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Personalized Drag Models: The Final Frontier in Ballistics?

I am super-excited about this article! I’ve actually been working on it for a couple of months, and I believe it represents some of the most interesting research I’ve come across in a while. Over the past several years, companies have started using Doppler radars to gain a much deeper understanding into the flight of a bullet. One ballistician told me recently that we’ve learned more in the last 5 years than the previous 75 years combined! In the last article, we looked G1 BC vs. G7 BC vs. Bullet-Specific Drag Models, including which of those the top-ranked precision rifle shooters in the country said they were using in rifle matches. In this post, I’ll highlight recent research related to drag modeling, and attempt to look forward to where all this seems to be headed.

So, are bullet-specific drag models the end of the line? Have we arrived? I don’t think so. While they seem to be a huge step in the right direction, there are actually other factors that influence the drag on the bullet – including the weapon it is fired from. That’s part of the reason why first round hits at extreme long range are still so elusive. I’m going to share in this post how the drag on a bullet can vary based on several factors that are independent of the bullet itself.

Dave Emary

The research I’ll highlight came from books, magazines, and whitepapers I’ve read over the past two years, but much of it was presented by Dave Emary. Dave is a respected researcher with over 30 years in the ballistics field designing powders, bullets, and ammo. Dave was the Chief Ballistician at Hornady for many years, but retired there in 2017 and is now a “free agent,” primarily doing ballistic research at the New Mexico Institute of Mining and Technology on 8 inch howitzers and 120mm guns. Dave and the team of engineers over at Hornady are some of the industry leaders when it comes to research and development, and this post will highlight a little of what those guys are spending some of their best hours researching. As always, I will add thoughts from other leading minds in the industry to try to provide a balanced view.

Dave and a couple other leading industry experts were kind enough to read through this article and give me feedback before it was published. I also had a long phone conversation with Dave where I felt like I received an education! Thanks to those guys for helping an excited young man with too many questions!

Barrel Twist Rate

One big factor that influences a bullet’s drag is the twist rate of the barrel. This fact was also well-documented by Bryan Litz’s research in Modern Advancements in Long Range Shooting Vol 1. The chart below shows how drag curves measured with Hornady’s Doppler radar varied for the same exact bullet when shot from barrels with different twist rates.

Note: If you’ve never seen a drag chart like the one above, and aren’t sure how to read it, check out this intro article by Bryan Litz.

There is also some research that suggests that other aspects related to the barrel could affect the bullet’s drag, such as rifling profile or even how worn the rifling is. That means the drag of a bullet could be slightly different over the first hundred rounds from a rifle than after 1,000+ rounds from the same rifle. While that is interesting, more research with larger sample sizes still needs to be done before we draw strong conclusions.

Muzzle Brake

Another aspect that can affect the drag force on the bullet is if the rifle has a muzzle brake – and not only if it has a muzzle brake, but which kind of muzzle brake. Dave’s research seems to show this variation, and he explains, “Most of the brakes show significant ‘tipoff’ of the projectile at the muzzle which causes yaw and takes substantially differing amounts of time to damp. Most of the brakes tested will have an adverse effect on the drag and associated performance of the projectile. Brake D may have some advantage over the no brake because of only a small impact to the high supersonic drag and significant reduction in drag at lower supersonic speeds. If a brake is a necessity Brake D would certainly be the one to use with this setup.” (Note: For those of you wondering, Brake D appears to be American Precision Arms Little B* muzzle brake.)

Bullet BC varies by muzzle brake

The drag variation caused by muzzle brakes surprised me when I first read about it. But, just this week I read another article that speaks to the same point that was written by physicist James Boatright and published in the magazine by the Fifty Caliber Shooters Association (Very High Power, Vol 2019-2). For context, James spent his professional career working on NASA contracts and published many articles on ballistics and rifles in Precision Shooting Magazine – so he’s not just some guy, which was immediately noticeable in the article I read. Here is what James had to say on this subject: “An improperly designed muzzle brake can induce an initial yaw and yaw-rate for a bullet which would have been perfectly launched otherwise. Particular attention should be paid to minimizing the annular clearances between successive gas ports (or within each baffle of the brake or suppressor), as the gas pressure behind the bullet is being bled off. By achieving hyper-stable flight right out of the muzzle, a rifle bullet can fly all the way to its distant target with it’s lowest possible aerodynamic drag (Cd).” Translation: A muzzle brake can absolutely affect the drag of a bullet – as the chart above clearly shows.

Type of Gun Powder

Okay, the weapon can clearly affect the drag the bullet will experience, but now let’s turn our attention to the components of the loaded ammo. The chart below shows the results of Hornady’s tests using the same bullet, the same rifle and barrel without a muzzle brake, but switching out 5 different types of gun powder: RL-19, RL-22, H4350, H4831 and H1000.

Bullet BC varies by powder type

Differences here are substantial. RL-22 and H1000 show definite muzzle tipoff, likely a result of higher muzzle exit pressures and longer envelopment by the muzzle gas cloud,” explains Emary. “However, it is very interesting that both these propellants show significantly reduced low supersonic drag. Perhaps less bullet upset/distortion, in-bore because of slower rise times and lower maximum acceleration. For ranges of out to about 1000 yards the data shows it would be very hard to beat RL-19. A longer barrel, in order to reduce muzzle exit pressures, with the RL-22 or the H4831 might produce the optimum results, especially for long range firing.” There are really two thoughts there: Not only can the powder affect the drag on the bullet, but also the combination of the powder type and barrel length.

While these tests seem to be on a small sample size, they help us understand how various factors related to the weapon and initial launch conditions can affect the drag a bullet experiences. More research is necessary to draw firm conclusions.

Bullet-To-Bullet Variation

Finally, variations from one bullet to another can cause measurable differences in drag. “Bullet manufacturers have occasionally noted impacts on bullet drag with die wear and the replacing of dies and other equipment used in forming projectiles,” researcher Michael Courtney explains. I’ve also noticed that Bryan Litz updates his experimentally measured G1 and G7 BC’s for various bullets periodically based on the latest lots of bullets, and while they typically don’t change dramatically over time, they do change a measurable amount. So this news isn’t ground-breaking for many of us, and it’s why some shooters lay in a big supply of bullets from the same lot. However, the chart below shows the drag variation recorded by Doppler radar for 10 consecutive shots of the same exact 6.5mm 140gr bullet.

Bullet meplat

While Dave didn’t specify what brand/model of bullet was represented in the data above, he did provide some practical advice to keep in mind when looking for consistent bullets: “Look for projectiles that have very uniform and consistent meplat shape. The meplat is the very point of the nose. Experience has shown the meplat to be very important to drag uniformity from projectile to projectile. Go slowly with needle point projectiles. They look nice and sexy and may produce low average drag but they don’t necessarily product low drag variability from projectile to projectile. That can lead to increased vertical dispersion.” Referring to the chart above, Dave said, “As can be seen the uniformity of the drag performance is not very good and would certainly lead to elevation variation on target at longer ranges. Ultimately the drag curves should all nearly lay on top of each other. This is usually never realized but it should be substantially better than the projectile shown in the chart above. Radar data has shown that meplat diameters of .17 caliber or smaller do not increase the drag, however very small meplat diameters can cause drag variability as shown in the chart above.”

There are a number of other aspects that could potentially cause variation in drag from bullet-to-bullet. One of those is the possibility of plastic tips melting/deforming in flight. While that is a controversial topic, Dave Emary swore they were able to clearly identify that happening through their Doppler radar experiments. That is why Hornady switched to the ELD bullet tips a while back. More recently, they released aluminum tipped bullets they’re calling A-TIP, which are packaged in the exact sequential order that the bullets came off the press with minimal handling. It seems that since Hornady uncovered this bullet-to-bullet variation in drag, they’ve been taking steps to maximize the odds that a bullet is going to fly just like the one before and after it. (Watch in-depth video on A-Tip bullets). While Hornady is already headed in that direction, I expect other manufacturers will be taking steps towards this as well as our understanding of bullet-to-bullet drag variation matures.

Most veteran long range shooters have learned that having very consistent muzzle velocity (i.e. low standard deviation) is usually more valuable than having the highest possible muzzle velocity. For example, if I’d done load development and was deciding between one load that averages 3000 fps with an SD around 8 fps and another that averages 3050 fps with an SD of 20 fps, I’d pick the one with the lower SD’s. (Related: How much does SD matter?) What if we need to apply that same mindset to the consistency/uniformity of a bullet’s drag? One bullet might have an amazingly high BC but the drag may vary from bullet-to-bullet, while another may have a slightly lower BC on average but is extremely consistent. In the long range game, low drag bullets and high muzzle velocity are great, but consistency may be even more important.

