Learn the Science of the Long-Range Kill

The Abrams’ Smoothbore Sabot

The American M1 Abrams is equipped with a 120mm smoothbore cannon. It fires armor-piercing discarding sabots with depleted uranium penetrators. This ammunition kills by penetrating enemy armor with kinetic energy. The penetrator is like a super-hard bolt that drills a hole in the enemy tank purely by the velocity and energy with which it arrives. The depleted uranium has an incendiary effect that sets fire to anything flammable inside the target.

Figure 2 shows an Abrams’ 120mm Cone-Stabilized Discarding Sabot penetrator (lower image). Notice its arrow-like shape. Other projectiles are fin-stabilized, but the principles we want to discuss are the same.

The sabot has a range of five miles, but is generally considered effective to two. The question we want to address here is – how does it fly straight and true to its target? Notice that the sabot looks like an arrow. It has a long shaft, a pointed nose, and a flared stabilizing cone on its tail. An arrow has feathers (fletching). Both are forms of “empennage” – stabilizers.

If we set it on a blade somewhere around Point G labeled on the photo, we find there is as much weight toward the nose as there is toward the tail. The sabot balances perfectly around Point G. This is called its center of gravity.

Now, once the round’s been fired and it’s headed downrange, gravity and wind resistance start acting on it. It starts slowing down due to aerodynamic forces. These forces, like the weight of the sabot, tend to balance each other at Point P. This is called the center of pressure. At P, you’ll have as much pressure acting on the front of the sabot as on the rear.

The center of gravity is fixed by the sabot’s shape, materials, and weight. It never changes. The center of pressure, however, depends primarily on how fast the sabot is moving. It starts to slow down from the moment it leaves the muzzle, but P stays behind the center of gravity, towards the cone. (Over longer ranges and differences of altitude, other influences come into play, but for a shot over flat ground, velocity is the key factor.)

The distance between the center of gravity and the center of pressure is called the moment of inertia. With the center of gravity ahead of the center of pressure, the sabot remains stable and flies true to its target. This is how the Abram’s gun maintains accuracy without the rifling characteristic of other tank cannons and artillery pieces. This sabot doesn’t spin.

The Raufoss .50 Caliber API Round

In a previous article, The Perfect Long-Range Kill, I described a world-record sniper kill made by a Canadian JTF-2 sniper in Iraq, 2017. I gave details about the weapon, ammunition, and ballistic science involved. One question was – how did the armor-piercing incendiary bullet retain its stability over the full 2,875 yards to the target when the typical .50 caliber bullet goes subsonic at 2,200 yards. Let’s look at how bullets remain stable over range.

Like other bullets, the .50 caliber Raufoss round used by the sniper in Mosul is spin stabilized. Compare its structure to that of the Abrams’ sabot. The bullet’s center of gravity, G, is toward the rear. I guessed its position because the heaviest components inside the bullet, including the tungsten penetrator, are positioned toward the boat tail.

The bullet doesn’t have fins or a cone at the tail to stabilize it. What you find here is that the Raufoss has a center of pressure, P, toward the nose because the forces have nothing to push against at the tail.

The point is, the positions of the center of pressure and the center of gravity are reversed in the case of a bullet as compared to an arrow or cone-stabilized sabot. This makes stabilizing the bullet a tricky exercise.

In flight, the aerodynamic forces working on the bullet are very different from those working on the sabot. What you find is that the aerodynamic pressure acts on the center of pressure in the nose and pushes back against the bullet, slowing it down. The weight in the center of gravity wants to keep moving forward and wants to swap places with the center of pressure. The pressure from all that forward velocity wants to flip the bullet end-over-end. It is fundamentally unstable. See Figure 4.

Think of the moment of inertia as a crowbar with the tip positioned under the center of gravity while a giant presses down on the handle at the center of pressure. Something has to counteract that force, or the bullet will tumble, and there is no way we will ever hit our target. The question then becomes, how do we keep the bullet from flipping end-over-end due to the forces acting on its moment of inertia?

Spin-Stabilizing a Bullet

The trick, of course, is rifling. We manufacture our barrel with spiral grooves that cause the bullet to spin. The grooves are designed to spin the bullet at a certain rate. For example, a one-in-ten twist means a bullet spins once in every ten inches of rifle barrel. A one-in-seven means the bullet spins once in seven inches. The Barrett .50 caliber sniper rifle has a one-in-fifteen twist.

