Selecting a Rifle: The Perfect Long-Range Kill

The Perfect Long-Range Kill

A Canadian sniper with Joint Task Force 2 made a world-record kill shot at a range of 3,540 meters (2.2 miles). That range converts to 3,871 yards. Range was determined by a laser rangefinder and an inclinometer. There were two two-man shooter-spotter teams, with shooters and spotters rotating regularly due to the fatigue associated with long periods of concentration. Although the snipers occupied an elevated position, the range was so great that the line-of-sight distance and the horizontal distance did not require much adjustment.

The sniper’s McMillan TAC-50 .50 BMG sniper rifle (US Navy SEALs’ Mk 15, Canadian C-15A2 with 29-inch barrel, no twist information released) had an accuracy of 2 minutes of angle or 77 inches at that range. He was firing Norwegian Raufoss 671-grain Mk 211 Mod Zero .50 BMG Armor Piercing Incendiaries with tungsten carbide penetrators and RDX explosive (see Figures 2, 3, and 4). This round was designed to perform ballistically like the US M33 .50 BMG ball ammo. Muzzle velocity was unimpressive at around 2,800 fps. The ballistic coefficient was in the range of .650 to .680, typical for .50 BMG. It was a hot day in Mosul. They were probably using incendiary explosive rounds to assist in detecting bullet splash because visibility with mirage was poor.

This information is public. JTF2 uses proprietary ballistic calculators for which details have not been released. In fact, most of the classified equipment is used by the spotter. Trajectory calculation is cutting-edge technology. The key to success in this kind of shot lies in the ballistic inputs. Adjustments were made for range, wind (2-3 mph, L-R, 10:00), temperature, barometric pressure, altitude above sea level, spin drift, and Coreolis effect. Deltas or sensitivities to inputs were calculated. For example, a one mph error in estimating the wind would result in a miss by eight feet. A one-degree temperature error would cause a miss by three feet. Storm coming? A one-inch error in atmospheric pressure would cause a miss by fifty feet.

Figure 5 is a screenshot from the Hornady BC Ballistic Calculator downloadable for free from the Google Play Store. This is certainly far simpler than the proprietary JTF2 ballistic calculator, but it gives one the idea. Note, I ran the numbers on the Hornady 750-grain .50 caliber A-MAX, which is a match-grade round with a BC of 1.01, much higher than the Raufoss’s BC of 0.680. The A-MAX would have flown better that day.

The calculated holdover at 2.2 miles was 1,122 feet. Process that. 1,122 feet over the targets. The turrets on the rifle’s Schmidt & Bender PM-II scope could not be dialed far enough to allow the sniper to see the target in his reticle. Not even at low power, mounted on a Cadex Defense 60 MOA chassis to allow increased scope tilt. Elevation was such that the rifle was pointed at the sky. There are commercial periscope devices that can augment the scope, but JTF2 probably used proprietary equipment to address this issue.

It’s hard to imagine a .50-caliber round retaining velocity and remaining stable for a full 3,871 yards. The standard .50 BMG goes subsonic at 2,200 yards. In fact, the retained velocity on impact was 785 fps (slower than the muzzle velocity of a 1911, definitely subsonic), remaining energy was 850 ft-lbs, the muzzle energy of a .357 magnum. Enough smack to put the ISIS fighter down. In an interview, Dallas Alexander said he was hit center mass, like where you would aim to take down a deer. The time of flight was just under 10 seconds.

I am astonished the .50 BMG remained stable enough through the transonic zone to do the business. But the spin and 671-grain weight of the round certainly helped.

What does it take to make that kind of shot?

The Firing Solution

Clearly, the ballistic inputs and the firing solution are everything. A properly cared for and managed weapon will do its job so long as the shooter and spotter do theirs.

The Army trains soldiers to battle-zero the M-16 at 30 meters and 300 meters, performing the exercise on a 25-meter range with a small adjustment. Once zeroed, the bullet will cross the soldier’s line of sight at 30 meters and 300 meters. Between 30 meters and 300, it will fly above the line of sight, and after 300, it will fly below. See Figure 6.

For precise shooting inside 300 meters, the soldier has to aim a bit low. Beyond 300 meters, he has to aim a bit high. This is called holdover. To adjust for wind deflection, he has to aim a bit to the left or right. The 5.56mm round’s trajectory is such that even at 180 meters, the highest point of the trajectory, the soldier can aim center mass and will still hit the target about ten inches high.

A shooter can’t do that when he’s shooting a target at one mile, let alone two miles. As we’ve said, even a rifle that shoots to two minutes of angle will have an error of seventy-seven inches at two miles. The shooter has to Figure out how much to correct for holdover, wind deflection, and a host of other variables at the relevant range. That’s his firing solution.

Ballistic calculators can be used to compute firing solutions. The first ballistic calculators were used for artillery applications. As it happens, a key input to the calculation of a firing solution is a bullet’s ballistic coefficient. The shooter enters the ballistic coefficient and other data (range, wind speed, cartridge, sight height, etc.) into his ballistic calculator, and the app produces the firing solution. This includes the appropriate corrections for holdover and windage. We described the bare bones of the inputs that had to go into the JTF2 calculator above. It’s the computations inside that are classified and make all the difference.

Ballistic Coefficient

In the last article, Selecting a Rifle Cartridge, we looked at ways to compare cartridges and found BC was an effective metric. The 5.56mm cartridge has a BC in the .200s. The .300 PRC has a BC of .777 while the .300 Win Mag has a BC of .584, which is significantly lower. The .300 PRC outperforms the .300 Win Mag at ranges up to 1,500 yards despite having a lower muzzle velocity.