So Now What?

Is your head dizzy yet? The flight of the bullet could be influenced by many factors related to the barrel, muzzle brake, powder, and even slight variations in the bullet itself! All of these factors can interplay and “stack” on each other, making the cumulative effect hard (if not impossible) to anticipate. Research with Doppler radar has challenged our simplistic view and taught us that we can’t define a bullet’s drag in absolute terms independent of these other external factors – and there seem to be too many permutations to keep track of! So what’s a guy to do? I admit it almost makes me want to throw up my hands and say, “Forget the whole thing! I’ll just go shoot and forget all this stuff.”

If all those nuances could affect the drag of the bullet, then bullet-specific drag models are still a generalized view of the drag of a bullet. It is an average, at best. How could I account for those slight variations in drag for my specific rifle and ammo?

Well, Hornady has a proposed solution. They offer bullet-specific drag models based on their Doppler radar data, which you can use through their FREE phone app (iOS app| Android app). They say the bullet-specific data is “an average of different guns, cartridges, loads, in many cases plain muzzles and muzzle brakes and twist rates.” But, do they give us a way to account for variation for our specific weapon/ammo? Here is Dave Emary’s answer:

“In order to account for the variability across the spectrum of firearm setups/condition and loads out there we decided to use the ‘Axial Form Factor’ to allow adjustment of the supplied average Cd [drag] curves in 4DOF. As can be seen from the above data, the shape of most of the Cd curves remain substantially the same with just small differences in value, until we get to the previously mentioned high Sg situations. This allows for a simple multiplier to deal with the variability from system to system for tuning the Cd curve to the weapon for its actual drag performance. The figure below displays what the Axial Form Factor is actually doing.”

Hornady 4DOF

The addition of the “Axial Form Factor” seems like a practical and helpful solution. It gives the benefit from the high-definition, bullet-specific drag curve, while maintaining the ability to true/calibrate the drag model like we are used to doing when we use BC’s based on the G1 or G7 standard. It’s kind of the best of both worlds.

Applied Ballistics offers Custom Drag Models (CDM’s) that are also bullet-specific drag profiles based on data collected from live-fire tests. 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.” CDM’s should be very close to your actual impacts in the field without any truing/calibration. However, if there are slight variations in your drag from the CDM data for that bullet, the Applied Ballistics engine allows you to true/calibrate the drag model using a feature called Drop Scale Factor (DSF). You can actually use DSF to scale the drag at various points in flight based on the bullet’s speed, which seems like a flexible and clever way to do truing. This past week, a friend and I used DSF to true the ballistics on our Kestrel’s using Applied Ballistics CDM’s for our 375 CheyTac rifles out to 2 miles! (Watch video of Litz explaining how to true your ballistics with DSF.)

Bullet-specific drag models should require less truing/calibration than if we were using a single number for a G1 or G7 BC, but a number of variables could slightly influence the bullet’s drag that are specific to an individual weapon/ammo combination. In some cases these slight errors in drag might “stack” and end up causing your solution to be off at some distances. In those cases features like the Axial Form Factor from Hornady, or the Drop Scale Factor from Applied Ballistics should allow us to do the final tuning on our drag models so our predicted trajectory closely matches our impacts in the field.

Personalized Drag Models: The Final Frontier?

What if you could measure the exact drag for your exact bullet fired from your exact rifle setup? Bullet-specific drag models are clearly a step in the right direction, but what if you could somehow get your hands on a super-custom, highly-personalized drag model for your specific rifle/ammo/bullet combination? Could that be the final frontier of predictive ballistics?

Here is a quick analogy of how I think about the progression of drag modeling that puts into context where we have been, where we are at, and what I believe all of this is actually leading us to:

Progression of Drag Modeling

While we’ve come a long way, and the technology and data we can take advantage of today is amazing – fully personalized drag models don’t seem to be farfetched. In fact, it seems like an obvious next step in the progression. “The most accurate way to ensure the best result with any weapon ammunition system is of course to test it with Doppler radar and use the drag data for that exact combination,” explains Dave Emary. “Unfortunately most of us can’t justify spending over $100,000 for our own Doppler radar.”

Okay, so there are some obstacles – like that whole $100,000 device! Plus we’d need the ability to turn the Doppler data into a drag model on my Kestrel or phone. However, this seems to be the way everything is headed, so now it’s just a question of how/when someone will bring it market. There are probably several ways, but, as a business guy, I can see at least a couple possibilities that could get personalized drag models in our hands:

1) Pay To Record Your Drag Events

One of the companies who own a $100,000 Doppler radar could host events at a few times and locations across the country and offer to take a couple drag measurements of your bullet fired from your rifle and give you back a personalized drag profile for $100 each. If you have 4-5 rifles chambered in different cartridges or have multiple loads, maybe they’d give you up to 10 personalized drag profiles for $500. I think it’d be a good marketing move for a company like Hornady, Berger, or others to show their commitment to helping shooters get more rounds on target. They might could even partner with major rifle matches or ranges like the NRA Whittington Center to have this as an attraction, or maybe someone like Applied Ballistics could add a “Range Day” to their seminars to provide this kind of service to attendees. Maybe you could ship your ammo and rifle(s) to them, and they’d send it back with a personalized drag model. I doubt any of this would pay for the device, but it could at least help offset the cost and ultimately pioneer a new approach to further the shooting community.

2) Advancements in Consumer-Grade Equipment:

I read an interesting study conducted by Elya Courtney, Collin Morris, and Michael Courtney that was titled “Accurate Measurements of Free Flight Drag Coefficients with Amateur Doppler Radar” (view PDF summary). All 3 of those researchers seem very accomplished, but for reference Michael Courtney has a PhD in Physics from MIT. In that study, they used a LabRadar, which is a popular consumer-grade Doppler radar that sells for $560, to experimentally determine drag coefficients for fired bullets. The unit takes multiple measurements of a bullet’s speed out to 50-100 yards, depending on the caliber of the bullet, and then it “reverse engineers” the data to determine what the velocity must have been at the muzzle to match the velocities it tracked down range. The researchers basically accessed the raw data the unit records, and did further analysis on it to determine what the drag on the bullet must have been to match how the bullet speed slowed over the first 100 yards. They used that analysis to come up with a BC for a few bullets at a couple different velocities. I spot-checked a couple of the calculated BC’s they published based on the LabRadar data against Bryan Litz’s experimentally measured BC’s in Ballistic Performance of Rifle Bullets – and was shocked to see that they were often within 1% of his measured value or less! Considering that the published BC’s from manufacturers can be off by 5-10% or more, that is really pretty impressive accuracy!

LabRadar to calculate BC

In the conclusion of the study, Courtney points out, “The LabRadar may provide a convenient and inexpensive means to check for drag changes in the first 50-100 yards without more expensive and cumbersome methods for measuring drag effects over longer ranges. The LabRadar may also provide rapid feedback on design changes or modifications, not only in the projectiles but also in barrels (Bohnenkamp et al., 2011). Use of the LabRadar on the firing line of long range matches may provide a Physics based approach to diagnosing dropped points.”

Courtney’s research is very interesting. It shows the potential a consumer-grade device could have in a few applications, but the LabRadar has some limitations we’d have to overcome if we wanted to take it a step farther and use it to develop personalized drag models that span the full flight of a bullet. First, the LabRadar only records a short window of the flight (50-100 yards), so if you want to record the drag at all velocities for long range, you’d need to load down your ammo to simulate a bullet that had slowed. While that sounds straight-forward, there are little nuances like something called “spin decay,” which just means the bullet’s spin rate slows as it flies through the air, and you wouldn’t be simulating that … unless you bought a bunch of barrels in successively slower twist rates. (Fun side note: Bryan Litz told me that is what he used to do to more accurately measure BC’s. He would order a pile of barrels in crazy twist rates that he calculated to match what the spin rate would have slowed to at certain points down range. Knowing that he went to that extent made me appreciate the BC’s he’s published even more. Thanks, Bryan!)

