# Scaling Up Internal Mass Drivers?

Internal mass drivers are a potentially useful space drive, due to the ready availability of reaction mass (you can use anything from spare parts to literal dirt as a propellant, assuming you have a ferromagnetic bucket that you decelerate and retrieve at the end). However, on long trips on which in situ resource utilization may not be available, especially interstellar generation-ship trips, one would want a higher exhaust velocity, to maximize the fuel efficiency of the drive.

The excellent Atomic Rockets site contains this set of stats for a mass driver, but the exhaust velocity of 30 km/s isn't quite up to scratch for an interstellar spacecraft, even if you simply strap your craft to a convenient small asteroid to use for fuel. If we were to multiply the length of the drive by ten, according to the equation $$v_f^2 = v_i^2 + 2a \Delta d$$ (relativistic effects are negligible at these velocities, so we can ignore them), for a mass driver with the same acceleration, but ten times longer, we get an exhaust velocity of a bit under 95km/s, which is quite a bit nicer, even though we had to increase the mass of the drive and its power source by a factor of ten to increase the exhaust velocity by a factor of a bit over three. However, I don't know if it's actually possible to scale up a mass driver in the way I've described.

Would it be possible to scale up a Mass Driver by simply making it longer? Are there any factors that would require the mass to increase more than would be assumed from a simple "make it longer" perspective? Are there any other factors I'm not considering here?

• If you downvote, a comment with your reasons would be appreciated. That way, I can fix the problem and improve the question ;) – Gryphon Feb 11 '19 at 17:07
• Isn't fuel the bane of space travel? It seems you waste most of your acceleration energy just moving the reaction mass. – JBH Feb 11 '19 at 18:20
• @JBH, yes, fuel is the bane of space travel. That's why we're trying to make this more fuel efficient. – Gryphon Feb 11 '19 at 18:57
• As a side note, wouldn't it be much easier to just use an ion engine? Ions are easier to stabilize, easier to get up to relativistic velocities, and there's a lot more hydrogen in space than anything else. Asteroids are surprisingly hard to find, and if you strap one to your ship, you have to accelerate the asteroid as well as the ship. Plus, if you're already at speed, catching an asteroid will both be incredibly difficult, and will substantially decelerate your ship. – ckersch Mar 14 '19 at 18:11
• @ckersch The advantage of a mass driver is its ability to use anything as fuel. For an ion drive, you need a refined element, and most elements that work well in ion drives are fairly rare (hydrogen is a poor choice due to having low mass but not exceptionally low ionization energy, most of the noble gasses and alkali metals are superior). You wouldn't "catch" an asteroid for interstellar travel, you'd either match orbits and rendezvous normally or simply build your generation ship and mass driver on the asteroid itself (probably out of asteroidal materials). – Gryphon Mar 14 '19 at 18:18

Yes, but the engineering would be tricky.

Even getting to 30km/s is tricky. Current experimental railguns only manage between 2 and 3 km/s. A large part of that is due to limitations on the power supply and barrel length for practical weaponry applications (which are exactly the things you are looking at changing), but not all of it; even lower-powered railguns experience problems with rail erosion and electro-welding, which will seriously screw up an engine!

To solve those issues, you'll want to go with a coilgun (or "gauss gun") instead. I am not aware of any large-scale coilguns having actually been built; they are considerably more complex than railguns, as they require careful synchronization of different accelerator components. Small-scale coilguns, of the kind that a dedicated hobbyist could build in a garage, avoid the problem of electro-welding, but will still have to deal with frictional heating and barrel erosion. Fortunately, however, it seems that a large-scale coilgun can be designed to naturally center the projectile through magnetic levitation. While this sort of military-grade coil gun is currently only designed to hit around 3km/s in atmosphere, there is no fundamental reason why it could not be scaled up to arbitrarily high muzzle/exhaust velocities when operating in vacuum, as long as you ensure that the projectile never actually contacts the barrel walls. "All" you have to do is make sure that the wave of accelerator coil activations accelerates slightly ahead of the projectile for the whole length of the barrel, and that the barrel infrastructure can support the reaction forces. Since the force on the projectile need not increase with a larger length, it should be possible to extend the barrel indefinitely with only a linear increase in structural mass. Additionally, the mass of the barrel infrastructure can be kept down by simply putting a cap on the maximum mass of a single projectile (thus capping the force required to accelerate it)[*], and 95km/s is well below the speed at which electrical control signals can be sent along the barrel.

