On the Applied Ballistics Facebook Page, there was a fascinating series of posts showing traces of bullets at various speeds from Mach 0.86 to Mach 3.0. At the slowest speed, Mach 0.86, i.e. 962 FPS, there is turbulence behind the bullet, but no clear shockwave. At the highest velocity, Mach 3.0 (3375 FPS at sea level, 68° F), there is a dramatic double nose and tail wave formation.
To learn more, visit TheScienceofAccuracy.com. On that site you’ll find exclusive video content and you can subscribe to member’s only Podcasts. And you can purchase Applied Ballistics books on the Science of Accuracy webstore.
Mach 3.00 Bullet Flight Image
At Mach 3 (3355 FPS) this bullet now has a strong and well established shock wave forming at the tip, and at the base. Unlike the transition through Mach 1.0, nothing really interesting happens to the aerodynamics or shock waves meaning the aerodynamics and stability are: continuous, easy to predict, and model. As you go faster, the shockwaves make a shallower angle because the bullet is moving forward 3X faster than the shock wave is moving away from it. So the shock wave makes an angle that has a rise/run ratio of 1/3.
If a bullet flew within 10 feet of you traveling this fast, it would be about as loud as a 22 magnum. You’d certainly want hearing protection as the energy contained in a Mach 3 shock wave is high! How high…? Well, in 10 yards, this bullet slows from 3355 FPS to 3334 FPS in a time of 0.0090 seconds. The 55 ft-lb of kinetic energy lost during this 10 yards is due to aerodynamic drag on the bullet, which is comprised of wave, base, and skin friction drag components with the majority of the drag being due to shock wave formation. Expending 55 ft-lb of energy in 0.0090 seconds requires a power output of 6111 ft-lb/sec = 11.1 horsepower, most of which goes into creating the shock wave. Remember it’s a 3-D cone that travels great distance, and it gets its energy by stealing velocity from your bullet!
Mach 1.00 Bullet Flight Image
Many shots were fired to capture an image of the transonic shockwave structure at exactly Mach 1.00. With the bullet now moving at the speed of sound, the local airflow on some parts of the bullet exceeds Mach 1.0. Anytime something is moving thru the air faster than the air can get out of the way, you get a compression wave, aka “shock wave”. That’s what’s visible in this image — the areas where the air density changes rapidly (in the compression wave) are visible as near vertical lines and a detached bow wave out front. As the bullet progresses through transonic speed, this shockwave structure develops which has strong effects on the drag (wind sensitivity) and stability of the bullet.
The exact development of the shockwaves and the resulting effects are unique and sensitive to the bullet geometry, and become very difficult to predict through the transition from subsonic (incompressible flow without shock waves) to supersonic (compressible flow with shock waves). Each bullet geometry does this differently which is why it’s difficult to determine transonic stability criteria for bullets of different shapes.
Mach 0.86 Bullet Flight Image
Here’s a bullet at Mach 0.86 (86% the speed of sound, which is 962 FPS at 61° F). As you can see, this 0.86 Mach is not fast enough to make any discernable waves but you can see turbulence in the bullet wake (right side in photo). The beginning of small shock waves can be seen on the bullet tip, and at the bearing surface/boat tail juncture. For the most part, all of the airflow around this bullet is subsonic. You wouldn’t hear a supersonic ‘crack’ from this bullet flying past the observer.
In discussions of ballistics, you’ll see references to “tangent”, “secant”, and “hybrid” bullet shapes. We know that, for many readers, these terms can be confusing. To add to the confusion, bullet makers don’t always identify their projectiles as secant or tangent designs. This article provides a basic explanation of tangent, secant, and hybrid ogive bullet designs, to help you understand the characteristics of these three basic bullet shapes.
Tangent vs. Secant vs. Hybrid
Most match bullets produced today use a tangent ogive profile, but the modern VLD-style bullets employ a secant profile. To further complicate matters, the latest generation of “Hybrid” projectiles from Berger Bullets feature a blended secant + tangent profile to combine the best qualities of both nose shapes. The secant section provides reduced drag, while the tangent section makes the bullet easier to tune, i.e. less sensitive to bullet seating depth position.
