August 12th, 2018

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 11th, 2018

Bullet RPM and Drag — How BC Changes with Bullet Spin Rates

Bryan Litz bullet rpm BC Drag ballistics coefficient twist rate

You may not realize it… but to get the optimum BC from your bullets (i.e. the lowest aerodynamic drag), you must spin the bullets fast enough. Bullet drag increases (as expressed by lower BC) if the bullet spins too slowly. Bryan Litz of Applied Ballistics explains how BC changes with twist rates…

More Spin, Less Drag
In this article, we look at how twist rate and stability affect the Ballistic Coefficient (BC) of a bullet. Again, this topic is covered in detail in the Modern Advancements book. Through our testing, we’ve learned that adequate spin-stabilization is important to achieving the best BC (and lowest drag). In other words, if you don’t spin your bullets fast enough (with sufficient twist rate), the BC of your bullets may be less than optimal. That means, in practical terms, that your bullets drop more quickly and deflect more in the wind (other factors being equal). Spin your bullets faster, and you can optimize your BC for best performance.

Any test that’s designed to study BC effects has to be carefully controlled in the sense that the variables are isolated. To this end, barrels were ordered from a single barrel smith, chambered and headspaced to the same rifle, with the only difference being the twist rate of the barrels. In this test, 3 pairs of barrels were used. In .224 caliber, 1:9” and 1:7” twist. In .243 caliber it was 1:10” and 1:8”, and in .30 caliber it was 1:12” and 1:10”. Other than the twist rates, each pair of barrels was identical in length, contour, and had similar round counts. Here is a barrel rack at the Applied Ballistics Lab:

Applied Ballistics used multiple barrels to study how twist rate affects BC.

stability gyroscopic ballistics coefficient drag twist rate

“The Modern Advancements series is basically a journal of the ongoing R&D efforts of the Applied Ballistics Laboratory. The goal of the series is to share what we’re learning about ballistics so others can benefit.” –Bryan Litz

Barrel twist rate along with velocity, atmospherics, and bullet design all combine to result in a Gyroscopic Stability Factor (SG). It’s the SG that actually correlates to BC. The testing revealed that if you get SG above 1.5, the BC may improve slightly with faster twist (higher SG), but it’s very difficult to see. However, BC drops off very quickly for SGs below 1.5. This can be seen in the figure below from Modern Advancements in Long Range Shooting.

The chart shows that when the Gyroscopic Stability Factor (SG) is above 1.5, BC is mostly constant. But if SG falls below 1.5, BC drops off dramatically.
stability gyroscopic ballistics coefficient drag twist rate

Note that the BC drops by about 3% for every 0.1 that SG falls below 1.5. The data supports a correlation coefficient of 0.87 for this relationship. That means the 3% per 0.1 unit of SG is an accurate trend, but isn’t necessarily exact for every scenario.

It’s a common assumption that if a shooter is seeing great groups and round holes, that he’s seeing the full potential BC of the bullets. These tests did not support that assumption. It’s quite common to shoot very tight groups and have round bullet holes while your BC is compromised by as much as 10% or more. This is probably the most practical and important take-away from this test.

To calculate the SG of your bullets in your rifle, visit the Berger Bullets online stability calculator. This FREE calculator will show you the SG of your bullets, as well as indicate if your BC will be compromised (and by how much) if the SG is below 1.5. With the stated twist rate of your barrel, if your selected bullet shows an SG of 1.5 (or less), the calculator will suggest alternate bullets that will fully stabilize in your rifle. This valuable online resource is based directly on live fire testing. You can use the SG Calculator for free on the web — you don’t need to download software.

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July 31st, 2016

Berger Bullets Twist Rate Stability Calculator

Berger twist rate calculator

Berger twist rate calculatorBerger Twist-Rate Stability Calculator
On the 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 cool tool tells you if your chosen bullet will really stabilize in your barrel.


CLICK HERE to Go to TWIST RATE CALCULATOR PAGE

How to Use Berger’s Twist Rate Calculator
Using the Twist Rate Calculator 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).

Berger twist rate calculator

If you have an SG under 1.0, your bullet is predicted not to stabilize. If you have between 1.0 and 1.1 SG, your bullet may or may not stabilize. If you have an SG greater than 1.1, your bullet should stabilize under optimal conditions, but stabilization might not be adequate when temperature, altitude, or other variables are less-than-optimal. That’s why Berger normally recommends at least 1.5 SG to get out of the “Marginal Stability” zone.

