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.
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.
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.)
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.
“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.
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.
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.”
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:
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!
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.
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:
- Aerodynamic Drag Modeling for Ballistics by Bryan Litz
- Hornady 4 Degree of Freedom (4 DOF) Trajectory Program Technical Paper by Hornady Engineering Team
- Accurate Measurements of Free Flight Drag Coefficients with Amateur Doppler by Elya Courtney, Collin Morris, and Michael Courtney
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?! 😉