Berger Bullets ballistician Bryan Litz explains tangent and secant bullet ogive designs in a glossary section of his Applied Ballistics website, which we reprint below. Bryan then explains how tangent and secant profiles can be combined in a “hybrid” design.
How Bullet Ogive Curves are Defined
While the term “ogive” is often used to describe the particular point on the bullet where the curve reaches full bullet diameter, in fact the “ogive” properly refers to the entire curve of the bullet from the tip to the full-diameter straight section — the shank.
Understanding then, that the ogive is a curve, how is that curve described?
LITZ: The ogive of a bullet is usually characterized by the length of its radius. This radius is often given in calibers instead of inches. For example, an 8 ogive 6mm bullet has an ogive that is a segment of a circular arc with a radius of 8*.243 = 1.952”. A .30-caliber bullet with an 8 ogive will be proportionally the same as the 8 ogive 6mm bullet, but the actual radius will be 2.464” for the .30 caliber bullet.
For a given nose length, if an ogive is perfectly tangent, it will have a very specific radius. Any radius longer than that will cause the ogive to be secant. Secant ogives can range from very mild (short radius) to very aggressive (long radius). The drag of a secant ogive is minimized when its radius is twice as long as a tangent ogive radius. In other words, if a tangent ogive has an 8 caliber radius, then the longest practical secant ogive radius is 16 calibers long for a given nose length.”
Bryan Litz Explains Hybrid Design and Optimal Hybrid Seating Depths
Ogive Metrics and Rt/R Ratio
LITZ: There is a number that’s used to quantify how secant an ogive is. The metric is known as the Rt/R ratio and it’s the ratio of the tangent ogive radius to the actual ogive radius for a given bullet. In the above example, the 16 caliber ogive would have an Rt/R ratio of 0.5. The number 0.5 is therefore the lowest practical value for the Rt/R ratio, and represents the minimum drag ogive for a given length. An ogive that’s perfectly tangent will have an Rt/R ratio of 1.0. Most ogives are in between an Rt/R of 1.0 and 0.5. The dimensioned drawings at the end of my Applied Ballistics book provide the bullets ogive radius in calibers, as well as the Rt/R ratio. In short, the Rt/R ratio is simply a measure of how secant an ogive is. 1.0 is not secant at all, 0.5 is as secant as it gets.
Hybrid Bullet Design — Best of Both Worlds?
Bryan Litz has developed a number of modern “Hybrid” design bullets for Berger. The objective of Bryan’s design work has been to achieve a very low drag design that is also “not finicky”. Normal (non-hybrid) secant designs, such as the Berger 105gr VLD, deliver very impressive BC values, but the bullets can be sensitive to seating depth. Montana’s Tom Mousel has set world records with the Berger 105gr VLD in his 6mm Dasher, but he tells us “seating depth is critical to the best accuracy”. Tom says a mere .003″ seating depth change “makes a difference”. In an effort to produce more forgiving high-BC bullets, Bryan Litz developed the hybrid tangent/secant bullet shape.
Many barrel-makers mark the twist rate and bore dimensions on their barrel blanks.
Does muzzle velocity change with faster or slower barrel twist rates? Absolutely, but much less than you might think. Faster twist rates do slow down bullets somewhat, but the speed loss is NOT that significant. With Bartlein .308 Win barrels of identical length and contour, a 1:12″-twist barrel was only 8 fps faster than a 1:8″-twist barrel. That was the result of testing by Applied Ballistics.
The Applied Ballistics team tested six (6) same-length/same-contour Bartlein barrels to observe how twist rate might affect muzzle velocity. This unique, multi-barrel test is featured in the book Modern Advancements in Long Range Shooting, Vol. 1. That book includes other fascinating field tests, including a comprehensive chronograph comparison.
Barrel Twist Rate vs. Velocity — What Tests Reveal by Bryan Litz
When considering barrel twist rates, it’s a common belief that faster twist rates will reduce muzzle velocity. The thinking is that the faster twist rate will resist forward motion of the bullet and slow it down. There are anecdotal accounts of this, such as when someone replaces a barrel of one brand/twist with a different brand and twist and observes a different muzzle velocity. But how do you know the twist rate is what affected muzzle velocity and not the barrel finish, or bore/groove dimensions? Did you use the same chronograph to measure velocity from both barrels? Do you really trust your chronograph?
