I think spin testing and folks experimenting with the old
Vern Juenke sonic jacket wall thickness uniformity measuring device pretty well agree that Berger is generally at the top for jacket uniformity, but Sierra and Hornady have not been asleep at the wheel, so I see the ranking as a moving target.
Bart B has related how Mid Tompkins got a special collet made for a Dremel tool and span Lapua bullets in it with the Dremel connected to an ammeter. The eccentric spin of a bullet's center of mass (CM or center of gravity, CG) that is offset from the bore axis increases the side load on the bearings, so the current goes up. He sorted the bullets by smallest load current, then proceeded to shoot a 600-yard group that, IIRC, was only an inch or less with the best ones. (If Bart sees this post, he may correct what I recall or offer more details.) Harold Vaughn worked out both a torsion pendulum-based bullet balance measuring device and a compressed air spinner and microphone detector of eccentric spin, and a description adequate to duplicate these tools is in Appendix C (p.253) of
Rifle Accuracy Facts.
All these tools work, but sorting with them is time-consuming, as none of them is particularly quick.
Vaughn, by the way, shows barrel bending or vibration from eccentric bullet spin is unnecessary to account for the inaccuracy it introduces. A barrel usually only rotates a bullet a couple of times on its way to the muzzle, and it is turning it at accelerating speed at every point along the way, so there isn't a single tuned resonant frequency it would attempt to drive. It could initiate some barrel ringing, but it would mostly happen after the bullet cleared the muzzle.
The better way to look at the effect is just to pay attention to the bullet itself. Imagine there was a safe way to look down the muzzle and see the bullet's center of mass and watch the bullet spin up. An off-axis CM would appear to orbit around the bore axis. Now imagine your drone cam is looking down on a kid swinging a ball on a string in a circle above his head. The ball, like the offset bullet CG, will be orbiting around the kid's head. So, what happens if the kid lets go of the string? The ball, without the pull on the string to keep turning it into the circle, takes off straight along a line tangent to where it was on the circle at the moment of release and at a speed equal to the number of radians per second it was rotating at that same moment. Similarly, when the bullet clears the muzzle and is no longer constrained by the bore and rifling, its CG takes off to the side of the bore line tangent to where it was at the moment the bore let go of it, at a speed equal to the number of radians per second it was rotating at that same moment.
So, here's a calculated result. Suppose a bullet's CM is a quarter of a thousandth of an inch to the side of the bore line. Further, suppose that it is spinning at 250,000 rpm the moment it is released. Further, suppose that it takes 0.1 s to get to a 100-yard target.
Dividing 250,000 rpm by 60 to convert to revolutions per second gives 4,166 rps. Converting revolutions to radians just means multiplying by 2×pi, giving us 13,092 rad/s. The radius of the rotation is 0.00025 inches, so the rotational velocity of the CM at the muzzle is that radius times rad/s, or 0.00025"×13,092 rad/s, or 3.27 inches per second (ips). This means that during the time it takes for the bullet to reach the target, it will have drifted 3.27 ips × 0.1 seconds = 0.327" to the side of the intended point of impact. If you have another such bullet, but with the CG just happening to be on the other side of the barrel when the bullet clears the muzzle, so it drifts in the opposite direction, between the two, you have added 0.655" to the size of your group. The principle is diagramed on p.170 of Vaughn's book, linked to above.
The above was also all fleshed out many years ago by A.A. Abbatiello, who, writing in TAR in the 1960s, did a test of over 40 different lots of National Match ammunition (30-06 with 173-grain M1 Type bullets). He measured the concentricity error in each loaded round, as even if the bullets were not perfect, a bullet that enters the bore at a tilt still moves the CM a little to the side, and he marked the high side. Shooting then confirmed the relationship I just described and included that if you oriented the high side of eccentric rounds the same way in the rifle chamber each time, the added dispersion it caused was cut in half because all the lateral drift was in the same direction, so it wasn't additive. Harold Vaughn does that same experiment, but with a bullet type whose CM is not offset nearly as much by bullet in-bore tilt as the long M1 Type's bullet is, so that while you see the spread on a target (p.134), it is about a third the spread Abbatiello had.
