These four photos show the substantial changes in the shock wave and turbulence patterns for the same 7.5mm bullet at different velocities. The “M” stands for Mach and the numerical value represents the velocity of the bullet relative to the speed of sound at the time of the shot. Photos by Beat Kneubuehl.
“Going transonic” is generally not a good thing for bullets. The bullet can lose stability as it enters the transonic zone. It can also become less slippery, losing BC as a consequence of dynamic instability. In this video, Bryan Litz of Applied Ballistics analyzes what happens to bullet stability (and BC) as projectiles approach the speed of sound. Transonic effects come into play starting about Mach 1.2, as the bullet drops below 1340 fps.
Transonic Ballistics Effects Explainedby Bryan Litz
What happens when the bullet slows to transonic speed, i.e. when the bullet slows to about 1340 feet per second? It is getting close to the speed of sound, close to the sound barrier. That is a bad place to fly for anything. In particular, for bullets that are spin-stabilized, what the sound barrier does to a bullet (as it flies near Mach 1) is that it has a de-stabilizing effect. The center of pressure moves forward, and the over-turning moment on the bullet gets greater. You must then ask: “Is your bullet going to have enough gyroscopic stability to overcome the increasing dynamic instability that’s experienced at transonic speed?”
Some bullets do this better than others. Typically bullets that are shorter and have shallow boat-tail angles will track better through the transonic range. On the contrary, bullets that are longer… can experience a greater range of pitching and yawing in the transonic range that will depress their ballistic coefficients at that speed to greater or lesser extents depending on the exact conditions of the day. That makes it very hard to predict your trajectory for bullets like that through that speed range.
When you look at transonic effects on stability, you’re looking at reasons to maybe have a super-fast twist rate to stabilize your bullets, because you’re actually getting better performance — you’re getting less drag and more BC from your bullets if they are spinning with a more rigid axis through the transonic flight range because they’ll be experiencing less pitching and yawing in their flight.
To determine how bullets perform in the “transonic zone”, Bryan did a lot of testing with multiple barrels and various twist rates, comparing how bullets act at supersonic AND transonic velocities. Bryan looked at the effect of twist rates on the bullets’ Ballistic Coefficient (BC). His tests revealed how BC degrades in the transonic zone due to pitching and yawing. Bryan also studied how precision (group size) and muzzle velocity were affected by twist rates. You may be surprised by the results (which showed that precision did not suffer much with faster barrel twist rates). The results of this extensive research are found in Bryan’s book Modern Advancements in Long Range Shooting.
Bryan notes: “A lot of gunpowder was burned to get these results and it’s all published in layman’s terms that are easy to understand”. If you’re interested in learning more about transonic bullet stability, you may want to pick up a copy of Bryan’s book.
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Someone spending thousands of dollars on a once-in-a-lifetime hunt might consider getting Geovid rangefinding binoculars. Leica’s award-winning Geovid combines a superb binocular optic with a laser rangefinder AND a ballistic computer. With this single device you can spot your game, find the distance to your target, and calculate the elevation correction. Geovids even take a micro-SD card so you can upload your customized ballistics table.
At around $3200.00 (street price) Geovids are very expensive, but for a serious hunter the Geovid’s capabilities justify the price*. The glass is excellent, the rangefinder offers outstanding performance, and you never have to pull out a PDA or mobile device to run ballistics. The Geovid even does angle correction and can output elevation click values. With the Geovid, you have one tool that does three jobs exceptionally well. When you’re climbing a mountain in pursuit of a Trophy Elk, carrying less gear makes sense.
Now through October 31, 2015 you can save $300.00 on a new 8×42 Geovid HD-B, or 10×42 Geovid HD-B. That makes this state-of-the-art tool much more affordable. To get a $300.00 mail-in rebate from Leica, submit a sales receipt with the Leica Rebate Form.
