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 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?
Note, read the books, didn’t finish the show-
I think it’s a mixture of a few things-
Rail guns are midrange weapons in expanse. Their purpose is for when missiles have failed.
With that in mind I think the idea is that the speed is the key feature. Pdc rounds have travel time. Rail guns essentially don’t. They WILL hit at ranges too close for missiles and too far for accurate PDC.
I think the % of speed of light thing is “they don’t know the math”(be that the authors or the character) so I’m going to handwave the extreme overkill. The point is that with lots of jamming and physics going on, there’s range where a rail gun round is fast enough to mitigate all that. Oh and I do think the threat/ability to bombard is a mentioned secondary use of rail guns vs stations and planetary targets.
As for why it doesn’t fragment. Well first of, mostly because then the story doesn’t work. They want a certain kind of space battles and did a good job setting them up plausibly and shotgun rails ruin that. Ignoring that, I could see a “couldn’t figure it out” science explanation. Making a round detect the range, detonate, and have all the stuff needed to do that survive the obscene forces involved might just be on the too hard to be worth it scale
I would be very concerned about putting a tungsten round which is designed to explode and fragment through the rails on a railgun. A railgun works because it passes ridiculous amounts of energy through the round whilst it passes down the rail. Anything like a fuse would cause an insanely huge risk of the round exploding in the rails and breaking your railgun.
A coilgun might work for a birdshot style weapon, but the scale required for those is so much larger than would be needed for a railgun.
The shows weakest point to me vs the books was definitely the space combat. The ranges involved and speed just doesn't translate as well to the screen. They did an excellent job at finding a middle ground, but it means it's the last 'hard' sci fi element of the show and can't be critiqued as much.
In reality the plasma generated by the ships hulls and systems being hit would probably cause way more damage internally than the round itself.
One series I really loved for it's take on distances was the Honor Harrington books.
There was an odd mix of FTL tech and realistic slower than light stuff. FTL drives could be detected instantly, but communication and other sensor data followed light speed limits. There'd be these battle that were happening at insane distances like across solar systems.
So they'd be getting messages from other ships in the fleet, but they could tell from the sensor data that the ship had been destroyed and the guy they're talking has been dead for a few minutes.
That has piqued my interest. Just got the first book downloaded on Kindle. It's free for the first one! The art work looks very retro but it's only from 2012. I'm blasting through the 40k Horus Heresy saga ATM but when I fancy a change in pace I'll give that a read. Thanks for the recommendation!
Yea... much as I hate to admit it, I think you're probably right about it just being a way for the authors to lampshade the math. Plenty on online communities have speculated about somewhere between 1% and 10% of C but, as I laid out here, I don't think those values hold up. 0.1% of C is still plenty fast though.
I bet if I did a more careful reread of the books I could find engagement distance numbers and work out about how fast the rounds must be traveling... and I bet it would be a lot less than 1% of C.
I enjoyed the series, more in the early seasons than the later. But I have to say, as someone with a pretty solid understanding on algebraic kinematics, I appreciate the accuracy in the detail of your argument. You nail the physics discrepancies with accurate criticism and terminology. Perhaps the rounds were warheads that could fragment upon impact/proximity? Bit of a stretch, but given the magnetic acceleration method of a rail gun, it could be plausible?
In the show railguns are treated like super scary weapons that will annihilate anyone who gets close, which they really aren't in the books.
In the books their main draw is that they are a cheap alternative to torpedos, power is plentiful on ships and the tungsten slugs are cheap and easy to come by(you can buy them basically anywhere while only Mars and earth make the good torpedos).
I would argue that your entire post is a perfect argument for 0.1% being an "appreciable percentage of C." It might not be a huge percentage of C in raw numbers, but you can definitely appreciate the amount of energy.
I don't remember if they get into it much in the books, but I think the main thing is that it's sort of a precision stealth weapon. You mention the utility of a more destructive spread, but I believe the purpose was the opposite. One shot through the engine of a ship will completely disable it without killing the crew or destroying everything on board.
Outside of that, the railgun has other advantages. It can't be shot down by PDCs like missiles can and doesn't need any sort of active scanning to target. So it can punch holes in targets that are able to dodge or shoot down missiles.
So, that occurred to me too but, if that's the case, you'd want a smaller projectile that went faster. Punching a small hole in a critical component at distance is a great capability but, by reducing mass and increasing speed you can push out the distance at which you're capable of doing that and reduce your target's ability to "dodge".
Ultimately, the speed and mass of a railgun slug draw upon the same reserves of the firing ship: namely the power to run the railgun and the ability to absorb the recoil from the acceleration. Since power is effectively unlimited in The Expanse (fusion!) the recoil is the limiting factor. Dropping the mass increases the speed and increasing the speed pushes out the kill radius.
If 5 kg is only 2.3 cubic inches, I'm not sure you'd want to go much smaller. I don't know how you measure the damage caused by a 1 inch hole vs a 2 inch hole, but there's got to be a limit where you're not guaranteeing critical damage any more.
