How could a spacecraft defend against a train of small hypervelocity impactors?

Question

Hypervelocity (30 km/s) impactors tend not to penetrate that deep, even though they can have an enormous amount of kinetic energy. The penetration depth can be approximated by $l_i \sqrt{\rho_i/\rho_a}$ where $l_i$ is the length of the impactor, $\rho_i$ is the density of the impactor, and $\rho_a$ is the density of the armor. If the impactor is iron and so is the armor, then it only penetrates to approximately its length, regardless of its speed. As it does this it dumps all its energy near the surface of the armor, making a big, wide crater near the surface.

But what if instead of one long impactor, the attacker sent a "train" of little ones, lined up with each other, with significant empty space between one impactor and the next? The idea is that each little impactor makes a little crater. Then, a few microseconds later, the next one in the train hits the back of the crater, making another little crater deeper inside the armor. And so on. I've made some state of the art CGI to illustrate:

The maximum depth "drilled" by the train could be increased almost as much as you want just by making the impactors smaller and having more of them, for the same total mass. The main engineering challenge for the attacker would be making sure all the impactors lined up precisely one after the other.

It seems that such a train of impactors would also effectively defeat Whipple-type spaced armor. The point of Whipple armor is that an impactor "splashes" and disperses as it passes through the first layer of armor, so it is spread out more when it hits the next layer of armor and is more easily stopped. But with an impactor train, each impactor in the train just punches a hole in one layer of the Whipple armor, making way for the next impactor in the train to pass through the hole completely intact, without dispersing at all. The spacing/dispersion of the armor would be totally defeated.

How could a spacecraft effectively defend against this type of attack?

Answer 1

Your major issue would be having the whole train or even part of it impact the same spot when everything is moving that fast. Possible if you're firing head or stern on, but otherwise seems unrealistic to me.

You could accomplish it another way with the same hypothesis though. Shoot projectiles in front of the spaceship that explode leaving a cloud of fragments behind. The spaceship going through this cloud at 10-30km per second would rip it's shield to pieces with multiple impacts all happening everywhere on top of each other.

Then when/if the spaceship slows to avoid the cloud, rip into it with your train weapon.

Answer 2

This is the same working model as a practical pulsed laser weapon, and yes... if you deliver a fresh helping of energy to the bottom of a crater, you can dig it deeper.

However.

Pulsed lasers can make fairly strong guarantees about shooting straight, and given the reduced time of flight there's more scope for tweaking your aim. Once you've delivered a train of colinear projectiles, however, changing their direction is considerably more difficult. Moreover, it is an awful lot harder to shoot three bullets and be assured that they'll strike at precisely the same point even on a stationary target, as the weapon will be quite sensitive to even tiny variations in weight, heat and power and real-time compensation is tricky.

Lasers need to be pulsed, in part, because you don't want the energy to be absorbed in the flash of plasma generated by the previous pulse, but instead of cut a deeper hole. The same applies to your projectiles... you don't want the crud excavated by one projectile to hit the next one behind it, which risks deflecting it and greatly reducing its ability to deepen the damage track. You have to space your projectiles widely enough to avoid this issue, but the longer the length of time between impacts, the harder a job you'll have to ensure that everything fits into the same hole.

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crater 1/3 the volume = 70% the depth of the long impactor's crater

Well, no. That's not quite how it works, because hypervelocity jets penetrate well but don't really "crater" very much... the aspect ratio of a hit by something like a HEAT warhead is quite high.

(Image from Novokshanov and Ockendon, Elastic–plastic modelling of shaped charge jet penetration, which is a potentially interesting read by itself. Jet penetrated metal block from right side.)

You can't cheat your way past the penetration depth approximation by assuming the same total length of penetrator somehow cuts a deeper channel when it is spaced out a little bit! (have a think: in the limit, if you use a huge number of very thin plates, so closely spaced as to be all but touching, is your projectile train distinguishable from a solid rod impactor? would it have a different crater depth?)

This should also highlight the issues you'll have with shooting straight, because each projectile must fit neatly down the damage track created by the one in front of it, and any matter it excavates needs to squirt back out of the hole it came in, and it must not disrupt any projectiles that are still following and have yet to impact. As the hole gets deeper, the spacing between projectiles must increase, because it takes just a little bit longer for the crud to get out.

Anyway. The key thing is that your spaced projectiles almost certainly won't penetrate any deeper than a long rod of the same total length. Their benefit is that you can shoot a shorter total length and more effectively defeat spaced armor and active defense systems, because an impact to one projectile can't propagate back up to the next projectile in line, which might pass through the hole undamaged.

Anything that helps project against long rod projectiles will still help against colinear projectiles. There's not any other obvious easy win... relative motion of the ship by jinking or rolling would work just as well against both flavors.

That basically boils down to "don't get hit" or "carry a lot of armor", and in that regard, weaponry hasn't changed much over the last few tens of thousands of years.

Answer 3

Putting aside my inclination to frame challenge the notion that each individual impactor would hit the same point (which is a really really big problem) - there are a few options:

Hard-Kill Active Protection

The disadvantage a smaller projectile has over a longer projectile is that a a Hard-Kill system has to expend less energy to kill each projectile. Now, whether this is a Laser based system, an interceptor based system (think Patriot missles) or other - the principle remains the same - something from the ship reaches out and either destroys them outright or disrupts them so that they aren't focused on a single point or disperses them so instead of multiple projectiles, it's smaller fragments spread over a larger area.

ERA - Explosive Reactive Armour

There's a reason it's used against explosive penetrators - that is once the outer layer goes 'bang' - the plate flies off and disrupts the jet of copper. Now, it might have to be tinkered a little to work with your your train of impactors - but the basic principle of disrupting them is sound. As above, you don't have to stop them outright if you have armour, you only have to disrupt it enough so that all that energy isn't focused on a single point and causes a penetration.

Moveable Armour

Plenty of Sci-Fi ships have rotating thingies on the outside - whether it's for Artificial gravity or other cool reasons - why not have the armour move? Whereas in the real world, the hull of any fighting vehicle normally has certain constraints to do with either logistics, aerodynamics, fluid dynamics etc. a Space Vessel has less constraints - so making a perfectly round vessel, mounting the armour on a ball bearing type mount and have it continuously spin would mean that along with the movement of the vessel through space, that the impactors would not hit the same spot reliably enough to crack the armour.

Fluid Based Armour

Water does some rather interesting things when high velocity projectiles - it's quite effective at stopping bullets and because it's liquid, it will fill the void. Some super-dense liquid with a really strong attractive force (something something magnets something) could take the round, deform, heat up - absorb all that energy and then fill in the gaps left behind, by doing something magnet-y you can also get over the time it would take for the fluid to re-fill the void naturally.

And whilst it would require an outerlayer to keep the liquid contained, by magnetising it, you'd make it want to stick to the hull and you accept that in combat, you'd loose some of your effectiveness and need to repair the holes and top-up the liquid.