Internal, external, wound, and terminal all have what in common? Ballistics. Part of ballistics is the twist rate of your barrel, and properly matching your ammunition to your twist rate will provide you with better ballistics and most likely better accuracy.

Twist rates have been a heavily debated topic as of recent. It has gone as far as some manufacturers introducing slower than designed twist rates for specific cartridges. In effect, neutering those cartridges and the capabilities of those rifles.

Let’s jump right to it. As far as an AR-15 chambered in 5.56 NATO or .223 Wylde goes, a shooter should pick up something in a 1:7 or 1:8 twist rate and call it a day. Either one of these will be able to stabilize bullets from the common 55g FMJ to the popular 77g Sierra OTP Matchking. But what if I have this caliber or that rifle?

Are you ready for a math lesson? Let’s go a little deep into the science of barrel twist rates. This will involve a bit of math, but I’ll try to simplify it for you in the end.

**Rifling and Bullet Stability**

So what is the purpose of rifle twist rates? History lesson….. Carving grooves down the bore of a gun barrel dates back to at least the 15th century, but it was relegated mostly to cannons. Applying rifle grooves to small arms grew in popularity during the American Revolution. During this time period, most infantry small arms had smooth bores. This was a compromise allowing for faster loading from the muzzle.

The .69 caliber 545-grain lead ball that was launched from these smooth bore barrels has been estimated to be traveling at around 1000 feet per second. Accounting for the material of the projectile and figuring up the math for kinetic energy, it is easy to see that this would do significant damage to the human body. If it hit, that is.

The problem with these smoothbore muskets was that they were inaccurate. The lead balls were prone to fly off in different directions after firing. Given the type of combative tactics and close ranges at the time, and this wasn’t seen as an issue. In the 18^{th} Century, infantry tactics relied on massed volleys of fire from formations of troops. This tactic put a premium on the volume of fire, and not accuracy.

During this time period rifling for small arms did exist, but it was impractical. As it relates to internal and external ballistics, rifles require a tight fit between the lead ball and the bore of the rifle. Without that tight fit, the projectile won’t spin or the expanding gasses might blow by it entirely. Both of which are detrimental to ballistics, stabilization, and accuracy. Also, this tight fit meant that the rifle were much slower to load and fire.

In the 1700’s gunsmiths began producing the first series of Colonial American rifled weapons. These were known as the Long Rifle, later to become known as the Kentucky Long Rifle. These were primarily a frontier weapon used for accurate hunting and defense. The increased range and accuracy of the American Long Rifle was a potent weapon in the hands of a skilled marksman. It wasn’t until the mid-19th century that rifling became common with infantry small arms. This is largely in part due to breech-loading mechanisms.

**Principles of Rifling**

Time for a little science. So how does rifling work, and what does it do to a projectile? The rifling of a barrel imparts rotational force to the projectile. It is this rotational force that in turn provides gyroscopic stability for a bullet in flight.

A simple way to relate this is to think of throwing a football. Without spin, the football tumbles end over end until it lands some relatively short distance away. Or strays off the path of travel to either side. However, if you throw it with spin, the ball becomes much more accurate and stable in flight. Sound familiar? Just like a bullet maybe?

In ballistics, the center of pressure is the point where all of the aerodynamic forces, particularly lift and drag, are equalized. If this point is behind or below the center of gravity, then the object is self-stabilizing. This is why fin stabilization works with missiles and similar military ordnance. The fins pull the center of pressure much further rearward.

If the center of pressure is in front or above the center of gravity, as with a bullet, then the lift and drag forces induce torqueing effects where the projectile wants to tumble end over end. Spinning the bullet along its long axis prevents this tumbling.

Bullets that are shorter in length have the center of pressure closer to the center of gravity. With longer bullets, the center of pressure is further away from the center of gravity creating more instability and requiring a faster twist rate to increase gyroscopic stability.

