Bullet Stability, the Greenhill and Miller formulas, and the search for the right compromise

What makes a bullet stable? What are the symptoms of less than stable bullet flight? What are the symptoms of an unstable bullet? These are questions that are actually a bit more difficult to answer than you might think.

The Greenhill Formula is an “empirical formula” in that it took a lot of data points, and tried to describe them using math. There are a lot of empirical formulas out there, such as the tensile strength of materials is actually based on testing them, but since you can’t test every configuration of a material you come up with an empirical formula that describes reality well enough for the engineers to design parts based on material shapes and lengths that were never tested before. And it works pretty well. The Greenhill formula has largely been supplanted by various Miller formulas. The Miller stability factor formulas work like this, it essentially compares bullet length, twist rate, and velocity to figure out how fast a given bullet will be spinning on exiting the muzzle and says that “anything that calculates above 1.3 is stable, anything 1.0 to 1.299 is marginal, and under 1.0 is unstable.” And the Miller formula generally works really well at predicting whether a bullet will leave round or oblong holes in a paper target.

However, technology moves on. Bullet design has changed and advanced, and Bryan Litz has added new data points to the data set and determined that for some bullets, specifically the new low drag bullet designs with a very long “torque arm” on their center of gravity, that not having a stability factor of 1.5 or higher can and will cause a reduction in the ballistic coefficient of these bullets. http://bulletin.accurateshooter.com/2015/03/how-ballistic-coefficent-varies-with-twist-rate-stabilization/  It should be noted that the ballistic tools that Litz is using isn’t just looking at whether the bullet leaves a round or oblong hole in a target.

Now…this isn’t to say that a tighter twist will be more ACCURATE than a slower twist, if there is even the slightest imbalance in a bullet a tighter twist rate will expand the expected accuracy of a group. The math here is more “proven physics” than empirical formula, but the twist rates of the top rated benchrest shooters provide the empirical results consistent with “lowest twist = best accuracy potential” http://riflebarrels.com/a-look-at-bullet-imbalance-and-twist/

So…what do you do? First, you need to decide what exactly it is you want in terms of performance from your rifle. Do you want outstanding short range accuracy? Or do you want something designed to keep a long skinny projectile supersonic for as long as possible? The answer to that question is going to help you prioritize what bullet design you are looking for, and what twist rate is optimal for that bullet design.

For a normal hunting rifle, where pinpoint precision and long range wind bucking abilities are not prioritized, almost any twist rate fast enough to stabilize normal and “heavy for caliber” hunting bullets will do splendidly. This is the reason that a 1:10 twist is so ubiquitous among hunting rifles, as it handles the heavies very well. As bore diameter increases, 1;12 becomes the norm at 338, and 1:14 around the .358 or .366 range. Some 44 caliber bores will have a sedate 1:18 or 1:20 twist rate. Or do they?

About 8 years ago, a world record holder rifleman for long range accuracy posed the question,

“Here’s three barrels:
22 caliber (.224″ groove diameter), 1:8″ twist.
30 caliber (.308″ groove diameter), 1:11″ twist.
44 caliber (..448″ groove diameter), 1:16” twist.

Which one has the greatest angle the rifling presents to the bullet?

The only answer anyone came up with involved trigonometry, and of the answers given this one is the version I understand best “Inverse Tangent of Pi times bore diameter divided by twist equals rifling angle” And using that formula I calculate that each of the three barrels had the same angle of rifling, 5 point zero two degrees (which should really just be five degrees for all intents and purposes), except the 44 caliber which was 5 point zero three degrees of rifling twist angle. It is very counter intuitive to think that the same rifling angle produces very different twist rates, but once you consider the larger bore has so much more material to cover before making a complete revolution, it makes more sense. For the record, a 1:10 twist on a 308 barrel comes in at a 5.52 degree angle, which is about 10% more than the 1:11 twist, which makes sense that the 1:10 is 10% tighter than 1:11.

So, with all this theory, what does it really mean? Well, if you are shooting long skinny premium Berger, Sierra, or other top shelf VLD bullets for long range, make sure you have a barrel twist and velocity that gets you into the 1.5 or higher range using a Miller calculation. If you are shooting shorter, blunter bullets, or less than perfectly manufactured bullets (like you cast your own) then go with the slowest possible twist rate to get you right at 1.3 using a Miller stability calculation. This bifurcation of twist rates reflects the split of bullet making technology, and is a very interesting development.

Now…Palma shooters have traditionally gone with the slower twists. They are limited to 155gr bullets in International competition, and so often choose twist rates that are very slow compared to other 30 cal bullets (and the 223 Remington, aka 5.56×45 NATO hasn’t supplanted the 7.62×51 aka 308 Win as the top Palma cartridge yet). And those Palma shooters are launching those 155gr pills out to 1000 yards with great accuracy using those 1:14 twist barrels. Except for John Whidden, who built a 1:10 twist competition rig which took him to back to back LR championships: http://bulletin.accurateshooter.com/2017/07/john-whidden-wins-2017-nra-long-range-championship/

So maybe we’ll see more Palma barrels with 1:10 twists in the future, as bullet manufacturing technology eliminates major and minor sources of bullet imbalance and allows shooters to take advantage of a more consistent ballistic coefficient for long range shooting. No matter what, this is an interesting time to be a ballistics nerd.

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