*We have a good friend who works as a professional hunting guide and gunsmith in New Mexico. For years he made do with well-used Steiner binoculars and an older Leica LRF. On our last visit to NM, he proudly showed us his new Leica Geovid. I told him: “John, those Geovids cost a fortune… are they really worth the money?” He told me: “On one of my first hunts after getting the Geovid, I took along the Steiners for comparison. It was late in the day. I glassed a ridgeline about 700 yards away with the Steiners, and saw nothing. Then I got out the Geovid, looked at the same area and saw two large Elk in among some trees. That made the hunt a success for me and my client. Yes the Geovids are worth it… the glass really makes a difference in low light. And I can range as I’m spotting — that’s a big deal.”
If you are considering the Geovids, you’ll find that Geovid owners have high praise for these rangefinding binoculars. Here are reviews from verified purchasers who have used Geovids on hunts:
“Optical quality is second to none, these binos are in a class by themselves (the only competition IMHO are the Swarovski EL Range). Direct comparison of optic image quality to my lesser-brand binos really demonstrated the difference for me. The image is bright and clear across the entire field of view which is also wider than my standard 10×42 binos. Low-light gathering capability at dawn and dusk is considerably better than my lesser brands and should extend my evening hunting times by another 5 to 10 minutes. The laser ranging capability is amazing! The reading is almost instantaneous[.] The display is a red open target square that’s easy to see in all light conditions.” — Jackson611
“These Binos are the best range-finders on the market, not even talking about the glass yet. The range report is almost instantaneous. If you choose to load your ballistics data on the SD card you will be glad you did. It gives you bullet drop out to 1000 yards. Now let’s get to the glass. I have Swarovski 15×56 binos. These Leicas are just as clear, but small enough to wear around your neck. The price is high, but I learned a long time ago, that you get what you pay for with optics. And if you hunt out west, your optics will make or break your hunt.” — Matt
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Here’s a great tip from Forum member Greg C. (aka “Rem40X”). Greg has created a trajectory table with windage and elevation data for various distances and wind speeds. Greg prints out a compact version of his drop chart to place on his rifle. While many shooters tape a ‘come-up’ table on their buttstock, Greg has a better solution. He tapes the trajectory table to the outside of his front flip-up scope cover. This way, when he flips up the cover, his data is displayed for easy viewing right in front.
With your ‘come-up’ table on the flip-up cover you can check your windage and elevation easily without having to move up off the rifle and roll the gun over to look at the side of the stock. Greg tells us: “Placing my trajectory table on the front scope cover has worked well for me for a couple of years and thought I’d share. It’s in plain view and not under my armpit. And the table is far enough away that my aging eyes can read it easily. To apply, just use clear tape on the front objective cover.”
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Applied Ballistics has created a new series of YouTube videos about precision long range shooting. Featuring ace long-range shooter and professional ballistician Bryan Litz, these videos will address various topics of interest to long-range marksmen. In this week’s video, the first in the series, Bryan Litz answers the question, “Just What Is Long Range Shooting?” Bryan discusses how we define “long range” and the key factors shooters need to consider.
Applied Ballistics Video — What Is Long Range Shooting?
Bryan states: “I don’t think there is a clear definition of where Long Range starts.” But he offers this practical guideline: “The way I think of it, any time you’re making major adjustments to your zero in order to hit a target, due to gravity drop and wind deflection, THEN you’re getting into ‘Long Range’. For example, if you are zeroed at 100 yards and need to shoot to 600 yards, you have many feet of elevation [drop] to account for, and to me, that’s where it becomes Long Range.”
Extended Long Range and the Transonic Zone
Bryan adds a second concept, namely “Extended Long Range”. Litz says that: “Extended Long Range starts whenever the bullet slows to its transonic range. As the bullet slows down to approach Mach 1, it starts to encounter transonic effects, which are more complex and difficult to account for, compared to the supersonic range where the bullet is relatively well-behaved.” Bryan notes that bullets start to encounter transonic effects at about 1340 fps, quite a bit faster than the speed of sound, which is about 1116 fps at sea level in normal conditions (59° F).
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Warner Tool Company (WTC) has introduced a new series of “Flat Line” ultra-high-BC bullets. These sleek, lathe-turned solids are some of the most perfectly-streamlined projectiles ever sold. The Ballistic Coefficients (BCs) of Flat Line projectiles are as much as 20% higher than other match bullets of similar caliber and weight. For example, the .30-caliber 200gr Flat Line bullet has a claimed G1 BC of 0.780. Compare that to 0.555 for the Sierra 200gr MatchKing and 0.622 for the Berger 200gr Hybrid.