Summary of Test Results
After all the smoke cleared, we found that muzzle velocity correlates to twist rate at the average rate of approximately 1.33 FPS per inch of twist. In other words, your velocity is reduced by about 5 FPS if you go from a 1:12″ twist to a 1:8″ twist. — Bryan Litz
Savage Test Rifle with Six Bartlein Barrels
Most shooters don’t have access to the equipment required to fully explore questions like this. These are exactly the kinds of things we examine in the book Modern Advancements in Long Range Shooting, Vol. 1. In that book, we present experiments conducted in the Applied Ballistics lab. Some of those experiments took on a “Myth Buster” tone as we sought to confirm (or deny) popular pre-conceptions. For example, here’s how we approached the question of barrel twist and muzzle velocity.
Six .308 Win Barrels from Bartlein — All Shot from the Same Rifle
We acquired six (6) barrels from the same manufacturer (Bartlein), all the same length and contour, and all chambered with the same reamer (SAAMI spec .308 Winchester). All these barrels were fitted to the same Savage Precision Target action, and fired from the same stock, and bench set-up. Common ammo was fired from all six barrels having different twist rates and rifling configurations. In this way, we’re truly able to compare what effect the actual twist rate has on muzzle velocity with a reasonable degree of confidence.
Prior to live fire testing, we explored the theoretical basis of the project, doing the physics. In this case, an energy balance is presented which predicts how much velocity you should expect to lose for a bullet that’s got a little more rotational energy from the faster twist. In the case of the .30 caliber 175 grain bullets, the math predicts a loss of 1.25 fps per inch-unit of barrel twist (e.g. a 1:8″ twist is predicted to be 1.25 fps slower than a 1:9″ twist).
Above, data shows relationship between Twist Rate and Muzzle Velocity (MV) for various barrel twist rates and rifling types. From fast to slow, the three 1:10″ twist barrels are: 5R (canted land), 5 Groove, 5 Groove left-hand twist.
We proceeded with testing all 6 barrels, with twist rates from 1:8″ to 1:12″. After all the smoke cleared, we found that muzzle velocity correlates to twist rate at the average rate of approximately 1.33 fps per inch of twist. In other words, your velocity is reduced by about 5 fps if you go from a 1:12″ twist to a 1:8″ twist. [Editor: That’s an average for all the lengths tested. The actual variance between 1:12″ and 1:8″ here was 8 FPS.] In this case the math prediction was pretty close, and we have to remember that there’s always uncertainty in the live fire results. Uncertainty is always considered in terms of what conclusions the results can actually support with confidence.
This is just a brief synopsis of a single test case. The coverage of twist rates in Modern Advancements in Long-Range Shooting Vol. 1 is more detailed, with multiple live fire tests. Results are extrapolated for other calibers and bullet weights. Needless to say, the question of “how twist rate affects muzzle velocity” is fully answered.
Other chapters in the book’s twist rate section include: · Stability and Drag — Supersonic
· Stability and Drag — Transonic
· Spin Rate Decay
· Effect of Twist rate on Precision
Other sections of the book include: Modern Rifles, Scopes, and Bullets as well as Advancements in Predictive Modeling. This book is sold through the Applied Ballistics online store at thescienceofaccuracy.com. Modern Advancements in Long Range Shooting is also available as an eBook in Amazon Kindle format.
Want to improve your understanding of Ballistics, Bullet Design, Bullet Pointing, and other shooting-related tech topics? Well here’s a treasure trove of gun expertise. Applied Ballistics offers dozens of FREE tech articles on its website. Curious about Coriolis? — You’ll find answers. Want to understand the difference between G1 and G7 BC? — There’s an article about that.
“Doc” Beech, technical support specialist at Applied Ballistics says these articles can help shooters working with ballistics programs: “One of the biggest issues I have seen is the misunderstanding… about a bullet’s ballistic coefficient (BC) and what it really means. Several papers on ballistic coefficient are available for shooters to review on the website.”