“Keyholing”. Have you heard of this term or experienced its effects? This phenomenon occurs when a barrel is unable to provide gyroscopic stability to a projectile. The bullet tumbles end over end because aerodynamic forces are winning out. It continues tumbling until it hits the target. The hole left behind appears elongated since the bullet passed through sideways. Like throwing a football without spin, this results in extremely degraded accuracy and range for your rifle. When you begin to see this with a rifle, typically the barrel is either “shot out” or the twist rate is totally mismatched to the ammunition. In my experiences I have not seen a poor or damage muzzle crown contribute to this. In my experiences, a poor muzzle crown results in poor accuracy and/or precision which is commonly associated with larger group sizes.

**Matching Rifle Twist Rate to Caliber**

Hopefully you now know why rifling is important. Added stability, correct? But what is stability? The definition is that the bullet will align its axis with the oncoming airflow. Greater stability means a more perfect alignment. Projectiles, even from fast twist rates, will trace the trajectory with their axis. The axis will point up as the bullet is rising in its trajectory, and then the axis will tilt down as the bullet comes back down to the line of sight on the target.

How fast does a given bullet need to spin in order to remain stable? This is where science, math, and engineering meet. The twist rate of a barrel is described in terms of one rotation over a certain number of inches of barrel. As an example let’s take the current Mil-Spec twist rate of 1:7. This means that the projectile will rotate one time for every seven inches of barrel. If the barrel was a 20” barrel with a 1:7 twist, that would mean that the bullet would rotate nearly three complete turns before exiting the barrel.

If you want to convert the muzzle velocity to Revolutions Per Minute there are a couple of conversions.

- Muzzle Velocity multiplied by “720”. Take this number and divide it by the twist rate of the barrel and you then have the bullets Revolutions Per Minute (RPM).

So my 16” 5.56 rifle with a 1:7 twist barrel launches a bullet at say 2700 FPS muzzle velocity. Let’s convert this to RPM’s.

- 2700×720= 1944000
- 1944000 / 7= 277,714.285714 RPM’s

As you can see, the projectile spins at 277,714 RPM as it exits the barrel.

**OR**

MV x (12/twist rate in inches) x 60= Bullet RPM

- MV= muzzle velocity

So let’s use information from my 22” 6 ARC and convert this to RPM’s. It is a 7.5 twist barrel with an average velocity of 3344fps.

- 12/7.5= 1.6
- 1.6 x 3344= 5350.4
- 5350.4 x 60= 321,024 RPM as it exits the barrel

I prefer to use the latter equation for figuring bullet RPM.

**Gyroscopic Stability Factor**

Stability of a bullet in flight is measured by assigning a gyroscopic stability factor (SG). Any value below 1 is unstable. Between 1 and 1.3 is marginally stable, and anything higher than 1.3 is stable. With 1.5 being optimal.

But, there are some caveats though. These stability values are assumptions based on generic bullet designs and this does not always correlate. A gentleman by the name of Bryan Litz of Applied Ballistics (also a Ballistician for Berger) did a lot of research using VLD bullets popular in long range competition. It was found that these bullets tend to change their stability factor as velocity decreases. So, through his testing his conclusion was that you should target the 1.5+ range for your long-range shooting needs.

Also, atmospheric conditions influence the gyroscopic stability factor of a bullet. Since atmospheric conditions are ever changing, than so is the SG of the bullet. Elevation (atmospheric pressure) and temperature are two of the biggest factors. Given all factors the same, as the temperature decreases so does the SG of the bullet. As temperature increases, the SG of the bullet also increases. What about elevation? Again, given all factors the same, as elevation increases so does the gyroscopic stability of the bullet. As elevation decreases, the SG of the bullet also decreases.

Let’s look at a couple of examples:

- G1 BC- .475
- .308 caliber
- Bullet weight- 175
- Bullet length- 1.240”
- Muzzle velocity- 2650
- Barrel twist- 10
- Temperature- 80 degrees
- Elevation- 980 feet
- The above parameters would of a gyroscopic stability of 2.60

Now using the above parameters let’s decrease and increase the temperature while leaving everything else the same.

- 30 degree temperature
- The bullet would then have an SG of 2.36
- 105 degree temperature
- The bullet would have a SG of 2.72

Now let’s set the temperature back to 80 degrees and increase and decrease the elevation while leaving the other parameters the same.

