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January 21st, 2023

Sierra Ballistics Resources — 60+ Authoritative Articles for FREE

Sierra Bullets Ballistics Resources

Need some informative reading material for winter days? Here’s a vast resource available free from Sierra Bullets. Here are links to over 60 articles with information on bullets, ballistic coefficients, wind drift, up/down angles, temperature effects, tailwind effects and much more. Most of these resources come from the respected Sierra Reloading Manuals, 4th and 5th Editions. There are enough articles to read one per week for a year!

Major Ballistics Reference Articles
The Ballistic Coefficient by William T. McDonald & Ted C. Almgren (Adobe .PDF)
Deflections and Drift of a Bullet in a Crosswind by William T. McDonald (Adobe .PDF)
Inclined Fire by William T. McDonald

Table of Exterior Ballistic Coefficients
(5th Edition Reloading Manual)

Rifle
Handgun
.22 Rimfire

Exterior Ballistic Tables
(4th Edition Reloading Manual)

Rifle Tables – Select by Bullet
Handgun Tables – Select by Bullet
Silhouette Tables – Select by Bullet

5th Edition Manual Exterior Ballistics Section
Section 1.0 Introduction
Section 2-2.1 The Ballistic Coefficient Explained
Section 2.2 Bigger Is Not Always Better
Section 2.3 How the Ballistic Coefficient is Measured
Section 2.3.1.1 Measurement Procedure
Section 2.3.1.2 Important Precautions and Points to Consider
Section 2.3.2 Initial Velocity and Time of Flight Method
Section 2.3.3 Doppler Radar Method
Section 2.4 Lessons Learned from Ballistic Coefficient Testing
Section 2.5 Examples of Ballistic Coefficient Measurements
Section 3.0 Exterior Ballistic Effects on Bullet Flight
Section 3.1 Effects of Altitude and Atmospheric Conditions
Section 3.2 Effects of Wind
Section 3.3 Effects of Shooting Uphill or Downhill
Section 3.4-3.4.1 Trajectory Considerations for Sighting in a Gun
Section 3.4.2 Determining Zero Range from Firing Test Results
Section 3.4.3 Sighting in for a Change in Shooting Location
Section 3.5 Point Blank Range
Section 3.6 Maximum Horizontal Range of a Gun
Section 3.7 Maximum Height of Fire of a Gun
Section 4.0 Six Degree of Freedom Effects on Bullet Flight
Section 4.1 Basic Physical Concepts
Section 4.2 Yaw of Repose and Resulting Crossrange Deflection
Section 4.3 Turning of a Bullet to Follow a Crosswind and Resulting Deflections
Section 4.4 Turning of a Bullet to Follow a Vertical Wind and Resulting Deflections
Section 5.0 Trajectory Tables
Section 6.0 Sierra’s Infinity Exterior Ballistics Software

4th Edition Manual Exterior Ballistics Section
Section 2.0 Introduction
Section 3.0 Historical Summary
Section 4.0 The Ballistic Coefficient
Section 4.1 Basic Definitions
Section 4.2 Ballistic Coefficients Effects on Bullet Trajectories
Section 4.3 How the Ballistic Coefficient is Measured by Firing Tests
Section 4.4 Lessons Learned From Ballistic Coefficient Measurements
Section 4.5 Ballistic Coefficient Variations with Muzzle Velocity near the Speed of Sound
Section 4.6 Ballistic Coefficient Dependence on Coning Motion
Section 5.0 Exterior Ballistics Topics
Section 5.1 Effects of Altitude and Atmospheric Conditions
Section 5.2 Effects of Altitude and Uphill/Downhill Shooting
Section 5.3 Wind Effects
Section 5.3.1 Headwinds and Tailwinds
Section 5.3.2 Crosswinds
Section 5.3.3 Winds from Any Direction
Section 5.4 Changing the Zero Range
Section 5.5 Point Blank Range
Section 5.6 Muzzle Velocity Dependence on Cartridge Temperature
Section 6.0 Equations of Bullet Flight
Section 6.1 Differential Equations of Bullet Motion
Section 6.2 Drag Force and the Drag Function
Section 6.3/Section 6.3.1 Siacci’s Method/The Change of Independent Variables
Section 6.3.2 The Assumption
Section 6.4 Mayevski’s Analytical Form of the Drag Model
Section 6.5 Closed-Form Solutions for Trajectory Parameters
Section 6.6 Other Useful Equations
Section 6.6.1 References

Sierra Bullets Ballistics Resources

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November 21st, 2022

How Altitude and Barometric Pressure Affect Projectile Ballistics

altitude ballistics zeiss LRP S5 318-50 FFP scope
Photo shows the new ZEISS LRP S5 318-50 first focal plane (FFP) scope.

“A bullet launched at a higher altitude is able to fly slightly farther (in the thinner air) for every increment of downward movement. Effectively, the bullet behaves as if it has a higher ballistic coefficient.”

Last month a good friend ventured to the high country of Colorado to pursue elk. He recently zeroed his rifle in California, at a range just a few hundred feet Above Mean Sea Level (AMSL). He wondered if the higher altitude in Colorado could alter his ballistics. The answer is a definite yes. However the good news is that free ballistics calculators can help you plot reliable drop charts for various shooting locations, high or low.

Suunto AltimeterThe question has been posed: “What effect does altitude have on the flight of a bullet?” The simplistic answer is that, at higher altitudes, the air is thinner (lower density), so there is less drag on the bullet. This means that the amount of bullet drop is less at any given flight distance from the muzzle. Since the force of gravity is essentially constant on the earth’s surface (for practical purposes), the bullet’s downward acceleration doesn’t change, but a bullet launched at a higher altitude is able to fly slightly farther (in the thinner air) for every increment of downward movement. Effectively, at higher altitudes, the bullet behaves as if it has a higher ballistic coefficient.