In his book Applied Ballistics For Long-Range Shooting, Bryan Litz (Berger Ballistician) recommends at least a 1.4 SG rating when selecting a barrel twist for a particular bullet. This gives you a safety margin for shooting under various conditions, such as higher or lower altitudes or temperatures.

Story idea from EdLongrange. We welcome reader submissions.
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October 22nd, 2015

Berger Updates Bullet BC Data and Recommended Twist Rates

Berger BC Ballistics Coefficient Barrel Twist Rate  Updates

Berger has released two important informational updates for its line-up of bullets. First, the Ballistics Coefficients (BCs) have been updated for the vast majority of bullets Berger sells. In addition, G7 model BCs are being provided for most of the bullets. You will want to use the updated BC data, which is based on actual testing of recent production lots of bullets.

Second, Berger is now providing a dual twist-rate recommendation for most bullets. Berger is now lists a “minimum” barrel twist rate as well as an “optimal” twist rate. To get maximum long-range performance from your bullets, use a barrel with the “optimal” rate of twist.

CLICK HERE for the latest Berger Quick Reference Sheets with updated BCs and new Optimal Twist Rates. Eric Stecker, Berger President says: “We have tested every lot of bullets‬ produced in the last several years to bring you these updated numbers for all of our bullets.”

Ballistic Coeffificent (BC) Updates with G7 Data
Berger notes: “We have updated all of our Ballistic Coefficients to be even more accurate.
Prior to 2008, all of Berger Bullets’ BCs were calculated using a computer prediction. Early in 2009, we began measuring BCs with live-fire testing. As a result, Berger’s BCs were updated and G7 BCs were also made available. This represented a dramatic improvement in the accuracy of performance data at that time. Since 2009, the BCs assessed for Berger Bullets have not been updated. As part of our ongoing effort to provide shooters with the best information possible, Berger has been testing every lot of bullets produced for the last several years. The result is updated and highly accurate running averages of BCs for recent production lots.

Here are some of the Updated BC Values for popular Berger Target (Match) Bullets:

Description New G1 BC New G7 BC % Change
22 Cal 80gr VLD Target 0.455 0.233 +2%
22 Cal 90gr VLD Target 0.534 0.274 -3%
6mm 95gr VLD Target 0.467 0.240 -3%
6mm 105gr VLD Target 0.517 0.265 +5%
6mm 105gr Hybrid Target 0.536 0.275 -1%
6mm 115gr VLD Target 0.563 0.289 +3%
6.5mm 130gr VLD Target 0.562 0.288 +2%
6.5mm 140gr Hybrid Target 0.607 0.311 -2%
7mm 180gr VLD Target 0.683 0.350 +4%
7mm 180gr Hybrid Target 0.680 0.349 +1%
30 Cal 155gr Hybrid Target 0.478 0.245 -1%
30 Cal 185gr Hybrid Target 0.576 0.295 +1%
30 Cal 215gr Hybrid Target 0.691 0.354 -1%

CLICK HERE for Complete Table with all bullets on Berger Website

G7 Form Factor Addition
Berger also added the G7 form factor to the Ballistics Quick Reference Sheet. The analysis of form factors can be very useful when considering a bullet’s long range performance potential. Going by BC alone can be deceptive since BC includes the weight and caliber of the bullet. Form factor indicates how much drag the bullet has, which is a very important consideration for all bullets of all calibers.

NEW Dual Twist-Rate Recommendations
Recommended twist rates for bullets are commonly listed as a single value, such as 1:12” (one rotation in 12″ of barrel travel). This may be overly simplistic. There is a big gray area of marginal stability in which bullets can fly with good accuracy, but with a reduced (i.e. sub-optimal) Ballistic Coefficient. Recognizing this reality, Berger is now listing two twist rates for each bullet it makes. The first is the minimum twist needed for good accuracy, which Berger has always recommended. The second is the new optimal twist rate, which is the twist that will stabilize the bullet to a level which achieves its full performance (BC) potential. CLICK HERE For more information.

Berger BC Ballistics Coefficient Barrel Twist Rate  Updates

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