Bryan Litz is the Chief Ballistician for Berger Bullets and his background includes working for the US Air Force on air-to-air missile design and being an accomplished long range rifle competitor. He is (as I understand it) the author of the Applied Ballistics solver that seems to be enjoying great popularity among students of the science. It is, for example, the software provided in the current Kestrel weather monitors that include ballistics calculators. The first of his several books I purchased was the second edition of Applied Ballistics for Long-Range Shooting. I regret to say that that book sat mostly ignored on a bookshelf for a long time. I was primarily interested in its description of various bullets, especially their G7 ballistics coefficients that I used with other calculators.
A few weeks ago, however, I finally decided to read the part of the book before the bullet data tables and could only rue having previously ignored it. I had read several other books about firearms ballistics in the past and had used several ballistics solvers. I therefore didn’t expect to be exposed to much, if anything, new. I couldn’t have been more wrong. Not only does Litz discuss all the topics about long range rifle shooting ballistics that others cover, he does it in ways that I find unusually detailed and clear. Perhaps most useful are the examples he cites that are based on actual field experiments. Other authors may mention things like spin drift and the effects of rifling twist rate on precision, but almost invariably on the basis of theory alone.
At this point I’ll make my general criticism of the books. For the reader who frets about such things as “it’s” versus “its,” we (I, anyway) would have appreciated prepublication reviews by an editor who understood them, not to mention obvious typographical errors. In one instance I found numerical values that differed slightly on two successive pages. In addition, there is some duplication among the books. That helps reinforce the information, but affects one’s perception of how good a value they are. It’s also important to understand that although the author continually stresses how his bullet ballistics data is more valid than standard G1 and G7 ballistic coefficients, the differences among G1, G7, and his own custom drag curves become significant only at long ranges that are beyond the distances most riflemen shoot.
In fact, if the shooter never engages targets beyond 500 yards and doesn’t really care about why his bullets hit where, only that they do, many (but not all) of the topics in the books are probably not for him. If, however, the shooter is like me and wants to truly understand all the factors that affect rifle ballistics regardless of how much practical value that may ever be, then I cannot recommend the books too highly. In addition, I’ve found that it’s somewhat difficult to fully understand all the features of the Applied Ballistics solvers used in Kestrel devices, and that are available online and as smartphone apps. I couldn’t, for example, understand why a crosswind affected the vertical trajectory of shots at long ranges when nothing else changed. When I contacted the makers of the Kestrel instrument, the Nielsen-Kellerman company, I was told how to eliminate the strange (to me) results I was getting, but not fully why. It took reading about “aerodynamic jump” for it to finally become clear.
One other thing about terminology: Litz uses “precision” to refer to the inherent ability of a rifle and its ammunition to group the shots close together. It’s what benchrest shooters strive for: smallest groups without regard to where they hit on the target. “Accuracy” refers to hitting what the rifle is aimed at. A rifle and load that’s capable of consistent 2-inch groups at 500 yards would satisfy most people as being precise, but if the goal was to hit a 5-inch plate and they all hit 10 inches left of its center, it wouldn’t be accurate by Litz’s definition. I’ll use his terminology.
In addition, firearms ballistics are separated into subcategories. The books being reviewed are mostly about external ballistics, which are the things like wind and gravity outside the gun that affect a bullet’s flight. The other term for the same thing is exterior ballistics, and although Litz seems to prefer “external,” he uses “exterior” as well, sometimes on the same page. Other primary subcategories are internal or interior ballistics, which are factors inside the gun like chamber pressure. Terminal ballistics, which includes the sub-subcategory of “wound ballistics,” is about what happens when a bullet hits something such as a game animal.
The following reviews of the individual books briefly describe each of their sections and individual topics. Please ask questions if you want further details.
The books I most recommend reading are the two volumes of Modern Advancements in Long Range Shooting.
Applied Ballistics for Long-Range Shooting, second (2011) and third (2015) editions. As mentioned, the second edition of the book was my first Litz work. These two books come with a disc loaded with a version of the Applied Ballistics solver. It’s not, however, as comprehensive as the expensive one that can be purchased online directly from the company.
Chapter 1. Fundamentals and Definitions:
Deterministic and nondeterministic variables: The differences between things like gravity drop and spin drift that can be precisely determined in advance with a good calculator and good inputs versus the effects of wind. Not that wind effects can’t be calculated, but that wind is very difficult to measure precisely while shooting.
