With the secant ogive, that isn't certain, but I wouldn't bank on that boattail angle to behave in the transonic range.
For bullet concentricity, I only know of four approaches to the problem. One is to use a torsional pendulum, for which there are a couple of different types and methods that can work. I won't describe them because Harold Vaughn did that in the reference cited in the last paragraph of this post. Way, way too slow and too much trouble, IMHO.
Another is the old Vern Juenke sonic inspector. It operates on the assumption the core of a bullet is uniform and the forming dies that control the external dimensions were uniform, but that there is a runout in the jacket wall thickness that will throw the center of mass off-axis (opens groups by the same mechanism as bullet tilt; the centrifugal effect of spinning the center of mass eccesntrically around the bore axis). It uses an ultrasonic transducer arrangement and a motorized bullet turner to measure the jacket thickness all around the bullet axis. I have never had one, as they seemed rather expensive for what they were. A
couple of guys bought out Juenke when he retired, but despite their website, they don't seem to be actively producing it. Looking at their posted schematic as compared to their photos of the unit, I found errors, and their method of hand-producing the circuit board is slow and expensive compared to just having the boards made by a PC board house. I concluded they don't really know what they are doing. But also, the assumption Juenke made that bullet forming dies can be counted on to produce a uniform exterior is wrong. I've seen photos of cheap foreign "match" bullets with boattails so far off-center you can see their heels are higher on one side where they meet the bearing surface.
The other method of determining bullet mass symmetry is to spin them. Bart B has described previously how Mid Tompkins got a special collet made to hold some Lapua match bullets (
D46, IIRC) in a Dremel tool while an ammeter monitored the current flowing into it. The more out of balance a bullet is, the more current is drawn because an out-of-balance item in the chuck significantly increasing the side load on the motor. If I recall, Bart said Mid sorted the best (lowest current) of these bullets in this manner and shot a world record level (at the time) group with them. Something under an inch at 600 yards (again, IIRC; if Bart see's this post, he can correct the particulars).
Another spinner was the late Harold Vaughn's pneumatic device. You can see that described in his book,
Rifle Accuracy Facts, in the Bullet Imbalance chapter on page 169 (182 if you use the page counter in the scroll bar). Page 170 explains how an off-center center of mass opens groups up, whether the imbalance is due to bullet tilt in the bore or is manufactured into the bullet. On page 173 he shows a torsional pendulum with indicator for finding bullet imbalance. On page 174 he shows the pneumatic spinner. There are more details on it in one of the book's appendices.