Forum member Milanuk explains that the key factor is not altitude, but rather air pressure. Milanuk writes:

“In basic terms, as your altitude increases, the density of the air the bullet must travel through decreases, thereby reducing the drag on the bullet. Generally, the higher the altitude, the less the bullet will drop. For example, I shoot at a couple ranges here in the Pacific Northwest. Both are at 1000′ AMSL (Above Mean Sea Level) or less. I’ll need about 29-30 MOA to get from 100 yards to 1000 yards with a Berger 155gr VLD at 2960 fps. By contrast, in Raton, NM, located at 6600′ AMSL, I’ll only need about 24-25 MOA to do the same. That’s a significant difference.

Note that it is the barometric pressure that really matters, not simply the nominal altitude. The barometric pressure will indicate the reduced pressure from a higher altitude, but it will also show you the pressure changes as a front moves in, etc. which can play havoc w/ your calculated come-ups. Most altimeters are simply barometers that read in feet instead of inches of mercury.”

As Milanuk states, it is NOT altitude per se, but the LOCAL barometric pressure (sometimes called “station pressure”) that is key. The two atmospheric conditions that most effect bullet flight are air temperature, and barometric pressure. Normally, humidity has a negligible effect. It’s important to remember that the barometric pressure reported on the radio (or internet) may be stated as a sea level equivalency. So in Denver (at 6,000 feet AMSL), if the local pressure is 24″, the radio will report the barometric pressure to be 30″. If you do high altitude shooting at long range, bring along a Kestrel, or remember to mentally correct the radio station’s pressure, by 1″ per 1,000 feet.

Trajectory of Bullet fired at Sea Level

Trajectory of Bullet fired at 20,000 feet

You can do your own experimental calculations using JBM Online Ballistics (free to use). Here is an extreme example, with two printouts (generated with Point Blank software), one showing bullet trajectory at sea level (0′ altitude) and one at 20,000 feet. For demonstration sake, we assigned a low 0.2 BC to the bullet, with a velocity of 3000 fps.

To learn more about all aspects of Exterior Ballistics, Hornady has a useful discussion of External Ballistics including the effects of altitude and temperature. To dig deeper, Sierra Bullets has a comprehensive Exterior Ballistics Resource Page with multiple sections from the Sierra Manual (4th and 5th Editions), including:

Section 3.0: Exterior Ballistic Effects on Bullet Flight
Section 3.1: Effects of Altitude and Atmospheric Conditions
Section 3.2: Effects of Wind
Section 3.3: Effects of Shooting Uphill or Downhill

Example from Section 3.0: “When a bullet flies through the air, two types of forces act on the bullet to determine its path (trajectory) through the air. The first is gravitational force; the other is aerodynamics. Several kinds of aerodynamic forces act on a bullet: drag, lift, side forces, Magnus force, spin damping force, pitch damping force, and Magnus cross force. The most important of these aerodynamic forces is drag. All the others are very small in comparison when the bullet is spin-stabilized.”

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March 12th, 2022

Bullet Sectional Density — What You Need to Know

Bullet projectile sectional density formula Sierra Bullets

by Sierra Bullets Ballistic Technician Paul Box
All of us who have been in reloading and shooting for any period of time have read how sectional density has been regarded as a bullet’s ability to penetrate. Back before high velocity came along and modern bullet design, the easiest way to get more “power” and penetration was by increasing the diameter and mass. After all, a bowling ball will hurt more than a golf ball, right?

Let’s take a closer look at sectional density.

The formula for calculating sectional density is pretty simple and straight forward. Take the bullet weight and divide by 7000. This number is then divided by the bullet diameter squared. Two bullets of equal weight and the same diameter will have equal sectional sectional density. No regard is given to the bullet construction. This is where the fly hits the soup in considering sectional density as far as penetration is concerned.

Section Density Formula: (Bullet Weight divided by 7000) divided by Bullet Diameter squared.

Bullet construction is the biggest factor in how it is able to penetrate. The best example I can think of here is to look at the Sierra .224 55 Gr. FMJBT GameKing #1355 compared to the 55 Gr. BlitzKing #1455. Both are .224 and weigh 55 grs. Both have a sectional density of .157. But there is a huge difference in their construction. The FMJ has a thick jacket and is designed to penetrate. The BlitzKing is designed for fast and rapid expansion with little concern for how deep they will penetrate.

The next time you’re choosing a bullet, look at the construction and less at the sectional density number. It’s all about the construction anyway. If you have any questions or would like to discuss sectional density or bullet penetration further, please give us a call at 800-223-8799 or shoot us an email at sierra@sierrabullets.com.

Sierra Bullets reloading tips

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December 23rd, 2021

Amazing Applied Ballistics Rimfire Ammo Test — 50 Types Tested

.22 LR Rimfire Ammunition testing Bryan Litz Applied Ballistics Eley
Photo shows Bryan Litz (on right) and tester Mitchell Fitzpatrick. Bryan said: “Only 2,445 rounds to go! We’re testing over 50 ammo types in five different twist barrels… science can be exhausting!”

Do you know the actual BC (Ballistic Coefficient) of your rimfire ammunition? Well Applied Ballistics has the data, thanks to a comprehensive, marathon ammo testing session. Some years back, in an effort to determine the “real world” BCs of various rimfire ammo types, Bryan Litz and his team at Applied Ballistics did an extraordinary, in-depth shooting test. Litz and company tested over fifty types of .22 LR ammo, using five different twist-rate barrels. This was one of the most comprehensive and through rimfire ammo tests ever done.