Accuracy and precision.
The shooting objective. What purpose do we have in shooting? If, for example, we’re shooting only at targets whose distances are known exactly, a flat trajectory matters less than resistance to wind deflection.
Ballistic merit: muzzle velocity, ballistic coefficient, trajectory (including “point blank range”), wind deflection, kinetic energy, other factors.
Chapter 2. Ballistic coefficient: What it is, why it’s important, and especially the difference between G1 and G7 drag curves. Practical long-range experiments to confirm calculations.
Chapter 3. Gravity drop: “point blank range” trajectory; advantages of flat trajectories; the value of a precise and accurate rangefinder; “danger space”; zeroing considerations; different trajectories’ crossover points.
Chapter 4. Uphill/downhill shooting: the effects of gravity versus air drag when shooting uphill or downhill; the “improved rifleman’s rule” (or “method”).
Chapter 5. Wind deflection: a comprehensive discussion of how and why wind affects the bullet’s flight; near/far wind; mechanism of wind deflection; wind gradient (differing deflection effects based on the height of the bullet above the ground); variable crosswinds; vertical winds; vertical deflection caused by purely horizontal crosswinds (“aero jump”).
Chapter 6. Gyroscopic drift (spin drift): Explanation of the phenomenon and how to deal with it; how it differs with some common bullets, including the effects of different rifling twist rates and directions (left or right).
Chapter 7. Coriolis effect: How the rotation of the Earth affects the path of the bullet, both horizontally and vertically (the second is usually ignored by other discussions of the effect).
Chapter 8. Using ballistics programs: their features; validating programs; field experiments to confirm calculations; introduction to uncertainty analysis (how do small uncertainties in velocities, wind, target distance, ballistic coefficient, air density, and aiming affect expected results); use of density altitude for calculations.
Chapter 9. “Controlling” our sights: discussion of the “cold bore” effect; confirming windage and elevation tracking; the effects of sight cant (tilt from horizontal) and the importance of using a sight level; use of aperture (nonoptical “iron”) sights; trajectory validation or “truing.”
Chapter 10. Bullet stability: a technical discussion of what factors affect a bullet’s ability to fly point forward; why the .30 caliber 168 grain Sierra MatchKing bullet is unsuited for long distance shooting; the effects of transonic speeds; “going to sleep.”
Chapter 11. Extended long range shooting: understanding transonic (transition from supersonic to subsonic) effects; Applied Ballistics custom drag bullet profiles; effects of twist rates; effects of bullet shapes; effects of different rifling types; effects of atmospheric conditions; importance of accurate range determination.
Chapter 12. “Interesting Facts and Trends”: this chapter covers a wide range of topics. Scaling effects (larger/smaller calibers and weights); bullet energy, both linear and rotational; twist rates and muzzle velocity; nature of bullet dispersion, including the claim that some rifles produce smaller minute of angle groups at longer distances than at shorter ranges.
Chapters 13 and 14. Two technical chapters discussing in detail how small variations can affect precision and accuracy, and how they can be modeled.
Chapter 15: Lethality of long range hunting bullets: Discussion of accuracy and “Matunas’ Optimal Game Weight” formula based on bullet and game characteristics.
Chapter 16 (second edition): Hit probability for hunting: A discussion of how ballistics and other variables affect hunters’ ability to effectively hit game animals.
Chapter 16 (third edition): Weapon Employment Zone (WEZ) Analysis: Discussion of a method to “figure out your hit percentage.” …
1) So that you can know if a shot is a high confidence or low confidence shot given your rifle system and field uncertainties.
2) So that you can do ballistic performance analyses to determine how to best improve your equipment and increase your hit percentage in a given application.
The WEZ analysis is an advanced feature of the Applied Ballistics solver that uses target size, rifle precision, and the uncertainties of bullet velocity, range estimation, and wind estimation to calculate the percentage likelihood of hitting a particular type of target. The discussion also includes evaluation of the effects of shooting at different altitudes (shooting at high altitude improves one’s probabilities).
Chapter 17. Anatomy of a bullet: discussion of the shape and design of different bullets; boat tails; why flat-based bullets are used by benchrest shooters for maximum precision; boat tail shape and drag; rebated boat tail designs; ogive profiles (tangent, secant, hybrid); bullet nose profiles; meplat considerations, including modifications.
