The Expanse: Thoughts on railguns
Having finished out the Amazon Prime series "The Expanse" I'm now working my way through the novels and I keep coming up against a problem with with railguns. Specifically, the way that railguns...
Having finished out the Amazon Prime series "The Expanse" I'm now working my way through the novels and I keep coming up against a problem with with railguns. Specifically, the way that railguns are used in The Expanse doesn't mesh well with the way they're portrayed.
First, some background. Ships in The Expanse are generally unarmored. There are a bunch of reasons for this but the short version is "most things that can hit you in space will kill you anyway" and armor adds mass which makes every manuver more expensive in terms of reaction mass. So no one has armor. This is important because it means that ships in the Expanse can get ripped up by something as mundane as a stray bullet from a Point Defense Cannon (PDC). PDCs are... well, they're guns. Regular guns which are flinging around much less mass and at much lower velocities than railguns.
Thus, ships in the Expanse are equipped to handle impacts but nothing much bigger than a sand-grain moving at a few km/s.
When we're introduced to rail-guns in the series we're given to understand that they use magnetic acceleration to chuck a 5kg chunk of tungsten and/or uranium at a target at an "appreciable percentage of C." That's much faster than a bullet or any micrometeors ships are likely to encounter. Even 1% of C is ~3,000 km/s.
5 kg of Tungsten is less than you think. Some back of the envelope math suggests that's about cube about 2.6 inches on a side... which is not big. That works out to an incredible energy density which would make a lot of sense if railguns were routinely being fired at planets or asteroids but, since they seem to mainly target ships, the vast, vast majority of the energy that goes into flinging that slug at its target is going to carry through to the other side of the ship.
All total we're talking about 488.5 million Newtons of force for 1% of the speed of light. Helpfully, this scales roughly lineraly so long as we don't get too close to C and induce relativistic mass issues, so 10% of C is 4.8 billion Newtons and so on. So, that railgun slug is carrying a lot of energy. At 1% of C it represents 22.5 trillion joules of kinetic energy. Written out long-ways so we can appreciate all those zeros it's 22,500,000,000,000 J. At 10%, we're talking 2.25 quadrillion joules. To give some sense of scale, that means that, at 1% of C, three rail-gun slugs are delivering about as much energy as the bomb that destroyed Hiroshima in 1945. At 10% of C one round carries about 537 kilotons, or about the yield of a modern, city-busting hydrogen bomb.
Those are absolutely titanic amounts of energy but, realistically, they'll never deliver that much power to a target. After all, a railgun round can only push on its target as hard as the target can push back on it. If the round just punches through the entire ship like it's made of paper, most of the energy stays in the railgun slug as it exits the other side of the ship and you get a neat hole rather than a gigantic flash as trillions of joules of kinetic energy turn into heat.
And obviously, if we're trying to kill things, we want the latter. The solution to this problem is fairly obvious: you need fragmentation. While it's great to have a tungsten cube all tightly packed together as you accelerate it, if you're shooting at a ship, you want a fairly diffuse impact, especially if we're talking about a 10% of C railgun slug. There aren't a lot of things out there in the solar system which can take 500 kilotons of hate and come out the other side in one piece. Moreover, at the distances at which a rail-gun fight happens, that spread would help ensure that you hit your target. Like a shotgun loaded with birdshot, a fragmenting railgun round would provide a cone of impact rather than a line, making dodges less effective.
And, as I mentioned earlier, you don't need a ton of mass to make this work. If a PDC round can go straight through a military craft then we can safely assume that a chunk of tungsten with the same kinetic energy will do the same thing. PDCs look rather a lot like the close in weapons systems in use on many naval ships today so we'll use those as a guide. The 20mm cannon on a Phallanx CWIS tosses out rounds at about 1,035 m/s. Those rounds weigh about 100 g (0.1 kg) which gives them a kinetic energy at the muzzle of 53,422 J.
So, if we could predictably shatter our 1% C railgun round into 421,136 pieces, each would have about the same kinetic energy as a PDC round and be able to hole the ship. At 10% C we could go even smaller and do the same thing with upwards of 40 million shards. 1% is plenty though. Each hull-penetrating piece of our original 5 kg bullet needs only weigh about 1/100th of a gram, which works out to being about 1/100th of the size of a grain of sand.
Put another way, if the fragmentation of a rail round could be precisely controlled, a target ship would experience hundreds of thousands of individual hull breaches with the mean distance between them determined only by the geometry of the ship and the angle of the attack. The result of this would be either the delivery of a titanic amount of energy to the ship itself as the armor attempts to absorb the impact or, if no armor is present (as seems to be the case in the Expanse) the rapid conversion of the interior of the ship to a thin soup.
This, however, seems never to happen in the series and what leaves me scratching my head. As a book and TV series, The Expanse does an otherwise bang-up job with hard science fiction. Most things in universe make sense. This, however, does not. We have take as a given that the materials science technology exists to allow the mounting and firing of a railgun on a ship -- there are a lot of challenges there -- but the straight-line-of-fire use of them is a rare problem with the world-building.
Any fans have any suggestions to help me square this circle?