“In the past 4-5 years we’ve made quantum leaps when it comes to predicting bullet trajectories.” –Dave Emary, Ballistician
Ever wonder why you center punch targets at some distances, but your dope is a couple clicks off at other distances? Maybe your shots are dead on at 600 yards but off at 1000 yards, or vice versa. In those scenarios we often blame the rifle, scope, ammo, or ourselves, but is our firing solution as accurate as it should be? This article gives practical insight into some important nuances of predicting bullet trajectory, and shows what drag models the top precision rifle shooters in the country are using to get consistent first round hits at long range.
While it can be hard to recognize, we’re right in the middle of a huge leap forward when it comes to accurately predicting bullet trajectory. I was discussing this with veteran ballistician David Emary recently, and he thought there may have been more advancements in ballistics in the past 5 years than the previous 75 years! What an exciting time to be involved in long range shooting! Honestly, I’ve been wanting to write on this topic for a while to shine a spotlight on what some researchers and industry insiders are saying could be the biggest impact in modern ballistics. I want to help put all this into context, and present what the advances are in plain English along with what they mean to the shooter.
A Brief History of Predicting Trajectory & “Standard” Bullets
To understand where we are and where we’re headed, we must know where we’ve been … but I promise this is relevant and I’ll keep it brief!
In the 1740’s, a ballistician discovered the drag force on a bullet could be over 100 times more powerful than the force of gravity, and that amount of drag force varied based on the bullet’s velocity. That event triggered 200+ years of research. Progress was slow because aerodynamic drag is a very complex process, and the calculus required to compute a single trajectory was lengthy, tedious, and done by hand. An early observation was the drag force was different for every type of bullet – the drag a bullet experiences in flight is unique based on its shape. However, the thought of somehow trying to measure and compute the drag for each and every type of bullet over the full velocity range from the muzzle to the target seemed impossible!
Around 1850, Francis Bashforth proposed a practical solution to simplify things: What if we established a “standard” bullet, and did all the comprehensive drag measurements and complex calculations for that one “standard” bullet? Then we could take the results for that “standard” bullet and make it a model that we simply scale somehow for other bullets to avoid the hassle of performing exhaustive measurements and calculations for hundreds of bullets. That brilliant idea was a catalyst for a new era in applied ballistics, and is the foundation of what we’ve used to this day.
From 1865-1880, live fire tests were conducted by practically every major military and reported in extensive ballistics tables. Shortcut equations were developed from those results to calculate trajectories more quickly, and they learned how to scale the known drag of a standard bullet to compute the trajectory of other bullets using something called a “Ballistic Coefficient.” This worldwide effort eventually culminated in standard drag models for a few shapes and sizes of bullets, with the G1 standard becoming the most popular.
A Ballistic Coefficient (BC) is a number used to describe the drag on a bullet compared to some standard bullet. For example, a G1 BC is comparing the drag of that specific bullet to the G1 standard bullet. The higher the BC, the better the bullet will be able to retain its velocity downrange and be less affected by the wind.
Shooters in the civilian world have been using G1 BC’s to calculate trajectories since Winchester and Sierra Bullets started publishing ballistics tables and data in the 1960’s and 70’s. An accurate BC is the foundation of a reliable firing solution. “Ballistic coefficients of bullets are important because under or over estimates of ballistic coefficients can dramatically impact predictions of long range trajectory, wind drift, and impact energy,” explains Michael Courtney, in research published by the US military.
However, it was noticed that the BC for bullets vary at different velocities, and sometimes that change could be significant. To provide a more accurate solution for the problem of velocity-dependent BC’s, Sierra Bullets started publishing multiple BC’s for each bullet that are broken up into several velocity “bands.” Here is an example:
One problem with the multiple BC approach is that most ballistic calculators don’t allow you to enter multiple BC’s, although there are a few with that feature (like the Shooter phone app). Another solution is to use the average BC over the velocities you’ll be shooting, but that means the trajectory may not be accurate over the entire range (i.e. your solution might be on at 600 yards and off at 1000 yards, or vice versa).
G7: A Better Standard For Long Range Bullets
In the late 2000’s, ballistician Bryan Litz proposed the G7 BC is a better standard for modern long range bullets. Others in the academic and research world also made that observation and saw it as a simple fact, but that idea challenged the popular opinion and established practices of the shooting community. “The reason why the BC of a modern long range bullet changes so much at different velocities is because modern bullets are so different in shape compared to the G1 standard that it’s BC is based on. In other words, the drag of a modern long range bullet changes differently than the G1 standard projectile, so the coefficient relating the two (the ballistic coefficient) has to change with velocity,” explains Bryan. Basically, if you don’t choose the standard that most closely matches your bullet the result will be velocity dependence and associated problems with BC’s. The standard that bears the closest resemblance to most modern long range bullets is the G7 standard.