Credit Shooting Sports USA Editor John Parker for finding this great resource. John writes: “Our friends at Applied Ballistics have a real gold mine of articles on the science of accurate shooting on their website. This is a fantastic source for precision shooting information[.] Topics presented are wide-ranging — from ballistic coefficients to bullet analysis.”
Here are six (6) of our favorite Applied Ballistics articles, available for FREE to read online. There are dozens more, all available on the Applied Ballistics Education Webpage. After Clicking link, select Plus (+) Symbol for “White Papers”, then find the article(s) you want in the list. For each selection, then click “Download” in the right column. This will send a PDF version to your device.
Berger Twist-Rate Stability Calculator On the Berger Bullets website you’ll find a handy Twist-Rate Stability Calculator that predicts your gyroscopic stability factor (SG) based on mulitiple variables: velocity, bullet length, bullet weight, barrel twist rate, ambient temperature, and altitude. This cool tool tells you if your chosen bullet will really stabilize in your barrel.
How to Use Berger’s Twist Rate Calculator
Using the Twist Rate Calculator is simple. Just enter the bullet DIAMETER (e.g. .264), bullet WEIGHT (in grains), and bullet overall LENGTH (in inches). On its website, Berger conveniently provides this info for all its bullet types. For other brands, we suggest you weigh three examples of your chosen bullet, and also measure the length on three samples. Then use the average weight and length of the three. To calculate bullet stability, simply enter your bullet data (along with observed Muzzle Velocity, outside Temperature, and Altitude) and click “Calculate SG”. Try different twist rate numbers (and recalculate) until you get an SG value of 1.4 (or higher).
Gyroscopic Stability (SG) and Twist Rate
Berger’s Twist Rate Calculator provides a predicted stability value called “SG” (for “Gyroscopic Stability”). This indicates the Gyroscopic Stability applied to the bullet by spin. This number is derived from the basic equation: SG = (rigidity of the spinning mass)/(overturning aerodynamic torque).
If you have an SG under 1.0, your bullet is predicted not to stabilize. If you have between 1.0 and 1.1 SG, your bullet may or may not stabilize. If you have an SG greater than 1.1, your bullet should stabilize under optimal conditions, but stabilization might not be adequate when temperature, altitude, or other variables are less-than-optimal. That’s why Berger normally recommends at least 1.5 SG to get out of the “Marginal Stability” zone.
In his book Applied Ballistics For Long-Range Shooting (3rd Ed.), Bryan Litz (Berger Ballistician) recommends at least a 1.4 SG rating when selecting a barrel twist for a particular bullet. This gives you a safety margin for shooting under various conditions, such as higher or lower altitudes or temperatures.
Story idea from EdLongrange. We welcome reader submissions.
Emil Praslick III is widely recognized as one of the greatest wind wizards on the planet — a master at identifying wind value and direction, and predicting wind cycles. As coach of the USAMU and top civilian teams, Emil has helped win many high-level championships. In the three videos we feature today, Emil, who works with Capstone Precision Group (Berger, Lapua, SK, Vihtavuori) and Team Applied Ballistics, explains how to determine wind direction and velocity using a variety of indicators. Praslick, now retired from the U.S. Army, was an 18-time National and 2-time World Champion coach with the USAMU.
Video ONE: Wind Theory Basics — Understanding “Wind Values”
In this video from UltimateReloader.com, Emil explains the basics of modern wind theory. To properly understand the effect of the wind you need to know both the velocity of the wind and its angle. The combination of those variables translates to the wind value. Emil also explains that the wind value may not be constant — it can cycle both in speed and velocity. Emil also explains some of the environmental conditions such as mirage that can reveal wind conditions.
Video TWO: Determining the Direction of the Wind
Key Point in Video — Find the Boil
Emil explains how to determine wind direction using optic. The method is to use spotting scope, riflescope, or binoculars to look for the “Boil” — the condition in mirage when the light waves rising straight up. The wind will generate that straight-up, vertical boil in your optics when it is blowing directly at you, or directly from your rear. To identify this, traverse your scope or optics until you see the boil running straight up. When you see that vertical boil, the direction your optic is pointing is aligned with the wind flow (either blowing towards you or from directly behind you).
