January 24th, 2019

How to Calculate Bullet RPM — Spin Rates and Stability

Spin rate stability bullet speed RPM Formula stabilization barrel twist
Photo by Werner Mehl, www.kurzzeit.com, all rights reserved.

Most serious shooters can tell you the muzzle velocity (MV) of their ammunition, based on measurements taken with a chronograph, or listed from a manufacturer’s data sheet. (Of course, actual speed tests conducted with YOUR gun will be more reliable.)

Bullet RPM = MV X 720/Twist Rate (in inches)

However, if you ask a typical reloader for the rotational rate of his bullet, in revolutions per minute (RPM), chances are he can’t give you an answer.

Knowing the true spin rate or RPM of your bullets is very important. First, spin rate, or RPM, will dramatically affect the performance of a bullet on a game animal. Ask any varminter and he’ll tell you that ultra-high RPM produces more dramatic hits with more “varmint hang time”. Second, RPM is important for bullet integrity. If you spin your bullets too fast, this heats up the jackets and also increases the centrifugal force acting on the jacket, pulling it outward. The combination of heat, friction, and centrifugal force can cause jacket failure and bullet “blow-ups” if you spin your bullets too fast.

Accuracy and RPM
Additionally, bullet RPM is very important for accuracy. Nearly all modern rifles use spin-stablized bullets. The barrel’s rifling imparts spin to the bullet as it passes through the bore. This rotation stabilizes the bullet in flight. Different bullets need different spin rates to perform optimally. Generally speaking, among bullets of the same caliber, longer bullets need more RPM to stabilize than do shorter bullets–often a lot more RPM.

It is generally believed that, for match bullets, best accuracy is achieved at the minimal spin rates that will fully stabilize the particular bullet at the distances where the bullet must perform. That’s why short-range 6PPC benchrest shooters use relatively slow twist rates, such as 1:14″, to stabilize their short, flatbase bullets. They could use “fast” twist rates such as 1:8″, but this delivers more bullet RPM than necessary. Match results have demonstrated conclusively that the slower twist rates produce better accuracy with these bullets.

On the other hand, Research by Bryan Litz of Applied Ballistics has shown that with long, boat-tailed bullets, best accuracy may be achieved with twist rates slightly “faster” than the minimum required for stabilization. The reasons for this are somewhat complex — but it’s something to consider when you buy your next barrel. If, for example, the bullet-maker recommends a 1:8.25″ twist, you might want to get a true 1:8″-twist barrel.

Calculating Bullet RPM from MV and Twist Rate
The lesson here is that you want to use the optimal RPM for each bullet type. So how do you calculate that? Bullet RPM is a function of two factors, barrel twist rate and velocity through the bore. With a given rifling twist rate, the quicker the bullet passes through the rifling, the faster it will be spinning when it leaves the muzzle. To a certain extent, then, if you speed up the bullet, you can use a slower twist rate, and still end up with enough RPM to stabilize the bullet. But you have to know how to calculate RPM so you can maintain sufficient revs.

Bullet RPM Formula
Here is a simple formula for calculating bullet RPM:

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

Quick Version: MV X 720/Twist Rate = RPM

Example One: In a 1:12″ twist barrel the bullet will make one complete revolution for every 12″ (or 1 foot) it travels through the bore. This makes the RPM calculation very easy. With a velocity of 3000 feet per second (FPS), in a 1:12″ twist barrel, the bullet will spin 3000 revolutions per SECOND (because it is traveling exactly one foot, and thereby making one complete revolution, in 1/3000 of a second). To convert to RPM, simply multiply by 60 since there are 60 seconds in a minute. Thus, at 3000 FPS, a bullet will be spinning at 3000 x 60, or 180,000 RPM, when it leaves the barrel.

Example Two: What about a faster twist rate, say a 1:8″ twist? We know the bullet will be spinning faster than in Example One, but how much faster? Using the formula, this is simple to calculate. Assuming the same MV of 3000 FPS, the bullet makes 12/8 or 1.5 revolutions for each 12″ or one foot it travels in the bore. Accordingly, the RPM is 3000 x (12/8) x 60, or 270,000 RPM.

