I think this theory has some holes in it.
First, the author contends that barrel bending modes cannot explain dispersion. For the example cited of a 50 fps change from 2900 fps (about 1.7%) in bullet exit velocity causing a large change in dispersion, any phenomenon that caused muzzle exit direction and/or transverse muzzle velocity (the velocity of the barrel at its muzzle) significantly in a time corresponding to the change in time that the bullet spends in the barrel (approximately 1.7% of the 1.24 ms cited, which is 0.021 ms) could cause such a change. One half a cycle would be ideal (a frequency of about 24000 Hz), but any slower frequency would work, particularly with increased amplitude (exactly what happens in a barrel – amplitude is largest for the lower harmonics). VarmitAl’s FEA results show this well – clearly bending modes can cause a change in dispersion in groups of shots with different mean barrel exit times.
Second, we are asked to believe that a bore diameter change makes a difference in bullet exit angle. The wave propagation cited causes a symmetrical change in bore diameter, not an asymmetrical one. The influence on exit angle of a symmetrical change would have to be caused by some secondary asymmetry, for instance, tipping of the bullet in a loose bore. The relatively large 0.00025” peak to peak spike might allow this, but the calculated change from sweet spot to sweet spot is only about 0.000005” (Fig. 5), making this hypothesized chain of events not very convincing.
Third, the magnitude of the variation in muzzle diameter is critical to this theory, even accepting that a symmetrical wave can cause asymmetrical effects on the bullet path. In Fig. 4, it appears that the variation is based on an impulse (infinitely short duration) of pressure, rather than the actual chamber pressure curve. Thus, it seems questionable whether the peak change calculated, 0.00025”, is accurate. With the smoother actual pressure, it is likely to be less, and might be so small as to preclude any significant influence on the bullet.
Fourth, the variation of bullet exit velocity within a group, and its influence on vertical dispersion, is not considered. The authors contend that the sweet spots are when the rate of change of bore diameter is small. If variation in bullet velocity is considered, however, minimum vertical dispersion would result when the changing bore diameter compensated in some way for the differences in bullet velocity within the group. For instance, squeezing the faster bullet to slow it down before it exits the muzzle, and reducing squeeze on the slower bullet, would tend to reduce variation in bullet exit velocity and reduce vertical dispersion. In this example, the sweet spot would be when the muzzle bore diameter is increasing.
Fifth, if a slightly tighter muzzle bore enhances accuracy, as some claim, then the sweet spot, for overall dispersion and in particular horizontal dispersion, would be when the bore is small. Together with the example from the fourth point above, the ultimate sweet spot would be where the bore is small AND increasing (at about 1.16 ms in Fig.. 5).
Anyway, interesting theory, but I am skeptical.