- 500 feet of elevation
- The bullet would have an SG of 2.56
- 3000 feet of elevation
- The bullet would have an SG of 2.80

While all of these numbers are generic and the bullet started with a base SG of 2.60, I think that you can see the importance of how atmospheric conditions can influence and change the stability of a bullet. If you were to start with a bullet that had a marginally stable SG of 1.2 and the atmospheric conditions changed, then you could possibly experience issues in bullet performance and accuracy or precision. This is where a barrel’s twist rate comes into the equation.

As stability factors decrease below 1.5, the bullet’s ballistic coefficient starts to decay. You should expect a 3% BC loss for every 0.1 stability factor loss below 1.5. An example: If the SG is 1.3, your BC will be reduced by approximately 6%. These numbers are based on live fire measurements in tests that Bryan Litz has conducted, and it takes affect right out of the muzzle. Not just transonic velocity. It should be noted though that sufficient increases in velocity can create an artificial increase in BC. So how is all of this figured out? Through math of course. There are three formulas, with each one building upon the work before it. But take note, these are approximations. The full formula for gyroscopic stability is known, but some of its inputs are difficult for the average person to determine. Examples are axial and transverse moments of inertia, and an aerodynamic coefficient called CMA.

*The Greenhill Formula*

In 1879 a British mathematician named Sir Alfred Greenhill developed this formula. It worked well enough in the 19th century for lead core bullets but doesn’t cut it for modern precision. The formula did, however, provide a foundation for further development.

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 is one that describes reality well enough for the engineers to design parts based on material shapes and lengths that were never tested before. This is a summarized version that’s a little easier to work with.

- C = 150, or use 180 for muzzle velocities higher than 2,800 f/s
- D = the bullet’s diameter measured in inches
- L = the bullet’s length in inches
- SG = specific gravity, a factor unique to each bullet

This is a link to a Greenhill Formula calculator.

*The Miller Formula*

Don Miller developed this formula as a more accurate way to find an ideal rifle twist rate. Whereas Greenhill was more of a generic formula, Miller’s uses more characteristics of a rifle bullet to arrive at a more specific solution.

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.

- m = bullet mass in grains
- s = gyroscopic stability factor (dimensionless)
- d = bullet diameter in inches
- l and L= bullet length in calibers

If you’re scratching your head about that “length in calibers,” that’s ok. Take the length of the bullet and divide it by its width. For example, a 175 grain SMK .308 bullet is 1.24″ long. So we divide 1.24 by .308 and get 4.026 calibers in length.

This is a link to a Miller Formula calculator.

*Improved Miller Formula*

This version came about through a collaboration of Don Miller and Michael Courtney for Precision Shooter. A lot of new bullet designs include polymer tips to aid with aerodynamics. With these projectiles, using the total length of the bullet makes calculations inaccurate since the mass does not distribute the same way as Miller’s earlier assumptions. To compensate, the pair made an adjustment to the original work:

Here’s how the whole thing looks when put together.

- S = stability factor
- m = mass in grains
- t = twist rate in calibers per inch (do twist rate divided by caliber)
- d = caliber
- L = the length of the bullet in calibers (bullet length in inches divided by caliber)
- L sub m = length of the metal portion of the bullet in calibers
- V = actual velocity
- FT = actual temperature in degrees Fahrenheit
- P = actual barometric pressure in inches of mercury

*Shortcutting the Math*

The fastest way to get your numbers is to use calculators. Berger has a twist rate stability calculator, as does JBM Ballistics. With the JBM Ballistics, my assumption is that they use the improved stability formula above since they include the plastic tip length in calculations.

**Over-Spinning and Terminal Effect**

Let’s talk about a couple of myths.

*Over-Spinning*

There is an optimum twist rate for a barrel given specific projectile. But a lot of people worry about over-spinning a bullet. For example, it’s commonly known that a 1/7 twist rate is good for 62g M855 as well as 77g SMK 262 Mod 1, but a lot of shooters think it’s too fast for a 55g M193. They also think it’s excessively fast for a lighter 45g varmint bullet.