Implications for Gun Builders and Reloaders
Calculating the RPM based on twist rate and MV gives us some very important information. Number one, we can tailor the load to decrease velocity just enough to avoid jacket failure and bullet blow-up at excessive RPMs. Number two, knowing how to find bullet RPM helps us compare barrels of different twist rates. Once we find that a bullet is stable at a given RPM, that gives us a “target” to meet or exceed in other barrels with a different twist rate. Although there are other important factors to consider, if you speed up the bullet (i.e. increase MV), you MAY be able to run a slower twist-rate barrel, so long as you maintain the requisite RPM for stabilization and other factors contributing to Gyroscopic Stability are present. In fact, you may need somewhat MORE RPM as you increase velocity, because more speed puts more pressure, a destabilizing force, on the nose of the bullet. You need to compensate for that destabilizing force with somewhat more RPM. But, as a general rule, if you increase velocity you CAN decrease twist rate. What’s the benefit? The slower twist-rate barrel may, potentially, be more accurate. And barrel heat and friction may be reduced somewhat.

Just remember that as you reduce twist rate you need to increase velocity, and you may need somewhat MORE RPM than before. (As velocities climb, destabilizing forces increase somewhat, RPM being equal.) There is a formula by Don Miller that can help you calculate how much you can slow down the twist rate as you increase velocity.

CLICK HERE for Miller Formula in Excel Spreadsheet Format

That said, we note that bullet-makers provide a recommended twist rate for their bullets. This is the “safe bet” to achieve stabilization with that bullet, and it may also indicate the twist rate at which the bullet shoots best. Though the RPM number alone does not assure gyroscopic stability, an RPM-based calculation can be very useful. We’ve seen real world examples where a bullet that needs an 8-twist barrel at 2800 FPS MV, would stabilize in a 9-twist barrel at 3200 FPS MV. Consider these examples.

MV = 2800 FPS
8-Twist RPM = 2800 x (12/8) x 60 = 252,000 RPM

MV = 3200 FPS
9-Twist RPM = 3200 x (12/9) x 60 = 256,000 RPM

Of course max velocity will be limited by case capacity and pressure. You can’t switch to a slower twist-rate barrel and maintain RPM if you’ve already maxed out your MV. But the Miller Formula can help you select an optimal twist rate if you’re thinking of running the same bullet in a larger case with more potential velocity.

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February 23rd, 2017

Figuring Optimal RPM with Berger Twist-Rate Stability Calculator

Berger twist rate calculator
Erik Dahlberg illustration courtesy FireArmsID.com.

Berger twist rate calculatorBerger Twist-Rate Stability Calculator
On the updated Berger Bullets website you’ll find a handy Twist-Rate Stability Calculator that predicts your gyroscopic stability factor (SG) based on mulitiple variables: velocity, bullet length, bullet weight, barrel twist rate, ambient temperature, and altitude. This very cool tool tells you if your chosen bullet will really stabilize in your barrel.

LIVE DEMO BELOW — Just enter values in the data boxes and click “Calculate SG”.

How to Use Berger’s Twist Rate Calculator
Using the Twist Rate Calculater is simple. Just enter the bullet DIAMETER (e.g. .264), bullet WEIGHT (in grains), and bullet overall LENGTH (in inches). On its website, Berger conveniently provides this info for all its bullet types. For other brands, we suggest you weigh three examples of your chosen bullet, and also measure the length on three samples. Then use the average weight and length of the three. To calculate bullet stability, simply enter your bullet data (along with observed Muzzle Velocity, outside Temperature, and Altitude) and click “Calculate SG”. Try different twist rate numbers (and recalculate) until you get an SG value of 1.4 (or higher).

Gyroscopic Stability (SG) and Twist Rate
Berger’s Twist Rate Calculator provides a predicted stability value called “SG” (for “Gyroscopic Stability”). This indicates the Gyroscopic Stability applied to the bullet by spin. This number is derived from the basic equation: SG = (rigidity of the spinning mass)/(overturning aerodynamic torque).

(more…)

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September 6th, 2015

Ballistics Tip: Understanding Bullet Stability (Twist Rate and MV)

Berger bullet SG MV twist rate stability Litz

Bryan Litz has produced an informative new video on the subject of bullet stability. The video explains how stability is related to spin rate (or RPM), and how RPM, in turn, is determined by barrel twist rate and velocity. For long-range shooting, it is important that a barrel have a fast-enough twist rate to stabilize the bullet over its entire trajectory.