.22 LR Rimfire Ammunition testing Bryan Litz Applied Ballistics Eley

.22 LR Rimfire Ammunition testingBryan tolds us: “We tested many types of .22 rimfire ammo for the 2nd Edition of the Ballistic Performance of Rifle Bullets book. We used a pair of Oehler chronographs to measure velocity at the muzzle (MV) and velocity at 100 yards.” With these numbers (average and SD) Bryan can calculate G1 BCs for all the 50+ types of rimfire ammo. What’s more, because every sample is shot through five different barrels (each with a different twist rate) Bryan can also determine how velocity is affected by twist rate.

The tests are primarily to determine velocities for BC calculations — this was not an accuracy test. Bryan explains: “Our tests are not really looking at accuracy, mainly because that’s so subjective to different rifles. Our testing is primarily focused on measuring the BC of rimfire rounds from different twist-rate barrels. The MVs and BCs from the different twist test barrels was then published by Applied Ballistics in print books. Bryan Litz told us: “The .22 LR Rimfire data was originally published in Ballistic Performance of Rifle Bullets, 2nd Edition, which is now out of print. The 3rd Edition of that book doesn’t have rimfire data. The rimfire testing results and data were re-published in Modern Advancements in Long Range Shooting – Volume II (along with many other topics).

Bringing Science to the Rimfire World
Bryan’s goal with this project was to increase the rimfire knowledge base: “We hope to give the world of .22 LR rimfire a good dose of science. How is the BC of .22 rimfire ammo affected by barrel twist? Do subsonic rounds have more consistent BCs than supersonic or transonic rounds? What brands have the highest BCs? What brands have the most consistent MVs?”

.22 LR Rimfire Ammunition testing Bryan Litz Applied Ballistics Eley
Data from two Oehler chronographs is recorded in a computer. Ammo samples were tested in five (5) different barrels (of varying twist rates). Give credit to Dane Hobbs who supplied a test rifle, multiple barrels, and most of the ammo types for the test.

.22 LR at 300 Yards?
Bryan also conducted some longer range rimfire tests. His interesting findings have appeared in the Modern Advancements in Long Range Shooting book series. Bryan notes: “While .22 rimfire isn’t typically considered ‘long range’, we were able to consistently hit a two-MOA steel target at 300 yards with the trajectory predicted by AB software and the measured BC of some standard .22 LR rimfire ammo. The info we’re generating may make it possible to push the range of target engagement for a round that’s not seen much advancement in many decades.”

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October 24th, 2021

Sunday Gunday: Wind-Reading with Keith Glasscock

Keith Glasscock winning wind youtube channel f-Class f-Open wind reading

Keith Glasscock is one of America’s very finest F-Class shooters. This talented trigger-puller took second in F-Open division at the F-Class National Championships three years in a row. A smart engineer with aviation knowledge, Keith is a master wind reader, who has served as the wind coach for top F-Class teams. In fact Keith is in Arizona right now coaching a team at Ben Avery.

Keith shares his wind-reading expertise on his popular YouTube Channel — Winning in the Wind. This channel provides intelligent advice on multiple topics including reloading, load development, shooting strategies, and yes, reading the wind.

Keith has the credentials to back up the advice he offers in his video lessons. A High Master, Keith finished second overall at the 2021 NRA F-Class Long Range Championship in F-Open division. He also finished second at the 2020 Nationals, and he took second place at the 2019 Nationals. His consistency is unrivaled, which means he definitely knows the secrets of long-range wind calling and loading ultra-accurate ammo.

Today we feature two of Keith’s latest YouTube videos, both focused on wind reading.

Wind Direction vs. Wind Speed — Which is More Important

Most shooters find wind reading somewhat intimidating. That is understandable. The wind can change constantly during a match, with variations in both wind velocity and angles. Sometimes you think you have a cycle figured out, but then there can be an unexpected lull. Or you may start a string in what you think is a stable condition, but then a surprise shift changes everything. In addition, wind flows can be influenced by terrain features, such as berms, which have varying effects depending on wind angle (e.g. a tailwind hitting a berm will act differently than a 90-deg crosswind). That is why a good wind reader needs to identify both the wind speed AND the wind angle. In this video, Keith explains when to focus primarily on direction and when to pay most attention to velocity. With headwinds and tailwinds, Keith notes, you should monitor angle changes carefully. With crosswinds, speed is the key variable to watch.

KEY Points to Remember
— Small changes in wind direction changes alter POI drastically at long range
— During head or tailwinds, focus on wind direction
— During crosswinds, focus more on wind speed
— The wind is cyclic — always be aware of the pattern

Keith Glasscock wind reading video winnning spotting scope flag angle kestrel

Determining Wind Direction with Precision

Keith Glasscock winning wind youtube channel f-Class f-Open ES SD loading

Many shooters try to read the wind merely using whatever wind flags might be aloft on the range. Flags are important of course, but there are other vital factors that a wise wind-watcher will monitor. You want to watch mirage, and the movement of grass and trees. In looking for angle changes, Keith says the spotting scope is a very important tool. His tripod is equipped with angle markings on the rotating tripod head. This allows him to ascertain wind angles with great precision.

In the video below, Keith shows how to use a spotting scope to read the wind. He explains how he uses his spotting scope in his role as a wind coach. But a spotting scope can also be used effectively by competitors shooting prone or from a bench. Many top shooters use their spotting scopes to watch mirage during their relays. Keith notes that smart competitors can also use their spotters BETWEEN relays to scout natural wind indicators (moving grass, trees etc.), check for boils, watch mirage, and estimate wind velocity cycles.