The new Flat Line bullets all show extremely high Ballistic Coefficients for their weights:
WTC also claims that Flat Line bullets can be launched at faster velocities than other bullets of similar caliber and weight. In its marketing materials, WTC says that Flat Line bullets deliver “Higher velocities when compared with projectiles in its weight class [and] much higher velocity when compared with projectiles of similar BC.” For example, WTC claims that “the 155.5gr .30-caliber bullet has the velocity of a 125-135gr bullet [with] the BC of a 185-200gr bullet.” It will be interesting to see if these claims can be verified in field tests.
Here are comparative G1 BCs for a variety of large .30-caliber bullets:
Cal Zant of the Precision Rifle Blog has obtained some early-production Flat Line bullets from their designer, Josh Kunz. Zant has written a lengthy article explaining the design and features of the new Flat Line bullets. If you are considering ordering some of these new lathe-turned solids, you should definitely read Zant’s report.
These bullets were designed by Aerospace engineer Josh Kunz using advanced computational fluid dynamics (CFD) to simulate supersonic air flow around the bullets. Through the use of advanced modeling and precision CNC machining, Kunz has developed extremely uniform, ballistically “slippery” bullets that fly faster and flatter than other projectiles of similar weight/caliber.
Premium Pricing: Flat Line Bullets Cost $125 to $165 per Hundred
These new Flat Line solid bullets are pricey. The 155s cost $1.25 per bullet and the price goes up from there. If you need large quantities of projectiles for a week-long match, the cost can be daunting. One hundred fifty of the 200-grainers will set you back $435.00! Here is a price list for the new Flat Line bullets. All quantities are in boxes of 50. Pricing is introductory and subject to change.
.30 Cal 155 grain
$62.50 per 50-ct box ($1.25 per bullet)
.30 Cal 180 grain
$67.50 per 50-ct box ($1.35 per bullet)
.30 Cal 200 grain
$72.50 per 50-ct box ($1.45 per bullet)
.338 Cal 255 grain
$82.50 per 50-ct box ($1.65 per bullet)
Is the cost worth it? When you look at the overall expense of attending a major match, and the fact that the top places in big matches are sometimes are decided by a single point (or X-Count), some competitors will spend the extra money for these ultra-high BC solids.
How do you build better (more precise) ammo drop tables? With radar, that’s how. Barnes Bullets is using Doppler Radar to develop the drop tables for its new Precision Match line of factory ammunition. The Doppler radar allows Barnes to determine actual velocities at hundreds of points along a bullet’s flight path. This provides a more complete view of the ballistics “behavior” of the bullet, particularly at long range. Using Doppler radar, Barnes has learned that neither the G1 nor G7 BC models are perfect. Barnes essentially builds a custom drag curve for each bullet using Doppler radar findings.
Use of Doppler Radar to Generate Trajectory Solutions
by Barnes Bullets, LLC
Typical trajectory tables are generated by measuring only two values: muzzle velocity, and either time-of-flight to a downrange target, or a second downrange velocity. Depending on the test facility where this data is gathered, that downrange target or chronograph may only be 100 to 300 yards from the muzzle. These values are used to calculate the Ballistic Coefficient (BC value) of the bullet, and the BC value is then referenced to a standardized drag curve such as G1 or G7 to generate the trajectory table.
This approach works reasonably well for the distances encountered in most hunting and target shooting conditions, but breaks down rapidly for long range work. It’s really an archaic approach based on artillery firings conducted in the late 1800s and computational techniques developed before the advent of modern computers.
There is a better approach which has been utilized by modern militaries around the world for many years to generate very precise firing solutions. Due to the sizeable investment required, it has been slow to make its way into the commercial market. This modern approach is to use a Doppler radar system to gather thousands of data points as a bullet flies downrange. This radar data is used to generate a bullet specific drag curve, and then fed into a modern 6 Degree of Freedom (DOF) [ballistics software program] to generate precise firing solutions and greatly increase first-round hit probability. (The 6 DOF software accounts for x, y, and z position along with the bullet’s pitch, yaw, and roll rates.)
