Want to learn more about Long Range Shooting? Check out the NSFF “Elements of Long Range Shooting” videos hosted by ballistics guru Bryan Litz of Applied Ballistics. In this multi-part series, Bryan covers a variety of topics of interest to precision shooters. For today’s Saturday at the Movies special, we feature seven of Bryan’s videos. Watch other informative Long Range Shooting and Ballistics videos with Bryan Litz on the NSSF YouTube Channel.
Atmospherics and Density Altitude
Bryan Litz explains: “An important element in calculating an accurate firing solution for long-range shooting is understanding the effects of atmospherics on a projectile.” Atmospherics include air pressure, air temperature, and humidity. Bryan notes: “Temperature, pressure, and humidity all affect the air density… that the bullet is flying through. You can combine all those factors into one variable called ‘Density Altitude’.” Density Altitude is used by the ballistic solver to account for variables that affect bullet flight.
Bullet Ballistic Coefficients
A bullet’s ballistic coefficient (BC) basically expresses how well the bullet flies through the air. Higher BC bullets have less aerodynamic drag than lower BC projectiles. You will see BCs listed as either G1 and G7 numbers. These correspond to different bullet shape models. Generally speaking, the G7 model works better for the long, boat-tail bullets used for long-range shooting. Notably, a bullet’s drag is NOT constant in flight. The true BC can vary over the course of the trajectory as the bullet velocity degrades. In other words, “BC is dynamic”. That said, you can make very accurate drop charts using the BCs provided by major bullet-makers, as plugged into solvers. However, long-range competitors may want to record “real world” drop numbers at various distances. For example, we’ve seen trajectories be higher than predicted at 500 yards, yet lower than predicted at 1000.
Transonic Range
When considering your rifle’s long-range performance, you need to understand the limit of your bullet’s supersonic range. As the bullet slows below the speed of sound, it enters the transonic zone. This can be accompanied by variations in stability as well as BC changes. Bryan explains “once your bullet slows done below supersonic and you get into transonic effects, there are a lot more considerations that come into play. The drag of the bullet becomes less certain, the stability of the bullet can be challenged, and things related to long times of flight, such as Coriolis and Spin Drift, come into play. So whenever you are shooting long range you need to where your bullet slows down to about 1340 fps.”
Ballistics Solvers — Many Options
Bryan Litz observes: “When we talk about the elements of long range shooting, obviously a very important element is a getting a fire solution, using a ballistic solver. There are a lot of ballistic solvers out there… Applied Ballistics has smartphone Apps. Applied Ballistics has integrated the ballistic solver directly into a Kestral, and the same solver runs (manually) on the Accuracy Solutions Wiz-Wheel. The point is, if it is an Applied Ballistics device it is running the same solutions across the board.”
Bullet Stability and Twist Rates
In this video, Bryan Litz talks about bullet in-flight stability and how to calculate barrel twist-rate requirements for long-range bullets. Bryan explains that bullet stability (for conventional projectiles) is basically provided by the spinning of the bullet. But this spin rate is a function of BOTH the nominal twist rate of the barrel AND the velocity of the projectile. Thus, when shooting the same bullet, a very high-speed cartridge may work with a slower barrel twist rate than is required for a lower-speed (less powerful) cartridge. For match bullets, shot at ranges to 1000 yards and beyond, Bryan recommends a twist rate that offers good stability.
Scope Tracking — Tall Target Test
Have you recently purchased a new scope? Then you should verify the actual click value of the turrets before you use the optic in competition. While a scope may have listed click values of 1/4-MOA, 1/8-MOA or 0.1 Mils, the reality may be slightly different. Many scopes have actual click values that are slightly higher or lower than the value claimed by the manufacturer. The small variance adds up when you click through a wide range of elevation. In this video, Bryan Litz shows how to verify your true click values using a “Tall Target Test”. The idea is to start at the bottom end of a vertical line, and then click up 30 MOA or so. Multiply the number of clicked MOA by 1.047 to get the claimed value in inches. For example, at 100 yards, 30 MOA is exactly 31.41 inches. Then measure the difference in your actual point of impact.