KEY Points to Remember
— Wind flags leave a lot to be desired in precision wind direction reading
— Precision wind direction can be obtained with a spotting scope
— There is a boil both directly upwind and directly downwind
— Angle indicator on your tripod helps with angular precision in wind readings
— Scouting with a spotting scope before your turn to shoot can be fruitful

Keith Glasscock winning wind youtube channel f-Class f-Open ES SD loading

Questions and Answers with Keith Glasscock

Keith Glasscock winning wind youtube channel f-Class f-Open wind reading

Q. How did you get started as a wind coach, and what were the most important stages in your progress in wind-reading?

Keith: I started coaching this team in 2017. I was looking for a team to shoot on, but they needed a wind coach. I’ve been a backseat driver ever since. I learned the most about reading the wind from shooting when the conditions are absolutely miserable – flags popping, wind switching, people missing the targets entirely, and there I was, having to make the big call. I learn from my own mistakes, and it shows. I still make mistakes, but try to limit them to ones I haven’t already made. In essence, I am in the most important stage now. Humbly looking at the wind knowing its power and mystery, while learning new things every day.

Q. What are the most common wind-reading mistakes you see people make at matches?

Keith: The most common, in a word, is UNDER-confidence. Most shooters can make that wind call with accuracy. But their fear prevents them from doing that, and prevents them from learning or taking advantage of smooth, solid conditions. The second common mistake is failure to anticipate changes. That comes from not gauging the wind pattern. It’s all about patterns in a sport where wind changes so small have such profound impacts on score.

Q. What’s more important — wind flags, or mirage (or maybe the unexpected horizontal that appears on the last shot recorded on target).

Keith: Both flags and mirage lie. The only thing that tells the truth is a bullet. Unfortunately, the wind can switch faster than you can shoot in most cases. I take a fluid approach. I look for what on the range right now tells me what the wind is doing.

Q. When are conditions so bad/unpredictable that it is necessary to just stop shooting and wait for things to get better?

Keith: This is situational, and comes down to what you are observing. I never like to shoot in the top of a gust condition, even when I know what the hold is. The drop off is what gets you that surprise 8.

Q: What type of wind meters do you recommend?

Keith: While Kestrels are inexpensive and quite serviceable, they are directional in nature. If I want absolute wind speed, an omnidirectional style unit is preferred.

Q. Are there ways to practice reading the wind (and judging wind speeds) when one is away from the range?

Keith: I really concentrate on seeing mirage any time I’m outside, without optics. I can, many times, see the boil of the mirage, and wind direction with the naked eye. My time in aviation has my eye tuned to see things like shear zones and venturis in the airflow. I take a moment, anytime the air is moving, to feel the air on my skin, see the trees and grass moving, and areas where the wind does funny things. Trees and grass tend to get too much credit as precision wind indicators. I use them as wind change indicators. It also gives me an opportunity to humble myself and realize how dependent I am on mirage and flags.

Keith Glasscock winning wind youtube channel f-Class f-Open ES SD loading

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October 19th, 2021

How Altitude Affects Bullet Ballistics (Drag and Drop)

altitude ballistics zeiss LRP S5 318-50 FFP scope
Photo shows the new ZEISS LRP S5 318-50 first focal plane (FFP) scope.

“A bullet launched at a higher altitude is able to fly slightly farther (in the thinner air) for every increment of downward movement. Effectively, the bullet behaves as if it has a higher ballistic coefficient.”

It’s hunting season, and a good friend is heading to the high country of Colorado next week to pursue elk. He recently zeroed his rifle in California, at a range just a few hundred feet Above Mean Sea Level (AMSL). He wondered if the higher altitude in Colorado could alter his ballistics. The answer is a definite yes. However the good news is that free ballistics calculators can help you plot reliable drop charts for various shooting locations, high or low.

Suunto AltimeterThe question has been posed: “What effect does altitude have on the flight of a bullet?” The simplistic answer is that, at higher altitudes, the air is thinner (lower density), so there is less drag on the bullet. This means that the amount of bullet drop is less at any given flight distance from the muzzle. Since the force of gravity is essentially constant on the earth’s surface (for practical purposes), the bullet’s downward acceleration doesn’t change, but a bullet launched at a higher altitude is able to fly slightly farther (in the thinner air) for every increment of downward movement. Effectively, at higher altitudes, the bullet behaves as if it has a higher ballistic coefficient.

Forum member Milanuk explains that the key factor is not altitude, but rather air pressure. Milanuk writes:

“In basic terms, as your altitude increases, the density of the air the bullet must travel through decreases, thereby reducing the drag on the bullet. Generally, the higher the altitude, the less the bullet will drop. For example, I shoot at a couple ranges here in the Pacific Northwest. Both are at 1000′ AMSL (Above Mean Sea Level) or less. I’ll need about 29-30 MOA to get from 100 yards to 1000 yards with a Berger 155gr VLD at 2960 fps. By contrast, in Raton, NM, located at 6600′ AMSL, I’ll only need about 24-25 MOA to do the same. That’s a significant difference.

Note that it is the barometric pressure that really matters, not simply the nominal altitude. The barometric pressure will indicate the reduced pressure from a higher altitude, but it will also show you the pressure changes as a front moves in, etc. which can play havoc w/ your calculated come-ups. Most altimeters are simply barometers that read in feet instead of inches of mercury.”

As Milanuk states, it is NOT altitude per se, but the LOCAL barometric pressure (sometimes called “station pressure”) that is key. The two atmospheric conditions that most effect bullet flight are air temperature, and barometric pressure. Normally, humidity has a negligible effect. It’s important to remember that the barometric pressure reported on the radio (or internet) may be stated as a sea level equivalency. So in Denver (at 6,000 feet AMSL), if the local pressure is 24″, the radio will report the barometric pressure to be 30″. If you do high altitude shooting at long range, bring along a Kestrel, or remember to mentally correct the radio station’s pressure, by 1″ per 1,000 feet.