Barnes has invested heavily in this modern approach. Our Doppler radar system can track bullets out to 1500 meters, recording the velocity and time of flight of that bullet every few feet along the flight path. Consider the graph below showing a bullet specific drag curve referenced to the more common G1 and G7 curves:
Neither of the standard curves is a particularly good match to our test bullet. In the legacy approach to generating a downrange trajectory table, the BC value is in effect a multiplier or a fudge factor that’s used to shift the drag curve of the test bullet to try and approximate one of the standard curves. This leads to heated arguments as to which of the standardized drag curves is a better fit, or if multiple BC values should be used to better approximate the standard curve (e.g., use one BC value when the velocity is between Mach 1 and Mach 2, and a different BC value when the velocity is between Mach 2 and Mach 3.) Barnes’ approach to creating trajectory tables is to generate bullet-specific drag curves, and use that data directly in a modern, state-of-the-art, 6 DOF ballistics program called Prodas to generate the firing solution.
Story tip from EdLongrange. We welcome reader submissions.
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We know our readers are curious about the new Tipped MatchKings (TMKs) introduced by Sierra Bullets this year. Our friend Bill at Rifleshooter.com got hold of some of the .30-Cal 175-grain TMKs and tested them in his .308 Win rifle. He found the bullets were very consistent in weight. As for bearing surface, the SD was fairly low (.002″), but measurements varied from 0.400″ to 0.407″. Seven-thousandths extreme spread is more than we like to see, as it may affect accuracy. Therefore we recommend you sort by bearing surface length before loading these in match rounds.
Photo shows Bryan Litz (on right) and tester Mitchell Fitzpatrick. Bryan said: “Only 2,445 rounds to go! We’re testing over 50 ammo types in five different twist barrels… science can be exhausting!”
Do you know the actual BC (Ballistic Coefficient) of your rimfire ammunition? Well Applied Ballisitics will soon have answers for you. Bryan Litz and his team of testers have been working on a Herculean project. They’ve been testing over fifty types of .22 LR ammo, using five different twist-rate barrels.
Applied Ballistics has just released a fully upgraded version of its popular Tactical App for Android devices. Bryan Litz tells us: “AB Tactical has received a major overhaul (including a new Bullet Library with over 420 options). The upgrade will require that you uninstall the previous version that you have of the application and then install this new version. This is due to the complete re-write of the internal database handling.” NOTE: You need to record your gun-specific data before you install the new version. Details of the updated AB Tactical App are featured in the new 19-page USER Manual.
NOTE: This upgrade is for the Applied Ballistics Tactical Version only. There is no iPhone version of this App, and this is not the standard app that can be purchased from Google Play, or iTunes.
The new version of AB Tactical has a host of important enhancements:
Our friend Darrell Buell has a new Beast — a monster 64-inch-long .375 CheyTac that weighs more than 70 pounds! Designed for ultra-long-range shooting (two miles and beyond), this beast represents the state-of-the-art in extreme long-range rifles.
Darrell reports: “This rifle is pretty much purpose-built to shoot 2+ miles extremely accurately. It is a .375 CheyTac (lengthened) built on a BAT 2.5″ action. The custom 35″, 1:10″-twist Brux barrel is a fat, 2″-diameter ‘straight taper’ with fluting. A custom 5″-long muzzle brake is fitted at the end. All barreled action work was done by R.W. Snyder Custom Rifles. The stock was created to fit the build by PDC Custom, and the massive muzzle brake as well.” The “bridge” at the end may look like a barrel block, but it’s not — the barrel completely free-floats. (The Picatinny rail on top of the bridge allows use of an overhanging bipod as an alternative to the JoyPod).
Darrell has lots of elevation on tap: “With 150 MOA in the Ivey rings, another 20 MOA in the scope rail, 55 MOA in the Nightforce Competition scope, and 10 MOA in the FCR-1 reticle, there’s an impressive +235 MOA available.”