In practice, unless you have extremely good quality control on the inputs to your mass driver, you will not want to use a single centralized control system; the acceleration profile of each projectile will likely be slightly different, so you will want lidar sensors (or something equivalent) distributed along the barrel to measure the projectile's actual progress and trigger successive accelerator coils locally.

There is also the issue of bucket/sabot recovery. If you want all components of the drive to be reusable, and you want to be able to just dump whatever mass you have on hand into it as remass without pre-processing, then

1. You need an accelerable bucket to carry the arbitrary mass in, as you can't depend on the remass itself to have the necessary magnetic properties.
2. You can't throw the bucket away.

If you are OK with carrying some dedicated "fuel mass" and just augmenting it with arbitrary stuff, then you can throw away your sabots, and things become simpler. A similar situation applies if you have onboard facilities to refine mined materials into sabots--but then you can't just use whatever you find willy-nilly, and you have the added complication of the refinement and manufacturing facilities.

So, how do you go about recovering the bucket(s)? Well, for one thing, you know that an empty bucket obviously has less mass than a bucket full of remass, so you can decelerate it much more quickly given the same amount of force--and since the deceleration stage will put the barrel under tension, you can use a much higher deceleration force! That means that bucket recovery will not take up half the length of the barrel; 10% or even less would be plausible, and the size of the deceleration section will scale linearly with the rest of the driver. The tricky bit will be actually catching the buckets at the end and returning them for re-use. I am not at all sure how to arrange that infrastructure in a way that leaves an opening for the remass to pass through and does not add a bunch of moving parts that are then prone to potential failure.

[*] You can save even more mass by arranging the mass driver in a tractor configuration, with the barrel extending in front and the bulk of the ship arranged around the nozzle. This will put the whole thing in tension, and structural metals tend to be much stronger in tension than in compression (if you are building the support structure of the barrel out of asteroidal rock, on the other hand, that would be a bad idea, as rock is much stronger in compression). If you arrange things carefully, you can make sure the deceleration section is also in tension, but if that becomes impractical, take comfort in the fact that the bucket deceleration section is relatively tiny anyway, so you still get a net saving in total mass.

• As a side-note, the wikipedia page on coil guns is a bit deceptive about the definition of a gauss gun. Coilguns which you describe here were invented by Kristian Birkeland. Gauss guns which use momentum transferred between colliding magnets were invented by Carl Gauss and are distinctly different than a coilgun, but sci-fi often confuses the two. – Nosajimiki - Reinstate Monica Mar 12 '19 at 15:24
• "make sure that the wave of accelerator coil activations accelerates slightly ahead of the projectile for the whole length of the barrel" Would this imply increasingly rapid shifts in the current that has to travel through successive coils (going from zero current to some maximum value in smaller and smaller increments of time) as the velocity of the projectile increases? If so would this imply some limits to how fast a projectile could be realistically accelerated by a giant coilgun, just based on the maximum rate current can increase in known materials? – Hypnosifl Oct 15 '19 at 0:10
• @Hypnosifl No. The time it takes a coil to ramp up to maximum field strength doesn't matter nearly as much as the interval after which you begin activating each successive coil. Being able to switch a single coil more rapidly will give you greater efficiency, but does not fundamentally limit the maximum projectile velocity. – Logan R. Kearsley Oct 15 '19 at 19:38

Ouroboros mass driver.

The thing about the long long long mass drivers is that each set of coils gets one use for each chunk of propellent and then it is done. Inefficient! They are expensive, those coils. And it is one thing to have a 2 km barrel lying quietly on the moon, another one to mount it sticking priapically out of your starship. The aesthetics, you know.

