The science of external ballistics.

<< Barrel envy

Fashion victims >>

Hello again. Continuing the ballistics trend, this week I’m talking about external ballistics. So far, we’ve covered wound ballistics, intermediate ballistics (with a deep dive on silencers), and internal ballistics.

What is/are¹ external ballistics? It’s everything that happens to the bullet or shell between leaving the influence of the gun and hitting the target. It’s everything that happens “outside,” as its name suggests.

As with the rest of the ballistics journey, the gun designer is always trying to maximise how much of the chemical energy in the propellant ends up causing damage to the target. We saw last week that getting to keep 30% of the energy by the time the bullet leaves the gun is a good return. How do we keep as much of that 30% as possible all the way to the target? And better still, how do we maximise our chances of hitting the target? That’s our focus today.

We’ll start by talking about spin-stabilisation, which is one of the oldest tricks in the book. Then we’ll look at some alternatives, such as using fins to keep the projectile on track. Finally, we’ll touch on some tricks for squeezing out a bit more range.

Before that, however, I’ll encourage you to subscribe to the blog using the link below. As always, I’d love to see your comments below, or you can contact me via webform here or email here. Finally, if you’ve enjoyed this read, please share it with a friend.

If you enjoy this blog and want to support it, please consider a donation. Keeping this blog going doesn’t cost much, but it isn’t free either, so any help would be very much appreciated👍

Spinning the bullet improves accuracy

Why is this?

A bullet² which spins quickly as it travels through the air is more likely to stay on its intended course and not veer off wildly in some other direction. This is clearly a good thing, and a step up from the early days of firearms.

A spinning bullet works better for the same reason that a spinning top doesn’t fall over: the gyroscopic effect. Any little disturbance in the air, which would cause a non-spinning bullet to tumble wildly, turns a spinning bullet around a second axis instead, in a motion called precession:

Spinning bullets are so much like spinning tops that there’s a YouTube trend of wonderful idiots firing pistols into ice to see the bullets bounce out and behave like little spinning tops. I say “idiots” because this is not safe, and “wonderful” because it gives us this amazing phenomenon:

Bullets need to spin fast enough to keep them from “falling over” into the airflow (i.e. tumbling). You can see at the end of the clip above when it finally runs out of energy and topples. There’s no point in spinning them any faster than this, however, since it brings no extra benefit³. It takes energy to spin up the bullet (more on this below), so the spin rate is carefully selected to be just right.

How fast is this? It depends on the round and the design of the gun barrel, but spin rates of hundreds of thousands of RPM are common. This sounds fast (and it is), but a bullet itself is very fast, so the spin is pretty staid by comparison. This is yet another example of how everything to do with firearms stretches the bounds of human perception. See the video below, where the spin rate is just about visible before the bullet hits the wall:

The other notable thing about the video above is how the bullet is very clearly engraved with the marks caused by the rifling process. Let’s talk about this next.

How do we achieve spin?

Gun designers make bullets spin by engraving the inside of the barrel with grooves:

The bullet or shell is ever so slightly wider than the distance between the tops of the grooves, so they grip onto the projectile and make it spin as it accelerates down the barrel. This leaves discernible imprints on the soft copper jackets of a rifle round:

The imprint on the bullet will include any micro-imperfections in the gun barrel’s rifling. This means that bullets can be forensically matched to the gun barrel which fired them, or at least to the tool which made a series of barrels. This is just a consequence of rifling and spin-stabilisation, and is not a design feature of rifles.

Larger calibre projectiles get the spin treatment too, usually via a “driving band” made from copper or another soft material which engages in the gun’s rifling.

The band on bigger “bullets” illustrates the main problem with rifling: it puts high stresses on the projectile and causes extra friction which wastes that precious energy we’re trying to conserve. A single copper band instead of an entire copper jacket means less friction on the shell.

One solution to this problem is progressive twist rifling, i.e. a groove that starts with a very gradual twist and increases the twist angle until the end of the barrel.

The GAU-8 Avenger cannon used on the A-10 (a.k.a. the “BRRRT plane”) uses a progressive twist⁴. It’s complicated to manufacture barrels with a progressive twist, however, so it’s not a widely used technique.

If you want to be really radical, however, you can ditch rifling altogether. We’ll discuss that further down, but first, let’s look at some movie examples.

What do the movies say?

We’ve seen that spin is good, and rifling causes spin. As well as spin, bullets precess, i.e. their nose rotates around a fixed point in front. This precession also has a second-order wobble on top of itself called nutation. If we slowed down time and put a light trail on the tip of the bullet, it would draw a path something like this:

This is something which, as you might expect, Hollywood doesn’t always get. Sometimes we don’t see any spin at all⁵…

…and other times, we see far too much⁶:

Other times, we see some faint traces in the animation which sort of count:⁷

And sometimes we get to see the spin, along with some wonderfully unrealistic bullet curving:

What we don’t see, because admittedly it would be more difficult to animate⁸, is the wobbling of the bullet as it travels and spins. It would make for a cool shot though. Then, if the filmmakers wanted to get graphic, they could show a bullet starting to tumble just before it hit someone, for maximum damage.