It’s a common belief that spinning a bullet too fast will result in it maintaining a nose high orientation on the downrange half of its travel. Thereby increasing drag. This is false.

So here’s the truth. Spinning a bullet too fast may degrade your accuracy just a little bit. An emphasis on may.

The faster twist rate induces slightly more spin drift. Spin drift is the tendency of the bullet to travel horizontally in the direction it’s spinning. It really only shows up at very long distances, and then at that point we also have other factors that contribute to accuracy and precision.

A faster twist rate also aids in reducing the yaw of the bullet. Reducing yaw also reduces drag on the bullet. This is more evident at long distances. All of this is especially important at transonic speed. Transonic is when air is flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. Transonic speed is generally between Mach .8 and 1.2.

Bryan Litz did a study on this with 30 caliber bullets and found that at extended ranges a barrel with a faster twist rate had bullets that entered a target leaving a truer circular hole. Whereas a slower twist barrel had bullets that would enter the target leaving an elongated hole which was found to be caused by the yaw of the bullet. For practical purposes, you really can’t over spin a bullet from an accuracy perspective.

That said, small lightweight bullets with thin jackets might self-destruct in mid-air if spun too quickly. I have experienced this phenomenon when I experimented with Hornady 110g V-Max bullets in a 300 Weatherby Magnum. I experienced the bullet coming apart at velocity, keyholing, and no accuracy whatsoever. Another well documented case of thin jacketed bullets coming apart is when Sierra first released the heavier Matchkings for NRA High Power competition shooting. Many competitors reported to Sierra that those bullets were coming apart in flight. Sierra decided that a thicker jacket was the solution.

But let’s put a little more math into this. An accepted industry number for bullet RPM before bullet construction integrity concerns may be a factor is 350,000 RPM. This is not a given, nor is it a standard. I use it as a guideline. I have seen bullets fail below this, while I’ve seen bullets be successful above this number.

Twist rates have become a heated topic in today’s forums and groups. Especially in the predator hunting world. More specifically the 6 ARC has seen a lot of controversy with the commonly seen 7.5 twist barrels and the use of lightweight bullets between 58g and 70g. “It’s too fast.”

So let’s take a look at the barrels used in BRD Gun Works 6 ARC builds, and the 58g V-Max load that has been developed for predator hunting. They utilize a 7.5 twist barrel and the barrels are 20” long, with an occasional 22” barrel. I will calculate bullet RPM’s for both barrels so you can see what the difference in velocity makes to the RPM’s of the bullet.

Using my preferred calculation method let’s calculate bullet RPM’s for the 22” barrel and see where it is in contrast to the 350,000 RPM number.

- 12/7.5= 1.6
- 1.6 x 3367= 5387.2
- 5387.2 x 60= 323,230 RPM as it exits the barrel

Now for the 20” barrel.

- 12/7.5= 1.6
- 1.6 x 3322= 5315.2
- 5315.2 x 60= 318,912 RPM as it exits the barrel

A velocity difference of 45fps in the same atmospheric conditions resulted in a difference of 4318 RPM’s between the 20” and 22” barrel.

A few things to note:

- The 22” barrel provided a gyroscopic stability of 3.65, while the 20” barrel provided an SG of 3.63 with the reduced velocity. Both of these are over the optimal 1.5 SG.
- The 58g load uses a V-Max varmint bullet which utilizes Hornady’s AMP jacket.
- Thin match grade jacket
- These barrels will consistently shoot this 58g load into .3 to .5 MOA five shot groups throughout the year.
- An increase in velocity above the current load results in a decrease in accuracy but nothing that I can attribute to the twist of the barrel.
- No key holes
- No jacket separation
- No catastrophic bullet failure
- The group just begins to open up, but is still sub-moa

I’ve put a lot of info out there so far, but what it comes down to is this. You should aim for a stability factor between 1.5 and 2. Going higher than 2 is probably ok, but depends a lot on the construction of the bullet. The only way to know if it works for you is to test it.

*Tumbling and Terminal Effect*

Some people assume that a marginally stable bullet in flight is more likely to tumble and fragment on impact. This is not absolute truth. The nature of a projectile like the 5.56 to tumble and fragment is not related to its aerodynamic stability. Rather, it’s the result of the bullets center of gravity and the impact itself. AKA, its design.