I propose the round mass driver, which your ship will wear tastefully girdled about its midsection. The payload goes around and around the circular track, passing through the same set of coils over and over, accelerating as it goes. Each pass through your coils adds energy. Of course, larger is better here because of the centrifugal force pushing your projectile against the bottom of the track as it turns, but your track is tough stuff and you can rig your secondary semicircular coils to exert a magnetic force on the projectile opposing its tendency to push out radially.

The final speed of your projectile will depend on what sort of radial forces your track can withstand and how successfully you can counter that radial force with magnetism. At the point of release your track will open up (hopefully at a purpose-built point for opening) and the spun-up-to-speed projectile will emerge.

Also, this device will make a terrifyingly awesome sound, audible in all parts of the ship.

• Well, you made me look up a word, so good for you. I don't often have to do that. My one issue is that, at these speeds, it'll do horrific things to both projectile and track if you do anything but magnetically levitate the projectile in the center of a hard-vacuum containing barrel, which will probably negate the cool noise. Other than that, this is a good alternative to a linear mass driver, so +1. – Gryphon Mar 13 '19 at 21:00
• Also, it'd be really great if you could find an equation relating ring radius, maximum exhaust velocity, and whatever other factor is relevant (probably the maximum force of the electromagnets and/or structural strength, I'm not sure), but that'd be a bonus, not a requirement. – Gryphon Mar 13 '19 at 21:03
• @Gryphon: Looking up word - very good. Use it often. Re noise, you are right, which is a shame. Re the math: I will embarrass myself. But anyone interested in plunking some figures into this, please do. – Willk Mar 13 '19 at 22:40
• Re: math, I'll see if I can find anything to edit in. I'm not all that smart, but Google is. – Gryphon Mar 13 '19 at 23:05
• Also, re: word: wouldn't a large circle around the ship have the opposite sort of imagery? I'm not sure if that's actually an improvement. – Gryphon Mar 14 '19 at 0:09

There are three things that I can think of that would stop your mass driver design scaling linearly.

1. You need your structure to maintain some minimum level of rigidity rather than the whole thing bending and flexing on every shot. As I am not a structural engineer, I can't actually tell you what wort of material limits you might hit, but at some point, your materials are simply not going to be up to the job.

2. Inefficiencies. Some proportion of your mass driver's energy is going to end up heating the bucket instead of pushing it. If you pump that energy in faster than the bucket can radiate it out, you're eventually going to have the whole thing explosively vapourise. You will not reach Alpha Centauri today. If you're not using superconductors, you'll also find that losses in your big power lines will be a bit of a problem, too.

3. Power switching. In a coilgun, you'll want to be able to turn off a coil ASAP once the drive bucket is through, or it will just cause drag and slow everything down. The faster your bucket is going, the harder it is to turn things on and off fast enough. I seem to recall reading something about superconducting drive coils which you'd cook with lasers to quench them as fast as possible, but I sense lifetime limits and cycle time issues there!

There are other ways to improve your mass driver though... consider using superconducting buckets instead of ferromagnetic ones, because you don't hit magnetic saturation issues at a puny tesla or two, but instead can use tens- or even low-hundreds-of-tesla magnetic fields. You'll squeeze a few extra percent of efficiency out of the system too.

(in the limit, you may find it easier to simply ionise your reaction mass with electron beams, and accelerate the cloud of plasma out the back. that works with any fuel too and might end up being simpler to make!)

The problem is that your giant, hard-to-build, hard-to-run mass driver still only provides a puny 10000s $$I_{sp}$$. That's a slow boat to the Oort cloud, let alone visiting another star.

Assuming a 100km/s exhaust velocity, and a pretty optimistic 1000:1 mass ratio, you've got a $$\Delta_v$$ of 690km/s. If you blow it all on acceleration, and use some other means to stop, it'll take you nearly two thousand years to get to Alpha Centauri. I'll bet you ten bucks that in that timespan, someone will have invented a better drive. If you're lucky, they might collect you on their way past.

The take-home message should be "don't use mass drivers for starships". Or visiting the outer solar system, for that matter. Leave em to the 1950s asteroid miners.