Second, remember we also saw that there was some drag induced early in flight with some muzzle brakes or certain gun powders that Dave Emary referred to as “tipoff”? In those cases the bullets typically recover from the initial launch conditions some distance from the muzzle and start flying normal. However, if there was something about your rifle/ammo system that caused that kind of “tipoff,” then the data collected from the reduced loads would also all have noise mixed into their drag data from that “tipoff” that wouldn’t have been present if the bullet was truly 500 or 1000 yards down range at that lower velocity, because the bullet would have likely re-stabilized by that point. Ultimately, if all the measurements come from within 100 yards of the muzzle there could potentially be noise mixed into the data.

Now, that doesn’t mean there isn’t hope! It simply means there are still challenges to overcome. To be clear, I personally don’t believe the current model of the LabRadar is the answer for us recording our own data that could be used to create an accurate personalized drag model for the full flight of a bullet. It is world-class at what it was designed to do: interpolating muzzle velocity from Doppler trace data it collects. I’m a HUGE fan of the LabRadar for that use. However, the internals of the device simply weren’t designed to track bullets over extended distances or to give high degrees of certainty in the drag recorded. That was an intentional design decision to keep costs down, and not a lack of knowledge on the part of the manufacturer. In fact, the LabRadar was developed by Infinition, which is the same company making the $100,000 Infinition BR-1001 Doppler radar that companies like Hornady, Barnes Bullets, and others are using to do the kind of research I highlighted in this post. Here is what Infinition says about the LabRadar:

“Infinition has been the industry leader in Doppler Radar Technology since 1996 with products being used by defense agencies all over the world. Infinition has unique expertise in Ballistic Instrumentation Radar Systems and highly sophisticated software for the capture and processing of a ballistic event. High quality innovative products and services, timely delivery and superior customer support have all contributed to gaining customers and establishing our solid worldwide reputation. Our radar systems include the most complex long range multiple target tracking systems to small laboratory range applications capturing tiny projectiles at ultra high velocities. From this technology the creation of LabRadar was developed for everyday use by individuals.

Maybe the next model of the LabRadar won’t be able to collect the data at the distances and level of detail necessary either – but what about the one after that? What about a different product a competing company will eventually release?

50 years ago virtually nobody would have guessed that we’d have come as far as we have, which probably means that we will all be surprised how much progress is made over the next 50 years. Dave Emary told me that he believes we’ve made more progress in ballistics in the past 5 years than the previous 75 year! Who knows where we will be in another 5 years?! And while we may not be able to fully account for all the little nuances I mentioned over the next 5-10 years, I have to believe the result will still be more accurate than what we have access to today.

Dave also shared that Doppler radar equipment has come down from $100k three to four years ago to around $75-80k today for all the equipment necessary to do the drag measurements we’re talking about here. That is obviously still out of the reach of consumers, but it represents a 25% drop in cost in just a couple years. While it may be a while until this professional-grade equipment drops into our price range, it just seems like a matter of time until we’ll have access to equipment with capabilities to provide us with “personalized drag models.” I’m hoping this article might even encourage some entrepreneurial engineers or creative problem-solvers to help bring that into existence! If nothing else, I hope it gives you a better understanding of how the drag of your bullet could vary from your buddy that is firing the same bullet from a different rifle.

How much does it really matter?

So how much do these slight variations in drag matter to the shooter? Well, I admit that I don’t really know, because much of it could vary from one weapon/ammo combination to another. Earlier today, I was having a conversation with a couple industry experts that are deep in similar research, and they basically said, “It depends on a lot of things.” I’d expect the only people who really care about the slight improvement personalized drag models could offer are those shooting small targets at extreme distances, especially if there is an emphasis on first-round hits. Even in those cases, the amount of improvement depends on the specific rifle/ammo/bullet, and it would be difficult to make sweeping generalizations about how much “better” personalized drag models might be. Extreme long range shooting is testing the limits of predictive ballistics, and this kind of research and development is on the cutting edge of that field. I’d suspect personalized drag models may have little to no measurable improvement for those shooting distances below 1500 yards. I hope more research is published to the public in the near future that help us gain a better understand about how the rifle or ammo components can affect a bullet’s drag. At the very least, I wanted to share with you guys these interesting developments related to long range precision rifle work.

Dive Deeper

There isn’t a ton of research like this published (at least that is accessible to the general public), but I do know a ton of R&D money is being put towards these kinds of topics. I’m hopeful (and fully expecting) more to be published in the near future to give us a better understanding. But if you’ve found this interesting, there are a couple things I’ve read that I’d suggest for a deeper dive:

Of course, if you want a more general overview of more technical topics like this, I’d highly recommend Bryan Litz’s books, and I’d definitely start with Applied Ballistics for Long Range Shooting. Bryan does a GREAT job explaining some very technical topics like this in terms that the average shooter can understand and apply.

Finally, if you are really, really into this stuff and want to get into the real technical details of it, I’d recommend Modern Exterior Ballistics by Robert McCoy. I got that book as a Christmas gift a couple years ago, because my family knows how big of a nerd I am! I’ve loved it, so it might be a great gift idea. I mean, who wouldn’t love a physics textbook for Christmas?! 😉

About Cal

Cal Zant is the shooter/author behind PrecisionRifleBlog.com. Cal is a life-long learner, and loves to help others get into this sport he's so passionate about. Cal has an engineering background, unique data-driven approach, and the ability to present technical information in an unbiased and straight-forward fashion. For more info, check out PrecisionRifleBlog.com/About.

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55 comments

  1. In light of recent ballistic research we are finding new factors affecting bullet performance. That’s good because then we can begin eliminating “BAD” factors such as muzzle brake designs that “tip” bullets.

    One factor I feel needs more investigation is INTERNAL BALLISTICS.
    ->For example how does the gentler engraving on a bullet of 5R rifling affect exterior ballistics, if at all?
    ->And does bullet jacket treatment with substances such as moly and HBN coating affect exterior ballistics positively? David Tubbs and many other noted shooters now feel HBN gives more consistent velocities from cold bore first shots and following shots.

    • Great points, Eric. There are still a lot of things we don’t fully understand about internal ballistics. However, Doppler radar research can give us new insight there as well. In conversation today, a friend was telling me about really high frequency Doppler radar that had the ability to track how the bullet travels through the barrel in high detail. It’s a little different than the Doppler guys are using to track bullets over long range, but is designed for higher resolution at much shorter distances. I’d bet that kind of research helps us find new insight in internal ballistics. Honestly, we’re JUST NOW able to record and understand events that are happening in the blink of an eye, and we can do at an impressive level of detail that is constantly increasing. So I fully expect us to continue to uncover nuances of things like you mentioned over the next 10 years.

      Dave Emary has published some research that shows how two different types of rifling produced two different drag profiles. It did show a difference in drag between a 5R barrel and a 6 groove square rifling barrel – but I will add the disclaimer that it seemed to be over a really small sample size, so I’d suggest more research would need to be done over a larger sample size to reach conclusions you could have confidence in. I actually talked to some industry experts about that specifically and they were skeptical that the rifling would have a significant impact on drag because “skin friction” is one of three components that affects drag, and it is a relatively small percentage of the total equation. They didn’t say it wasn’t plausible, but they thought more research across larger sample sizes would be necessary to ensure the rifling profile was the true cause of the difference.

      And the thing about HBN coating or other treatments like Melonite are that tests would have to be done with a large sample size of barrels, and over thousands of rounds each to reach a conclusion. I’m not sure we’ll have the answer to that unless a military put the cash into the research, and even if they did the tests the results would likely not be published for guys like us to learn from – unfortunately.

      So great questions! Unfortunately, this is probably all the insight I can offer – but I expect we’ll know a lot more about those things over the next few years. Certainly an exciting time to be involved in the long range community!

      Thanks,
      Cal

  2. Im very pleased with the advancements in ballistics these days. This article is a lot to absorb. Sort of like reading Applied Ballistics.
    I have been shooting close to 60 years, but the last 10 have definitely been the most fun. I thank Brian Litz for that. To be able to refer to my generated ballistics chart and dile up and be in the black all the way out to 1000 yards is something we only dreamed of decades ago.
    The science of shooting is where ths satisfaction is at.

    • Thanks, Kurt. I know this is a lot to absorb. I actually spent more time trying to take things out of this post than put things in it! I tried to be rigorous, but it is a pretty technical topic and I know I have a lot of critical readers who appreciate knowing the details, so I was trying to balance approachable/simple with complete.