Remember earlier when I mentioned the center of pressure vs the center of gravity? When the bullet impacts, the dramatic increase in drag moves the center of pressure way in front of the center of gravity. At the same time, the deceleration and reduction in RPM from friction further destabilize the bullet. At that point, the bullet can’t help but tumble. It has little to do with how stable it was flying beforehand.

But let me add another little tid bit. Empirical data has shown that a faster twist barrel will have a positive effect to terminal ballistics. As we’ve already discussed, a faster twist rate increases rotational speed which decreases yaw, and yada yada yada. Things we’ve already talked about. But this increase in rotational speed also increases rotational energy and forward energy, which translates into more energy on target, more “shock” to the target, and increased wound channels.

*But I’ll Lose Velocity*

Yet another commonly heard concern when it comes to a faster twist rate. While yes, a little velocity will be lost with a faster twist barrel, it isn’t significant enough to have an impact on ballistic performance. Even at intermediate to longer ranges. Let’s use a 10 twist and 12 twist barrel as an example. The difference in kinetic energy of rotation between these two is barely noticeable as compared to the kinetic energy of forward motion. This results in very little loss of muzzle velocity.

**Wrapping Up**

At this point, you’ve got a sense of why rifling exists. Since the aerodynamics of bullet flight want to make the projectile tumble end over end, we need a way to stabilize it. Fins aren’t practical for small arms, so we use spin stabilization.

Spin is imparted by the rifling grooves down your barrel. The rate at which these grooves curve around the bore, the twist rate, imparts many thousands of RPM to the bullet. The ideal twist rate for your caliber depends on the weight and design of the projectile, as well as the velocity that you intend to push it. Longer projectiles, and those with more bearing surface area in contact with the rifling, generally like a faster twist rate. A thing to note here. Longer bullets do not always mean more bearing surface area contact. Just as a lighter bullet weight does not always correlate to a shorter bullet. These are common misconceptions.

You may have noticed that in this article I limited the topic of twist to standard uniform twist. I purposely did not mention or delve into gain twist (aka progressive or transitional twist) barrels. Gain twist barrels are those that start with a slower twist at the chamber and finish with a faster twist at the muzzle. It “gains” twist, hence the name. There’s arguments to both sides. I’ve not had enough interest in them to experiment and test gain twist barrels. Two of the more commonly mentioned pros of gain twist barrels is that the slower twist at the chamber reduces bullet deformation as it is not quickly spun up in RPM’s. It is also stated that this will also offer less resistance during the peak pressure curve which will reduce pressures, and may allow for a little more powder in the case. The other pro commonly associated is that those who shoot lathe spun solid bullets with driving bands see better sealing and accuracy as the gain twist keeps the driving band of the bullet more firmly in place with the rifling. Again, I have no real world experience with these and therefore cannot speak to their values.

So…what do you do? First, you need to decide what exactly it is that 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? Somewhere in between? The answer to that question is going to help you prioritize what bullet design you are looking for. Then you need to determine what velocity it is that you want to achieve. If you shoot factory ammunition, this for the most part will already be determined for you. But if you handload, then that envelope opens up and becomes a factor for your twist rate.

If you are shooting long skinny premium Berger, Sierra, lathe spun solid bullets, 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.

For what it is worth, at BRD Gun Works I prefer to run a faster than normal twist for most cartridges. Within reason of course. This is true even in the predator guns. An exception to this would be if a client came to me with specific conditions, bullet selection, and load parameters that a fast twist barrel would not provide for the required ballistics. An example of this is that I would not use a 6.5 or 7 twist barrel in a 22 Creedmoor that will shoot 45g to 55g bullets at 4,000fps.

There are a lot of formulas out there for figuring out the right twist rate, and I provided insight on the important ones. I’ve also attached a few links to online calculators that do a great job. There is a lot of information that you should consider when looking at selecting a twist rate for your barrel. I do hope that this article and the links will prove useful to you.

BRD Gun Works~ Performance on Demand