How Powerful a Starship Coilgun Can We Make?

Question

I've spent a good deal of time working through the mechanics of 'realistic' space combat, and figure that good old kinetic projectiles will probably still at least be part of the arsenal, if not the primary weapon. The effectiveness of such weapons, however, is mostly dependent on the muzzle velocity. Let's assume we're using coilguns, to get around the friction problems inherent in a railgun. The question is: How powerful can we theoretically get them?

For reference, let's use the U.S. Navy railgun project. From what I understand, they plan on firing a 10kg projectile at about 2.5 km/s from a gun barrel about 10m long, for an acceleration on the projectile of about 31250 g's. Let's use that as our modern-day benchmark. Because of the way the distance / acceleration equations pan out, in order to get twice the muzzle velocity, we need either four times the length or four times the acceleration. If I assume that coilgun acceleration technology improves at a rate of 1% per year and that my ships are being built about 200 years from now, then we could expect to get guns with about 7.3 times the acceleration of today's railgun, for an acceleration of 228125 g's. If my gun barrels are 100m long, then that would give us a muzzle velocity of about 21 km/s. Is this a reasonable set of assumptions to work off of? What would go wrong?

Also, the 10kg projectile used today is rather small for what I want them to do. Can I increase the mass of the projectile without decreasing the muzzle velocity? If such a technique exists, could I use it to also increase the muzzle velocity beyond the rather tepid (by sci-fi standards) 21 km/s that I've already got?

EDIT: Ideally, I'd like a way to justify having 100 meter long guns be able to throw out 1-ton projectiles at 30 km/s or better. If they could get up to 100 km/s, that would be fantastic.

Answer 1

I'd like a way to justify having 100 meter long guns be able to throw out 1-ton projectiles at 30 km/s or better

I don't understand your strange "tons", so lets use a nice easy measurement like a tonne. Your projectile will leave the barrel with a hefty $4.5*10^{11}$ joules of kinetic energy. If your coilgun only wastes 1% of that energy in heating the projectile, 4.5 gigajoules of energy will be absorbed by it (a little over the energy released by the detonation of a tonne of TNT, as it happens). The specific heat capacity of iron (for example) is 450 joules per kilo per degree, and it has a melting point of 1811K. From a starting point of a comfy 293K, it'll take $6.6*10^8$ joules to raise a tonne of iron to its melting point. The latent heat of fusion for iron is 247kJ/kg, or $2.47*10^8$ joules. You will note therefore that the energy required to melt a tonne of iron is an order of magnitude lower than that 1% waste heat.

In theory, then, your gun will explode immediately. You'll also find that you just heat your projectile up to its curie point and then you'll have real problems accelerating it further (or possibly at all), though I expect you'll still be able to heat it up just fine. Hopefully it won't hit the walls of your gun. Hopefully also your gun doesn't have problems with "dry firing"!

Problem one, then, the inductive heating of the projectile is gonna have to be hella low. Your coilgun is probably going to have to be >99% efficient.

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Next, lets hazard a guess at the capabilities of your coilgun using a lazy trick from Luke Campbell (which I found on the ever-useful project rho). It isn't quite realistic, but it does give ballpark figures for the performance and plausibility of your magnetic guns.

Now assume that the barrel is filled with field, and that the projectile sweeps the field out of the barrel, turning the field energy into kinetic energy (this is not actually how coilguns work, but it gives the physical upper limit based on energy conservation). The energy density is about 400 kJ/m3/T2 times the square of the magnetic field strength (398,098 J/m3/T2 to six significant figures). Call this value K.

You now know the volume needed in the barrel based on how much energy the projectile ends up with

volume = kinetic energy / (K * (magnetic field)^2)

Lets imagine the barrel is 30cm across (a one tonne iron projectile would therefore be a little under 2m long). The swept volume of the projectile as it traverses a 100m barrel is therefore about 7.07 cubic metres.

Using the above formula, you're gonna need a magnetic field strength of 400T. That's a lot. This is waaaay above the magnetic saturation point for an iron projectile (1-2 tesla), higher even than the saturation point of a modern "high"-temperature superconductor (100-200T). You'll need to handwave greater-than-room-temperature superconductors to deal with that kind of field. Remember that if your field strength exceeds your superconductor's critical field the superconductivity goes away, and your gun will probably go bang, in a very bad way. Also remember that the dumb iron projectile mentioned above is a lot more tolerant of serious heating than your fancy superconductors, which will probably stop superconducting at much power temperatures than the curie point of iron. Your inductive heating requirements become even more stringent, which implies even greater efficiency required of an already stupendously efficient system.