      And we absolutely should thank Bryan Litz for his monster contributions to the advancements of long range shooting over the past 10 years. That is why Bryan was the recipient of the NDIA Carlos Hathcock Award in 2019 for his significant contributions related to small arms weapons systems which have improved the capabilities of the U.S. military. You know we’ve been making incremental improvements all the time, and so it’s easy to forget how far we’ve come. But if you take an honest look back at where we were 10 years ago compared to today … it is staggering!

      And I think the next 10 will be just as exciting. It just feels like things are accelerating. It’s not just the research, but the new products and improvements in precision machining that are pushing us forward. I saw some products over the past two days at the King of 2 Miles match that have me excited about what the future holds!

      Thanks,
      Cal

  3. Thanks for another very interesting article Cal. A key takeaway for me was on the second chart – a significant reduction in drag by using faster twist barrels, and the need to include barrel twist when trying to use custom drag curves.

    • Thanks, Dean. Glad you found it helpful. I will say that the generalization that faster twist barrels result in lower drag is a common idea, but not true in all cases. I had a LENGTHY side-conversation with a very smart guy about that before I hit publish on this post. I originally said something like that in the article, and that was part of the feedback I got when I reached out to a few experts to read over this before I published it. He taught me that the optimal twist rate where a bullet will achieve it’s full BC potential comes down to that bullet’s specific geometry, and that is highly predictable based on the bullet design. Even if you had bullets of near equal weight and similar but not exact geometries, one of those bullets could experience higher limit cycle yaw effects than the other from the same exact barrel. His big point was that it’s all deterministic and has known explanations behind it, but the statement that faster twist barrels produce less drag is an over-generalization that he felt strongly just wasn’t true.

      My perspective is that traditional barrel twists (like those available on factory rifles) typically are too slow to properly stabilize the long, heavy-for-caliber bullets we use for long range work, and I’d bet it’s rare to achieve the full BC potential of those bullets without going to faster twist barrels. That is not true universally, but is the reason I usually lean towards faster twist rates in general.

      I will say that Bryan Litz has some research on this topic in Modern Advancements in Long Range Shooting Volume 1, which I think gives the most complete research and insight into the topic of twist rate and BC’s. It’s an awesome read if you haven’t seen it. If you liked this, I can guarantee you’d be into those Modern Advancement books.

      Thanks,
      Cal

  4. Cal:

    Since you only learn physics by doing problems, I would recommend Carlucci DE and Jacobson, SS “Ballistics and Design of Guns and Ammunition”. Sections on Interior Ballistics, Exterior Ballistics and Terminal Ballistics. I would say this book is a good prerequisite for understanding McCoy.

    The Introductory Concepts Section for Exterior Ballistics contains the wry comment. “The projectile in flight is no longer constrained in lateral motions by the walls of the gun and, as a free body, can develop motions that are complex and occasionally inimical to the intent of its user and embarrassingly, to its designer.”

    Rick

    • Hey, Rick. Great recommendation. I own that one as well. It’s actually where the featured graphic at the top of the last post came from. Both are great resources for different reasons. And that’s a fantastic quote. Absolutely true and well said. Thanks for sharing.

      Thanks,
      Cal

  5. Barrel stiffness is also a big part in this.

    • Hey, Jack. That’s an interesting point. I agree that the precision of the barrel is important to getting first round hits, but in this article I was primarily talking about the “Final Frontier in Predictive Ballistics” and by that I mean the science and math that goes into predicting how the bullet will fly once it’s left the muzzle. Barrel stiffness (or lack thereof) can impact the precision of the rifle and maybe even the location where the bullet exits the muzzle, but I’m not sure it affects the drag of the bullet. I’m not an aerospace engineer, so I could just not be aware of the connection there.

      What is really interesting is the correlation most people see between the stiffness of a barrel and precision. Have you ever read Harold Vaughn’s research related to barrels? You might find it really interesting. His book Rifle Accuracy Facts is a landmark book of his research, but unfortunately it’s not in print any longer. However, I noticed you can find a PDF version online. You might check it out if you haven’t read it already. Chapter 4 covers barrel vibration. Here is a link to the PDF I was able to find: http://storage.dynamic-arms.com/t-class/books/Rifle%20Accuracy%20Facts%20Full%20v1.1.pdf

      Thanks,
      Cal

  6. Cal, no mention of it here (rightfully; this is an important article by itself), but how do Emary’s statements re: muzzle device/gas tipping and down range re-stabilizing, impact your earlier posts/discussion/research on the whole ‘bullet going to sleep’ argument? It seems like a shoe-in to reignite that discussion.

    I have NO dog in that fight – just immediately (thought I) recognized the similarities.

    Thanks for all you do for the LR community.
    Brad

    • Hey, Brad. Thanks for the kind words. As far as the comment about the “bullet going to sleep”, you’ll have to remind me where we had that conversation. I tried to think of a post where I’d talked about that, but couldn’t remember. If you’re talking about the idea of group convergence (i.e. shooting smaller groups at further distances), I’d have to defer to the definitive research Bryan published in Modern Advancements in Long Range Shooting Volume 2. He went to the ends of the earth to try to reproduce something that would do that, and wasn’t able to. This is more that the drag is increased early in flight because of yaw that eventually dampens. Some initial launch conditions can amplify that more than others. It’s like when you spin a top; it will stabilizes and smooths out after a brief moment from the initial spin. Of course that isn’t a perfect analogy, but it might be helpful.

      If I’ve totally missed the point, please just point me back to where we’ve had that conversation. My memory is terrible!

      Thanks,
      Cal

  7. You have provided a rare publication:
    1. Well thought through
    2. Well researched and referenced
    3. And practically applied.

    I commend you for your efforts and thoroughness. It is a landmark article in this this field for those of us “practical” long distance shooters from 1000-1500 yards.

    Your efforts are commendable and highly recommended.

    Well done!! It is a great satisfaction to see someone take the time and effort to produce something like this! and not just marketing tripe!!

    • Wow, Terry. I really appreciate you saying that. That is exactly what I was going for. It did take A LOT of time to try to put all this together, so I appreciate your encouragement. I try to be intentional to cover the three points you mentioned, and stay away from the marketing hype. Thanks for noticing that and taking the time to give me the feedback.

      Thanks,
      Cal

  8. Nico van der Merwe

    Great article

  9. good job , it’s a good post ,thanks for sharing

    Unfortunately, mathematics has some difficulties for me. I can’t always understand formulas and too many charts quickly.

    • Thanks! I know it’s a lot of information. Honestly, it took me a little while to really understand how all this stuff applies, but I hope I presented it in a way that makes sense.

      Thanks,
      Cal

  10. Cal,
    I am a physician and have to sift through a tremendous amount of crappy literature to come to the few that make a difference. Your work fallls in the A category of believability. In my world that means it’s worth taking home and modifying my workflow!

    Well done… a second time!!

    Terry

  11. yes , of course .
    Your contribution is meaningful. For shooters who love long-range shooting, this information is very educational.

  12. Hi, , I am in the UK and, although I don’t shoot any disciplines, I find all your articles of interest, regarding your latest about drag factors I saw that muzzle breaks can have an effect does this also apply to silencers?
    Best Regards,
    Glenn Phillips

    • Thanks, Glenn. I’d assume it could apply to any muzzle device. If it changes the muzzle gas cloud then it has the potential to have some affect on drag – at least that is what seems to make sense in my head. I haven’t seen hard data on it though. It’s certainly a great question. Like brakes, I’m sure some are better than others at that.

      Thanks again,
      Cal

  13. Cal, probity requires I declare a proprietary interest in your articles. (I too have all the reference materials identified, and a few more besides!) I’m hugely impressed with the material you produce, and have had my eyes opened on more than one occasion. Sincere congratulations to you, and I would like to express my gratitude for the generosity of your technical supporters. There are a couple of (minor) details, where our R+D have come up with divergent results, but we would need a more substantial data base to address them publicly in this company!
    My biggest concern with the focus on ELD as it currently stands, is the convergence of objectives. Long range target shooting and M/LE are perfectly legitimate objectives, but we now see ELR objectives being applied to hunting, and this rings alarm bells. When distances exceed 1,500 m, there are very few (if any) rifle/cartridge combinations that are capable of delivering the minimum yard stick energy and projectile expansion velocities required for a humane kill. Then there are the Time of Flight implications and other variables. Whilst I sincerely appreciate that there a few long range hunters that take the time to learn these things and accept responsibility for their actions, there are a great many more aspirational ELR hunters who have yet to consider these concerns. Gentle recognition and occasional reminders of these limitations bring integrity to our efforts, whilst we simultaneously seek to stretch the boundaries of our current paradigms.
    It’s a sensitive issue in many ways, but we are now able to shoot accurately over far greater distances, than we can reliably deliver humane outcomes for game. 1,500 m is a very long way away to try and resolve unfortunate outcomes, especially in less than ideal circumstances.
    Thank you for your work. The standard and openness is most highly regarded!

