A crash course on armour penetration

How armour penetration works came up on the discord server a few days back, and I said I’d give a crash course on it.

To begin, let us begin at first principles: what is armour? Armour is any material used to stop an object from hitting and damaging a second object. How it does this depends on the type of armour, but no matter the specific method used it can be broken down into basic physics

To bring an object to a stop you need an external unbalanced force pointed in the opposite direction of the object’s travel. Or to put it another way, Newton’s Second Law of Motion, applied.

And thanks to Newton’s First Law of Motion we know that a force is term used when you have an accelerating mass:

F = ma

Now here is the thing with acceleration: it is the measure of how velocity changes over time.

a = v/s

If you swap out acceleration for velocity over time in the force equation you get:

F = mv/s

This is a big deal because it shows us another way to interpret force and a key ingredient in understanding armour penetration.

p = mv

p is the symbol physicist use to represent momentum and that means that a force can also be described as the change in momentum over time. And here we come to the point we have to remember: the ability of an object to travel through a medium is tied directly to momentum the object has.

Now the thing about nature is that it has no consciousness. It cannot make choices. It cannot choose to apply more or less force to something. It always applies as much force as it can to everything, which means that if two different objects were to hit two separate, but identical, barriers both of those objects would have the same force applied to them.

If these two objects have different momentums, then for them to receive the same force, something else has to balance the disparity. In this case there is only one option: time. The object with the greater momentum must spent more time interacting with the medium. As a consequence of this, the object with the higher momentum travels a greater distance through the medium.

Now what happens if the medium has a set depth and an object passing through it still has momentum on the other side? It keeps going and has penetrated through it. Voila, armour penetration.

At this point, things are going to get more complicated. This is because material properties are starting to come into play.

Because everything is made of matter, in order to penetrate a medium the matter of the medium has to get out of the way of the penetrating object, and matter doesn’t like to change its state of motion, ie it has inertia. The denser and harder the medium, the more inertia it has and the more force required to penetrate it.

In addition the shape of the object effects how easily the medium can be forced out of the way. A blunt object must work more to push the medium out of the way than a sleek one would, a long object will create more drag than a short one would, etc.

And then we get to non-Newtonian materials. Newtonian materials are those that respond in a linear fashion to forces applied to them. Non-Newtonian materials don’t, they’ll respond in an exponential fashion.

The non-Newtonian material people will be most familiar with is probably Oobleck, or cornstarch in water. The more force you apply to it, the more it resists moving. Trying to get through is quickly means it’ll act more like a solid, while trying to get through it slowly will mean it’ll be more liquid like.

You might be thinking, “hey why not use Oobleck as armour?” It is a good idea in theory, but there are a few downsides. One, it is a fluid most of the time, so it would bunch up at the bottom of the container it is in giving you uneven coverage. Two, it isn’t that great of a non-Newtonian material. It’s exponential resistance to force is quite low.

There is a non-Newtonian material out there that does have the right properties to make armour out of. You will have heard of it too. It’s called Kelvar.

On to a few practical examples.

Soft armour (Kevlar and the like)

Knives get by Kevlar in a couple of ways. They move very slow compared to bullets allowing more time for the material to get out of the way. They are very sharp meaning they encounter less of the medium at a time. They also cut the strands of Kevlar removing material that can stop the knives as they go through the Kevlar. They also have a huge amount of mass behind them to generate more force than the Kevlar can handle.

Spitzer rounds work better than rounded rounds because they are pointed. Armour piercing rounds work by having a very sleek high density round, thereby being more pointed than a Spitzer, to the point of going in one side and out the other. This is why Kevlar vests get pouches to carry armour plates.

A crossbow bolt is heavy, but also very large. It’ll start out being very good at penetrating soft armour but will quickly gain drag. Arrowhead design will also affect this.

Hard armour (steel, ceramics, etc) is dense and hard enough that you have to use very dense and sleek rounds to get through it, rounds that have enough force to punch through anyways, or fancy rounds that generate a super dense, super thin jet of metal to punch through the armour on impact.

The carapace of a crabman would be harder than soft armour, and softer than hard armour. The very definition of medium armour. How effective anything would be will end up depending greatly on the thickness of the armour, and the design of the projectile.