Video THREE: The No Wind Zero Setting
In this second video, Emil defines the “No-Wind Zero”, and explains why competitive shooters must understand the no-wind zero and have their sights or optics set for a no-wind zero starting point before heading to a match. In order to hit your target, after determining wind speed and direction, says Emil, “you have to have your scope setting dialed to ‘no wind zero’ first.”
Coach of Champions — Emil Praslick III
SFC Emil Praslick III, (U.S. Army, retired) works with Berger Bullets and Applied Ballistics. Emil served as the Head Coach of the U.S. National Long Range Rifle Team and Head Coach of the USAMU for several years. Teams coached by Emil have won 33 Inter-Service Rifle Championships. On top of that, teams he coached set 18 National records and 2 World Records. Overall, in the role of coach, Praslick can be credited with the most team wins of any coach in U.S. Military history.
On the Applied Ballistics Facebook Page, there is a fascinating series of posts showing traces of bullets at various speeds from Mach 0.86 to Mach 3.0. At the slowest speed, Mach 0.86, i.e. 962 FPS, there is turbulence behind the bullet, but no clear shockwave. At the highest velocity, Mach 3.0 (3375 FPS at sea level, 68° F), there is a dramatic double nose and tail wave formation.
To learn more, visit TheScienceofAccuracy.com. On that site you’ll find exclusive video content and you can subscribe to member’s only Podcasts. And you can purchase Applied Ballistics books on the Science of Accuracy webstore.
Mach 3.00 Bullet Flight Image
At Mach 3 (3355 FPS) this bullet now has a strong and well established shock wave forming at the tip, and at the base. Unlike the transition through Mach 1.0, nothing really interesting happens to the aerodynamics or shock waves meaning the aerodynamics and stability are: continuous, easy to predict, and model. As you go faster, the shockwaves make a shallower angle because the bullet is moving forward 3X faster than the shock wave is moving away from it. So the shock wave makes an angle that has a rise/run ratio of 1/3.
If a bullet flew within 10 feet of you traveling this fast, it would be about as loud as a 22 magnum. You’d certainly want hearing protection as the energy contained in a Mach 3 shock wave is high! How high…? Well, in 10 yards, this bullet slows from 3355 FPS to 3334 FPS in a time of 0.0090 seconds. The 55 ft-lb of kinetic energy lost during this 10 yards is due to aerodynamic drag on the bullet, which is comprised of wave, base, and skin friction drag components with the majority of the drag being due to shock wave formation. Expending 55 ft-lb of energy in 0.0090 seconds requires a power output of 6111 ft-lb/sec = 11.1 horsepower, most of which goes into creating the shock wave. Remember it’s a 3-D cone that travels great distance, and it gets its energy by stealing velocity from your bullet!
Mach 1.00 Bullet Flight Image
Many shots were fired to capture an image of the transonic shockwave structure at exactly Mach 1.00. With the bullet now moving at the speed of sound, the local airflow on some parts of the bullet exceeds Mach 1.0. Anytime something is moving thru the air faster than the air can get out of the way, you get a compression wave, aka “shock wave”. That’s what’s visible in this image — the areas where the air density changes rapidly (in the compression wave) are visible as near vertical lines and a detached bow wave out front. As the bullet progresses through transonic speed, this shockwave structure develops which has strong effects on the drag (wind sensitivity) and stability of the bullet.
The exact development of the shockwaves and the resulting effects are unique and sensitive to the bullet geometry, and become very difficult to predict through the transition from subsonic (incompressible flow without shock waves) to supersonic (compressible flow with shock waves). Each bullet geometry does this differently which is why it’s difficult to determine transonic stability criteria for bullets of different shapes.
Mach 0.86 Bullet Flight Image
Here’s a bullet at Mach 0.86 (86% the speed of sound, which is 962 FPS at 61° F). As you can see, this 0.86 Mach is not fast enough to make any discernable waves but you can see turbulence in the bullet wake (right side in photo). The beginning of small shock waves can be seen on the bullet tip, and at the bearing surface/boat tail juncture. For the most part, all of the airflow around this bullet is subsonic. You wouldn’t hear a supersonic ‘crack’ from this bullet flying past the observer.
