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In a world similar to us, but in which an evil mastermind is trying to create an armour to force their country into submission. Our villain is trying to make it out of a ceramic composite. What would be the density needed to sustain possible tank projectiles with minimum damage. And for a bonus, what would be a real cost for such a piece (the whole armour). The exoskeleton strength will be considered after knowing the potential weight.

LE: the weight itself is of no problem.

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    $\begingroup$ A soldier hit by a large projectile (say, a 20-pound ball of iron fired by a gun) will die of blunt trauma irrespective of the kind of armor they wear. All the armor can do is spread the energy of the projectile over a larger area, but the total surface area of a human is still limited. $\endgroup$ – AlexP Aug 21 '17 at 17:42
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    $\begingroup$ To sustain tank projectiles, one has to wear tank-sized armor. $\endgroup$ – Alexander Aug 21 '17 at 18:06
  • $\begingroup$ @AlexP it could add to the bulk of the person wearing it. Kind of like the Terminator armour in WH40k. It isn't limited to just 2-3 cm of material. $\endgroup$ – Schneejäger Aug 21 '17 at 18:12
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    $\begingroup$ @Separatrix: Google has proven to be a friend, again. I didn't know that there was a word for anthropomorphous tanks. (And an entire subculture, apparently, regardless of the impracticality of such machines.) Now I know. Showing my age... $\endgroup$ – AlexP Aug 21 '17 at 18:52
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    $\begingroup$ Massive ceramic armor will work, but there is a major caveat - ceramic plates shatter on impact, so they are effectively single-use Ceramic armor $\endgroup$ – Alexander Aug 21 '17 at 19:10
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Conservation of momentum suggests that the momentum of the projectile is transferred to the target at the instant of impact.

Let's say a 20 kg shell travelling at 1200 m/s at the instant before impact,
Momentum to be transferred $=20 \times1200=24000kgms^{-1}$
Mass of the man is, let's say 60 kg,
so the velocity of the man would be 400m/s after impact.

From the above, should you wish for the man to survive, he must be able to withstand both the initial transfer of momentum and the eventual deceleration. What armour does, is prevent the momentum transfer being concentrated at a point on a squishy human and instead distributes it throughout the body; but the body plus armour as a whole must still conserve momentum. So, can the man survive the instant acceleration from zero to 400m/s in a fraction of a second? Probably not. While a heavier individual will have a lower final velocity, it really won't make much difference; the blow will cause internal bleeding, and the sudden stop at the other end will damage his brain.

And that assumes the shell won't explode.

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  • $\begingroup$ You can limit this the way a tank does: by adding mass. The mass of the man is 60 kg, the mass of the armored exoskeleton is 60 tonnes. Then, your tank is blasted away at 4 meters per second, which the human inside can survive. The thing is, a 60t armature is going to sink its feet in the pavement like if it were quicksand. $\endgroup$ – Rekesoft Aug 22 '17 at 10:11
  • $\begingroup$ @Rekesoft: at 60 tonnes it's a 'mech, not armour. $\endgroup$ – nzaman Aug 22 '17 at 13:34
  • $\begingroup$ The OP refers to the armour as an exoskeleton, and explicitly says that "weight is not an issue". And he's wrong, of course: weight is a problem. $\endgroup$ – Rekesoft Aug 22 '17 at 13:37
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What you need to look into here are the various material properties and the reasons you might want them in armour.

Strength: the strength of material is the amount of force it can withstand and still recover its original shape;
Hardness: the hardness of a material defines the relative resistance that its surface imposes against the penetration of a harder body;
Toughness: toughness is the amount of energy that a material can absorb before fracture.
Stiffness: the rigidity of an object — the extent to which it resists deformation in response to an applied force.

Now these properties are all very well, but they're not interesting within limits. They only become interesting at the point of failure.

Ceramics score fairly well on hardness, toughness, stiffness but very badly on toughness. Once the limit is exceeded it shatters and absorbs no more energy.

Steel doesn't score so well on hardness and stiffness, but it scores a lot better on toughness. When its stiffness is exceeded it deforms, first elastically, then plastically, absorbing ever more energy as it does so before ultimate failure.

We don't tend to wear steel as personal armour in the modern age though so let's compare ceramic armour to aramid fibre better known as the variety and brand name Kevlar.

Aramid is a very soft cloth with a very high tensile strength, it's immensely tough. The reason it protects you from bullets is that on impact the threads don't break, ensuring that the projectile remains outside your squishy parts. It doesn't protect you from the force of impact though, you'll get quite a bruise, and it's vulnerable to sharp edges, it won't protect you from a knife or a bullet with a sharp point.

Ceramic armour is much harder and stiffer, but with its relatively low toughness it protects you sacrificially. The energy of the impact is absorbed by the shattering of the plate. It protects you from armour piercing rounds, once. After which you need to replace the plate.

So which do you choose for your personal armour?

Both. Ablative ceramic plate over aramid cloth. A single material gives only a single set of properties, if you wear both you get both.

You're asking to be able to survive tank shells though. Tank shells are designed to kill tanks. You need to be carrying enough protection to survive that. Nzaman has given you basic values for mass and momentum, that's your first consideration.

A tank will weigh around 60,000kg, perhaps you won't want to be trying to carry that much weight on a mecha as you'd need to spread the weight, legs will just sink in, but it gives you an idea of the values you're competing with.

However ceramics come into their own in tank armour, their high hardness helps them resist shaped charges, ceramics alone won't protect you, but they are a critical part of your armour sandwich.

To armour your mecha you're going to want multiple layers of yes, ceramics, but also composites and steel giving you an equivalent of Chobham armour the different properties of the different materials in this sandwich will give you the best chance of surviving the attack.

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