As a metric, BC describes the rate at which a bullet slows down over distance. Bullets with higher BCs tend to retain their velocity and remain stable for longer. The .50 BMG that JTF2 used in Mosul had a BC of .680. The BC is good, but not exceptional. However, at 671 grains, that is a heavy bullet. The BC indicates the rate at which the bullet will slow down and it will hit the transonic zone relatively quickly. But it retained enough stability to do the job. The bullet’s weight may have had much to do with that. Ditto its spin, but we have no information on barrel twist.

The purpose of this article is to provide the reader with an intuitive understanding of BC and why it is important to marksmanship, particularly long-range marksmanship. I think the case study above has made that point.

While the mathematics of BC and drag are complex, I will make this as painless as possible. I apologize to rigorous engineers, because I intend to simplify this discussion to the max.

Let’s start with the things that affect a bullet’s stability and how fast it slows down. Its weight and size certainly. Those are captured by a metric called the bullet’s “Sectional Density.” No complicated math – we need its weight in grams and its diameter in inches. That’s easy. That information is right on the box, and it becomes a constant.

The next part is harder to measure. Air resistance and wind slow the bullet down. Gravity causes the bullet to fall. We need an expression to describe how “draggy” the bullet is. Example. Imagine yourself driving a Ferrari sports car on the highway, passing an eighteen-wheeler. Which vehicle is “draggier?” Which one has to work harder against the wind?

That’s an easy call, but it’s not fair. Instead, let’s compare the Ferrari to a four-door Taurus sedan. They look more similar than the Ferrari and the 18-wheeler. It’s still no contest, but it’s a better comparison.

So let’s say we have an equation for the “Drag of Ferrari” and another for “Drag of Taurus”. Furthermore, we say the Taurus will be our standard vehicle for comparison. We can then construct a ratio like this:

Drag of Ferrari
——————- = Form Factor
Drag of Taurus

If the Ferrari has the same drag as the Taurus, the Form Factor = 1. If the Ferrari is much less draggy than the Taurus, the Form Factor is less than 1. If the Ferrari is more draggy than the Taurus, the form factor is greater than 1. Obviously, if the Taurus is our standard for comparison, FF numbers greater than 1 are bad.

Let’s do the same thing for bullets. In the late nineteenth century, armies were getting into breech-loading artillery. They wanted to calculate things like Form Factors and Ballistic Coefficients for artillery shells. The Germans came up with a standard artillery shell shape to which they could compare the performance of other artillery shells (see Figure 7).

They came up with a design called the Krupp Projectile Model (Figure 7). They said, “That’s our standard. We’ll calculate drag functions for it and compare the drag functions of other shells.” So the ballistic Form Factor became:

Drag of Bullet
—————— = Bullet’s Form Factor
Drag of Krupp

They calculated the bullet’s Ballistic Coefficient as:

Sectional Density of Bullet
——————————— = Ballistic Coefficient
Form Factor

From this formula, we can see what we already know.

If our bullet is more draggy than the Krupp projectile, the Form Factor will be greater than 1, and the BC will go down. That’s not good.

If our bullet is less draggy than the Krupp projectile, the Form Factor will be less than 1, and the BC will go up. That’s better for us.

Engineers tinkered with the Krupp Projectile Model over time and changed it a little bit, but not much. Now it’s called G1. The BC for a bullet calculated using the Krupp/G1 is the BC printed on your box of ammo called BC/G1.

Now isn’t that easy?

So what’s so proprietary and secret about the JTF2 calculators used for the two-mile kill?

Well, the Sectional Density never changes, but the Form Factor does. The projectiles – our bullet and the Krupp/G1 projectile – slow down after they leave the muzzle of our rifle. As they slow down, they become less stable and more draggy. And they become more draggy at different rates. That’s why the Form Factor changes. To do an exact job, we have to calculate Form Factors and BCs everywhere along the trajectory from the moment we fire to the moment of impact.

Most public ballistic calculators (like the Hornady in Figure 5) ask you to punch in the BC on the box (usually measured at the muzzle), and that’s the simplified approach that is widely used. Obviously, to pull off shots like the JTF2 two-miler, the calculations get more involved. If you’re wondering what they’re doing, you’re not alone. That’s why it’s classified.

In this video, Dallas Alexander of JTF2, is interviewed on the Shawn Ryan show and describes the action that day: The Shawn Ryan Show: Dallas Alexander of JTF 2. The video shows the moment of the kill at the end of the clip.

Conclusion

That’s what Ballistic Coefficient is all about, and that’s why we care. We need it for our firing solution, especially over longer ranges. We need it so the calculator can give us our holdovers and windage.

We still don’t know enough to pick out our rifle. We don’t know the barrel length or the barrel twist we need. We put a twist in the barrel to spin-stabilize our bullet on its way to the target.

In the next article, I’ll talk about how the drag and stability are calculated and how we work out barrel length and twist.

About the Author

You may reach Cameron at: cameron.curtis545@gmail.com

Cameron Curtis has spent thirty years in the financial markets as a trader and risk manager. He was on the trade floor when Saddam’s tanks rolled into Kuwait, when the air wars opened over Baghdad and Belgrade, and when the financial crisis swallowed the world. He’s studied military affairs and warfare all his adult life. His popular Breed series of military ad-venture thrillers are admired for combining deep expertise wit/h propulsive action. The premises are realistic, the stories adrenaline-fueled and emotionally engaging.

Check out the books here: Cameron Curtis’s Amazon Page

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