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Deep in space a colony ship continues to accelerate unaware of the volley of railgun rounds hurtling towards it. As the light from the attack reaches the bridge the PDCs (Point defense cannons) are brought online and set to intercept the rounds. Unfortunately the ship is so massive and has accelerated so much that dodging or turning is not a option.

The 10 PDCs are 12 barreled caseless kinetic cannons firing 2mm composite slugs and nano disassembly rounds at a 12:1 ratio at a rate of 400 rounds per second and a muzzle velocity of 1000fps.

The railgun rounds are coming in at 2000fps every 20s for a total of 16 rounds. They are 2.5 pounds of titanium and mix of dense metals.

Assuming all the PDCs can be brought to bear can the cannons defend the ship? Defense means no rounds hit the ship.

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    $\begingroup$ As noted in comments, 2000 fps is roughly chemical rifle based velocities, and not really worthy of typical "railgun" velocities. Square-Cube shows that your attack projectiles have a kinetic energy < 1 MJ. By comparison, the M1 Abrams fires shells with a KE of 12 MJ using a chemical charge. Can't your attackers do better than 21st century earth-based tanks? $\endgroup$ Jan 5 at 23:33
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    $\begingroup$ "has accelerated so much that dodging or turning is not a option." How much you have "accelerated" makes no difference to maneuverability. The only variables that matter are the time to impact from detection and how far your ship can move from rest in that time, because in space you are always "at rest" in your own reference frame. $\endgroup$
    – throx
    Jan 5 at 23:52
  • $\begingroup$ @throx Suppose we have a space ship that has a cross section of a mere 1000 m^2 going at 0.5 c. This ship is going to be plowing through the interstellar medium getting hit with kinetic energy on the order of 10^14 watts; that is more hard radiation than the entire power output of human civilization today turned into radiation energy. This ship must orient with shielding in front. The ship might be designed to thrust forward and reverse thrust to stop. Of course, such a ship is going was faster than the OP envisioned. $\endgroup$
    – Yakk
    Jan 6 at 4:42
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    $\begingroup$ @Yakk Well, yes, but anyone with the technology to push a ship to half light speed relative to the local interstellar dust and survive it is hardly going to have a problem just straight up ignoring a couple of railgun rounds moving at 1000m/s relative to themselves. I was more talking about something more pedestrian where the OP seemed to be under the assumption that the velocity of your ship relative to the starting reference frame was actually meaningful in terms of further acceleration ability. :) $\endgroup$
    – throx
    Jan 6 at 5:59
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You leave out a critical variable: distance at time of detection.

Suppose I am an ass. I have an old tennis ball and I am going to throw it at your head because I think people will like me if I do. Can you catch it before it hits your head, and then the people will like you instead? You are not a ninja but you are blessed with inborn ninja-like skills.

The first time I am 30 yards away. You see the ball coming. You catch the ball with ease and nod knowingly.

The next time I am 5 feet away. The ball is so close by the time you see it that there is no time for you to catch it and it bounces off your head. Hilarity ensues!

So too your railguns. If your ship sees incoming railgun rounds two miles (~10,000 feet) out (this is space, and it is not hazy!) you have over 4 seconds and so thousands of bullets to send at it. If you detect the incoming projectile 500 feet out it is going to hit you before you can hit it.

How early can you detect these railgun rounds? That determines the time you have and the time you have determines the likelihood of an effective defense.

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    $\begingroup$ Gotta love an answer that starts out with "Suppose I am an ass." :) $\endgroup$ Jan 6 at 2:30
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    $\begingroup$ Don't bring tennis balls to a railgun fight $\endgroup$
    – DKNguyen
    Jan 6 at 14:57
  • $\begingroup$ Suppose I am an ass. I have an old tennis ball and I am going to throw it at your head because I think people will like me if I do But asses don't have thumbs! $\endgroup$ Jan 6 at 16:38
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I did some quick math; Assuming that the weight of the slugs is negligible the impact of a slug against a railgun round would have around ~4.7 $\times$ 105 joules (1.13 kilograms moving at a relative speed of 914 m/s and a lot of rounding on the browser console). That's about 0.13 kWh, which according to my favorite table ever, is about 10% of what you need to obliterate a small vehicle in a laboratory.

If we assume a small vehicle weights around a metric ton, then we are speaking about total obliteration for something that weights 2.5 pounds (which is about 1.13 kg).

The problem that you have is that once you get to this level of destruction, you are not deflecting the incoming projectiles anymore. You are pulverizing them. They will still hit you - they will just be clouds of small bits instead of whole rounds.

The armor of the ship might be able to take this since the energy of a round will be spread over a much larger area (and a lot of it will miss). But if you just can't be touched by those rounds at all, then yes, it's a loss.

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    $\begingroup$ Turning it into plasma probably isn't a good idea. $\endgroup$
    – Mazura
    Jan 6 at 3:42
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    $\begingroup$ "They will still hit you - they will just be clouds of small bits instead of whole rounds." Whipple shields work exactly like this. en.wikipedia.org/wiki/Whipple_shield $\endgroup$ Jan 6 at 11:03
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Better solution than the PDCs...

  • Go down to the colony nursery and grab all the sand that can be spared.
  • Throw it out the rear hatch such that it disperses in your wake.
  • Wait for the railgun projectiles to hit your newly created micro-asteroid field at relativistic speeds.
  • Watch the fireworks from your now safe ship.
  • Use the PDCs on any projectiles which somehow get through the sand.
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  • $\begingroup$ 914m/s is barely relativistic, but it should make for a fine show indeed. $\endgroup$ Jan 5 at 15:51
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    $\begingroup$ You missed the bit that says "The railgun rounds are coming in at 2000fps ". Actually, come to think about it... that is one real poor specimen of a railgun! $\endgroup$
    – PcMan
    Jan 5 at 16:30
  • $\begingroup$ not if the projectiles have had to climb out of a planetary and star system gravity well @PcMan $\endgroup$
    – JCRM
    Jan 6 at 10:05
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Depends on the rest of your setting.

If a PDC hits one of the incoming railgun projectiles with at least one round (never mind nano or composite, mass matters here), it will impart some kinetic energy on the railgun projectile. That KE will change the course of the projectile.

That course change may or may not be enough to make the projectile miss. That depends in part on the size of your target, but also on how far out the hit takes place. And that, in turn, depends on sensors and targeting accuracy.

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