The Detailed Explanation
So here are the two key questions:
(1) How the bullets can become slightly loose and tipped in the bore?, and
(2) How loose are we talking about?
Bullets being loose when they travel down the barrel is called balloting. All bullets ballot somewhat and this accounts for a large chunk of the total dispersion in a typical rifle. For those who want to really dive into this subject in detail, and a whole lot more, we recommend the book Ammunition, Demystified by Jeff Siewert, which can be found on his website https://www.bulletology.com/. The first three topics below are discussed at length in his book. Jeff has been a frequent guest on Hornady’s podcast and those episodes are also available through his website. The last section on longitudinal shock waves has separate references, but the L. E. Brownell research at the University of Michigan is also referenced in Ammunition, Demystified.
The topics discussed here are not an exhaustive list and there are other sources of bullet dispersion. But, the basic concept of the bullets being slightly loose in the barrel account for a large percentage of bullet dispersion. Think of the D-Vise as being a manual override of these effects. Squeezing the end of the barrel enough to shrink the bore near the crown by about 0.001 inch and leaving a pressure of 40,000 – 60,000 PSI overcomes the negative effects described below.
Initial jump of the bullet from the brass into the rifling
The bullet’s initial jump from the brass into the rifling and the engraving of the bullet are extremely violent. Any part of this event that is not essentially perfect will lead to the bullet becoming slightly tipped in the bore. This is why hand loaders spend a considerable amount of time and effort trying to determine the best charge and seating depth and trying to ensure their bullets are as straight as possible in the brass.
When the bullet encounters the reduction in bore diameter caused by the D-Vise, it is force to fully engage the bore. This removes any bullet tip and causes the bullet to become properly aligned with the bore.
Pressure of the gases expanding inside the barrel
So how does pressure in the bore lead to the bullets not being well-guided? In engineering terms, this is understood through the relationship between stress and strain. In this case, stress is the pressure inside the barrel and the strain is how much the barrel changes size. Gabriel Lamé published the equations for the elastic stress in a thick-walled cylinder in his 1852 book, Leçons sur la théorie mathématique de l’élasticité des corps solides. “Lamé’s equations” provide a way to calculate the stresses and strains in a pressurized thick-walled cylinder.
The typical 50,000-60,000 peak pressure inside the barrel, which occurs very near the start of the bullet travel, will cause the bore of a typical hunting rifle to increase by roughly 0.0005 inch. Although the pressure decreases as the bullet travels down the bore, so does the barrel diameter, which means that the increase in bore diameter remains roughly the same all the way down the bore. That’s enough to make the bullet slightly loose and allow it to point in a slightly incorrect direction.
Now you’re probably thinking that all you need is a thicker barrel. A thicker barrel helps, but not as much as you might think. Thick barrels will reduce the problem somewhat, but will not eliminate it. That’s just the way the math works. And for a hunting rifle, it’s usually not a practical option anyway.
Variation in bore diameter and interior finish
Simply stated, the perfect rifle barrel has never been made and never will be. All machining operations have variation and tolerance. No rifle bore is perfectly straight, smooth, or uniform in diameter. They are close, but not perfect. And even if they were perfect, after a few shots they wouldn’t be. If you’ve ever used a bore scope to look at the inside of a rifle barrel, you’ve probably seen all kinds of imperfections in the bore.
The barrel will have some point at which the inside diameter is smallest, and it almost certainly will not be at the crown. At that location, the bullet will be exactly sized to that diameter. Everywhere past that point, the bullet will be slightly loose.
Longitudinal shock waves
Around 2003, an engineer named Chris Long who was also shooting competition came up with the theory of Optimum Barrel Time. He put a paper on the topic on his website: http://the-long-family.com/optimal%20barrel%20time.htm. The theory states that the bullet impacting the rifling creates longitudinal stress shock waves in the barrel that (1) increase the bore diameter by about 0.0002 inch and (2) traveling at the speed of sound in steel, reflect off the ends of the barrel several times as the bullet travels through the barrel. One thing to note is that since this is a shock wave and the steel of the barrel behaves like a very stiff spring, the bore diameter would actually be both increasing and decreasing as a wave both increases and decreases. If the bullet exits the barrel at a point in time when the bore diameter has increased then the bullet will be slightly loose in the barrel and dispersion increases. On the other hand, if the bullet exits the barrel at a point in time when the bore diameter has decreased then the bullet will be tightly guided and dispersion decreases. Chris has tried to measure and record the actual shock waves, but since the measurement signal is both very small and very fast, instrumentation has not been up to the task. However, there has been a considerable amount of testing of this theory for a couple decades that supports his conclusions.
Interestingly, L. E. Brownell and other researchers at the University of Michigan discovered the same thing doing ballistics research 38 years earlier in 1965 (back in a day when a university would actually do weapons research for the military). Chris Long was unaware of this paper at the time he created his theory. The researchers referred to the longitudinal shock wave as an “ultrasonic signal”. See the links below. In the document, see section VI starting on page 19. The researchers didn’t put together the implications for bullet dispersion the way that Chris Long did. But, using the analog instrumentation that was the only type available in 1965, they did actually record the signal and proved it really does occur.
University of Michigan library link: https://deepblue.lib.umich.edu/handle/2027.42/3866
The PDF link: https://deepblue.lib.umich.edu/bitstream/handle/2027.42/3866/bac6873.0001.001.pdf?sequence=5