“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.
The 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:
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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For those headed to the Nationals, we are sharing some smart tips from a past F-Class Champion who is both a great shooter AND a ballistics wizard. In 2015, Bryan Litz won the F-TR Mid-Range AND Long-Range National Championships hosted at Ben Avery. And at the 2014 Berger SW Nationals (SWN), Bryan took top honors among all sling shooters. If you only know Bryan Litz from his Applied Ballistics Books and DVDs, you may not realize that this guy is a also great marksman along with being an actual rocket scientist!
Given his impressive track record in both F-Class and Palma (Fullbore) out to 1000 yards, we asked Bryan if he had any advice for other long-range competitors.
First Bryan provided three tips concerning Ballistics, his special area of expertise. Next Bryan offered three more general tips about long-range competition — how to analyze your shooting, how to choose your ‘wind strategy’, and how to avoid the most costly mistakes, i.e. how to avoid the “train-wrecks”.
Bryan Litz won the 2015 F-TR Mid-Range and Long-Range Championships with this sleek rig:
Litz Ballistics Tips
Ballistics TIP ONE. If you’re having trouble getting your ballistic software to match actual drops, you need to look at a number of possible reasons. Here are some common issues that can cause problems.
Click Values Are Not Exact. Scopes and iron sights don’t always produce accurate adjustments. In other words, if your ballistics program predicts 30 MOA of drop, and you dial 30 MOA but hit low, it might be that your sight actually only moved 28 MOA (for example). To see if your sight is adjusting accurately, shoot a tall target at 100 yards and measure group separation when dialing your sight.
Barometric vs. Station Pressure. This is a commonly misunderstood input to ballistics programs. You can avoid this pitfall by remembering the following: station pressure is the actual measured pressure at your location, and you don’t need to tell the program your altitude when using station pressure. Barometric pressure is corrected for sea level. If you’re using barometric pressure, you also have to input your altitude.
Muzzle Velocity. Chronographs are not always as accurate as shooters think they are — your true MV may be off by 10-20 fps (or more). If your drop is different than predicted at long range, it might be because your muzzle velocity input is wrong.
Mixing Up BC (G1 vs. G7). Knowledgeable long range shooters know that the G7 standard is a more representative standard for modern LR bullets. However, using G7 BCs isn’t just a matter of clicking the ‘G7′ option in the program. The numeric value of the BC is different for G1 and G7. For example, the G1 BC of the Berger 155.5 grain Fullbore bullet is .464 but the G7 BC is .237. If you were to enter .464 but click on G7, the results would be way off.
Ballistics TIP TWO. A properly installed level is absolutely essential for long range shooting. Without a good level reference, your long range wind zero will be off due to minor canting of the rifle from side to side. You can verify that your level is installed correctly on a 100-yard ‘tall target’. Draw a plumb line straight up the target and verify that your groups track straight up this line as you go up in elevation.
Ballistics TIP THREE. If your long range ballistic predictions aren’t tracking, always come back and verify your 100-yard zero. Sometimes a simple zero shift can be misconstrued as errors in long range ballistics predictions.
Litz Competition Shooting Tips
Competition TIP ONE. Improving your scores in long range competition is a constant process of self-assessment. After each match, carefully analyze how you lost points and make a plan to improve. Beginning shooters will lose a lot of points to fundamental things like sight alignment and trigger control. Veteran shooters will lose far fewer points to a smaller list of mistakes. At every step along the way, always ask yourself why you’re losing points and address the issues. Sometimes the weak links that you need to work on aren’t your favorite thing to do, and success will take work in these areas as well.
Competition TIP TWO. Select your wind shooting strategy carefully. For beginners and veterans, most points are typically lost to wind. Successful shooters put a lot of thought into their approach to wind shooting. Sometimes it’s best to shoot fast and minimize the changes you’ll have to navigate. Other times it’s best to wait out a condition which may take several minutes. Develop a comfortable rest position so you have an easier time waiting when you should be waiting.
Competition TIP THREE. Actively avoid major train wrecks. Sounds obvious but it happens a lot. Select equipment that is reliable, get comfortable with it and have back-ups for important things. Don’t load on the verge of max pressure, don’t go to an important match with a barrel that’s near shot out, physically check tightness of all important screws prior to shooting each string. Observe what train wrecks you and others experience, and put measures in place to avoid them.
Photos by Steve Fiorenzo
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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.
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Lapua now offers a FREE Ballistics App. This was the first mobile ballistics App utilizing the 6DOF calculation model, making it one of most accurate ballistics Apps on the market. With this free mobile App you can calculate trajectories, range, bullet drop, turret adjustments and more.
Lapua’s sophisticated FREE Ballistics App has many great features — much more than you’d expect for a free App. If you do much shooting past 300 yards, or use a wide variety of bullets and/or cartridge types, definitely download the App and give it a try. For more details, read the Lapua Ballistics App User Manual. This handy PDF file explains how to set up the App and utilize all its powerful features.
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!