A good rule of thumb is if you are using a short, flat-based bullet, go with the G1 BC. If you are using a long bullet with a boat-tail and pointy nose (like most modern long range bullets), then the G7 BC is likely a better fit. As a result, using a G7 BC should be more constant and reliable for all velocities and ranges. Bryan summarizes it this way: “A trajectory that’s calculated with a G7 BC doesn’t suffer as much from the same velocity dependence problems and inaccuracies as calculations that are made with a G1 BC.”
The excerpt below is from Ballistic Performance of Rifle Bullets (3rd Edition) by Bryan Litz and it is based on BC’s carefully measured through live-fire experiments. The book has data like this for hundreds of bullets, but I picked the DTAC 6mm 115gr RBT bullet as an example, because it is extremely popular in the PRS. The page includes a chart that shows how the G1 and G7 BC change based on the velocity of the bullet, and it also quantifies the variance of each type of BC over supersonic flight.
Clearly the G7 BC is a better fit for this bullet, and 99% of the other bullets covered in the book. In this example, the G1 BC varies from 0.657 at high velocities down to 0.535 below 1500 fps. That’s a variation of 20%! There is a significant slope to the G1 BC line on the chart, and you can see the line trail off significantly as the bullet slows. If you were using a G1 BC, what number do you put in your ballistic calculator? The average is 0.590, but you know that isn’t going to produce accurate results at all ranges – meaning you may be on at 600 yards but off at 1,000 yards, or vice versa. On the other hand the G7 BC only varies from 0.311 at the highest velocities down to 0.300 below 1500 fps, which is less than a 4% variance. In this case, if you enter the average of 0.302 G7 BC in your ballistic calculator it is going to be very close at all ranges.
Note: If you noticed the G1 BC is a higher number than the G7 BC, don’t be distracted by that – it doesn’t mean anything to the shooter. The number for a bullet’s G7 BC will typically be about half the number for its G1 BC for the same bullet, but just because the G1 BC is higher doesn’t make the bullet fly any different! Just be sure to select the correct drag model in your ballistic calculator for the number you entered.
The example above is typical – I didn’t cherry-pick a bullet that exaggerates the point. Honestly, that is just a bullet I’ve used a lot. Other independent research has measured similar variance, saying things like, “As expected, the G7 BC shows much less change with different velocities than the G1 BC for boat tail bullets.” (Courtney). I will point out that bullets designed for Extreme Long Range in big bores like the 375 CheyTac, 416 Barrett, or 50 BMG can have twice as much variance in the G1 BC over their velocities as what is shown in this example.
Does that mean you can’t use a G1 BC to hit targets? Nope. I’ve seen exceptional shooters who I highly respect use G1 BC’s to achieve first round hits out to 2 miles! They may just have to do more truing/calibration. Are G7 BC’s always better? Not exactly, but they do usually vary less with velocity, meaning once you find the right number for a G7 it is more likely to align with hits at all ranges than a single G1 BC. G7 BC’s are still an approximation based on a standard bullet, so there will still be slight variance from the actual drag – but it should be a much better fit than G1 BC’s for most long range bullets and therefore require less truing/calibration.
Can I Trust The BC Printed On The Box?
As long range shooters, we love high BC bullets. It’s powerful to have a single number that represents how aerodynamic a bullet is. BC is seen as a performance measure, similar to horsepower in a car – the higher the number the better! So, manufacturers know it’s in their best interest to publish the highest possible number they could justify. That may sound cynical, but BC is very interpretive. In the example above, Sierra provided 4 different BC’s for various velocity bands, so if they just advertise one number which do they pick? That’s right, the highest one! While it might be more helpful for long range shooters to publish the average BC over a wider range of velocities, that’s not what happens. And it’s not just Sierra – practically everyone does it. “The majority of industry published BC’s is measured over relatively short ranges of 100 to 300 yards, which corresponds to velocities around 2500 fps depending on muzzle velocities,” explains Hornady.
Think about it: If everyone else is publishing best-case-scenario BC’s based on high velocities, you might as well play along or you’re handicapping yourself. Of course, a few companies seem to be more “optimistic” in their published BC’s, with independent research showing some manufacturers overestimate BC’s by more than 10% (Courtney) – so I’ve learned to be highly skeptical of the BC from most manufacturers.