Trajectory of Bullet fired at Sea Level

Trajectory of Bullet fired at 20,000 feet

You can do your own experimental calculations using JBM Online Ballistics (free to use). Here is an extreme example, with two printouts (generated with Point Blank software), one showing bullet trajectory at sea level (0′ altitude) and one at 20,000 feet. For demonstration sake, we assigned a low 0.2 BC to the bullet, with a velocity of 3000 fps.

To learn more about all aspects of Exterior Ballistics, Hornady has a useful discussion of External Ballistics including the effects of altitude and temperature. To dig deeper, Sierra Bullets has a comprehensive Exterior Ballistics Resource Page with multiple sections from the Sierra Manual (4th and 5th Editions), including:

Section 3.0: Exterior Ballistic Effects on Bullet Flight
Section 3.1: Effects of Altitude and Atmospheric Conditions
Section 3.2: Effects of Wind
Section 3.3: Effects of Shooting Uphill or Downhill

Example from Section 3.0: “When a bullet flies through the air, two types of forces act on the bullet to determine its path (trajectory) through the air. The first is gravitational force; the other is aerodynamics. Several kinds of aerodynamic forces act on a bullet: drag, lift, side forces, Magnus force, spin damping force, pitch damping force, and Magnus cross force. The most important of these aerodynamic forces is drag. All the others are very small in comparison when the bullet is spin-stabilized.”

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April 18th, 2021

Are You a Gun Wizard? Take the Shoot 101 Ballistics Quiz

Shoot 101 Ballistics Question Quiz BC trajectory

Shoot 101 Quiz
How much of an expert are you when it comes to firearms and ballistics? Test your knowledge with this interactive test. Vista Outdoor, parent of CCI, Federal, Bushnell, RCBS and other brands, has a media campaign called Shoot 101, which provides “how to” information about shooting, optics, and outdoor gear. There were a variety of interactive offerings that let you test your knowledge.

On the Shoot 101 website, you’ll find a Ballistics Quiz. The questions are pretty basic, but it’s still fun to see if you get all the answers correct.

You don’t need a lot of technical knowledge. Roughly a third of the questions are about projectile types and bullet construction. Note, on some platforms the layout doesn’t show all FOUR possible answers. So, for each question, be sure to scroll down to see all FOUR choices. REPEAT: Scroll down to see ALL answers!

CLICK HERE to Go to SHOOT 101 Ballistics QUIZ Page »

Sample Ballistics Question 1:

Shoot 101 Ballistics Question Quiz BC trajectory

Sample Ballistics Question 2:

Shoot 101 Ballistics Question Quiz BC trajectory

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November 12th, 2019

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.

(more…)

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August 1st, 2019

Ballistics TIP: How Altitude and Air Pressure Affect Bullet Flight

Trajectory of Bullet fired at Sea Level

Trajectory of Bullet fired at 20,000 feet

You can do your own experimental calculations using JBM Online Ballistics (free to use). Here is an extreme example, with two printouts (generated with Point Blank software), one showing bullet trajectory at sea level (0′ altitude) and one at 20,000 feet. For demonstration sake, we assigned a low 0.2 BC to the bullet, with a velocity of 3000 fps.

Suunto AltimeterOne of our readers asked “What effect does altitude have on the flight of a bullet?” The simplistic answer is that, at higher altitudes, the air is thinner (lower density), so there is less drag on the bullet. This means that the amount of bullet drop is less at any given flight distance from the muzzle. Since the force of gravity is essentially constant on the earth’s surface (for practical purposes), the bullet’s downward acceleration doesn’t change, but a bullet launched at a higher altitude is able to fly slightly farther (in the thinner air) for every increment of downward movement. Effectively, the bullet behaves as if it has a higher ballistic coefficient.

Forum member Milanuk explains that the key factor is not altitude, but rather air pressure. Milanuk writes:

“In basic terms, as your altitude increases, the density of the air the bullet must travel through decreases, thereby reducing the drag on the bullet. Generally, the higher the altitude, the less the bullet will drop. For example, I shoot at a couple ranges here in the Pacific Northwest. Both are at 1000′ ASL or less. I’ll need about 29-30 MOA to get from 100 yard to 1000 yards with a Berger 155gr VLD @ 2960fps. By contrast, in Raton, NM, located at 6600′ ASL, I’ll only need about 24-25 MOA to do the same. That’s a significant difference.

Note that it is the barometric pressure that really matters, not simply the nominal altitude. The barometric pressure will indicate the reduced pressure from a higher altitude, but it will also show you the pressure changes as a front moves in, etc. which can play havoc w/ your calculated come-ups. Most altimeters are simply barometers that read in feet instead of inches of mercury.”

As Milanuk states, it is NOT altitude per se, but the LOCAL barometric pressure (sometimes called “station pressure”) that is key. The two atmospheric conditions that most effect bullet flight are air temperature, and barometric pressure. Normally, humidity has a negligible effect.

It’s important to remember that the barometric pressure reported on the radio (or internet) may be stated as a sea level equivalency. So in Denver (at 6,000 feet amsl), if the local pressure is 24″, the radio will report the barometric pressure to be 30″. If you do high altitude shooting at long range, bring along a Kestrel, or remember to mentally correct the radio station’s pressure, by 1″ per 1,000 feet.”

If you want to learn more about all aspects of External Ballistics, ExteriorBallistics.com provides a variety of useful resources. In particular, on that site, Section 3.1 of the Sierra Manual is reprinted, covering Effects of Altitude and Atmospheric Pressure on bullet flight.