    • Stephen, glad to hear that this was helpful. I do agree with your points about the danger of blindly applying this to hunting situations. I originally got into long range shooting because I was a hunter looking to ethically extend my range, but I’ve never taken an animal at anywhere close to 1500m. But that isn’t a magic line, because like you said, what the ethical range is depends on the conditions. I’ve always thought of it as the distance where I could put 10 shots out of 10 on a 10” pie plate. If I don’t think I can do that, I don’t take the shot. Pressure in the moment and environmental conditions add enough uncertainty to the equation.

      I’d love to see your research. It seems like a lot of people are doing research, but not publishing the results for the public to learn from. I’d encourage you to share what you have. Thanks for the comments!

      Thanks,
      Cal

  14. Mahmoud A Shmaitelly

    Cal,

    I am really delighted to read your Article. It is superbly written. As a scientist, I got enjoyment by learning something I did not know. It is my first time I learn the selection of the gun powder would affect the Gyro stability and drag function of a bullet.

    I applaud your efforts and appreciate your desire to publish, Cal.

    Mahmoud

  15. You did it again Cal, caused my brain to spin when I was trying to get it to stop. Great info, always enjoy the scientific aspects to shooting accuracy. In your article, speaking of muzzle brakes, James talks about annular clearances between successive ports. We know muzzle brake design can greatly reduce recoil, felt recoil, muzzle rise, etc. I always felt that muzzle brake design affected accuracy. If I made a brake that had side and top ports, my thoughts are that would be great for 3 gun, or fast types of shooting where first round accuracy or distance accuracy wasn’t as much of a concern. However, I feel that Newton’s third law, ‘for every action there is an equal and opposite reaction’, comes in to play. In this case, it would be gases and the affects of may have on the bullet and accuracy. All that aside, my mind was wandering, my real question is about bore diameter in relation to bullet diameter and how this may affect accuracy. I know speaking to some shooters, if they have rifles in 6mm, 6.5mm and .308, their thoughts are to just get a muzzle brake that is for a .308, that way they can use it on any of the rifles and don’t accidentally put a 6mm brake on a larger diameter rifle. So, say I have what is believed to be proper annular clearance in port design, will a brake that is designed for a .308 be as accurate (I’ll leave efficient out of this since we’re discussing accuracy) on a smaller caliber or is there an ideal bullet diameter to muzzle brake bore diameter ratio?

    • Ha! I know it, David. I’m the same way. Some of the conversations I have with industry guys make my head spin, and I spend the next couple months thinking about something they said. This has been on my mind a lot over the last couple months, although I had been reading and talking about this for a year or two before that. There are a lot of industry leaders that are having conversations about this very topic, and I bet we hear a lot more about it over the next 2-3 years.

      You have some good points. The only one of your questions that I have hard data on is related to the effectiveness of a muzzle brake based on the caliber of the hole. I actually did the pioneering research on that topic myself! Here is an excerpt from my muzzle brake test that speaks to that exact point:

      I ran tests to see how much it mattered if a muzzle brake was caliber-specific, and those results were also surprising. I tested the effectiveness of having a caliber-specific brake on 4 very different muzzle brake designs that I had in all calibers: the APA Little B*, Holland 1.25” Radial QD Brake, Impact Precision Brake, and West Texas Ordnance Brake. I only found an improvement of 1-3% if a brake was 6mm rather than 30 caliber (7.62mm).

      To be clear, I tried the 6mm, 6.5mm, and 30 caliber brakes all on the 6XC, and in all 4 muzzle brake designs, there was only a difference of 1-3% in recoil reduction in terms of both overall momentum and peak force. That surprised me. I expected the caliber size of the bullet hole in the brake to make more of a difference. But, that’s why I actually run the tests and don’t just talk about this stuff!

      Honestly, that was buried in one of many posts about that test, and I should probably do a post that simply spotlights that one fact, but I still come across a lot of people that aren’t aware of that. One of my readers who is a wicked smart engineer tried to give a technical explanation for what that is in the comments of that post. The only thing I can say for sure is I only measured a 1-3% difference in recoil, which is not perceptible. So I, like your friends, have started buying 30 caliber brakes and not worrying about it.

      Now, does the size of the hole matter for this conversation related to “tipoff” at the muzzle and changes in drag. The short answer is I have no idea. I have some thoughts, but I’m not an expert on the subject. (I actually know a couple experts who said they read all my comments like this, so please chime in. 😉 ) I will try to share what is going through my head, but keep in mind I might be wrong about all of it! I’d think if the holes were concentric, it might not matter dramatically. But as the bullet passes through a hole (or you could think of it as going through a ring), the pressure around the bullet changes. If a 6mm bullet is going through a 6.05mm ring, the pressure around the bullet likely changes more dramatically if it was going through a ring with a 6 inch diameter, right? I’d expect the more clearance that is present between the surface of the bullet and the ring it is passing through, the less it would affect the bullet. Now, how much less? What kind of clearances or ratios are we talking about? No idea. 😉 Maybe someone smarter than me will chime in on that, or we’ll just have to wait for further research to be published on it. There is still so much to learn!

      Thanks,
      Cal

  16. Cal, the following is in response to your request, and provided solely on the basis of our results to date. They are hardly definitive.
    We are manufacturers of lathe turned copper bullets (Outer Edge Projectiles) in Australia. The point of divergence is with Dave’s comment about meplats of sub 1.7 calibres. Given Dave’s experience and qualifications, I am reticent to argue the toss. I can only share the anecdotal findings so far.
    We have tested, three projectiles with meplats of 1.16 (338) and (1.27) with very encouraging results. One was even sub 1.0 cal
    The 308-11-155 RBT fired from a 308 Win (Blaser R 93), achieved 28 hits in a row on clay targets at 1,275 m. (yes, it was a purple day for conditions!)
    Similar results were achieved with the 338 (Lapua). At 2,000 m, the Lap achieved very encouraging results on a 380 mm target.
    It is our suspicion that the issue with a sub 1.7 cal meplat has less to do with dimension, and more to do with precision and fragility. A sub 1.0 meplat, no matter how well made is prone to distortion through anything but the most judicious handling, and thus reintroduces dispersion. It takes very little damage to have quite a profound effect.
    Our caution in these statements is that these results are limited to just over 1,000 rounds for all three ‘tests’, so they are hardly definitive, and our testing continues. Whether these results are copper vs jacketed lead relevant, we have no idea.
    When the BBT hunting versions of these bullets are used, the effective range is halved. Not for accuracy, but the limits for velocity expansion, and minimum energy requirements for a humane outcome fall below the minimum expectations.
    Keep up the good work!

    • Stephen, I really, really appreciate you sharing your thoughts and findings. If everyone in the industry were so forthcoming with their findings, I know it’d help us learn more in half the time. I wish we were more collaborative, but it seems like most people either don’t want to put themselves out there for fear of criticism or they protect it as a proprietary competitive advantage. Both are small thinking, so I appreciate you being so open.

      I’m actually not sure how Dave arrived at that number. I have an idea, but it gets really technical. I think Bryan published some data on how much pointing bullets affects BC’s in Modern Advancements in Long Range Shooting Volume 2. I’ve been at the King of 2 Miles competition, so I don’t have my books with me to reference. I do remember he talked about his findings at one of the Applied Ballistics seminars, and there just wasn’t a significant improvement in BC. It was marginal at best, and far less than I expected it to be. It seems like that corroborates Dave’s comments about the size of the meplat, in that pointing bullets has a diminishing point of returns, so to speak.

      But honestly, your explanation is a good reason as well. I can totally see how the mechanical issues related to manufacturing bullets with really tiny meplat, and not just that but the handling of the bullets all the way to the moment they slide into the chamber can cause distortion. Honestly, that’s as good of a reason as anything!