The only thing I can think of is that while pdc go through much of the ship, there are probably vital elements, like the engines, that are better protected, and it is this especially that a railgun would be the ideal weapon against. Another element that is in favor of railguns is that the speed of delivery increases their effective range since slower pdc rounds are easier to move out of the way of due to their lower velocity.
A slug is more versatile than "buckshot". If I had to put a hole in a single ship compartment and minimize the damage/loss of life in other parts of the ship, a single round that punches straight through a 2-hull ship is much cleaner than 421,136 super fast but tiny pieces of metal that might bounce off of each other or other objects/shrapnel and head in completely unpredictable directions inside/outside the ship.
I was more thinking of something like an anti-personnel artillery round. You'd fuse the railgun slug to explode some distance from its target. Since the intertia of the initial shot would be conserved, this would allow you to hit a target with a tightly controlled cloud of shrapnel moving at speed.
Of course, with that same capability you could just set the fuse to not detonate at all, giving you back the sabot round.
I'll confess that I only know about the books, and then only in outline. But I was fascinated by your incredibly thorough analysis and started thinking about the problem in general. I wonder if there is an argument to be made that such a relativistic railgun might be designed for precision targeting of specific, very-well-shielded ship components, like a precision sniper round right through the heart of the machine.
Seat of pants calculation, but 0.01c is around 3 km/s, I believe. I'm going to assume that at impact, the railgun's payload would interact with the ship's mass in the shape of a truncated cone whose fat end points downrange of the original impact. (That is, the cross-section of the damage would get larger as we move into the ship from the original impact. It's not physically realistic otherwise.) Presumably, the geometry of the cone would be affected by the materials in the ship, the speed of sound in those materials, and so on. Regardless, the cone might potentially intersect a significant amount of the ship's mass -- quite a bit more than a straight line through the ship would, since the cone's cross-sectional area increases quadratically with the distance from the impact point, and the cone would probably pass through many layers of heavy material in a large ship.
Since we have conservation of momentum, if that cone were to spread to include, say, 1,000x the original mass of the tungsten cube, the speed of all of the ejected matter at the end would average to (0.01/1000)c, which is now only 3,000 m/s (if I'm doing the math right in my sleepy head). We're starting to get down into the range of "armor can actually stop this".
If there was a really important small component on the ship, and it were nestled deep within the ship's interior, and the ship was (important!) able to withstand enormous, catastrophic damage to its outer layers... maybe a railgun might actually be relevant? Does this intersect with the lore of the story in any meaningful way?
Generally in the Expanse there are two major components that are relevant to this kind of long-distance shootout.
Everything else in the ship is in unpredictable places and/or is just window dressing on "keeping the humans alive."
We do see attempts to sniper-shot the reactor cores of ships but that is, more often than not, a threat made by a military vessel against a civilian one wherein the military ship need not worry about staying alive while it lines up the shot. In a pitched battle (and the Expanse is very much a Cold War analog story, so everyone is always preparing for a pitched battle) railguns are imagined as anti-capital-ship weapons which are difficult to evade and which can do catastrophic damage.
My physics is shaky at best but something to speculate on is that perhaps it could be explained by a legal prohibition. Similar types of munitions called flechette rounds are contentious and some argue they may be illegal. The Expanse is basically space cold war so if the two major powers agreed to ban a certain type of munition it would be extremely uncommon since they make most of the guns.
I rather like that explanation as well, though, as tossing nukes around in space seems like something that people take pretty-much in stride, I'm not sure that holds a bunch of water.
I don’t have any ideas, but i do want to acknowledge your first rate nerdistry. A solid tip o my fedora to you.
Been a while and this might be a mix of book and show recollection, so take with a grain of salt.
Rail guns aren't meant to be primary weapons due to the energy/weight investment and minimal effectiveness, also the difficulty in hitting a moving target. The projectiles can't maneuver, the path has to be planned against vehicles or missiles that can adjust out of the way. They do require precise targeting and planning over a long distance and often miss. When the target is mobile, and several minutes or even hours away as some of the battles are, it's easy to miss. Not to mention minor course corrections on the target or debris/obstacles. The characters in the book talk about it, the rail gun is a weapon of desperate last stands and luck. Often in the story they make dramatic, last second lucky hits for the sake of naval battle drama.
But overall the show / books are also known for fudging the math and physics somewhat just for the sake of storytelling. It's more about drama and storytelling than anything else.
I'm thinking that with that sort of energy a significant portion of the impactor would turn to plasma upon hitting even the minimal armour required for impact protection, and that plasma would then be more likely to spread out than solid tungsten (resulting in at least making a bigger hole on the other side of the ship). I'm not sure how well that idea translates to reality though.
I don't have the math to represent this adequately but the short version is that deflection is proportionate to the relative inertia of the elements in an elastic collision. Since the impactor has dramatically more inertia there is a pretty hard upper limit to how much deflection is possible. We also see anti-spalling coatings mentioned which should help address this concern.
I read somewhere that they didn't want the expanse to have a hard sci-fi vibe and thus some things are just voodoo black magic by design.