Applied Ballistics (AB) has published an update to its Bullet Library, which can be accessed from all AB-enabled devices, including the AB Quantum App. The library updates are based on testing with Doppler radar. The bullet updates are based on averaging of multiple Doppler Radar tests at long range (through transonic). All of the bullets that were recently updated have been tested multiple times from various different barrels and twist rates to find the average performance. These updates to the bullet library are FREE to those who have subscribed to AB Quantum.
The AB team explained that these updates will help provide the most accurate ballistic fire solutions available. Ongoing updates are planned as AB continues testing and compiling results.
“Many of our existing bullets were modeled after just one test, but after a few years of testing out of multiple guns, we have a much better assessment of the bullets’ average performance and those models replace the originals. Rest assured, when we update a bullet model, it does NOT affect an existing gun profile. It’s only new gun profiles that get built — they’ll pull the updated performance. So [there is] no need to worry about your established data changing within an existing gun profile.”
Updates to the Applied Ballistics Bullet Library are normally made whenever:
* AB tests new bullets
* AB Accumulates more test data on existing bullets
* AB runs tests to further ranges than previous tests
Typically, changes to assessed performance are small (under 2%) representing only about 1 or 2 clicks of difference at 1000 yards. But sometimes the shift is more substantial.
Bryan Litz added: “The updates don’t always change performance a lot, some are just small tweaks. Typically you would build a new gun profile from selecting the bullet in the library to get the new performance. But if you’re using BC, you can just transcribe the new one into your existing gun profile.”
Q: What’s more important — wind speed, or direction?
A: Obviously they both matter, but they do trade dominance based on direction. For example, a 10 mph wind between 2:30 and 3:30 is only changing its value from 9.7 to 10 to 9.7 mph (bracket of 0.3 mph). However a 10 mph wind between 11:30 and 12:30 is changing its cross wind component value from 2.6 mph left to zero to 2.6 mph right (bracket of 5.2 mph). There is the same 30° change in direction, but this results in a massively different bracket.
Point being, in this case, a direction change is far more critical if it’s near 6 or 12 o’clock. A small direction change when it’s close to 3 or 9 o’clock is negligible.
On the contrary, a change in wind SPEED when it’s near 3 or 9 affects your crosswind component directly. But for a near head or tail wind, a fluctuation in wind speed only causes a small fraction of a change to the crosswind component.
SUMMARY: If you’re in a near full-value wind, pay more attention to wind SPEED. If you’re closer to a head- or tail-wind, nailing the exact DIRECTION will be more important.
Get More Tips on Bryan Litz Ballistics Facebook Page
This post is from the new Bryan Litz Ballistics Facebook Page. FB users should check that page regularly for more tips from Bryan, American’s leading ballistics expert and founder of Applied Ballistics LLC.
Here’s a smart tip from Bryan Litz, explaining how damage to a bullet jacket can harm the projectile’s Ballistic Coefficient (BC). This tip is posted on Bryan’s new Bryan Litz Ballistics Facebook page. We recommend you subscribe to that page to access Bryan’s latest informative posts.
Bryan notes: “If the case mouth scratches the bullet when you seat it, the damage can cause the BC to be inconsistent, which shows up as vertical dispersion at long range.”
We see this sometimes when running Doppler Radar for competitors at Applied Ballistics Mobile Lab events. If someone is shooting a bullet that typically has a very consistent BC (1% or less) but they’re seeing a higher BC variation, it can be due to the bullets being damaged in the loading process.”
The lead photo above shows the badly-scratched jacket of a bullet seated in a rough-mouthed case. To prevent such jacket damage, one should chamfer, deburr, and smooth case mouths after trimming.
Below is a recorded Doppler radar result showing excessive BC variation. Such variation can increase vertical dispersion at long range. This can result in larger group sizes and lower scores.
On the Applied Ballistics Facebook Page, there was a fascinating series of posts showing traces of bullets at various speeds from Mach 0.86 to Mach 3.0. At the slowest speed, Mach 0.86, i.e. 962 FPS, there is turbulence behind the bullet, but no clear shockwave. At the highest velocity, Mach 3.0 (3375 FPS at sea level, 68° F), there is a dramatic double nose and tail wave formation. 
Hybrid Bullet Design — Best of Both Worlds?
On his 