      That is also very interesting about the effective range being halved in hunting situations. That makes a lot of sense. I do think we’ve reached the point that more people need to be thinking that just because you can hit something way out there doesn’t mean your bullet will have the terminal performance it needs for a “humane outcome” (I like the way you worded that). So I appreciate you pointing that out.

      Stephen, once again I appreciate you sharing your observations. Over 3000 rounds of data is more than anecdotal, but I agree that it is still probably short of what we could draw firm conclusions from. However, that doesn’t mean it isn’t still helpful, so thanks for sharing!

      Thanks,
      Cal

  17. Cal,
    After reading this article and all the questions and your detailed responses I almost wanna say, “My head is full.” ;o)
    Your comment that most manufacturers have rifling twist rates that are too slo (for the bullet weights commonly used with the cartridge) is likely true.

    But not for all rifle manufacturers.
    Ex. I notice that while Browning’s 6.5 Creedmoor X-Bolt Pro (22″ barrel) has a 1:8 twist their Long Range version (26″ barrel) has a 1:7 twist, figuring those shooters will want heavier bullets for longer ranges and better BCs and lower CD numbers.

    As well Browning’s new 6.5 PRC X-Bolt Pro rifles comes with a 1:7 twist.because they likely figure this “6.5 CM magnum” will usually be shooting heavier bullets and they will be going 200 fps faster than the 6.5 CM with similar bullets.

    Seems new cartridges AND new ballistics are having an intersection with the more up-to-date rifle makers.

    • You are exactly right, Eric. That was true in general, but I have noticed Browning in particular is quicker to adapt than just about any other manufacturer. If you watch, they are typically always one of the first manufacturers to start offering new cartridges as a standard chamber offering. I actually have been very impressed with how up-with-the-times Browning has been when it comes to advancements in long range rifles. You don’t see that in a lot of larger, well-established companies. As a business guy, I know how many obstacles there can be to change in a large organization, even though they may seem trivial. I’m definitely impressed with Browning.

      But, outside of Browning and maybe one or two other exceptions, go look at the other big names and the twist rates they’re selling. I think you’ll see what I’m talking about, especially in more traditional calibers like 30 or 22 caliber, or ones that were well established 20 years ago like 7mm. Those are almost always slower than ideal. 6.5mm is a more recent phenomenon, so I’d expect those twist rates to not be as far behind. I think if you compared the average twist rate that comes on a factory rifle in a particular caliber and then compared that to the twist rates that custom barrel makers are selling for that same caliber, you’d see that factory barrels were slower twists in general. The shooting community has become more capable of engaging further targets, and many have moved to heavy-for-caliber bullets to extend their range even further … but most manufacturers just haven’t kept up. But Browning and a few others have. 😉

      Great points! Thanks for sharing.

      Thanks,
      Cal

  18. Unless there’s more samples that are not represented, the Drag Variation by Muzzle Brake and Powder Type plots are very concerning, as the ES in the drag of the bullets as well as the nuances in the Cd v. Mach curves are nearly identical to that of the single bullet fired 10 times with no experimental variation.

    One wonders if the variation observed due to Muzzle Brake and Powder Type exists natrually as the drag variation inheriant in the that type of bullet, or if it’s truely the cause of some external influence. I’ve observed much higher drag variation with plastic tipped bullets of all types (e.g., Sierra, Hornady, Barnes, etc.) than with standard OTM or lathe-turned designs.

    • Hey, Zach. I don’t look at drag data from Doppler all day, so I was really basing all of this on what Dave said was significant. He does work with this kind of data all the time, so if he said it was significant … I took it as significant. In regards to the powder variation, he literally said “Differences here are substantial.” Then here is what Dave Emary said specifically about the graph with the 10 consecutive shots: “As can be seen the uniformity of the drag performance is not very good and would certainly lead to elevation variation on target at longer ranges. Ultimately the drag curves should all nearly lay on top of each other. This is usually never realized but it should be substantially better than the projectile shown in the chart above.” I’m just trusting the expert here. I will say that other research seems to corroborate the results as well. If it was just one guy out there saying it, I wouldn’t have the confidence to publish this. But there are multiple reputable companies doing research in this area, but Dave’s work is the only one currently available to the public and that I have permission to talk about.

      I do think you’re on to something with the plastic tip bullets showing more variance. I wouldn’t be surprised if further research shows that pretty clearly. This is a complete guess, but I wonder if that plot of the 10 consecutive shots was from the data they uncovered that led to Hornady redesigning their tips because they were melting. I’d expect that you’d see some strange variances in the data down range, maybe not unlike what is shown on that graph. Then again, that is a complete guess. I know there are a lot of strong opinions whether that is what was happening or not, but I believe it was. I think where/how the bullet deforms is consistent enough within the same environment that shooters don’t notice it or simply true their ballistics to account for it. We think the BC is off or maybe the calculator and gloss over it. We are so quick to blame the firing solution, but what if the firing solution is right and something really is changing with the bullet itself that is causing the model to diverge from what is really happening mid-air?

      Anyway, kind of got off on a tangent there. I do appreciate you sharing your well thought-out comments. Those are great points. I can tell you I had some similar thoughts, which is why I wrote “While these tests seem to be on a small sample size, they help us understand how various factors related to the weapon and initial launch conditions can affect the drag a bullet experiences. More research is necessary to draw meaningful conclusions.” My bet is there will be a lot of research published in the next 2-3 years that corroborates this data and gives us further insight. This was pioneering research, and like most real science … it often uncovers more questions than answers. That’s just the truth of it!

      Thanks,
      Cal

  19. Cal,

    Really awesome article, even more than most you write, which is a high bar. I never would have thought that muzzle brakes would affect BC, but the mechanism of inducing yaw makes sense. What I’m trying to figure out is the part right below the bolded section:

    “Particular attention should be paid to reducing the annular clearances around successive gas ports (or within the baffle or supressor).”

    Is this saying that in your (very impressive) muzzle brake test, while there wasn’t a recoil improvement from e.g. a 6.5mm brake vs a 308 brake, that there would be in the early BC and ultimately in accuracy? If so, any chance data from that test could be re-analyzed for that? I’m now tempted to order both sizes of Lil B’s and test with my LabRadar.

    • Eric, I really appreciate the kind words. I had the same reaction to this research initially, but like you said … it is a short road to get there and understand that it’s more than plausible.

      And, that is a great point about the muzzle brake test. I don’t remember testing the precision of the brakes. I did a lot of tests, but not that. Most of the test shots for that research were done in that test fixture I made with the sensor attached to the butt of the rifle, so I wasn’t shoulder firing it for precision. Most of the time the rifle was just firing rounds into a berm.

      It seems to me that as long as the machining is concentric or perfectly mirrored on both sides, then yaw would be minimized … or at least not amplified significantly by the muzzle brake. Now that isn’t Dave or Litz talking, those are my own thoughts, so take them with a grain of salt. I’d imagine some machinists are better are tolerances and concentricity than others. I actually think that could be why Dave was leaning toward the American Precision Arms muzzle brake design as having the least impact on drag. I’ve talked to the owner, Jered Joplin, several times since my muzzle brake test and that guy has a higher attention to detail than most other gunsmiths I’ve met. He doesn’t seem to be as quickly satisfied that something is “within tolerances” and has spent a lot of time creating jigs to ensure operations are repeatable and done consistently every time. So I wasn’t surprised that Dave pointed that one out as the best performer from the few he tested.

      And hey, I’d love to hear your results if you get the bug to test it out yourself! This is pretty interesting stuff, and there is still a lot to learn and explore. That’s why I was so excited to share this research with all my readers.

      Thanks,
      Cal

  20. This is an extremely interesting article. It seems to be carrying Litz’s work into other areas. As a casual long range shooter, reloaded, and rocket scientist (you can determine which one is casual), I do have several comments:

    1. The figure showing the drag variation with the same bullet may potentially invalidate the figures above. It looks like bullet to bullet drag coefficient variation is greater than the influence of other factors (powder, brake, etc). In fact, how does the study discriminate between, say, variation due to powder, from the bullet variation? I hope that the drag coefficient variation is actually the average of multiple bullets so that effects due to bullet variation are averaged out (assuming the factors are independent). I may have missed it, but I didn’t see this mentioned.

    2. Others have touched on this: internal ballistics probably are an underlying mechanism. For example, yes, the study shows drag variation with different brakes (assuming the results were averaged over many bullets). But, each brake weighs more.m, and hence, changes the resonate frequency of the barrel. It could be that the differing brake performance is not due to how they are designed, but is due to some brakes being closer to an optimal resonate frequency than others. Ditto for the powder study.

