Bullet Stability and Barrel Twist

[gunderwood]

There is a great and straightforward book if you want to learn about exterior ballistics (bullet flight) from Brian Litz. You do not have to be a math wizard to get a lot of valuable information and tips from this book. Litz covers the math (well the basic forms of it), but the book is written as much as possible to not require any formulas or number crunching. The reality is that there are tools (computers, calcs, etc.) capable of doing the math, you really just need to know how to use them. Granted, there is value understanding the math, but it isn't required. It can be found here: http://www.appliedballisticsllc.com/ind ... s/Book.htm

Litz notes the definition of stability:

Stability is the ability of a projectile to maintain its point forward orientation in flight, and return to that orientation if disturbed.

That's it. If you want your bullet to fly straight, point forward to the target you aimed it at it needs stability. We are only talking about one type of stability in this post, that is gyro stability and we accomplish that through spinning of the bullet. A good book like Litz's will cover this in more detail, I'm just giving you the low down.

We spin the bullet with the use of barrel rifling (or in the case of a rifled slug, the slug is rifled for a smooth bore shotgun). The amount of spin imparted is function of the twist rate and the bullets velocity. It really is that simple. However, the amount of spin needed to achieve stability is a bit harder.

Twist rate is commonly expressed as a ratio such as 1:10", which reads one turn/twist/revolution per 10" of barrel. It means exactly that, the rifling will complete one revolution, a complete circle, ever ten inches. If you have a 20" barrel you will have 2 revolutions of twist (not exactly as the chamber is usually included, but let's keep it simple). If you have a 30" barrel you have 3 revolutions. 10" is 1 rev, 15" is 1.5 revs, etc., but that really isn't important. What matters is the rate, not the number of revs you have (simplified). To illustrate this, lets say I have a 1:10" twist barrel that is 10" long chambered in cartridge A and a 1:10" twist barrel that is 20" long chambered in cartridge B. If the muzzle velocity (the second variable in determining how much spin we impart to the bullet) of cartridge A and B is equal, both bullets will spin at the same rate. It does not matter that B has twice the barrel length as A! The twist rates and muzzle velocities of both A and B are the same, therefore they have the same imparted spin.

To illustrate this let's look at how much spin is imparted. I'm using very simple numbers, which makes them unrealistic, but the math is correct. Let's say that it takes 1 second to cover that 10" 1:10" barrel for cartridge A. That would impart a spin of one revolution per second (1RPS). If I loaded a max cartridge A load and that doubled the velocity so that it only took 0.5secs to cover that 10" barrel, the bullet would be spinning at 2RPS. If I loaded a light load and it halved the initial velocity, it would take 2secs and would spin at 0.5RPS. Of course I'ved ignored all kinds of things, but the important thing to understand is that the bullets velocity and the barrels twist rate are all that you need to know to calculate how fast it will spin. As I said before though, how much spin you need is more complex.

There is a simplified estimate, an equation, called the Miller Stability Formula that tells us roughly if a bullet will be stabilized (gyroscopic) or not. The thing to realize is that it is a simplification of much more advanced math and isn't calculating the actually gyroscopic stability, but rather approximating it. However, it works well in most cases. The formula is:

SG = 30 * m / (t^2 * d^3 * l * (1 + l^2)), where

SG = the gyroscopic stability factor which is basically the stability of the spinning bullet divided by the overturning torque due to drag.
m = mass in grains
t = rifling twist rate in calibers per turn
d = diameter of the bullet in inches
l = the length of the bullet in calibers

If you've been paying attention you should immediately question where the bullets velocity is! Simply put, it isn't there because this formula only works for 2800fps and no other velocity. Thankfully we have a simple correction to the calculated SG which is:

SG(from above) * (V / 2800)^1/3, where V is the bullets muzzle velocity in fps.

Even better is that we have a free calculator do the math for us! It's found here: http://www.jbmballistics.com/cgi-bin/jbmstab-5.1.cgi

A velocity correct SG of less than 1 is unstable, between 1 and 1.4 is marginally stable, and greater than 1.4 is stable. Remember this is only an approximation!