“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:
Here’s a report posted by long-range shooter Grizzman on the LiveLeak video hosting site. Grizzman engaged an 18″x24″ steel target at the distance of 2530 yards — 1.43 miles. Grizzman produced a great video that really gives you a sense of the distance (see the zoom footage at the 0:30 time mark). At this distance, the ballistics are remarkable. Grizzman’s .338-cal, 300gr Berger Hybrid bullets went transonic at 2400 yards and dropped 228 feet (69.5 meters) over their 2530-yard trajectory.
WATCH Video — Second camera at target records bullet impacts (see and hear the hits):
On LongRangeHunting.com, you’ll find a good article by Shawn Carlock about wind reading. Shawn is a veteran law enforcement marksman and a past USPSA national precision rifle champion. Shawn offers good advice on how to estimate wind speeds and directions using a multitude of available indicators — not just your wind gauge: “Use anything at your disposal to accurately estimate the wind’s velocity. I keep and use a Kestrel for reading conditions….The Kestrel is very accurate but will only tell you what the conditions are where you are standing. I practice by looking at grass, brush, trees, dust, wind flags, mirage, rain, fog and anything else that will give me info on velocity and then estimate the speed.”
Shawn also explains how terrain features can cause vertical wind effects. A hunter on a hilltop must account for bullet rise if there is a headwind blowing up the slope. Many shooters consider wind in only one plane — the horizontal. In fact wind has vertical components, both up and down. If you have piloted a small aircraft you know how important vertical wind vectors can be. Match shooters will also experience vertical rise when there is a strong tailwind blowing over an up-sloping berm ahead of the target emplacements. Overall, Shawn concludes: “The more time you spend studying the wind and its effect over varying terrain the more successful you will be as a long-range shooter and hunter.”
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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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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.
Learn More About SG and BC This article is just a brief overview of the interrelated subjects of twist rate, Gyroscopic Stability, and BC. The coverage of twist rates in Modern Advancements in Long-Range Shooting is more detailed, with multiple live fire tests.
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. Modern Advancements in Long Range Shooting is also available in eBook format in the Amazon Kindle store.
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At the 2015 Berger Southwest Nationals, Forum member Erik Cortina cornered Bryan Litz of Applied Ballistics. Erik, the F-Open winner in the 600-yard Mid-Range match, was curious about bullet sorting. Knowing that bullets can be sorted by many different criteria (e.g. weight, overall length, base to ogive length, actual bearing surface length etc.) Erik asked Bryan to specify the most important dimension to consider when sorting. Bryan recommended sorting by “Base to Ogive”. Litz noted that: “Sorting by overall length can be misleading because of the nature of the open-tip match bullet. You might get a bullet that measures longer because it has a jagged [tip], but that bullet might not fly any different. But measuring base to ogive might indicate that the bullet is formed differently — basically it’s a higher resolution measurement….”
Horizontal Wind-Drift vs. Distance
OK, here’s a challenge question for you.
Let’s see if you get it right.
Q: If the wind is blowing 10 mph from 9 o’clock and if my horizontal wind deflection is 0.7 inches at 100 yards, what is the horizontal drift at 1000 yards?
You may be thinking, “Well, since the target is ten times more distant, the wind-drift should be around 7 inches, maybe a little more since the bullet will be slowing down.” That sounds reasonable, right?
As you move from near to far, the increase in lateral deflection (from a 90° crosswind) is (roughly speaking) a function of the square of the multiple of distance. If your target is two times farther away, you use the square of two, namely four. If your target is five times farther away, you use the square of five, or twenty-five. In this example, the increased wind drift (from 100 to 1000 yards) is at least 0.7″ times (10 X 10) — over 70 inches (give or take a few inches depending on bullet type). We call that the Rule of the Square. This Rule lets you make a quick approximation of the windage correction needed at any yardage.
Precision Shooting and the Rule of the Square
I was going through some back issues of Precision Shooting Magazine and found many references to the Rule of the Square. This made me curious — I wondered how well the Rule really stacked up against modern ballistics programs. Accordingly, I ran some examples through the JBM Ballistics Trajectory Calculator, one of the best web-based ballistics programs. To my surprise, the Rule of the Square does a pretty good job of describing things.
