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To clear up some confusion about armor penetration

So I was looking through the suggestions ticket thingy we have now and stumbled on this ticket. It appears that there is some confusion on the subject of armor penetration (irl, not in game). So heres a (relatively) short summary of how armor penetration works and where armor is now a days.

To make this a bit easier to read, I've split it up. Feel free to skip to the parts that interest you, if you don't care about the details of a particular topic.
1.A detailed look at how penetration works
2.Penetration and speed
     -2.5.Penetration and crossection

3.Modern Projectiles and what they are meant to do
4.Modern composite armors

1. A detailed look at how penetration works:
So what happens when a projectile hits an armored plate? One of four things: penetration, partial penetration, deflection or shatter.
Lets start with penetration, since that is the goal of any projectile (except for HESH). In term of the underlying physics, there is a single condition for penetration: the momentum of the projectile must be greater than zero after it has pushed through the armor. As the projectile passes through a medium (be it armor or air) it must push it away. Some of that push will be in the direction of travel, giving some of the momentum of the projectile to the medium. Since momentum P = m*v where m is the mass of the projectile and v is its velocity, giving away momentum means losing speed (since mass is constant). If it loses all of its momentum, it loses all of its speed and thus stops. If the projectile starts to penetrate the armor, but runs out if momentum, this is called a partial penetration.
This brings us to shatters. While the projectile will lose impulse to both air and steel plate, there is a significant difference between the two (at leas at the velocities modern guns achieve, but more on that later). To understand that difference, it is necessary to understand why a projectile transfers momentum to the medium its travelling through. Looking at any projectile from the front, it has a non zero area as seen from the front, normaly called its cross section. It should be self explanetory that, if this area was a flat surface and the projectile was traveling through a medium, it would need to push allong whatever is in its way. In air, the air particals are simply battered out of the way, each taking a tiny amount of momentum with them. In solid materials, however, the particals are strongly attached to eachother. In other words, the particals in a solid pull on each other if one is moved out of position, as if they were connected by rubber bands. This means that a partical that is being pushed will pull along their neighbours and they will pull along their neighbours and so on, until the rubber bands snap. The projectile is also a solid, so as it pushes the armor apart, it to is being pushed agains by the armor (as per newtons third law action is equal to reaction). If the "rubber bands" that hold the particles of the projectile together are significantly weaker than those of the armor, the projectile will break and spread out across the armor and all of the momentum will also be spread acros the armor.
This leaves deflections, or ricochetts as they are usually. These occur if the projectile hits armor at an angle and the angle the shell leaves at is generally the incoming angle mirrored accros the normal of the armor. For a start, at an angle, the armor distance d that the projectile must penetrate is d = D/cos(α) where D is the armor thickness and α is the incoming angle (between 0° and 90°) to the armors normal. In words, that means that the greater the angle, the more armor must be penetrated. What really leads to deflection, is another thing, though: after a deflection, the projectile keeps moving. This means it doesnt lose all of its momentum. This is because, as the angle of impact increases, the momentum directly in line with the armor decreases. Why this leads to a deflection is extremely complicated, so I'll use a simplification here (so this only applies in generall). Consider that the momentum perpendicular to the armor is p = P*cos(α) where i is the momentum perpendicular to the armor, I is the total momuntum and α is the impact angle. To redirect the projectile it would take two times the momentum p. (I must stress again in generall) If penetrating the armor would take more momentum than 2*p, then the projectile is deflected.