[gunderwood]

Now let's take a look at an example. Let's assume the following:

Bullet diameter: 0.308"
Bullet length: 1.2"
Bullet mass: 155gr
Bullet velocity: 3000fps
Barrel Twist: 1:14" (insert as 14 in the calc)
Standard atmosphere: 59F/29.92Hg

If you insert those numbers you should get the following SG: 1.250, which is marginally stable and hence yellow. That combo may or may not work and you likely would find it works in some guns and not others...or you may never find a gun it works in with that specific bullet.

If we change the twist rate to 1:16" we find that the SG is now 0.957 and red (unstable). Remember that this is an approximation and the real calculation would have to take into account our bullets shape, but it is reasonable to say that that setup would not work at all; our bullets would keyhole if they ever made it to the target.

If we change that to 1:12" we get a SG of 1.702 which is green (stable). While it is possible our calculations are wrong for a given bullet, it is likely that you will find that combo to be stable. A stabilized bullet will shoot more accurately than a non-stable bullet, but there is more to accuracy than just stability.

There are negative effects to over spinning a bullet, but they are much less than under spinning it, but they must be compensated for. Generally long range shooters try to shoot a setup that is stable, but just barely so. Be careful as that setup is only stable in standard atmosphere conditions! You should have noticed that the Miller Stability formula doesn't have atmospheric conditions and that I didn't mention anything about the math to correct for it. Fear not, it exists and is simple algebra, but I didn't see the need to type it up here. It is a simple multiple like the velocity correction as the Miller formula assumes standard conditions.

If you play with the temperature and pressure in the stability calc you will notice that very dense air decreases the stability factor. That makes sense as more dense air increases the drag/overturning torque so stability is negatively impacted. As a side note, you now should have an idea why some bullets, particularly rifles, tend to tumble during terminal ballistics; the target is much more dense than the air and they are no longer stable so they don't want to "fly" point forward anymore.

[gunderwood]

So what's it all mean?

Thankfully you don't really have to understand any of that to shoot targets. You only run into issues with factor guns when you use them for purposes other than the manufacturers intended segment. E.g. subsonics in some cases. Manufacturers are generally smart enough to choose the proper twist rate for the market segment. You won't find varmint guns with twist rates unacceptable for the fast and low mass bullets commonly shot for that sport. Same with a standard hunting rifle or a long range precision rifle. However, you can get into trouble say if you tried to shoot a long range bullet (which has more mass and length and requires a faster twist) out of a varmint rifle. The twist rate is likely too slow. The opposite could happen if you try to shoot a varmint bullet out of a long range rifle. The twist rate is likely too fast and the extraordinary spin imparted to the varmint bullet may cause it to explode before reaching the target (gray mist).

If you aren't building something odd or trying to use a factory rifle outside of its intended category the twist rate is probably close enough to ideal that you will be fine.

[Taggure]

Thanks for the write up and I am sure that we will have white board discussions on this in the future as I start getting my new rifle set up for long range shooting.
So, after reading this my new rifle has a 20" barrel with a 1in10 twist and from the calculation I should be ok with shooting 180 - 220 grain bullet then. The 180 grain gave Stability: 1.490 and the 220 grain gave Stability: 1.822. I can see that the heavier bullet would be more stable.

Thanks
Vern

[gunderwood]

Thanks for the write up and I am sure that we will have white board discussions on this in the future as I start getting my new rifle set up for long range shooting.
So, after reading this my new rifle has a 20" barrel with a 1in10 twist and from the calculation I should be ok with shooting 180 - 220 grain bullet then. The 180 grain gave Stability: 1.490 and the 220 grain gave Stability: 1.822. I can see that the heavier bullet would be more stable.

Thanks
Vern

Those are awful heavy bullets for a .308Win. Something like a 175gr SMK is usually considered more ideal. Extra spin doesn't hurt that much and it gives you margin for very dense air or possibly even subsonics.