EXAMPLE ONE — .308 Win (100 to 400 Yards)
For a 168gr Sierra MK (.308), leaving the muzzle at 2700 fps, the JBM-predicted values* are as follows, with a 10 mph, 9 o’clock crosswind (at sea level, 65° F, Litz G7 BC):
Drift at 100: 0.8 MOA (0.8″)
Drift at 200: 1.6 MOA (3.3″)
Drift at 400: 3.4 MOA (14.4″)
Here you can see how the Rule of the Square works. The rule says our drift at 200 yards should be about FOUR times the drift at 100. It the example above, 0.8″ times 4 is 3.2″, pretty darn close to the JBM prediction of 3.3″. Quoting Precision Shooting: “Note that the deflections at 100 yards are typically a quarter of those at 200; lateral deflections increase as the square of the range”. Precision Shooting, June 2000, p. 16.
EXAMPLE TWO — .284 Win (100 to 1000 Yards)
For a .284 Win load, with the slippery Berger 180gr Target Hybrids, the Rule of the Square still works. Here we’ll input a 2750 fps velocity, Litz G7 BC, 10 mph, 9 o’clock crosswind, (same 65° temp at sea level). With these variables, JBM predicts:
Drift at 100: 0.5 MOA (0.5″)
Drift at 500: 2.5 MOA (13.3″)
Drift at 1000: 5.9 MOA (61.3″)
Again, even with a higher BC bullet, at 1000 yards we end up with something reasonably close to the 100-yard deflection (i.e. 0.5″) multiplied by (10×10), i.e. 50 inches. The Rule of the Square alerts you to the fact that the effects of crosswinds are MUCH greater at very long range. In this example, our JBM-calculated drift at 1000 is 61.3″ — that’s over 100 times the 100-yard lateral drift, even though the distance has only increased 10 times.
Note that, even with a 5 mph 90° sidewind, the “Rule of the Square” still applies. The 1000-yard lateral deflection in inches is still over 100 times the lateral deflection at 100 yards.
Why This All Matters (Even in the Age of Smartphones)
Now, some would say, “Why Should I Care About the Rule of the Square? My iPhone has a Ballistics App that does all my thinking for me”. Fair enough, but knowledge of this basic Rule of the Square enables a shooter to make an informed guess about necessary windage even without a come-up sheet, as long as he knows the distance AND can fire a sighter at 100 or 200 yards as a baseline.
For example, if I see empirically that I need 1″ windage correction at 100 yards, then I know that at 600 yards I need at least roughly (6 x 6 x 1″) or 36 total inches of drift correction, or 6 MOA. (To be precise, 1 MOA = 1.047″ at 100 yards). I can figure that out instantly, even without a ballistics chart, and even if my Smartphone’s battery is dead.
*Values shown are as displayed on the JBM-figured trajectory tables. The numbers can be slightly imprecise because JBM rounds off to one decimal place for both inches and MOA.
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Sierra Bullets has released Version 7 of its respected Infinity Exterior Ballistics software, available now for $39.95 for Windows computers. Renowned Sierra Ballistic Consultants Ted Almgren and Dr. Bill McDonald, who have written all Sierra Software since 1970, also wrote Infinity Version 7. Both are retired scientists from a major aerospace company. Infinity Exterior Ballistics Software version 7 is a sophisticated solver that can output multiple trajectory charts. A built-in database includes bullets and cartridges offered by 15 manufacturers, both U.S. and foreign.
This 13-minute Video Demonstrates the Many Features of Infinity 7 Ballistics Software:
This sophisticated program computes the effects on the bullet trajectory of variations in firing conditions. For example, you can change altitude of the firing point, target angle (uphill/downhill), wind speeds, or even modify the Ballistic Coefficient. In fact, you can change any inputted firing condition or combination of conditions.
One very handy function is the “back-to-zero” calculation. Infinity 7 software will compute where your gun is zeroed if you know that it shoots high by a measured amount at a known range.