Another problem is many manufacturers only publish G1 BC’s, and not G7 BC’s. So if we don’t have accurate G7 BC’s for our bullets, changing to that as the standard is just a good idea with no way to implement.
That brings us back to Bryan Litz. Several years ago, Bryan saw that the lack of accurate BC’s for bullets was becoming a limiting factor. So he started conducting live-fire tests to independently measure the real-world BC of popular rifle bullets to help the long range shooting community create more accurate firing solutions. His experiments were carefully instrumented so the resulting BC’s were accurate to +/- 1%, and Bryan has been publishing the results of that ongoing research for several years. This was a huge service to the shooting community, because now you can just look up the “Litz BC” and have a high degree of trust that it is accurate. Bryan has compiled a library of G1 and G7 BC’s measured from his live-fire testing and there are several ways to find those numbers, but if you want the entire list you should just buy his bullet library book that contains comprehensive info for 720 bullets (see the full bullet list).
A Quick Summary Of Where We Are Today
Today, shooters have powerful tools and data available which allow us to predict bullet trajectory at a whole different level of accuracy. New chronographs, like the LabRadar and MagnetoSpeed, have been released that provide very accurate muzzle velocities and avoid common pitfalls/errors associated with traditional, light-based chronographs. Then we have access to accurate G7 BC’s measured from Litz’s independent live-fire tests. Finally, handheld weather stations like the Kestrel Weather Meter allow us to gather on-site atmospherics in real-time. That is important because the drag a bullet experiences in flight changes based on the density of the air, so being able to measure the exact conditions allows us to customize the firing solution to be even more accurate!
All of those things have increased the quality of our inputs into a ballistic engine and therefore increase the quality of the output. If you combine all those things with a good ballistic engine, the output should very closely match your impacts in the field at most ranges without the need for much truing or calibration.
New Bullet-Specific Drag Models
Over the past decade, equipment and shooters have become much more capable, and started stretching out to distances that would have seemed ludicrous 10 years ago. That’s when we ran into a new problem. Bryan explains that “small differences in shape between a given bullet and the G7 standard can lead to significant misrepresentations of drag for that bullet at transonic speeds.” Transonic speed is when the bullet has slowed down to around 1300 fps, which is typically a long way out there, but the exact distance depends on the cartridge, bullet, and atmospheric conditions. For context, that might roughly equate to a distance around 1100-1200 yards for a 6.5 Creedmoor or 1500-1600 yards for a 338 Lapua Mag. We could use a good G7 BC with an accurate muzzle velocity to predict trajectory and get reliable first-round hits through supersonic flight, but as we stretched beyond to extreme distances the bullet became unpredictable again. It turns out that a specific bullet’s behavior at transonic speeds is unique, like a fingerprint. G1 or G7 standards are basically generic fingerprints – they won’t ever be a perfect match for a particular bullet, and that becomes especially apparent at transonic speeds.
That brings me to recent, very-exciting developments around drag modeling. In the opening, I mentioned back in the 1700’s and 1800’s “the thought of somehow trying to measure and compute the drag for each and every type of bullet over the full velocity range from the muzzle to the target seemed impossible!” That’s what led us to using standard drag models like the G1 and G7, which are simpler to apply and didn’t require modeling the actual unique bullet drag for each and every bullet shape. In most cases, the drag shapes are similar enough that simply scaling the drag curve in trajectory predictions was accurate enough. However, today we have equipment that makes measuring drag over the full flight easier, and computers are able to do the real calculus-based math much faster than mathematicians doing it by hand. While we’ve been using G standards to model drag for 100+ years, we have entered a new era!
Lapua, Applied Ballistics, Hornady, Barnes Bullets, government research labs, and others have recently started using Doppler radar to record extremely precise bullet trajectories. These aren’t LabRadar’s, but professional grade, $100,000 Doppler radar systems like the Infinition BR-1001. Doppler radar can record the exact flight of the bullet all the way down range, resulting in thousands of data points with an accuracy that is within a few millimeters! Barnes Bullets says their “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.” These companies then analyze that data to define the specific drag of an individual bullet at a whole new level.
“These continuous air drag coefficients make it possible to calculate the trajectory of your bullet much more accurately than using the simplified one-number B.C.,” explains Lapua. We no longer have to compare a bullet to a generic standard, but we have the precise and exact drag of that particular bullet.