In general, the tighter the twist, the faster the bullet spins, and the higher the revolutions per minute when it leaves the barrel. The spin creates angular momentum that stabilizes the bullet. In general, the faster the spin, the stiffer the bullet’s forward flight, and the harder it is for aerodynamic forces to flip its moment of inertia.

Imagine a child’s top. You spin the top, and it stays balanced on the surface. I used to spin jacks. Hold one pointy end, set the other pointy end on the floor, and snap my fingers. The jack would spin like a top. Try that with a bullet, and the bullet won’t spin very easily. The wider the diameter of the top, the easier it is to spin. A bullet is narrow, so it takes a lot of spin to stabilize it. By the same token, it’s easier to stabilize a .50 BMG than it is a .223. That’s because the .50 BMG has a greater diameter. The Barrett .50 caliber has a 1:15 twist, while an AR-15 might have a 1:8 twist. The .50 caliber twist is slower.

Why are we studying this? Every bullet has an optimum twist rate for its application. When you buy a rifle, you need to buy one with a barrel length and twist appropriate to the round you want to fire and the game you want to take down.

What happens if we don’t spin a bullet fast enough? In that case, the angular momentum of the spin is not enough to counteract the aerodynamic forces working to flip the bullet over and it becomes unstable.

We can’t hit the side of a barn.

What happens if we spin the bullet too fast? We get bullet failure. This usually happens when we apply too tight a twist to a small, light caliber like a .22 or a 6mm. The casing separates from the core, and the bullet breaks up in flight. You fire and see a puff in midair, partway downrange, as the bullet tears itself apart.

Things Get Complicated

In The Perfect Long-Range Kill, I described a world-record sniper shot made by a Canadian JTF-2 sniper in Iraq, 2017. I gave details about the weapon, ammunition, and ballistic science. I spent a fair bit of time discussing the required holdover. I alluded to factors that affected holdoff – wind, Coriolis effect, spin drift – but did not get into detail because that discussion would have been too overwhelming on the day.

We now have what we need to discuss spin drift.

In simple terms, spin drift is a diversion of our bullet’s flight path to the right caused by its spin. This happens when we have a barrel with a right-hand twist. If the barrel has a left-hand twist, the bullet is pushed to the left. Spin drift results from complex aerodynamic forces acting on the bullet as it flies downrange.

The mathematics of spin drift is too complicated to get into here. Suffice it to say that the aerodynamics are related to fluid dynamics and Bernoulli’s Principle, the same forces that govern air pressure around an airplane’s wings and allow it to fly. In the case of spin drift, the rotation of the bullet causes a differential in air pressure around the bullet – top/bottom and left/right. The deflection in the vertical axis is not significant, but the deflection in the horizontal axis is.

Spin drift is particularly significant at longer ranges. Figure 5 shows a representation of spin drift. In a hunting situation, spin drift can cause you to miss the vitals of your target. At the range of the two-mile sniper kill, it was definitely significant. Let’s break it down.

Figure 5 shows the kind of spin drift one would experience with something like a .300 Win Mag. Obviously, it depends on your target, but the error is real, and it becomes significant at ranges over 800 yards.

The world record sniper shot had spin drift of 6.29 MOA. At the range of 3,871 yards, that amounted to about 20 feet. The sniper would have to shift his aim 20 feet left.

That’s enough for the bullet to miss the ISIS fighter, miss the wall of the building he’s standing next to, and expend its energy on the landscape beyond.

Conclusion

In the last article, we spent a lot of time discussing the holdover, which was related to the limitations of the scope the snipers used. In a future article, we’ll discuss a commercially available periscope attachment that can be purchased to augment the sight. In this article, we focused on lateral adjustments, in particular spin drift. We saved it for this article because we wanted to include an introduction to rifling and bullet stability. That is why we spin a bullet and not a tank round?

The spin drift adjustment discussed above is in addition to the wind and the Coriolis effect. The latter is an adjustment due to the revolution of the Earth beneath the bullet while it is in flight. We will discuss the Coriolis adjustment in a future article.

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 with 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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