On the Applied Ballistics Facebook page a few seasons ago, Ballistician Bryan Litz posed a “Tuesday Trivia” question about ballistics. This being Tuesday we thought we’d bring back this interesting brain-teaser — a true/false question about bullet stabilization. On shooting forums you often find heated arguments about “over-stabilization”. Bryan wants readers to consider the issue of over-stabilization and answer a challenge question…
Is This Statement TRUE or FALSE?
“The problem with ‘over-stabilizing’ a bullet (by shooting it from an excessively fast twist rate) is that the bullet will fly ‘nose high’ on a long range shot. The nose-high orientation induces extra drag and reduces the effective BC of the bullet.”
True or False, and WHY?
Click the “Post Comment” link below to post your reply (and explain your reasoning).
Bullet Movement in Flight — More Complicated Than You May Think
Bullets do not follow a laser beam-like, perfectly straight line to the target, nor does the nose of the bullet always point exactly at the point of aim. Multiple forces are in effect that may cause the bullet to yaw (rotate side to side around its axis), tilt nose-up (pitch), or precess (like a spinning top) in flight. These effects (in exaggerated form) are shown below:
Yaw refers to movement of the nose of the bullet away from the line of flight. Precession is a change in the orientation of the rotational axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle (nutation) is constant. In physics, there are two types of precession: torque-free and torque-induced. Nutation refers to small circular movement at the bullet tip.
Applied Ballistics Founder Bryan Litz and Former USAMU and Team USA coach Emil Praslick III share their wisdom in an informative Guns Magazine Podcast. Along with being a true ballistics guru, Bryan Litz is an outstanding competitive shooter, having won F-TR National Championships, and both Sling and F-TR divisions at the Berger SW Nationals, along with many other matches. Emil is considered one of the world’s great wind-readers and team coaches, having coached 20+ championship teams.
Guns Magazine podcast host Brent Wheat asks Bryan and Emil about multiple topics including: exterior ballistics, bullet design, wind reading, ballistic solvers, BC myths, and more.
Brent reports: “Together, Bryan and Emil understand what happens from the time a bullet leaves the muzzle until it impacts the target, including the atmospheric affects along the way. Grab a pencil, listen in, and get ready to take notes.”
This Long Range Grad School podcast features Berger’s Chief Ballistician, Bryan Litz, and Berger’s Emil Praslick. Both have extensive long range competitive shooting experience, with championship titles (as shooter and/or coach) in a multitude of long range disciplines. CLICK arrow below to start podcast audio:
Emil Praslick (left) confers with Bryan Litz (right) at King of 2 Miles ELR Event.
In this Video Emil Praslick explains his methods for determining wind direction.
Bryan Litz coaching Team USA in Canada using a WIND PLOT.
Bryan Litz at 2011 World Long Range (Palma) Championships in Brisbane, Australia
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You’ve probably heard the term “Terminal Ballistics”. But do you really know what this refers to? Fundamentally, “Terminal Ballistics” describes the behavior of a projectile as it strikes, enters, and penetrates a target. Terminal Ballistics, then, can be said to describe projectile behavior in a target including the transfer of kinetic energy. Contrast this with “External Ballistics” which, generally speaking, describes and predicts how projectiles travel in flight. One way to look at this is that External Ballistics covers bullet behavior before impact, while terminal ballistics covers bullet behavior after impact.
The study of Terminal Ballistics is important for hunters, because it can predict how pellets, bullets, and slugs can perform on game. This NRA Firearm Science video illustrates Terminal Ballistics basics, defining key terms such as Impact Crater, Temporary Cavity, and Primary Cavity.
External Ballistics, also called “exterior ballistics”, is the part of ballistics that deals with the behavior of a non-powered projectile in flight.
Terminal Ballistics, a sub-field of ballistics, is the study of the behavior and effects of a projectile when it hits its target.
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“The pessimist complains about the wind; the optimist expects it to change; the realist adjusts the sails.” — William Arthur Ward
Readers often ask us: “Is there a decent, easy-to-comprehend book that can help my wind-reading?” Many of our Forum members have recommended The Wind Book for Rifle Shooters by Linda Miller and Keith Cunningham.
New Edition Released in May 2020
A NEW hardback edition of The Wind Book was released May 26, 2020. This 144-page book, first published in 2007, is a great resource. But you don’t have to take our word for it. If you click this link, you can read book excerpts and decide for yourself. When the Amazon page opens, click the book cover (labeled “Look Inside”) and another screen will appear. This lets you preview the first few chapters, and see some illustrations. Along with the new hardback edition ($22.99), Amazon offers a Kindle (eBook) edition for $14.99.
Other books cover wind reading in a broader discussion of ballistics or long-range shooting, such as Applied Ballistics for Long-Range Shooting by Bryan Litz. But the Miller & Cunningham book is ALL about wind reading from cover to cover, and that is its strength. The book focuses on real world skills that can help you accurately gauge wind angle, wind velocity, and wind cycles.