Coriolis Effect
The Coriolis Effect comes into play with extreme long-range shots. The rotation of the earth actually moves the target a small distance (in space) during the long duration of the bullet’s flight. Bryan Litz notes that, in most common shooting situations inside 1K, Coriolis is not significant. At 1000 yards, the Effect represents less than one click (for most cartridge types). Even well past 1000 yards, in windy conditions, the Coriolis Effect may well be “lost in the noise”. But in very calm conditions, when shooting at extreme ranges, Bryan says you can benefit from adjusting your ballistics solution for Coriolis: “The Coriolis Effect… has to do with the spin of the earth. The consequence of that is that, if the flight time of the bullet gets significantly long, the bullet can have an apparent drift from its intended target. The amount [of apparent drift] is very small — it depends on your latitude and azimuth of fire on the planet.”
About Bryan Litz
Bryan began his career as a rocket scientist, quite literally. He then started Applied Ballistics, the leading company focusing on ballistics science for rifle shooting. A past F-TR Long-Range National Champion and Chief Ballistician for Berger Bullets, knows his stuff. His Applied Ballistics squad was the winning team at the 2017 King of 2 Miles event, and Applied Ballistics has earned major U.S. defense contracts.
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“The overturning moment MW tends to rotate the bullet about an axis, which goes through the CG (center of gravity) and which is perpendicular to the plane of drag….
Ruprecht Nennstiel, a forensic ballistics expert from Wiesbaden, Germany, has authored a great resource about bullet behavior in flight. Nennstiel’s comprehensive article, How Do Bullets Fly, explains all the forces which affect bullet flight including gravity, wind, gyroscopic effects, aerodynamic drag, and lift. Nennstiel even explains the rather arcane Magnus Force and Coriolis Effect which come into play at long ranges. Nennstiel’s remarkable resource contains many useful illustrations plus new experimental observations of bullets fired from small arms, both at short and at long ranges.
Shadowgraph of .308 Winchester Bullet
A convenient index is provided so you can study each particular force in sequence. Writing with clear, precise prose, Nennstiel explains each key factor that affects external ballistics. For starters, we all know that bullets spin when launched from a rifled barrel. But Nennstiel explains in greater detail how this spinning creates gyroscopic stability:
“The overturning moment MW tends to rotate the bullet about an axis, which goes through the CG (center of gravity) and which is perpendicular to the plane of drag, the plane, formed by the velocity vector ‘v’ and the longitudinal axis of the bullet. In the absence of spin, the yaw angle ‘δ’ would grow and the bullet would tumble.
If the bullet has sufficient spin, saying if it rotates fast enough about its axis of form, the gyroscopic effect takes place: the bullet’s longitudinal axis moves into the direction of the overturning moment, perpendicular to the plane of drag. This axis shift however alters the plane of drag, which then rotates about the velocity vector. This movement is called precession or slow mode oscillation.”
Raise Your Ballistic IQ
Though comprehensible to the average reader with some grounding in basic physics, Nennstiel’s work is really the equivalent of a Ph.D thesis in external ballistics. You could easily spend hours reading (and re-reading) all the primary material as well as the detailed FAQ section. But we think it’s worth plowing into How Do Bullets Fly from start to finish. We suggest you bookmark the page for future reference. You can also download the complete article for future reference and offline reading.
Want to learn more about Long Range Shooting? Check out the NSFF “Elements of Long Range Shooting” videos hosted by ballistics guru Bryan Litz of Applied Ballistics. In this multi-part series, Bryan covers a variety of topics of interest to precision shooters. For today’s Saturday at the Movies special, we feature seven of Bryan’s videos. Watch other informative Long Range Shooting and Ballistics videos with Bryan Litz on the NSSF YouTube Channel.
Atmospherics and Density Altitude
Bryan Litz explains: “An important element in calculating an accurate firing solution for long-range shooting is understanding the effects of atmospherics on a projectile.” Atmospherics include air pressure, air temperature, and humidity. Bryan notes: “Temperature, pressure, and humidity all affect the air density… that the bullet is flying through. You can combine all those factors into one variable called ‘Density Altitude’.” Density Altitude is used by the ballistic solver to account for variables that affect bullet flight.