The chart below compares the bullet-specific drag curve from research conducted by Barnes Bullets with their Doppler radar to the G1 and G7 drag curves. Note: If you’ve never seen a drag curve chart like this, here is a good explanation on how to read them and what they mean to the shooter.
It’s clear the drag curve based on the actual readings from the Doppler radar above doesn’t exactly match the shape of the G1 or the G7 curve. It is most similar to the G7 (no surprise), but it doesn’t match it perfectly. That’s because the drag curve of every bullet is unique, like a fingerprint. The drag would only perfectly match the G7 standard if the bullet was a perfect match physically to the G7 standard bullet, and that is virtually never the case.
The chart below is from Applied Ballistics research, and shows how the measured drag of another specific bullet doesn’t perfectly match the scaled version of the G1 or G7 curves for that bullet. On the right side of the chart, you can see the actual measured drag closely matches the G1 and G7 drag models, so at short to mid-range the G1 BC would give fairly accurate results. But as you move to the left of the chart and the bullet slows down the models diverge. Again, the actual drag more closely matches the G7 curve, but isn’t an exact match.
Below is a similar chart from Hornady’s research that shows how the measured drag of a few different bullets compare to the G7 standard drag. While they are similar to the G7 drag curve, each bullet has dynamic behaviors that are unique in some way.
The Applied Ballistics team refers to their bullet-specific drag models derived from live-fire testing as Custom Drag Models (CDM). Applied Ballistics was the first to pioneer bullet-specific drag models, even before the use of Doppler radar. I asked Bryan Litz about this recently, and he said, “Before we got radar, we would measure several points of drag along the curve and connect the dots. That worked very well, but Doppler radar provides a continuous measurement. We are in the process of going back through the library and updating all bullet models with radar measurements as well as the latest versions (lots) of those bullets.” The Applied Ballistics team has now conducted careful live-fire testing necessary to establish the CDM’s for 815 modern bullets and counting! For more info on how you can start using these CDM’s from Applied Ballistics visit here. (Note: I share my personal experience with the accuracy/reliability of Applied Ballistics CDM’s in this post.)
Hornady is pioneering a similar approach with rich Doppler radar data they’ve recorded, and they’re also moving away from BC’s to bullet-specific drag profiles. They do a great job of articulating their approach:
Why calculate a trajectory using a mathematical comparison of your bullet to a “Standard Projectile” (oversimplification of BC) when you can use an exact model of your projectile in the trajectory calculation (Drag Coefficient)? Using Doppler radar, Hornady ballisticians have calculated the exact drag versus velocity curve for each projectile in the 4DOF Bullet Library. Ballistic Coefficient can change as velocity changes. A drag curve doesn’t change; the curve is specific to each projectile and is directly related to its trajectory. (Read more)
Hornady allows you to use these bullet-specific drag profiles for FREE in the Hornady Ballistics app, which is available on iOS and Android devices. Hornady currently has these 4DOF bullet-specific drag profiles in their library for around 50 Hornady bullets, 8 Berger bullets, 1 Fort Scott bullet, 7 Lapua bullets, 2 Nosler bullets, 13 Sierra bullets, and 6 Warner Tool bullets. So the bullet selection isn’t near as broad as Applied Ballistics data, but Hornady is adding to their library all the time as well. When they were asked why there aren’t more bullets in the Hornady 4DOF database here was their response: “Hornady technicians will continue to add Hornady projectiles and other bullet brands to the database. Testing is time-consuming, but rest assured, there will be more projectiles added to the library.” I can only imagine how time-consuming this is, but thank you guys for pioneering!
Barnes Bullets and Lapua have also shared some of their data. Barnes data can be found on their website, and Lapua has created an app that gives you access to data for their bullets.