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July 5th, 2018

Input Key Variables Correctly for Ballistics Apps

Ballistic AE Moble App Ballistics Program solver JBM iphone, iPod, iPad

“Garbage In, Garbage Out.” You have to input key variables with precision if you want your Ballistics Apps to deliver reliable long-range trajectories. So says Tom Beckstrand, Field Editor for Guns & Ammo magazine. A former U.S. Army Special Forces Officer, and avid long-range competitor, Beckstrand knows the importance of using your ballistic calculator correctly. Here are his tips on how to achieve the best results using Ballistics Calculators.

Key Variables: Muzzle Velocity, Ballistic Coefficient, Sight Height

“The most important inputs to make any ballistic calculator work correctly are muzzle velocity, ballistic coefficient, and sight height,” says Beckstrand.

Ascertain Accurate Muzzle Velocity with a Good Chronograph
“Cheap chronographs will not give an accurate muzzle velocity, so the serious shooter needs to spend the money on a quality chrono.” When you chronograph, make sure to measure the distance from the muzzle to the chrono unit. That input is also important to your Ballistic calculations.

Use Reliable G1 and G7 Ballistic Coefficients
Beckstrand added, “Ballistic Coefficients are available from ammunition and bullet manufacturers, and most of these coefficients the manufacturers provide are really quite accurate.” Ballistic Coefficient or BC, is a number that reflects how well a bullet cuts through the air. The higher the BC, the less the bullet is affected by air drag.

Measure Sight Height Correctly Using Calipers
Beckstrand has found that many shooters aren’t inputting sight height or they are guessing at the correct height. As target distance increases, just a half-inch of sight height inaccuracy can mean several inches up or down.

“Sight height is the input most often overlooked and is usually the source of greatest error. I think a lot of shooters, especially those new to long-range shooting, simply don’t understand the importance of this input.”

Sight height is the distance from the centerline of the scope to the centerline of the bore. Some shooters, Beckstrand believes, just “eye it up” and estimate the distance. “Really, you should use a set of calipers to measure the sight height distance … within 0.1 inch”.

Get Leading Ballistics App for iOS Devices

Ballistic AE Moble App Ballistics Program solver JBM iphone, iPod, iPad

Ballistic AE Moble App Ballistics Program solver JBM iphone, iPod, iPadNeed a top-notch Ballistics App for your iPhone, iPad, or iPod? Start with Ballistic AE, the number 1 (i.e. most installed) App for iOS systems. Ballistics AE (Advanced Edition) is the most popular iOS ballistics program for many good reasons. Full-featured and easy to use, Ballistics AE has been refined over many years, and it supplies rock-solid solutions derived from JBM Ballistics solver (created by James B. Millard). Unlike some other Apps, Ballistics AE is STABLE on iPhones (with various OS levels). What’s cool is that Ballistics AE is now on sale for $12.99.

We’ve used the Ballistic AE program on an iPhone 5S, iPhone 6, and iPad, and it performed well. Here are some of the features we liked:

  • 1. Mirrors output from online version of JBM Ballistics we often use for initial calculations.
  • 2. Controls are simple to use and (mostly) intuitive.
  • 3. Handy comparison feature lets you compare ballistics for different projectiles side by side.
  • 4. Advanced Wind Kit allows you to account for complex wind situations.
  • 5. Projectile and BC Databases are very comprehensive.
  • 6. Software is regularly updated to match Apple OS changes.

Ballistic-AE App for iPhone & iPod, $12.99 | Ballistic-AE App for iPad, $12.99

Ballistic AE Moble App Ballistics Program solver JBM iphone, iPod, iPad

This Video Explains How to Set Up and Use Ballistic AE:

Permalink Bullets, Brass, Ammo, Gear Review, Tech Tip 6 Comments »
April 30th, 2018

RDF Bullets from Nosler — High BCs and Uniform Meplats

Nosler RDF reduced drag factor match bullets PRS High BC uniform meplats

Nosler’s line of RDF™ (Reduced Drag Factor) bullets feature very high Ballistic Coefficients, hybrid-type ogives, and tight, factory-closed meplats. Nosler’s RDF bullets were designed to be very competitive match projectiles for their respective bullet weights. Now offered in four calibers, Nosler RDF bullets genuinely deliver excellent performance for the price. Shooters, particular PRS competitors, have found the RDFs deliver the flat trajectory and high BC necessary to reach the podium.

Nosler RDF reduced drag factor match bullets PRS High BC uniform meplats

Nosler is proud of its RDF bullets, which feature tight, uniform meplats: “Nosler knows what gives competitive shooters an edge, isn’t an edge at all. It’s a point. With the highest in-class Ballistic Coefficient and smallest, most consistent meplat, RDF is the flattest-shooting match bullet in its class. Now available in more calibers and weights, the RDF’s meticulously-optimized compound ogive and long, drag-reducing boat-tail make achieving peak accuracy a snap”.

Experience RDF, the Flattest-Shooting Match Bullet:

Current Nosler RDF Bullets:
• 22 Cal 70 grain — G1 Ballistic Coefficient 0.416 | G7 Ballistic Coefficient 0.211
• 22 Cal 85 grain — G1 Ballistic Coefficient 0.498 | G7 Ballistic Coefficient N/A
• 6mm 105 grain — G1 Ballistic Coefficient 0.571 | G7 Ballistic Coefficient 0.280
• 6.5mm 140 grain — G1 Ballistic Coefficient 0.658 | G7 Ballistic Coefficient 0.330
• 30 Cal 175 grain — G1 Ballistic Coefficient 0.536 | G7 Ballistic Coefficient 0.270

RDF bullets are also available in Nosler factory ammunition in a variety of popular cartridge types. Nosler factory ammo lets you spend more time at the range and less at your reloading bench. Look for RDF bullets loaded in Nosler’s “Match Grade” Ammunition. Below is the .264-caliber, 140 grain RDF loaded in 6.5 Creedmoor, a popular chambering for PRS and tactical shooters.