Bullet Ballistic Coefficients
A bullet’s ballistic coefficient (BC) basically expresses how well the bullet flies through the air. Higher BC bullets have less aerodynamic drag than lower BC projectiles. You will see BCs listed as either G1 and G7 numbers. These correspond to different bullet shape models. Generally speaking, the G7 model works better for the long, boat-tail bullets used for long-range shooting. Notably, a bullet’s drag is NOT constant in flight. The true BC can vary over the course of the trajectory as the bullet velocity degrades. In other words, “BC is dynamic”. That said, you can make very accurate drop charts using the BCs provided by major bullet-makers, as plugged into solvers. However, long-range competitors may want to record “real world” drop numbers at various distances. For example, we’ve seen trajectories be higher than predicted at 500 yards, yet lower than predicted at 1000.
Transonic Range
When considering your rifle’s long-range performance, you need to understand the limit of your bullet’s supersonic range. As the bullet slows below the speed of sound, it enters the transonic zone. This can be accompanied by variations in stability as well as BC changes. Bryan explains “once your bullet slows done below supersonic and you get into transonic effects, there are a lot more considerations that come into play. The drag of the bullet becomes less certain, the stability of the bullet can be challenged, and things related to long times of flight, such as Coriolis and Spin Drift, come into play. So whenever you are shooting long range you need to where your bullet slows down to about 1340 fps.”
Ballistics Solvers — Many Options
Bryan Litz observes: “When we talk about the elements of long range shooting, obviously a very important element is a getting a fire solution, using a ballistic solver. There are a lot of ballistic solvers out there… Applied Ballistics has smartphone Apps. Applied Ballistics has integrated the ballistic solver directly into a Kestral, and the same solver runs (manually) on the Accuracy Solutions Wiz-Wheel. The point is, if it is an Applied Ballistics device it is running the same solutions across the board.”
Bullet Stability and Twist Rates
In this video, Bryan Litz talks about bullet in-flight stability and how to calculate barrel twist-rate requirements for long-range bullets. Bryan explains that bullet stability (for conventional projectiles) is basically provided by the spinning of the bullet. But this spin rate is a function of BOTH the nominal twist rate of the barrel AND the velocity of the projectile. Thus, when shooting the same bullet, a very high-speed cartridge may work with a slower barrel twist rate than is required for a lower-speed (less powerful) cartridge. For match bullets, shot at ranges to 1000 yards and beyond, Bryan recommends a twist rate that offers good stability.
Scope Tracking — Tall Target Test
Have you recently purchased a new scope? Then you should verify the actual click value of the turrets before you use the optic in competition. While a scope may have listed click values of 1/4-MOA, 1/8-MOA or 0.1 Mils, the reality may be slightly different. Many scopes have actual click values that are slightly higher or lower than the value claimed by the manufacturer. The small variance adds up when you click through a wide range of elevation. In this video, Bryan Litz shows how to verify your true click values using a “Tall Target Test”. The idea is to start at the bottom end of a vertical line, and then click up 30 MOA or so. Multiply the number of clicked MOA by 1.047 to get the claimed value in inches. For example, at 100 yards, 30 MOA is exactly 31.41 inches. Then measure the difference in your actual point of impact.
Coriolis Effect
The Coriolis Effect comes into play with extreme long-range shots. The rotation of the earth actually moves the target a small distance (in space) during the long duration of the bullet’s flight. Bryan Litz notes that, in most common shooting situations inside 1K, Coriolis is not significant. At 1000 yards, the Effect represents less than one click (for most cartridge types). Even well past 1000 yards, in windy conditions, the Coriolis Effect may well be “lost in the noise”. But in very calm conditions, when shooting at extreme ranges, Bryan says you can benefit from adjusting your ballistics solution for Coriolis: “The Coriolis Effect… has to do with the spin of the earth. The consequence of that is that, if the flight time of the bullet gets significantly long, the bullet can have an apparent drift from its intended target. The amount [of apparent drift] is very small — it depends on your latitude and azimuth of fire on the planet.”
About Bryan Litz
Bryan began his career as a rocket scientist, quite literally. He then started Applied Ballistics, the leading company focusing on ballistics science for rifle shooting. A past F-TR Long-Range National Champion and Chief Ballistician for Berger Bullets, knows his stuff. His Applied Ballistics squad was the winning team at the 2017 King of 2 Miles event, and Applied Ballistics has earned major U.S. defense contracts.