Chapter 18. Monolithic bullets: pros and cons of using bullets that are made of a solid piece of one type of metal rather than separate jacket and core.
Chapter 19 (second edition). “Using the experimental data”: a discussion of how the exact drag curves of specific bullets were developed; comments on specific bullet brands (Sierra, Berger, Hornady, etc.).
Chapter 19 (third edition). Ballistic Performance of Rifle Bullets: The third edition does not contain the same detailed bullet data discussed below, and this chapter serves as an introduction to the separate book of that title. The bullet descriptions in the third edition are limited to sectional density, G7 form factor, and average G1 and G7 ballistic coefficients (BC). For the BC at more specific velocities; bullet dimensions, including lengths (required for certain calculations); and stability factors, Ballistic Performance of Rifle Bullets is now the book required.
Most of the remainder of the second edition (almost half, or ~260 pages) is data on specific bullets: dimensions, including ogive radius, meplat diameter; sectional density; stability factors with various rifling twist rates, and ballistic coefficients (G1 and G7) and drag curves at different muzzle velocities. At the very end of both editions are several pages with various formulas from kinetic energy to stability.
The third edition of the book differs little from the second edition except as discussed under the specific chapters above, and does not contain the detailed bullet data library of the second edition.
Ballistic Performance of Rifle Bullets, third edition (2017).
This book is a vast, 750 page data library of detailed information about many commercial rifle bullets. The bullets’ dimensions are detailed along with ballistic coefficient and performance at a wide range of velocities. In addition, the data contains information on rifling twist rates required for bullet stability.
Next are volumes I and II of Modern Advancements in Long Range Shooting. It seems that at least one more volume is planned based on the cover designs. These books cover many of the same ballistics topics as Applied Ballistics for Long-Range Shooting, but the discussions tend to be less detailed and technical. Many other topics about the practical aspects of long range shooting are also included.
Volume I (2014).
From the introduction: “[This book] aims to end the misinformation which is so prevalent in long range shooting. By applying the scientific method and taking a Myth Buster approach, the state of the art is advanced both in terms of the available tools, and the knowledge to best apply them.”
Chapter 1: Twist Rate and Muzzle Velocity. This chapter discusses how rifling twist rate affects muzzle velocity both on a theoretical and practical experiment basis. The answer? Yes, but to no practical degree.
Chapter 2: Stability and Drag - Supersonic. A discussion of the effects of rifling types and twist rates on bullet stability in the supersonic velocity range.
Chapter 3: Stability and Drag - Transonic. A discussion of the causes and effects of drag in the velocity range from supersonic to subsonic (long distances). This is the range in which the differences between the G1 and G7 drag models becomes most important. Theory and practical experimentation.
Chapter 4: Spin Rate Decay. Increase of stability with distance traveled. Effect of barrel length on stability. Elevation (altitude) effects. Practical measurement of spin decay.
Chapter 5. Effect of Twist Rate on Precision. How twist rates affect precision (small groups), and why slower rates are better for precision, but not for stability. Why thin bullet jackets are usually better for precision. Why better quality bullets are less sensitive to twist rate variations. Results of live fire precision tests with different twist rate barrels. Why better-stabilized bullets travel through the transonic velocity zone with less drag
Chapter 6. Modern Long Range Rifles: A discussion about “a few essential items which are truly advancing the performance of modern long range rifles.” Overall cartridge length constraints of various magazines and guns. The value of cartridges using smaller caliber bullets with higher ballistic coefficients (BCs). The importance (again) of barrel rifling twist rates for long bullets with the highest BCs.
Chapter 7. Advancement in Optics: A discussion of the importance of good optical sights for long range shooting, especially adjustment range and mechanical reliability. In this chapter and elsewhere in the Litz books he stresses the need to ensure that elevation tracking is accurate, that is, that if turning the elevation knob 12 clicks is supposed to raise the point of impact by 3 minutes of angle, that that’s what happens. It’s 3 MOA, not 2.8 or 3.1 MOA. He also discusses the advantages of “holding” reticles such as the Horus TreMoR2. His opinion of Ballistic (or Bullet) Drop Compensating (BDC) reticles is expressed as “Although the simplicity of ballistic turrets and reticles is appealing, their effective range is typically limited to short and medium ranges where environmental effects are less consequential.”
Chapter 8. Long Range Hunting Bullets: Most of the discussion in all the Litz books are about bullets intended and suitable for target shooting. This chapter discusses a number of bullets suitable for hunting.