Fins are better for dart-like projectiles

We mentioned above that you can ditch rifling altogether. This is an option when you’re firing long, thin projectiles. Luckily for designers, this is the preferred modern tank vs. tank ammunition type. It’s known by the not-at-all suspect term “long-rod penetrator⁹” and works by shedding an outer layer (a “sabot”) as soon as it leaves the tank’s gun barrel:

The combination of fins, sabots, and a long, dense core make this a very effective anti-armour weapon. I’ll come back to this when we talk about terminal ballistics. For now, suffice to say that:

• The sabot means you can use a big barrel to give all the propellant energy to a thin projectile, so it goes very fast (nearly twice as fast as a shell fired from the equivalent gun).
• The thin cross-section means air resistance is minimised.
• The fins provide much-needed stability due to the missing spin, meaning the projectile doesn’t tumble.

Getting rid of spin-stabilisation has one big advantage, which is that you no longer need to rifle your gun barrels. Compare the German 120 mm tank gun barrel below to the sectioned British 105 mm gun above¹⁰.

Focusing on the back end can eke out more distance

The last thing to talk about is how designers make their projectiles (and usually we are talking about artillery shells here) go that little bit further by optimising their aerodynamic shape to minimise drag. This is done at the front end, obviously, but the tail end of a projectile is also important for its aerodynamic shape. Improving aerodynamic performance often comes at the expense of payload, i.e. the effect you want to have on the target:

The aerodynamic back end shape, as seen in numbers 3 and 4 above, is called a “boat tail.” An even more extreme step you can take is to fill the boat tail section with propellant (instead of explosive) and burn this propellant as the shell flies through the air, sending the exhaust gases out little holes in the base of the shell:

This so-called base bleed system fills up the vacuum behind the shell, which reduces drag. Every source I can find on this tells me it’s definitely not a rocket motor. A rocket produces thrust, and this merely raises the back-pressure from a negative value to neutral or mildly positive.

I dunno, this sounds like a rocket to me, just a very weak one. Anyway, you can go ahead and put in a rocket system altogether and avoid this semantic trap. As you might imagine, this involves devoting even more internal space to propellant at the expense of explosive:

Base bleed can add 5 to 10 km to a 155 mm howitzer’s already impressive 25 km range. Rocket assist can bring the range up to 40 km.

Conclusion: Counter-intuitive design choices

A lecturer in college said something which has always stuck with me. The great thing about engineering, according to him, is that it can lead you down the most counter-intuitive design choices which still make sense.

For example, anyone with common sense can see that a bigger engine, or one that burns more fuel, will generate more power. Spraying water into the engine, on the other hand, would seem silly. But that’s exactly what an engineer will tell you to do, via an intercooler, to further compress the intake air before combustion and generate extra power.

The same holds for gun design. You wouldn’t intuitively think that putting complicated grooves in a barrel and making the bullet slightly too big to fit through them would result in a better shot—but it does.

Common sense might not lead you to design big blocks around a projectile which get discarded as soon as they leave the barrel—but these result in a much faster kinetic energy tank round.

A very weak rocket motor which barely sputters out some limp gas might seem like a waste of space, but it eliminates a negative pressure area, reduces drag, and greatly improves overall range.

Thanks to some clever engineering, gun designers can minimise the energy lost in the external air while the bullet or shell is travelling toward its target.

What happens when the projectile reaches its target? This will be the topic of our next ballistics article, which may not be next week, but will be soon. In the meantime, thanks for reading and please remember, if you haven’t already, to subscribe using the link below. Please also share this article with a friend. And if you want to learn more about tank guns (rifled and smoothbore), Frank Tank Rants has an excellent explainer (and mythbuster) here. Thanks, and see you next week.

Featured Image: Neo – ‘The One’, from The Matrix, Warner Bros. (1999), via YouTube.

1. I think this should be singular, but my editor disagrees. Hence this compromise which will please nobody. ↩︎
2. I’m throwing the word “bullet” out here a lot, but will also be talking about tank and artillery shells. When they are spin-stabilised, the same principles apply. ↩︎
3. It may actually damage the bullet through centrifugal forces if the spin is too extreme. ↩︎
4. This allows it to have a lighter barrel because the chamber pressure is lower, because, in turn, the initial resistance on the bullet is lower. For airborne weapons, weight is everything. ↩︎
5. Admittedly, the camera and probably the viewer is looking at Gal Gadot much more than the bullet. No complaints there. This second clip, with the bank robbers, suffers from the “single-speed slow motion” effect I’ve noted previously. If Wonder Woman really did move that poor schmuck’s head out of the way of a bullet, the sudden impact of her hand on his head would be as bad, or worse, than the bullet. ↩︎
6. Compare the spin “trails” (also not a thing) with the slower rate of spin we saw in the high-speed video above. I feel bad nitpicking this scene though, because it’s so freaking iconic, and they made a decent attempt. ↩︎
7. This is yet another example of single-speed slow motion. Everything takes the same length of time, be it a shirt opening, a bullet moving, or food falling to the floor. ↩︎
8. Although here’s a stock one I found via a quick search. ↩︎
9. Yes, seriously. Also known as a “kinetic energy penetrator” or, if you want to go deep into the jargon, “APFSDS-T,” which stands for “Armour-Piercing Fin Stabilised Discarding Sabot (Tracer).” ↩︎
10. The eagle-eyed among you might have noticed that, last week, I showed a picture of a cutaway gun barrel with a long-rod penetrator round in the chamber. The barrel was rifled. What gives? British tanks, including the modern Challenger 2, have always had rifled tank guns. This is because their favoured tank ammunition is high explosive squash head (HESH), which fires a shell, which needs to be spin-stabilised, which requires a rifled barrel. But they also fire long-rod penetrator ammo, in which case they have a special “slipping driving band” which engages in the rifling but doesn’t transfer all of the spin to the projectile. Makes sense…. right? ↩︎