2.Penetration and Speed:
After reading the last section, it might seem strange that everything revolved around momentum. It is generally accepted, that velocity is paramount in armor penetration. Yet, if it is primarily dependant on momentum, why would that be the case? Should it not be just as effective to use a heavier projectile, since P = m*v? Well, not quite. Here we come back to how solids are held together. In solid materials, as mentioned before, the atoms or molecules are bound together. If an atom is moved out of position, the atoms around it exert a force on it to move it back into position (I used rubber bands as an analogie). The farther the atom is moved out of position, the stronger the force pulling it back. As per newtons third law, the surrounding atoms also get pulled to the out of place atom. This causes the surrounding atoms to move towards the out of place atoms. They then get pulled on by and pull on the atoms surrounding them. Etc. This spreads the momentum of a projectile impacting or penetrating a piece of armor across the entirety of the armor. However, the ability to spread the momentum across the armor is limited. For a start, the force (which transfers the momentum) is proportional to the displacement of the out of place atom. This means that the spreading of momentum gets less and less efficient as you get further away from the impact point, since each step of atoms pulling on each other must transfer less. The other important detail is that the returning force for the out of place atom increases only to a point, then it starts decreasing rapidly. These two factors mean that there is a maximum amount of momentum an atom can transport away from the impact per unit of time.
This is where speed comes in. The faster the projectile hits an atom, the faster its hit away. In air, where the particals essentially cannot transfer momentum between each other as described above, this means that only the amount of air between you and the target matters. If you throw a rock at a steel plate, however, the steel can transport several times more momentum away from the impact than the rock has. Thus the rock bounces off. Shooting a gun into ballistics gell, the projectile has enough momentum and hits fast enough, that the gell can't tranfer it away from the impact fast enough to stop the projectile from ripping through it. The ripping quickly robs the projectile of momentum and it soon loses the ability to rip through the gell. This can be seen in high speed shots of bullets being fired into ballistics gell, as the will bounce back before stopping completely.
Essentially what is relevant to penetration, is how much momentum a material can transfer per time unit, relative to how much momentum it would take to push the material out of the way in that amount of time. If the amount that can be transfered is insignificant compared to the amount that is need to push through, only the mass of the material in the way of the projectile is relevant. The speed at which a materials internal strength is no longer relevant is roughly proportional to the speed of sound in the material (or its hardness and density in other words) and generally several times as high.

     -2.5.Penetration and crossection:
As a sub point of speed, crossection is also relevant. As seen above, momentum is transferred across atomic bonds by the force holding the atoms together. Since many atoms are being hit at a time, all of them transfer momentum. The momentum transfered is thus also dependant on the area of the impact, as this determins the number atoms hit. Minimizing crossection (or achieving highest crossectional density to be more specific) is incredebly important.

3.Modern projectiles and what they are meant to do:
In the modern world there are two main concepts for armor penetration: the kinetic energy penetrator and the shaped charged. The modern iteration of the kinetic energy penetrator is most comonly known as APFSDS or armor piercing fin stabalized discarding sabot. The projectile that does the penetrating is a very thin, relatively light rod of very dense metal, that is stabalized in flight by fins (as spin stabalization does not work on very long projectiles). And yes, thin rods are incredibly light compared to what would be conventional equivelant caliber (not penetration) AP rounds. They travel very fast and have an inredible amount of mometnum. They are also made of very hard materials, in order to stop them from shattering on impact or desintegrating before full penetration.
Shaped charges use explosives to form a thin coppper sheet into a quasi liquid jet of metal that travels at around 10-15km/s. Note that the jet is not truelly liquid. The metal does not melt, rather the forces on it are so great that the forces holding the atoms together are insignificant. The copper, acting as a non compressible fluid now, is formed into a jet due to the conic form of the coper sleeve in the shaped charge. This jet converges to mere millimeters at its focul point, but quickly disperses afterwards. Because the jet has comparatively little momentum and now structural cohesion due to its quasi liquid state, it relies soley on its immense speed and small crossection for penetration.

4.Modern Composite armors:
Modern armor is a composite of many materials (hence the name). Generally, it consists of a less dense and relatively soft matrix material (generally metal alloys) in which ceramic structures are suspended. Ceramics are used, because they are extremely hard (the speed of sound in them is very high). Thus they offer the best protection against high velocity projectiles. The reason they must be suspended in a matrix of supporting material, is becuase ceramics are incredebly brittle as well as hard. Any hit on a plate of ceramic will shatter it. Having many small plates suspended in a matrix allows the armor to retain its integrity, even if some plates are shattered. There are additional advantages though. Having multiple plates of ceramics spaced apart means that a projectile will have mulltiple transitions between materials of different hardnesses and densities. This increases the chance of the projectile shattering, as each transition is an enormous shock to the projectile. This is especially true for shaped charge jet, as it has no structural cohesion to begin with. The jet will often spread across the plates, following the seam between ceramic and matrix material. As a result modern composite armor is significantly more effective against kinetic energy projectiles and can stop heat rated to penetrate several times the armors thickness in steel. The armors major drawback , is that it has an internal structure that limits it to a certain minimum thickness and thus minimum wheight. This means it is only really an option for main battle tanks and not for lighter vehicles (though simplified composite is used in those vehicles, usually using spaced armor and a single layer of ceramic or a ceramic coating).

Well thats it, hope you enjoyed!

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