expand at about 5,200 fps--faster than any speeding bullet. These expanding gases have no ballistic coefficient, so they slow down quickly, but as the bullet exits the muzzle the faster blast squirts past it. The muzzle crown is the last thing the bullet touches. It is essential that the crown be uniform and exactly perpendicular to the bullet's flight or these escaping gases will exert uneven pressure on the bullet's base, causing it to yaw.
Air resistance plus the stabilizing spin from the rifling will overcome this. Serious riflemen call this "going to sleep." Exactly at what distance this occurs depends on many factors, but an irregular muzzle crown is one of the primary culprits in yawing. Absent wind, aiming errors and all the rest, a stable projectile in flight will follow a geometric dispersion pattern. If you're getting one-inch groups at 100 yards, the best you can hope for--without a bit of luck--is a two-inch group at 200 yards. If your dispersion is exponential, as in a four-inch group, look to external factors (like your benchrest technique). If you are actually getting comparatively smaller groups at 200 yards than at 100 yards, the most likely culprit is your muzzle crown. This is because yawing affects accuracy until the bullet goes to sleep.
This simple hand tool from Brownells is centered by a barrel spud. The only caution is to go easy and stop the hand screw in a different place with each revolution.
So how can you tell? Well, I learned a trick at the range with my buddy Geoff Miller, accuracy freak and proprietor of the John Rigby Company. I was shooting a new Remington 770 in .30-06 . It showed promise, but I was getting irregular flyers. It wasn't the bedding. It could have been the loads, but it might have been an off-center crown. Geoff whipped out a bottle of typewriter white-out fluid and painted the crown.
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