Chapter 9. Rise of the 30 Caliber: A discussion of 0.30 caliber bullets and comparing them with other modern offerings.
Chapter 10. Evolution of FULLBORE Bullets: A discussion of the International FULLBORE (Palma) shooting competition.
Chapter 11. State of the Art Ballistic Modeling: Discussion of ballistic solvers (calculators), including live fire testing and validations. The importance of accurate input data: target distance, zero distance, muzzle velocity, ballistic coefficient, accurate scope adjustments, atmospheric station pressure. Less important or “it depends”: air temperature, slant (up/down) angle, sight height, latitude and azimuth (Coriolis effects).
Chapter 12. Accounting for Secondary Effects: Verifying spin drift (live fire testing); aerodynamic jump (vertical displacement in horizontal crosswind); Miller stability formula (much more accurate for modern bullets than Greenhill); Coriolis effect—its horizontal and vertical components.
Chapter 13. Modern Drag Modeling: Validating the theories.
Chapter 14. WEZ (Weapon Employment Zone) Modeling: All the factors that affect hitting the target (accuracy) and how they can be incorporated into calculations to determine the probability of a hit at various ranges.
Chapter 15. Measuring Muzzle Velocity: Detailed discussion about use and evaluation of various current (2014) chronographs.
Chapter 16. Laser Rangefinders: Detailed discussion about use and evaluation of various rangefinders.
Chapter 17. Wind Measurement: The importance and difficulty of accurate wind speed measurements and how it remains the aspect of long range shooting that has seen the least improvement in recent years.
Chapter 18. Modern Ballistic Instrumentation: Recent ballistic solvers (calculators) and instruments.
The book ends with a list of specific mathematical formulas discussed and bullet data information as discussed above.
Volume II (2016).
Chapter 1. Understanding Dispersion: Measuring dispersion, including the statistical value of different numbers of shots in precision measurement groups, and the statistical methods of comparing groups fired with different numbers of shots. How measuring mean radius is a better method than overall group size. Further discussion of spin rate versus precision. Benchrest bullets.
Chapter 2. Angular Group Convergence: Yes, convergence, or the notion that the angular size of groups (e.g., in minutes of angle) can become smaller at long distances than at short ranges. For example, a claim that someone’s consistent groups measure 1 inch at 100 yards, but 1.5 inches at 200 yards rather than the 2 inches (or larger) we would expect. This chapter is a comprehensive discussion of the idea and explores the possible reasons for the phenomenon, including through the results of over 70 live fire test groups—if it truly exists. I found the book worth owning for that reason alone.
Chapter 3. Bullet Trimming and Pointing: Manufacturing methods used for open tip match bullets usually leave their meplats (tips) somewhat ragged and ununiform. That lack of uniformity affects the bullets’ ballistic coefficients and therefore can result in vertical stringing at long ranges. There are two primary ways of correcting the lack of uniformity, trimming the point in a manner similar to trimming a cartridge case mouth, and swaging (forming) the point into a more uniform shape. This chapter discusses the methods, to include their effectiveness and other pros and cons.
Chapter 4. Powder Measurement: This chapter examines the value of different methods of powder measurement and the effects of such things as cartridge case (brass) and primer selection for producing the most consistent, uniform muzzle velocities. The importance of accurate chronograph readings is reiterated.
Chapter 5. Flash Hole Deburring: What it says.
Chapter 6. Neck Tension: What it says.
Chapter 7. Fill Ratio. The effects of changing how completely cartridge cases are filled with powder.
Chapter 8. Performance Evaluation of Laser Rangefinders: What it says (update from volume I).
Chapter 9. Rimfire Ammunition: The results of extensive testing of different 22 Long Rifle ammunition.
Chapter 10. Aerodynamic Drag Modeling for Ballistics: A detailed discussion of ballistic coefficients and related matters pertaining to atmospheric drag and bullet performance.
Chapter 11. Advancements in Barrel Technology: An evaluation of several high quality barrels, including fluted and carbon fiber wrapped models. An interesting part of the discussion was about barrel stiffness and the effects of firing multiple rounds to warm the material and its effects on point of impact shift.
The remainder of the book consisted of an updated bullet data library, laser rangefinder performance charts, and mathematical formulas.
Accuracy and Precision for Long Range Shooting: A Practical Guide for Riflemen (2012).