    • Hey, Serac. I appreciate the thoughtful comments. You’re clearly a sharp guy, so I actually take it as a huge compliment that you read my articles and find them interesting. I totally understand your points, and can’t say they aren’t well-founded. Honestly, I had some of the same concerns, but I can say that other researchers have corroborated the findings (like what physicist James Boatright said about the muzzle brakes). If this was the only study I’d seen that made these points and hadn’t had similar conversations with other respected researchers, I probably wouldn’t have published it. In fact, I originally had one or two other charts in there that were very interesting to me, but the sample size seemed small and I couldn’t find any other ballisticians/researchers who had found similar effects … so I decided to cut it from my article. It’s not that it wasn’t true, it just seemed lower confidence than the other data. Unfortunately, I’m not free to publish all of the research I’m aware of, but I can just say that I’m hopeful more research will be published to the public in the near future that will further our understanding in these areas. I simply wanted to start the conversation, and help bring the shooting community in on some of the conversations that are going on in research circles behind-the-scenes.

      And that is a very interesting point about this being related to the resonate frequency of the barrel. I was at the King of 2 Miles competition at the Whittington Center in Raton, NM for the past few days, and had a chance to have a few in-depth conversations with John Baker, owner of TacomHQ. John is the engineer who invented the Charlie Tarac, which is a proven optics product used by serious ELR shooters and deployed world-wide in the military. John is a super-sharp guy, and it was one of my favorite conversations for the whole year, because he challenged the way I thought about a lot of things, especially when it comes to resonate frequency in barrels. Over the past couple years he’s been working on a “structured barrel” and I got a chance to learn about that, and actually shoot behind a few guns outfitted with his barrel this past weekend. I want to do some further tests on it, but I’ll just say my initial impression is “WOW!” There is a lot going on with that barrel, but a huge part of the design was to interrupt/disperse/diffuse barrel vibration. You can actually feel the difference in vibration and recoil when you shoot. The barrels also have 400% more surface area than traditional steel barrels and deep “breather ports” along the bore that help is stay MUCH cooler over long strings than traditional barrels. We fired 10 shots of 375 CheyTac ammo from one barrel, which would normally heat a barrel to 150+ degrees … but we monitored the structured barrel after that string and measured a max temperature of 86 degrees. Where a traditional barrel would be too hot to grab after a string like that, the structured barrel was only mildly warm to the touch. But the harmonics part is what is really interesting. Some people have done load development on them and they say the point of impact doesn’t shift at all from load-to-load. John carries around multiple kinds of factory ammo, with different bullet weights and muzzle velocities, and they all hit the same point of impact, which I’d think is related to the difference in the resonate frequency of the barrel compared to traditional steel barrels.

      I think you’d find the structured barrel very interesting. Here is a video that highlights some of the 3rd party analysis that has been done on the barrel:
      https://www.youtube.com/watch?v=0_v8b2H2_TE

      Anyway, thanks for chiming in an sharing your thoughts. I definitely can’t say you’re wrong about any of it. They’re all good points. The truth is we’re just now getting the equipment to really understand and record events that happen really quickly and were impossible to capture in the past. Bryan Litz and the Applied Ballistics team have a couple Dopplar radars setup at different frequencies that can track the bullet’s flight in extreme detail out of the muzzle and all the way out to where the bullet hits the ground, and they’ve even combined that with slow-motion ballistic cameras down range to get actual photos of bullets in flight down range to gain new understanding in nuances of a particular bullet’s flight. This is stuff that was completely impossible just a few years ago, but now we’re able to measure and observe at a whole new level. I believe we’ll learn more about bullet flight, and some of the aspects you touched on, over the next 5 years than any other time in history. Which as a guy that loves to learn, that makes me pretty excited. Thanks again for the thoughtful comments and kind words about the content.

      Thanks,
      Cal

  21. Thanks for the reply, Cal. I’ve been a long time reader, but lurker, only.

    I agree that this is the first step. And honestly, even if they didn’t average across bullets, the relationship looks to be there. This is great data. I’d really love to see the same study done with averages across multiple bullets (preferably, more than 10). The next step would be to look for cross interactions – maybe one type of bullet is less sensitive to differing brakes than others? That is certainly down the road. These researchers are on a good path. A large Design of Experiments is the next logical step. It isn’t easy there are so many potential factors – bullets, meplat, powders, brakes, bullet seating depth, neck tension, primers, twist method, twist rate, twist direction, progressive twist, barrel harmonics (frequency and mode), and temperature. And I’m sure I missed some!

    I’m a big fan of the structured barrels! I’ve never seen one, and never been behind the trigger. But, I do subscribe to the concept. I want to get one, someday (for reduced harmonic sensitivity, but also, better heat dissipation here in the Southwest USA!). Back in the day I used barrel tuning methods with great success in three position competitive .22 and air rifle. I could feel a difference in the gun with a tuned barrel. I’m sure the structured barrels feel remarkably different on center fire.

    Thanks for this great blog.

  22. Cal – How accurate are the down range MVs reported via ShotMarker and Silver Mtn electronic target systems that are listed on the electronic score sheets. Can those supersonic readings be used for custom drag modeling?

    • Dan, good question. I honestly don’t have clue. Unfortunately, I’m not familiar with those.

      Can anyone else reading these comments speak to the accuracy of those systems?

      Sorry I couldn’t be more help.

      Thanks,
      Cal

  23. I’m not as pessimistic about consumer grade Doppler drag modeling.

    If you have a bullet specific custom drag model from the manufacturer and Doppler measurements from a Lab Radar, it seems like you could true up the right hand side of the graph with the Lab Radar and then use DOPE to true up the curve from there until the transsonic region using some type of fudge factor like the Axial form factor mentioned above.

    It wouldn’t be perfect but as others have mentioned, it seems like the variability is high enough that you’re never going to get perfect even if you measure and recalculate your drag model after every shot.

    • Good point, Dan. It’s still a form of truing, versus measuring your actual drag … so that is all I was saying. The end I’m talking about ideally would have zero “truing” involved, but the measured drag from the actual bullet from your weapon over the entire flight. So it’s not that you couldn’t use it in more advanced ways to help with truing like you suggested, so good point.

      Thanks,
      Cal

  24. I apologize thoroughly for asking this question under the wrong topic. I am new to this incredible site, my question is why didn’t any of the shooters competing in the King of 2 miles shoot the 408 Cheytac? Again my sincere apologies I realize that thread is old and I am hoping someone could educate me. No doubt the 416 and 375 are incredible but is there a specific reason? Thank you in advance,

    • John, the 408 CheyTac really doesn’t give you an advantage ballistically over the 375, and there also aren’t as many good bullet options. That’s why most guys land on some variation of the 375 CheyTac. The guys using 416 are optimized for being able to spot their bullet splash more easily at extreme range, which is a huge deal to getting on target at ELR. The 416 not only has a bigger bullet, but more case capacity to push that bullet. The 408 is caught somewhere in no man’s land. It’s still quite capable, but not as capable as either of the other options … which is why very few choose that cartridge for ELR competitions.

      Thanks,
      Cal

  25. Cal – These systems record the bullet MV (sonic crack) as it passes through the target. Each system has a chronograph function from the four corner sensors on the target frame and lists the bullet MV at the target (300 yds, 600 yds, 1,000 yds, etc.). The average MV for the string shows on the electronic (tablet, laptop, phone) score sheets which the shooter can capture via screen shot for later review.

    I’m an F-Class shooters and these systems are becoming more common at some of the ranges. If you can send your regular email address directly to me, I’ll send some links to the target systems and some screen shots that illustrate what I’m talking about – Thanks – Dan

    • That is pretty interesting. That would be really helpful in ELR matches like King of 2 Mile. I was actually talking with the Applied Ballistics team about how cool it’d be to setup a wind array on that mountainside to record the wind speed and direction in 3D over the course of the match. Obviously monitoring it during the match would be illegal, but maybe after the qualifying round you could publish the data and a shooter could go look at what the wind was doing at the time they shot to better understand what was happening out there, and what caused the bullet to behave like it did. Honestly, there are some crazy winds (including vertical winds) along that ridge, and it’d just give you a little better understanding like the system you are talking about.