At this point, Doppler-based data has only been measured on a limited number of bullets and most manufacturers aren’t publishing their data publically, but instead simply integrate it into their proprietary ballistic solvers. While that is helpful, I agree with a suggestion Dave Emary made in an article he wrote for Guns & Ammo magazine: “I hope the industry begins publishing Cd versus Mach number curves so the advantages of this system can be more readily adopted by everyone.” I realize proprietary data can be seen as a competitive advantage, but that certainly isn’t putting the customer first. For example, Hornady recently partnered with Kestrel to release a new ballistic weather meter that allows you to use their 4DOF bullet library (more on the Hornady Kestrel). So if I want to use the Applied Ballistics drag models, I’d have to buy the Kestrel with the Applied Ballistics engine, but if I want to use Hornady’s drag models I’d have to buy a different device. While that may be good for the profitability of those companies, it’s not in the shooter’s best interest. Often when multiple businesses in an industry don’t put the customer first, it is a preamble to disruption. Think about it: Netflix didn’t kill Blockbuster – ridiculous late fees did. Uber didn’t kill the taxi business – limited access and fare control did. Apple didn’t kill the music industry – being forced to buy full-length albums did. A more collaborative approach where researchers share their findings publically would allow us to learn from each other and help move the shooting industry forward more quickly. I recognize there has to be a way to monetize all the R&D going into this for it to be sustainable, but what if we could use one device and had the option to pay $5 for whatever drag profile we wanted instead of being forced to commit to one camp or the other? It doesn’t have to be an either/or decision. There is a way that open-handed collaboration could benefit everyone.
So What Are The Top Precision Rifle Shooters Using?
While all this advancement is clearly exciting to me as an engineer, I’ve actually heard some respected shooters say they still thought G7 BC’s were more accurate. One of the guys who told me that was a top shooter in the PRS and a guy I highly respect, so it wasn’t just some random guy at the range! That’s what made me think it’d be interesting to ask the top precision rifle shooters in the country what drag model they were using. The survey was based on 170 shooters that finished highest overall last season in the Precision Rifle Series and National Rifle League. I asked what ballistic engine they were using, and if the shooter said they used the Applied Ballistics engine I knew that engine allows them to choose from a G1, G7, or Custom Drag Model, so I asked a follow-up question to those shooters to see which they used most often. Here is what they said:
The various colors on the chart represent the league and rank of the shooters. For example, black indicates shooters who finished in the top 10 in the PRS, dark blue is those who finished 11-25 in the PRS, and the lighter the blue, the further out they finished in PRS Open Division season standings. The green colors represents the top shooters in the NRL, where the darkest green is the top 10, medium green is 11-25, and light green are 26th to 50th. The legend on the chart itemizes the league and ranks each color represents, but basically the darker the color, the higher up the shooters placed.
So of the 130 top precision rifle shooters who said they were using the Applied Ballistics engine, 63% said they use G7 BC’s to calculate their ballistics, 27% used one of the Applied Ballistics Custom Drag Models, and finally just 10% use G1 BC’s.
This could be my own personal bias playing in, but I can’t help but wonder if we’ll see that trend change over time to see more people opting towards bullet-specific drag models. In the past, it has been fairly complicated to load these custom drag models onto your device, and sometimes you have to pay extra for them, so that extra hassle/expense might be limiting how many have made the switch and not necessarily because they don’t believe they’re accurate. I will say that loading one of Applied Ballistics CDM’s onto a Kestrel has become much easier lately through the Kestrel LiNK Ballistics phone app. I’d also bet there are people who may not have heard of bullet-specific drag models or understand how they’re different – which is why I’m writing this post! 😉
I was talking about these results with Dave Emary, a respected ballistician, and he wasn’t that surprised by these results. He pointed out that most PRS-style rifle matches don’t have targets beyond 1200 yards, and BC-based firing solutions are adequate for those distances. It’s really only when you stretch out beyond 1200-1400 yards that a bullet has slowed to the point that the nuances of a specific bullet’s drag will start to result in misses, and that’s where bullet-specific drag models become really valuable for first-round hits without the need for extensive truing/calibration. Dave also explained that one of the big goals behind bullet-specific drag models and some other recent work with the military is to provide a way for a guy to jump out of a helicopter anywhere in the world, input the current atmospherics into a ballistic solver, and then be able to connect first-round hits on man-size targets beyond 2000 meters without the need to true/calibrate his ballistics for that environment or even re-zero his rifle. And they’re now successfully doing that, thanks to highly accurate, Doppler-based, bullet-specific drag models. Wow!!!
It does seem clear that the whole industry is trending in the direction of Doppler-based, bullet-specific drag models. This article cited research from several different companies, along with respected researchers and ballisticians. We all recognize the merit this new approach has, and are excited about the new possibilities this will open up as more bullets are tested and we’re able to apply these advances in the field. I believe this is literally the most exciting time in history to be a long range shooter, and I hope this helps more shooters recognize the significant shift this represents when it comes to predicting bullet trajectory and connecting first round hits at extreme distances.
In the next post, I’ll go one step further into the rabbit hole by highlighting some of the most interesting research I’ve come across in a while, and I’ll also take a look forward to what could be “The Final Frontier” when it comes to predicting bullet trajectory. Stay tuned!