Compare Trajectories with Five Different Bullets
One very powerful feature of Infinity 7 is its trajectory comparison capability. With most ballistics programs (such as the JBM online ballistics calculator), you can only view one bullet’s trajectory (and associated drop chart) at a time. Not so with Infinity 7. This software handles up to five different bullets at a time. You can compare downrange velocity, energy, drop, bullet path height, or crosswind drift with results shown in bolt tabular and graphical format. That helps you select the best bullet for your gun and application. The ability to compare downrange ballistics of five different bullets at once is particularly helpful for hunters, who can compare the “hitting power” of different projectiles at various distances.
You can purchase Infinity 7 Ballistics Software as a standalone product for $39.99, or you can buy the Infinity 7 Suite for $59.95, which includes the Sierra Bullets 5th Edition Reloading Manual on CD-ROM. If you prefer a printed loading Manual, a combo pack with Infinity 7 software CD-ROM plus published (hard-back) Reloading Manual is offered for $64.95.
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In response to questions from a fellow F-Class shooter, German Salazar offered some expert advice in an article entitled: Basics: A Few Wind Reading Tips. Here are highlights from that essay. You can read the entire article on German’s Rifleman’s Journal Website. German cautions that: “I certainly am not attempting to make this short item into a comprehensive lesson in wind reading, but there may be a nugget or two in here for the newer shooter. There is, however, no substitute for range time and coaching.”
Preliminary Matters — Holding Off vs. Knob-Turning
Let’s begin by eliminating one topic altogether — I realize that the predominant method of wind correction in F-Class is holding-off with the crosshairs of your scope rather than adjusting the windage knob. I am a firm believer in aiming at the center and turning the knob as needed, but we’ll leave that for another time and focus on seeing what the wind is doing.
The Wave — Wind Cycles and Shot Timing
I find that most shooters begin to shoot immediately when the time commences rather than waiting for an appropriate moment in the cycle, this often leads to lost points early on. If you’ve been scoring prior to shooting, hopefully you’ve observing the flags and your shooter’s shot placement. It’s a very useful way of gaining some insight into the day’s wind patterns before shooting.
My technique is based on the understanding of wind as a cyclical wave motion. That statement alone should give you plenty to think about[.] Imagine for a moment, a surfer. He waits for a gentle swell, gets moving on it and rides it through it’s growth and ultimately its crescendo and hopefully avoids being swallowed in its crash. Wind typically behaves in the same fashion as that wave and a smart shooter behaves as does the surfer — get on early in the wave, ride through the major change and get off at the right moment. Knowing when to stop shooting is every bit as important as shooting quickly through the predictable portion of the wave; getting back on to the next wave is a matter of delicate judgment and timing.
When you are on that rising (or falling) wave, the idea is to shoot very quickly to minimize the amount of change between shots and to make a small adjustment on each shot. Too many shooters waste time trying to analyze the exact amount of the change, by which time it has changed even more! Get on with it, click or hold over a set amount and fire the next shot quickly. This is the foundation of how I shoot and it is very effective as long as you know when to start, when to stop and you have a good man working the target – a slow marker is the death of this method.
Watch Shots from Other Shooters
We all watch the wind flags, of course, and the trees if your range is so blessed (ours are fairly barren), and many other small wind indicators. Watching the shots of your fellow shooter can also be a very useful tool and should be observed whenever possible. When a good shooter next to you comes up with a poor shot, it should signal you to stop and reassess conditions as they may not be what they appear.
While scoring for another shooter, take a moment to scan the line of targets. You’ll be surprised at how most of the shot markers move in unison to one side and then the other. The sad truth is that most shooters are behind the changes in the wind and they will get carried to either side of the bull as the wind changes. You’ll see this in the targets as they come up, and once learned, you’ll find that the line of targets is as useful as another row of flags.
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Thomas Haugland, a Shooters’ Forum member from Norway, is a long-range target shooter and hunter. He has created an interesting video showing how to gauge wind velocities by watching trees, grass, and other natural vegetation. The video commentary is in English, but the units of wind speed (and distance) are metric. Haugland explains: “This is not a full tutorial, but rather a short heads-up to make you draw the lines between the dots yourself”. Here are some conversions that will help when watching the video:
.5 m/s = 1.1 mph | 1 m/s = 2.2 mph | 2 m/s = 4.5 mph
3 m/s = 6.7 mph | 4 m/s = 8.9 mph | 5 m/s =11.2 mph