      There are some guys at ELR events like that who shoot with a MagnetoSpeed chronograph attached, so they can have live feedback on shot-to-shot muzzle velocity. If you struck went high above a steel target at 3,000 yards was it because a wind you didn’t see or your muzzle velocity was 10 fps faster than the average (and should therefore send the same shot without correcting). I personally was planning to run like that, but my MagnetoSpeed went down the week before the match … and the extreme spread of my load was 12 fps (SD around 4-5 fps), so I wasn’t expecting to see much variation with that load. I will say that I bet I have a MagnetoSpeed attached at the next ELR match, because there is always that little thing in the back of your mind that makes you wonder if you missed because of variations in muzzle velocity and knowing what it was on each shot would at least help you know whether that was true or not.

      Ultimately this is a fun game, and there are always unknowns. That is part of why it’s so challenging, but the more we can record/observe the more we can understand why a bullet flew the way it did. There will always be unknowns (at least I bet there will be), so measuring MV like you’re saying or measuring the wind during the match would just be ways we could flesh out a couple more “knowns”, which might help us better understand the remaining unknowns or be able to better quantify the variability in the weapons and components themselves.

      Anyway, I did send you an email, so please forward me the links to some of the products you’re talking about. I’d like to at least take a look at them. Thanks again for the comments.

      Thanks,
      Cal

  26. Cal,
    Thank you so much for educating me. I just remembered when the 408 CT came out. It showed so much promise. I thought it would be ideal for that type of event. I personally would go the 375 CT route but her in Louisiana I am damn lucky to be able to shoot to 1200 yards and it’s a 4 hour ride every other weekend. Shooting the 375CT at that distance just doesn’t make much sense when I can reach that with much less expensive options. Again thank you so very much for your time. You do an incredible job with this site, I have already learned so much from reading your posts.

  27. …great article and discussion !!! …adding one more to the Doppler bits — could not several LabRadars be used, at different distances from the firing position, say every 100m or 200m (and along the flight path) to measure the velocities and then use that data to back out the Cd ?

    This would still be more than a guy like me could afford, but could not too out of range for an group ?

    …just to worn pennies..

    -NJ

    • That’s a great idea. They have to be near and aligned with the bullet path, but you could probably slightly overlap them to make it work. To get the full bullet path, you’d need a lot of them … but it’d certainly still be less than $75,000! Maybe that’s another path forward. If they could be daisy-chained or maybe through a wireless mesh network, you could just buy more units to extend the observation range, and maybe the software could stitch it all together as a continuous measurement for analysis.

      I’d bet $100 someone from Infinition is reading these comments, so maybe this will become a feature in a future version. Thanks for sharing!

      Thanks,
      Cal

  28. The problem with a string of lab radars is. They must be near the muzzel of the rifle to trigger. Although the can be triggered by the projectile, the instructions claim thats not as accurate. Some time its difficult to get them to trigger anyway. If they gef a little out of alignment they will not trigger.
    Sorry to dampen the moment. When the cost of the more elaborate equipment comes down this will get easier.

    • Hey, Kurt. You make a good point. It would be hard to make it work with the current model, but I was suggesting there could be a new feature in a future model where they are linked together, and in that case the unit near the rifle that is first in the chain could trigger the rest. I admit it may not be the answer, but it’s an interesting idea. Waiting on a more elaborate piece of equipment might be the best option for some, because it is clearly simpler, more convenient, and would be more seamless … but that could be 10+ years from now, so we’re just trying to brainstorm ways you could get it in people’s hands sooner.

      Here is a little better explanation of the rough idea (which I openly admit is still half-baked). What if they added the feature to “extend” the system with additional units similar to Google’s Mesh Wi-Fi systems that you can purchase to cover your home in Wi-Fi? You can read more about those at the link, but that system is basically multiple Wi-Fi points that work together to create a connected system that gives you a strong signal throughout your home. From your phone or laptop’s perspective, it’s just one big network. If you need more coverage in your backyard, you can just add another Wi-Fi point. The cool part is how simple it is. You basically just plug it in wherever you want to extend the signal, and the new unit will automatically communicate with the other devices and create an extension of the system to cover that new area. If you were in the basement and went up to the 2nd floor, your phone or laptop would be seamlessly handed off from one device to the other so it had continuous connection all the way. The device would be communicating as if it was one big system, but in reality it might be talking to unit 1, 2, or 3 … the system makes all of that transparent to the user/device. (Note: There are lots of manufacturers doing this, like Ubiquiti and others, but I just use Google as an example.)

      What if a LabRadar (or maybe similar product from a different company), had the ability to connect to additional units to extend the distance over which it is able to record data. You still have the problem of having to make sure they are aligned to the bullet path, but that seems like something you could work around. In fact, since the units have to be aligned along the bullet path and you have line of sight, you could use directional signals to connect the devices, which might allow you to maximize the space between units and/or lower the cost of the parts. If the units were all connected and aware of each other, they could design software to trigger the devices (based on the muzzle blast near the first one). The units could also communicate their measurements back to the unit beside the shooter, and those be merged through software into a single continuous series of measurements for each shot. The unit could then further analyze that comprehensive flight data to calculate a personalized drag profile of the bullet’s drag over the entire flight.

      I don’t have a clue what all that would cost, but it seems like if you combined the mesh network idea with the existing features the LabRadar can already do, then it’s just about writing the software to make all of it work together. As far as hardware costs, you can find highly-rated versions of those mesh Wi-Fi systems with 3 of those Wi-Fi points for $175 on Amazon, which would put the price per point around $60. Those devices are unidirectional, so you might could save some cost and/or extend the range by using directional antennas for this application. But if you just use the street price of $560 for the LabRadar + $60 for the Wi-Fi point, you could potentially land under $650 total for an “extendable unit.” How many you’d need to monitor the drag over say 1500 yards (similar to the Infinition BR-1001) could vary based on how big the caliber of the bullet was, but let’s just say each one was able to cover 100 yards … so you’d need 15 total units. $650 per unit x 15 units = $9,750 total. I’d also expect that if they sold them in “5 Packs” they might give you a little discount, but even at that “full retail price” you’d be under $10,000 … which is still a ton of money, but is actually a small fraction of the cost of other options out there. Wait a couple years, and we can probably expect that price to come down by at least 20-30%.

      All this might be a pipe-dream and a terrible idea, but it at least seems like a viable option that an innovative company might at least consider and investigate. What will be funny is if we see a product like this emerge a year from now! 😉

      Thanks,
      Cal

  29. …may be a bit finicky, adjusting to the parabolic trajectory (max ord) and would change some from load to load, but AB could be used to start with, to figure out the max ord and drops, and how high off the ground to place each LabRadar to capture the true horizontal velocity.

    Unrelated, I would agree with Serac’s first comment about just bullet variability — the spread in calculated Cd would mask other effects, given the range in Cd shown in the plot. I would think that even using averages may be difficult, because each individual shot will not necessarily behave to the average, and the effect of each item (bullets, muzzle brake, etc.) compounded on each other may obscure things (could be additive one time, could be subtractive, or somewhere in between, etc.), i.e. adding individual events from several probabilistic distributions. One would hope the bullets used for that test are not any of the leading bullets currently being used…

    …sorry for nerding out… and could totally be out to lunch…
    -NJ

    • Those are great points, and would present challenges … but not necessarily ones you wouldn’t be able to overcome.

      I do think we’ll see more research come out at some point that helps us understand bullet-to-bullet variability. I actually think some research firms already have the data, but just haven’t published it yet. You could probably imagine what kind of firestorm that would create in the industry, so it’s understandable that nobody wants to jump out there and share data that potentially paints a lot of people in a bad light. But someone will break rank at some point and do it. The industry needs that truth to take the next big step forward. The more I thought about that, the more interested I became in Hornady’s new A-Tip bullets. I really think that was in response to the bullet-to-bullet variability they’ve seen, maybe with their own products and maybe some other manufacturers as well. I have no basis for that assumption, but just find the idea behind that product interesting and can’t help but notice the coincidence in the timing of it’s development and all this new data coming to light. Like I said, I personally bought a few hundred of those to try out after thinking about all this stuff for a couple months.

      Honestly, I can’t wait to see how this all plays out. I feel like researchers are learning a lot right now, but have yet to share much of it with the general public. But it is mounting, and I bet we in the shooting community learn a lot over the next couple years. As a guy who loves to learn, that is exciting!

      Thanks,
      Cal

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