Nosler RDF reduced drag factor match bullets PRS High BC uniform meplats

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August 10th, 2017

Is Bullet B.C. Important When Hunting? (Answer: It Depends)

Sierra Bullets Deer Hunting BC Ballistic Coefficient bullet
Game image courtesy OutdoorNebraska.gov/deer.

Written by Sierra Bullets Ballistic Technician Paul Box
Judging by the calls I’ve had through the years, I think some shooters might be placing too much importance on Ballistic Coefficient (B.C.). The best example of this comes from a call I had one day. This shooter called wanting the ballistic coefficient of one of our Sierra bullets. After I told him he seemed a little disappointed, so I ask him what his application was. Long range target, deer hunting in the woods? Talk to me.

As it turned out, he hunted deer in open timber. He very rarely shot beyond 100 yards. I pointed out to him that, under 200 yards, B.C. has little impact. Let’s compare a couple of bullets.

Let’s look at the trajectory of a couple of bullets and see how they compare. The .30 caliber 180 grain Round Nose #2170 RN and the 180 grain Spitzer Boat Tail #2160 SBT. The round nose has a B.C. of .240, while the SBT is .501. Starting both bullets out of the muzzle at 2700 FPS [with a 100-yard ZERO], at 200 yards the #2170 RN impacts 4.46″ low while the #2160 SBT impacts 3.88″ low. That’s a difference of only 0.58″ in spite of a huge difference in Ballistic Coefficient. If we compare out at 500 yards, then we have a [significant drop variance] of 14.27″ between these two bullets. [Editor: That difference could mean a miss at 500 yards.]

Distance to Your Prey is the Key Consideration
In a hunting situation, under 200 yards, having a difference of only .58” isn’t going to make or break us. But when elk hunting in wide open spaces it could mean everything.

The next time you’re choosing a bullet, give some thought about the distances you will be shooting. Sometimes B.C. isn’t everything. If you have any questions, please give the Sierra Bullets technicians a call at 800-233-8799.

sierra bullets ballistic coefficient hunting BC bullet logo customer support

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March 22nd, 2017

Chronograph Testing — Tips from the USAMU

USAMU Marksmanship Unit Velocity Chronograph Testing Sample Sizes

Each Wednesday, the U.S. Army Marksmanship Unit publishes a reloading “how-to” article on the USAMU Facebook page. This past week’s “Handloading Hump Day” article, the latest in a 7-part series, relates to chronograph testing and statistical samples. We highly recommend you read this article, which offers some important tips that can benefit any hand-loader. Visit the USAMU Facebook page next Wednesday for the next installment.

Chronograph Testing — Set-Up, Sample Sizes, and Velocity Factors

Initial Chronograph Setup
A chronograph is an instrument designed to measure bullet velocity. Typically, the bullet casts a shadow as it passes over two electronic sensors placed a given distance apart. The first screen is the “start” screen, and it triggers an internal, high-speed counter. As the bullet passes the second, or “stop” screen, the counter is stopped. Then, appropriate math of time vs. distance traveled reveals the bullet’s velocity. Most home chronographs use either 2- or 4-foot spacing between sensors. Longer spacing can add some accuracy to the system, but with high-quality chronographs, 4-foot spacing is certainly adequate.

Laboratory chronographs usually have six feet or more between sensors. Depending upon the make and model of ones chronograph, it should come with instructions on how far the “start” screen should be placed from one’s muzzle. Other details include adequate light (indoors or outdoors), light diffusers over the sensors as needed, and protecting the start screen from blast and debris such as shotgun wads, etc. When assembling a sky-screen system, the spacing between sensors must be extremely accurate to allow correct velocity readings.

Statistics: Group Sizes, Distances and Sample Sizes
How many groups should we fire, and how many shots per group? These questions are matters of judgment, to a degree. First, to best assess how ones ammunition will perform in competition, it should be test-fired at the actual distance for which it will be used. [That means] 600-yard or 1000-yard ammo should be tested at 600 and 1000 yards, respectively, if possible. It is possible to work up very accurate ammunition at 100 or 200 yards that does not perform well as ranges increase. Sometimes, a change in powder type can correct this and produce a load that really shines at longer range.

The number of shots fired per group should be realistic for the course of fire. That is, if one will be firing 10-shot strings in competition then final accuracy testing, at least, should involve 10-shot strings. These will reflect the rifles’ true capability. Knowing this will help the shooter better decide in competition whether a shot requires a sight adjustment, or if it merely struck within the normal accuracy radius of his rifle.

How many groups are needed for a valid test? Here, much depends on the precision with which one can gather the accuracy data. If shooting from a machine rest in good weather conditions, two or three 10-shot groups at full distance may be very adequate. If it’s windy, the rifle or ammunition are marginal, or the shooter is not confident in his ability to consistently fire every shot accurately, then a few more groups may give a better picture of the rifle’s true average.

(more…)

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October 19th, 2016

Lapua Releases FREE Advanced 6DOF Ballistics Mobile APP

Lapua Ballistics App 6DOF degrees of Freedom solver doppler radar bullet BC Apple iOS Android OS mobile smartphone iphone

Lapua, maker of premium brass, bullets, and loaded ammo, has released a new, state-of-the-art Ballistics program that runs on smartphones and mobile devices. The all-new Lapua Ballistics Mobile App is the first mobile ballistics app utilizing the 6DOF calculation model. 6DOF refers to “Six Degrees of Freedom”, referring to the multiple variables the software calculates. As explained below, a 6DOF solver can account for 3 components of movement PLUS 3 components of rotation. Of course, as with other ballistics software, the Lapua Mobile App looks at Bullet BC, velocity, and cross-wind effects. This software can also account for subtle, extreme long range factors such as the Coriolis Effect.