Problem 2, then, is materials science. You're gonna need some absurdly optimistic super high temperature supercondutors to make this work.

(also, I hope you're just throwing dumb projectiles here. good luck getting any technology to survive the acceleration, heating and magnetic fields you're subjecting the projectile to here)

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If they could get up to 100 km/s, that would be fantastic.

If by "fantastic" you mean "solidly within the realms of fantasy" then you're in luck! The energy levels you'll need to deal with are a good two orders of magnitude greater. Your superconductors and projectile will need to be made out of fairydust.

Problem three: you're already waaay out at the bleeding edge of what appears to be possible. You can't really go any further.

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There are of course further problems related to the sheer amount of power you're going to have to throw at your gun to get it to boost the projectile to the required speed, the size and complexity of the associated ultracapacitor technology (which will go boom big time if damaged whilst charged!), the sheer amount of power your switches are going to have to handle in order to turn the acceleration coils on and off fast enough, the power generation requirements of your ship, the necessary heat rejection capability, and so on and so on. I think you're going to be disappointed, sorry.

Answer 2

So it's probably important to explain a few things here about physics and Newton's Laws. The whole point of a railgun is to be able to do a lot of damage with a smaller projectile by giving it far more velocity.

Momentum = Mass x Velocity

In this equation, what we're saying is that you can increase the damage caused in a collision with something in two ways; you can increase mass, or you can increase velocity. Actually, you can also do both if you like and that's what you're trying to do by having heavier ammo, but to what end?

Remember that in space in particular, any form of launch of ammunition, even a railgun, is also a thrust vector. That means, that if you increase the mass of the bullet that you're already accelerating to very high speeds, you're changing the vector of your ship in the process by pushing it away from the direction you're attacking. Not to mention of course that improving launch acceleration of the projectile while also increasing its mass means harnessing orders of magnitude more energy on the scale you're talking about.

Is it possible? Yes, of course it's possible. BUT, do to it you're effectively reinventing the battleship in space. These massive guns are going to push boats around quite a bit out there and as such, you're effectively going to need a massive boat just to keep things steady as you fire. That's probably a good thing because your boat has to be capable of holding incredible amounts of energy so probably houses some form of fusion reactor or banks of capacitors that make modern industrial batteries look like phone charging banks.

The important thing to note is the equation for energy;

Energy = 1/2 x Mass x Velocity²

What that means is that your energy requirements are proportional to the square of the velocity you want to achieve, and that the more mass you're accelerating, the more energy you have to put in. So, increasing your projectile weight by 100 means you need 50 times more energy just to give the projectile the same velocity, and to increase the velocity by 10 times you need another 100 times, so you now need a ship capable of unleashing 5,000 times the energy of the original railgun to get your ton of projectile to 100km/s - doable but very dangerous.

Ultimately, the size of the barrel is only important in terms of the speed at which you can impart the energy. Is 100m reasonable? I don't know enough about the technology to say but the point being that you have just increased your energy requirement by 5,000 and only increased your barrel size by a factor of 10, meaning that your new barrel has to be able to impart 500x the energy density (or 500x the energy per set length of barrel) as the original design.

If you get it working, the relative impact is going to be incredible and you'd be able to wipe out old ships with no problem, but just bear in mind that if you need a ship hundreds of times larger to run the guns, so does your enemy meaning that it may look impressive, but it's likely going to be just as hard to shoot the enemy down with these bad boys in your more modern context as it would have been with the current technology.

Answer 3

Muzzle velocities may be more modest than your projected velocity of 21 km/s. When Gerard O'Neill was conducting trials with mass-drivers. This was pioneering work for the construction of his proposed Lagrange cylinder habitats. This research found there was a limiting velocity of around 4 km/s. After which any projectile launched with a mass-river tended to (a) reach a limit where the electromagnetic field could not transfer more momentum to the projectiles, and (b) wreck the mass-driver.

Coil-gun technology might be better at launching projectiles at higher velocities than mass-drivers, and making sure projectiles continued moving in a straight line without making contact with the walls of the coil-gun.

You may need to take into account there could be practical limits to what can be achieved by coil-guns. This is based on empirical trials with mass-drivers.