Share the post "Saturday at the Movies: Litz on Long Range Shooting + Ballistics"
“The overturning moment MW tends to rotate the bullet about an axis, which goes through the CG (center of gravity) and which is perpendicular to the plane of drag….
Ruprecht Nennstiel, a forensic ballistics expert from Wiesbaden, Germany, has authored a great resource about bullet behavior in flight. Nennstiel’s comprehensive article, How Do Bullets Fly, explains all the forces which affect bullet flight including gravity, wind, gyroscopic effects, aerodynamic drag, and lift. Nennstiel even explains the rather arcane Magnus Force and Coriolis Effect which come into play at long ranges. Nennstiel’s remarkable resource contains many useful illustrations plus new experimental observations of bullets fired from small arms, both at short and at long ranges.
Shadowgraph of .308 Winchester Bullet
A convenient index is provided so you can study each particular force in sequence. Writing with clear, precise prose, Nennstiel explains each key factor that affects external ballistics. For starters, we all know that bullets spin when launched from a rifled barrel. But Nennstiel explains in greater detail how this spinning creates gyroscopic stability:
“The overturning moment MW tends to rotate the bullet about an axis, which goes through the CG (center of gravity) and which is perpendicular to the plane of drag, the plane, formed by the velocity vector ‘v’ and the longitudinal axis of the bullet. In the absence of spin, the yaw angle ‘δ’ would grow and the bullet would tumble.
If the bullet has sufficient spin, saying if it rotates fast enough about its axis of form, the gyroscopic effect takes place: the bullet’s longitudinal axis moves into the direction of the overturning moment, perpendicular to the plane of drag. This axis shift however alters the plane of drag, which then rotates about the velocity vector. This movement is called precession or slow mode oscillation.”
Raise Your Ballistic IQ
Though comprehensible to the average reader with some grounding in basic physics, Nennstiel’s work is really the equivalent of a Ph.D thesis in external ballistics. You could easily spend hours reading (and re-reading) all the primary material as well as the detailed FAQ section. But we think it’s worth plowing into How Do Bullets Fly from start to finish. We suggest you bookmark the page for future reference. You can also download the complete article for future reference and offline reading.
The Coriolis Effect comes into play with extreme long-range shots like this. The rotation of the earth actually moves the target a small distance (in space) during the course of the bullet’s flight. Photo by Dustin Ellermann at Whittington Center Range.
When you’re out at the range, the Earth seems very stable. But it is actually a big sphere zooming through space while spinning around its axis, one complete turn every 24 hours. The rotation of the earth can create problems for extreme long-range shooters. During extended bullet flight times, the rotation of the planet causes an apparent deflection of the bullet path over very long distances. This is the ballistics manifestation of the Coriolis Effect.
Bryan Litz of Applied Ballistics has produced a short video that explains the Coriolis Effect. Bryan notes that Coriolis is “a very subtle effect. People like to make more of it than it is because it seems mysterious.” In most common shooting situations inside 1K, Coriolis is not important. At 1000 yards, the Effect represents less than one click (for most cartridge types). Even well past 1000 yards, in windy conditions, the Coriolis Effect may well be “lost in the noise”. But in very calm conditions, when shooting at extreme ranges, Bryan says you can benefit from adjusting your ballistics solution for Coriolis.
Bryan explains: “The Coriolis Effect… has to do with the spin of the earth. You are basically shooting from one point to another on a rotating sphere, in an inertial reference frame. The consequence of that is that, if the flight time of the bullet gets significantly long, the bullet can have an apparent drift from its intended target. The amount [of apparent drift] is very small — it depends on your latitude and azimuth of fire on the planet.”
Coriolis is a very subtle effect. With typical bullet BCs and velocities, you must get to at least 1000 yards before Coriolis amounts to even one click. Accordingly, Bryan advises: “Coriolis Effect is NOT something to think about on moving targets, it is NOT something to think about in high, uncertain wind environments because there are variables that are dominating your uncertainty picture, and the Coriolis will distract you more than the correction is worth.”