Detailed Bullet Stability Article
To complement the above video, Bryan has authored a detailed article that explains the key concepts involved in bullet stabilization. Bryan explains: “Bullet stability can be quantified by the gyroscopic stability factor, SG. A bullet that is fired with inadequate spin will have an SG less than 1.0 and will tumble right out of the barrel. If you spin the bullet fast enough to achieve an SG of 1.5 or higher, it will fly point forward with accuracy and minimal drag.”


CLICK HERE to READ Full Bullet Stability Article by Bryan Litz

Berger bullet SG MV twist rate stability Litz

There is a “gray zone” of marginal stability. Bryan notes: “Bullets flying with SGs between 1.0 and 1.5 are marginally stabilized and will fly with some amount of pitching and yawing. This induces extra drag, and reduces the bullets’ effective BC. Bullets in this marginal stability condition can fly with good accuracy and precision, even though the BC is reduced. For short range applications, marginal stability isn’t really an issue. However, shooters who are interested in maximizing performance at long range will need to select a twist rate that will fully stabilize the bullet, and produce an SG of 1.5 or higher.”


Berger twist rate calculatorBerger Twist-Rate Stability Calculator
On the updated Berger Bullets website you’ll find a handy Twist-Rate Stability Calculator that predicts your gyroscopic stability factor (SG) based on mulitiple variables: velocity, bullet length, bullet weight, barrel twist rate, ambient temperature, and altitude. This very cool tool tells you if your chosen bullet will really stabilize in your barrel.

LIVE DEMO BELOW — Just enter values in the data boxes and click “Calculate SG”.

Top photo with bullet by Werner Mehl, www.kurzzeit.com, all rights reserved.
Permalink Bullets, Brass, Ammo, Tech Tip 7 Comments »
June 26th, 2014

Modern Advancements in Long Range Shooting — By Bryan Litz

Litz Applied Ballistics Book Modern Advancements Long Range ShootingApplied Ballistics, LLC is offering an all-new book by Bryan Litz, the first in a series. The new 339-page, hard-cover book, Modern Advancements for Long Range Shooting, Volume I, documents the ongoing R & D being done at the Applied Ballistics laboratory, the “Area 51″ of the shooting world.

“This new series is heavily based in experimental ballistics, and takes a ‘Myth Busters’-type approach to many of the questions and problems faced by modern long range shooters,” stated Litz. Volume I of the series is scheduled for release in late July, 2014. The book will cost $39.95, but you can pre-order now for $35.95, a 10% savings.

Bryan adds: “Anyone interested in the underlying science behind shooting can benefit from this book. We address the important questions… How much does faster twist affect MV? How does stability affect BC from the muzzle and downrange? What chronographs are capable of high accuracy and precision? What characteristics should you look for in your long range rifle and optic set up? What new gadgets are being developed to enhance long range shooting?

New Book Features Extensive Live-Fire Test Results
Bryan tells us: “The book spotlights state-of-the-art technologies (and methodologies) in long range shooting. New equipment and old ideas are explored using experimental, live-fire testing. Extensive test results are reported in an easy-to-understand way. Among other things, our tests explore the effects of twist rate on muzzle velocity, BC (supersonic and transonic), precision, even spin rate decay for various rifling profiles as they are tested experimentally.

Chronographs and Optics Are Tested and Compared
Litz’s new book traces the evolution of modern rifle, bullet, and optic design. Results from chronograph comparison tests are presented, showing the strengths and weaknesses of available commercial chronographs. High-tech instrumentation such as laser rangefinders and wind measurement devices are explained in detail by contributing author Nick Vitalbo.

The New Book Puts Theory into Practice
We asked Bryan Litz how this new book differs from his previous treatises. Bryan replied: “My original Applied Ballistics for Long-Range Shooting book explains the fundamental elements of external ballistics. It’s the academic background which all future work relies on. The new book, Modern Advancements in Long Range Shooting, covers the ongoing development of equipment and ideas. We explore things like twist rate effects, modern rifle and optic design, and some of the high tech instruments which are being used to enhance the effectiveness of long range shooting.

Litz Applied Ballistics Book Modern Advancements Long Range Shooting

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