Lapua Ballistics App 6DOF degrees of Freedom solver doppler radar bullet BC Apple iOS Android OS mobile smartphone iphone


CLICK HERE for FREE 28-page Ballistics App USER GUIDE

Notably, the new Lapua Ballistics App includes a library of up-to-date bullet profiles based on extensive field tests with Doppler Radar. Having an ultra-sophisticated 6DOF solver combined with Doppler Radar data makes the Lapua Mobile App one of the most accurate ballistics Apps on the market. Lapua Ballistics offers the latest, Doppler-proven Lapua cartridge and bullet data for you to combine with your firearm and local weather information. The App also includes the option to define custom bullets.

Lapua Ballistics App 6DOF degrees of Freedom solver doppler radar bullet BC Apple iOS Android OS mobile smartphone iphone

The Lapua Ballistics App is available for Android and iOS smart phones and mobile devices free of charge. For more info, visit www.lapua.com/lapuaballisticsapp.

Lapua Ballistics App 6DOF degrees of Freedom solver doppler radar bullet BC Apple iOS Android OS mobile smartphone iphone

6DOF, the most accurate calculation method. Lapua cartridge / bullet information. Distance, wind speed and angle. outputs numerical, reticle, table and graph views, metric and imperial values. Set Point Blank-range to different sight-in distances and impact windows. Define custom bullets ( BC G1 or G7 and Siacci method), Pre-set max 4 powder temperature.Sight-in-POI, Coriolis calculation

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August 19th, 2016

New Hornady Ballistics Calculator Uses Doppler Radar Bullet Data

Hornady Ballistics Calculator 4DOF Doppler Vertical Jump Spin Drift Angle of Attack

Here’s a significant new addition to our knowledge base for Long-Range shooting. Hornady has released a new Ballistics Calculator that employs bullet profiles derived from Doppler radar testing and 3D projectile modeling. Hornady’s Patent Pending 4DOF™ Ballistic Calculator provides trajectory solutions based on projectile Drag Coefficient (not static G1/G7 ballistic coefficients) along with the exact physical modeling of projectiles and their mass and aerodynamic properties. This new 4DOF (Four Degrees of Freedom) calculator also accounts for spin drift and the subtle VERTICAL effects of crosswinds.


We strongly recommend you watch this video from start to finish. In greater detail than is possible here, this video explains how the 4DOF System works, and why it is more sophisticated than other commercially-offered Ballistics calculators. There’s a LOT going on here…

Aerodynamic Jump from Crosswind Calculated
According to Hornady, the 4DOF Ballistics Calculator “is the first publicly-available program that will correctly calculate the vertical shift a bullet experiences as it encounters a crosswind.” This effect is called aerodynamic jump. The use of radar-derived drag profiles, correct projectile dynamics, aerodynamic jump, and spin drift enable the Hornady® 4DOF™ ballistic calculator to provide very sophisticated solutions. Hornady says its 4DOF solver is “the most accurate commercially available trajectory program … even at extreme ranges.”

“Current ballistic calculators provide three degrees of freedom in their approach — windage, elevation, and range — but treat the projectile as an inanimate lump flying through the air,” said Dave Emary, Hornady Chief Ballistician. “This program incorporates the projectile’s movement in the standard three degrees but also adds its movement about its center of gravity and subsequent angle relative to its line of flight, which is the fourth degree of freedom.”

Using Doppler radar, Hornady engineers have calculated exact drag versus velocity curves for each bullet in the 4DOF™ calculator library. This means the 4DOF™ calculator should provicde more precise long range solutions than calulators that rely on simple BC numbers or drag curves based with limited data collection points. Emary adds: “The Hornady 4DOF also accurately calculates angled shots by accounting for important conditions that [other ballistic] programs overlook.”

“This calculator doesn’t utilize BCs (Ballistic Coefficients) like other calculators,” added Jayden Quinlan, Hornady Ballistics Engineer. “Why compare the flight of your bullet to a standard G1 or G7 projectile when you can use your own projectile as the standard?” That makes sense, but users must remember that Hornady’s 4DOF projectile “library” includes mostly Hornady-made bullets. However, in addition to Hornady bullets, the 4DOF Calculator currently does list seven Berger projectiles, six Sierra projectiles, and one Lapua bullet type. For example, Sierra’s new 183gr 7mm MatchKing is listed, as is Berger’s 105gr 6mm Hybrid.

This Video Explains How to Use Hornady’s New 4DOF Ballistics Calculator

Hornady Ballistics Calculator 4DOF Doppler Vertical Jump Spin Drift Angle of Attack

Using the 4DOF™ Ballistic Calculator:
The Hornady 4DOF Ballistic Calculator provides trajectory solutions based on projectile Drag Coefficient (not ballistic coefficients) along with exact physical modeling of the projectile and its mass and aerodynamic properties. Additionally, it calculates the vertical shift a bullet experiences as it encounters a crosswind, i.e. “aerodynamic jump”. The use of drag coefficients, projectile dynamics, aerodynamic jump, and spin drift enable the 4DOF Ballistic Calculator to accurately measure trajectories even at extreme ranges. It is ideal for both long range and moderate distances and is available for the low-drag precision bullets listed in the drop down menu of the calculator. For calculating trajectories of traditional hunting and varmint bullets using BCs (ballistic coefficients), you can use Hornady’s Standard Ballistics Calculator.

Hornady Ballistics Calculator 4DOF Doppler Vertical Jump Spin Drift Angle of Attack

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