“Where you could think about Coriolis, and have it be a major impact on your hit percentage, is if you are shooting at extended range, at relatively small targets, in low-wind conditions. Where you know your muzzle velocity and BC very well, [and there are] pristine conditions, that’s where you’re going to see Coriolis creep in. You’ll receive more refinement and accuracy in your ballistics solutions if you account for Coriolis on those types of shots. But in most practical long-range shooting situations, Coriolis is NOT important. What IS important is to understand is when you should think about it and when you shouldn’t, i.e. when applying it will matter and when it won’t.”
The Coriolis Effect — General Physics
The Coriolis Effect is the apparent deflection of moving objects when the motion is described relative to a rotating reference frame. The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object’s speed in the rotating frame.
A commonly encountered rotating reference frame is the Earth. The Coriolis effect is caused by the rotation of the Earth and the inertia of the mass experiencing the effect. Because the Earth completes only one rotation per day, the Coriolis force is quite small, and its effects generally become noticeable only for motions occurring over large distances and long periods of time. This force causes moving objects on the surface of the Earth to be deflected to the right (with respect to the direction of travel) in the Northern Hemisphere and to the left in the Southern Hemisphere. The horizontal deflection effect is greater near the poles and smallest at the equator, since the rate of change in the diameter of the circles of latitude when travelling north or south, increases the closer the object is to the poles. (Source: Wikipedia)
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Bryan Litz, chief Ballistician for Berger Bullets (and a trained rocket scientist) has authored an impressive new book: Accuracy and Precision for Long Range Shooting. Bryan’s new book is a companion to his successful treatise, Applied Ballistics for Long-Range Shooting. Now in its Second Edition, Litz’s Applied Ballistics book has become the “go-to” Ballistics book for precision shooters worldwide.
While Bryan’s first book covers the science of ballistics and trajectory calculation, his new book examines practical issues involved in long-range accuracy. Bryan explains: “In a nutshell, this book focuses on the uncertainties of practical shooting which affect hit percentage on various size targets. In other words, classic ballistics teaches you how to calculate windage and elevation corrections. This book will help you understand what your chances are of hitting a target under certain conditions, and how to improve those chances through training and design.
Practical Examples
Does a low ES/SD really make a difference at long range? Absolutely. In Chapter 6, you can see that reducing muzzle velocity variation from 20 fps Standard Deviation (SD) to 10 fps SD improves hit percentage on a 5″ circle at 500 yards from 83% to 93%.
Ever wonder how much spin drift, Coriolis affect, or using G1 vs. G7 BC’s affect your chances of hitting a target? In Chapter 10 for example, you’ll learn that ignoring spin drift in ballistic calculations reduces hit percentage on a 10″ target from 21% to 15% at 900 yards for a specified environment and cartridge.
The new book is divided into three main sections. Part 1 focuses on Precision, which explores how hit percentage is related group size. Litz explains the variable that affect group size: muzzle velocity variation, range estimation error, wind estimation error, and inherent rifle precision
Part 2 focuses on Accuracy, which is how well the group is centered around the aim-point. Topics include: leveling your sights, trajectory modeling and secondary effects, calibrating ballistic solutions, and live fire verification.
Part 3 focuses on Weapon Employment Zone (WEZ) analysis. WEZ evaluates firearm effectiveness in terms of hit percentage. The author applies WEZ in the contexts of score shooting, varmint and big game hunting, and tactical shooting. WEZ is also used to compare hit percentage for the 300 Win Mag vs. .338 Lapua Mag.
Book is 300-page, Hard-Cover Format
Accuracy and Precision for Long Range Shooting is a 6″x9″ hardcover book with 300 pages, and retails for $34.95. The book is currently at the printers, and should begin shipping by October 15, 2012. In the mean time, you can pre-order and save $5 off the regular $34.95 retail price.
When you’re out at the range, the Earth seems very stable. But it is actually a big sphere zooming through space while spinning around its axis, one complete turn every 24 hours. The rotation of the earth can create problems for extreme long-range shooters. During extended bullet flight times, the rotation of the planet causes an apparent deflection of the bullet path over very long distances. This is the ballistics manifestation of the 