“[This] is a book for riflemen who want to understand the important elements of their craft. All too often, ambitious shooters strive to hit smaller targets at greater distances, without a clear understanding of what’s really required for success. … Critical thinking 101: In order to get better at hitting targets, we must understand what causes us to miss targets.”
Chapter 1. Overview of Methodology: The Weapon Employment Zone (WEZ) analysis (described above) is used throughout the book.
Chapter 2. Example WEZ Calculation: This example uses a rifle with 24 inch barrel chambered for 308 Winchester and firing the 175 grain Sierra MatchKing bullet at 2600 feet per second. Variables are crosswind estimates, rifle/ammunition precision (group sizes), velocity consistency, atmospheric conditions (elevation above sea level), and target size.
Chapter 3. Wind Uncertainty: A closer examination of the effects of uncertainties in wind speed estimates.
Chapter 4. Range Uncertainty: A closer examination of the effects of uncertainties in target distance estimates.
Chapter 5. Inherent Precision: An examination of the effects of rifle/ammunition precision, or their ability to produce small, consistent groups.
Chapter 6. Muzzle Velocity Effects: An examination of the effects of variations in muzzle velocity.
Chapter 7. Accurate Shooting—Basics: Factors pertaining to the ability to hit one’s target, including the effects on the actual zero (point of aim = point of impact) of shooting from different positions; the optimum zeroing range; and understanding one’s sights, including the need to ensure they track accurately.
Chapter 8. Leveling Your Sights: The reasons why it’s important that the rifle is not canted (tipped) with respect to gravity when shooting.
Chapter 9. Trajectory Modeling: This information is similar to what is presented in other books about the topic. The important discussions concern the importance of accurate inputs such as muzzle velocity and ballistic coefficients. There is also more detailed discussion of the effects of different atmospheric conditions (humidity, temperature) that doesn’t appear in the other books in the series.
Chapter 10. Secondary Trajectory Effects: Coverage of spin drift, including WEZ targets; and Coriolis effects. The book points out that Coriolis effects may need to be considered on small targets as close as 500 yards.
Chapter 11. Calibrating Ballistics Solutions: “The idea is to correct the inputs based on observed drop, thereby calibrating the program to be more accurate.” This is a feature of the Applied Ballistics solver installed in the Kestrel 5700 weather monitor, but only after working with another version of the calculator did I discover that it’s not useful unless shooting at extended ranges (generally ≥1000 yards). The discussion is, however, very detailed and useful if it can be employed.
Chapter 12. Live Fire Verification: The results of live fire with various rifles and cartridges to verify the WEZ theoretical results.
Chapter 13. 300 Winchester Magnum: WEZ Analysis.
Chapter 14. 300 Win Mag vs. 338 Lapua Mag: WEZ Analysis.
Chapter 15. Score Shooting: WEZ Analysis factors relating to shooting at bull’s-eye targets.
Chapter 16. Wind Sensor Array: A discussion of wind issues and technological efforts to determine precise wind effects to the target.
Chapter 17. Varmint Hunting: WEZ Analysis of various varmint hunting loads.
Chapter 18. Medium and Big Game Hunting: WEZ Analysis of various loads for hunting those animals.
Chapter 19. Military and Tactical Shooting: WEZ Analysis of military rifles. M4 carbine with M855 ammunition; M110 rifle with M118LR; XM2010 with A191 (190 grain 300 Win Mag) ammunition; and Sako TRG-42, 338 Lapua Mag, 300 grain Berger Hybrid.
At the end of the book is a short bullet data library.
“Most men … can seldom accept the simplest and most obvious truth if it … would oblige them to admit the falsity of conclusions … which they have woven, thread by thread, into the fabrics of their lives.”
— Leo Tolstoy
Thanks for the review Sigfruend. I own a Kestrel 5700 with the ballistic calculator. You are correct when stating beyond 500 yards it starts to give some incorrect data. I just got back from doing load development all day. From 600-1000 yards I was .2-.3 mils low when using the Kestrel's data. When creating the custom curve one must adjust muzzle velocity to match the actual real world numbers and then one can create a custom ballistic curve.
It will get you in the "ballpark" according the conversation I had with Kestrel. The reason is no two rifles perform the same. There are too many variables at play. It's a tool in the tool belt, but certainly not the end all, be all.
Some gun owners might still be interested in these subjects.
At the long range course I took last month, there was a lot of classroom discussion about Litz and his work. Great stuff.
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