All other factors being equal, it is your ability to read the wind that will make the most difference in your shooting accuracy. The better you understand the behavior of the wind, the better you will understand the behavior of your bullet. — Wind Book for Rifle Shooters
The Wind Book for Rifle Shooters covers techniques and tactics used by expert wind-readers. There are numerous charts and illustrations. The authors show you how to put together a simple wind-reading “toolbox” for calculating wind speed, direction, deflection and drift. Then they explain how to use these tools to read flags and mirage, record and interpret your observations, and time your shots to compensate for wind. Here are two reviews from actual book buyers:
I believe this is a must-have book if you are a long-range sport shooter. I compete in F-Class Open and when I first purchased this book and read it from cover to cover, it helped me understand wind reading and making accurate scope corrections. Buy this book, read it, put into practice what it tells you, you will not be disappointed. — P. Janzso
If you have one book for wind reading, this should be it. Whether you’re a novice or experienced wind shooter this book has something for you. It covers how to get wind speed and direction from flags, mirage, and natural phenomenon. In my opinion this is the best book for learning to read wind speed and direction. — Muddler
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Many guys getting started in long range shooting are confused about what kind of scope they should buy — specifically whether it should have MIL-based clicks or MOA-based clicks. Before you can make that decision, you need to understand the terminology. This article, with a video by Bryan Litz, explains MILS and MOA so you can choose the right type of scope for your intended application.
You probably know that MOA stands for “Minute of Angle” (or more precisely “minute of arc”), but could you define the terms “Milrad” or “MIL”? In his latest video, Bryan Litz of Applied Ballitics explains MOA and MILs (short for “milliradians”). Bryan defines those terms and explains how they are used. One MOA is an angular measurement (1/60th of one degree) that subtends 1.047″ at 100 yards. One MIL (i.e. one milliradian) subtends 1/10th meter at 100 meters; that means that 0.1 Mil is one centimeter (1 cm) at 100 meters. Is one angular measurement system better than another? Not necessarily… Bryan explains that Mildot scopes may be handy for ranging, but scopes with MOA-based clicks work just fine for precision work at known distances. Also because one MOA is almost exactly one inch at 100 yards, the MOA system is convenient for expressing a rifle’s accuracy. By common parlance, a “half-MOA” rifle can shoot groups that are 1/2-inch (or smaller) at 100 yards.
What is a “Minute” of Angle?
When talking about angular degrees, a “minute” is simply 1/60th. So a “Minute of Angle” is simply 1/60th of one degree of a central angle, measured either up and down (for elevation) or side to side (for windage). At 100 yards, 1 MOA equals 1.047″ on the target. This is often rounded to one inch for simplicity. Say, for example, you click up 1 MOA (four clicks on a 1/4-MOA scope). That is roughly 1 inch at 100 yards, or roughly 4 inches at 400 yards, since the target area measured by an MOA subtension increases with the distance.
MIL vs. MOA for Target Ranging
MIL or MOA — which angular measuring system is better for target ranging (and hold-offs)? In a recent article on his PrecisionRifleBlog.com website, Cal Zant tackles that question. Analyzing the pros and cons of each, Zant concludes that both systems work well, provided you have compatible click values on your scope. Zant does note that a 1/4 MOA division is “slightly more precise” than 1/10th mil, but that’s really not a big deal: “Technically, 1/4 MOA clicks provide a little finer adjustments than 1/10 MIL. This difference is very slight… it only equates to 0.1″ difference in adjustments at 100 yards or 1″ at 1,000 yards[.]” Zant adds that, in practical terms, both 1/4-MOA clicks and 1/10th-MIL clicks work well in the field: “Most shooters agree that 1/4 MOA or 1/10 MIL are both right around that sweet spot.”
Readers often ask for a good, authoritative resource on doping the wind and reading mirage. Many of our Forum members recommended M.Sgt. Jim Owens’ Wind-Reading Book. With 22 sets of wind charts, this 166-page resource is offered for $14.95 in print format or $12.95 in CD format.
Owens’ Reading the Wind and Coaching Techniques clearly explains how to gauge wind speeds and angles. Owens, a well-known High Power coach and creator of Jarheadtop.com, offers a simple system for ascertaining wind value based on speed and angle. The CD also explains how to read mirage — a vital skill for long-range shooters. In many situations, reading the mirage may be just as important as watching the wind flags. Owens’ $12.95 CD provides wind-reading strategies that can be applied by coaches as well as individual shooters.
NOTE: The Wind DVD product is completely different than Owens’ $12.95 CD. The DVD is like an interactive class, while the CD is basically an eBook.
Played straight through, the DVD offers about 75 minutes of instruction. M.Sgt. Owens says “You will learn more in an hour and fifteen minutes than the host learned in fifteen years in the Marine Corps shooting program. This is a wind class you can attend again and again. [It provides] a simple system for judging the speed, direction and value of the wind.” The DVD also covers mirage reading, wind strategies, bullet BC and more.
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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.
“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.
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.
The 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.
The 
Shoot 101 Quiz
On the 
As a separate product, Owens offers a 
