Reducing required length of a mass driver using loop?

If you had a loop of electromagnets with an encapsulated payload inside vacuum tubes, how fast could you accelerate the capsule to before it reached some maximum velocity?

What effect would scale have on the answer to that hypothetical?

And would it be worthwhile to have such a loop as a first stage in a mass driver to reduce material and space requirements?

• Well, getting things to go around the loop is a whole other engineering problem... Commented Jul 17 at 15:18
• SpinLaunch FTW. Commented Jul 18 at 7:46
• "electromagnets ... vacuum ... how fast?" I guess light speed. More on physics.SE. But asking here provides the practical answers I think You expected. Commented Jul 21 at 22:00

A particle accelerator fits the description given in the OP (albeit for a very small payload) and can reach 99.99....% (more 9s than matters) the speed of light. So that's the maximum speed, essentially the speed of light as long as you're prepared to cope with high $$g$$ forces - which is well explored in this classic XKCD what-if (also available as a video).$$^1$$

But raw speed at ground level is not all that useful for getting stuff into orbit. If, through whatever mechanism, you accelerate a payload up to orbital velocity in the low, dense parts of the atmosphere, it will burn up before it gets anywhere. Think about how destructive the forces of re-entry are when a spacecraft is moving at about orbital velocity but going through the very thin upper atmosphere. Moving the same speed at sea level would be many orders of magnitude worse because the air is $$10000\times$$ denser. Even if that doesn't destroy the payload the air resistance would slow it down vastly, to far below orbital velocity. So you have to get it going even faster initially to compensate, which makes the whole problem worse.

Of course you don't have to accelerate it all the way to orbital velocity, you could "only" give it the speed that the first stage of a standard rocket would, and have the payload include a traditional second stage rocket. This would still leave you having to handle a vastly greater max Q, again, because of the high speed in the thick, dense atmosphere. Which leaves you needing to engineer the whole second stage of a rocket to survive that, as well as building an accelerator that has to accelerator a mass many times larger than the final payload.

Conventional wisdom concluded a long time ago that the atmosphere makes such schemes non starters. That's why some proposals for linear accelerators have them be very long and extend dozens of kilometres in altitude - at that point the air is much thinner and less of a problem. Of course, building such an aerial vacuum tunnel comes with countless difficulties of its own, and we're basically in Space Elevator level of scifi. That's not to say that the general idea wouldn't work somewhere without an atmosphere, like the Moon, or a very thin one, like Mars.

SpinLaunch, however, thinks that the many problems mentioned above are surmountable in the near term. But I'm not the only one who suspects that company will be far more successful at parting investors from their money than getting payloads into space.

$$^1$$ Pedantry Corner: A particle accelerator works because it's accelerating stuff that has an electrostatic charge - this would not be the case with a mass driver. Electromagnets could be used to give the payload a magnetic field but not an electrostatic charge, so the workings would be fairly different on an engineering level even if Maxwell's Laws are pretty symmetric between magnetic and electric fields. Particle accelerators also have to deal with keeping the particle beam tightly focussed - something which is clearly not an issue when the payload is a single macroscopic object

• The fact that a particle accelerator fits the question's description just cracks me up, honestly. Commented Jul 17 at 18:17
• @Cadence I guess it might be desirable to keep all the "accelerator parts" close together on the ground, rather than having them spread out in a kilometres long vacuum tube? Keeping the latter simple and free of machinery could be better? But as it's all fantasy from current technology, fine tuning the details like this seems rather pointless. Commented Jul 17 at 22:19
• Mountains are too low. Even at the very peak of mountain Everest (where, needless to say, constructing a massive facility would be very hard) the air is only 3 times thinner than at sea level and 3000x denser than at the Karman line (which is roughly where reentry physics starts being important). There's always a trade off between multiple factors (velocity given by accelerator, g forces felt, size of upper stage being accelerated, altitude, cost of construction) and no compromise between these factors looks plausible or worth it. Commented Jul 18 at 18:06
• Basically yes. Unless you believe SpinLaunch, but they're probably a scam trying to make money from investors who don't know better. Commented Jul 18 at 19:33
• And, if you do look at SpinLaunch and know enough math to realize how the g-forces for the spinning part scale up, the atmosphere is the least of their worries. They need some kind of unobtainum to build the arm out of in order to stand up to to the 30,000g forces (IIRC, been a while since I did the math, but it was about that absurd. More violent than being fired out of a literal cannon, sustained for minutes instead of fractional seconds.) they're going to end up with and I'm not sure what kind of payload they think they're going to launch other than liquids and solid blocks of metal... Commented Jul 18 at 20:55

You can certainly do this, but the maximum potential speed and other technical questions depend heavily on the desired operating parameters of the accelerator. There isn't a simple answer.

While in the loop track, you need a way to provide enough centripetal force to stop the cargo from punching out through the wall of the loop. That could be provided by magnets, or by wheels on a physical track, or whatever -- but also remember that whatever force the loop puts on the cargo, the loop has to withstand an equal and opposite force. The loop forces the cargo onto a curved path, and in return the cargo puts potentially enormous forces on the loop. The physical engineering of the loop determines what the maximums are for that -- the wider the loop, the lower the forces, but you gain less benefit as compared to a straight track.

That curve will also produce equivalent G-loading on the cargo based on the radius of the loop. If you're building a mass driver weapon or delivering the output from a mining/smelting operation, maybe that doesn't matter, because you're firing a solid metal slug and the limiting factor is purely the mechanical forces you're putting on the loop itself. But if you're trying to use a mass driver to launch goods or living humans, you probably need to keep it down to a single digit number of Gs to prevent damaging your products or injuring your passengers.

As an example of this that uses a physical rotor instead of magnets, look at the SpinLaunch project. The technical limitations of the system are non-trivial -- it's not remotely suitable for anything living, and even electronics have to be designed to withstand the forces involved, but I could certainly see a similar system that's intended to operate in a hard vacuum environment and adds a magnetic track to the outbound end of the thing.

• I figured being in the tube & using em would reduce friction & heat. and being in a sturdy capsule with gel padding internally would protect cargo. I think if the system had to go slow enough to support bio cargo it wouldn't be worthwhile. But even if it was just able to launch raw materials to be collected and used for construction in space that would still be useful, even if you couldn't deliver anything else. Ideally you could deliver anything that wasn't overly fragile, if the forces were consistent & stable things wont shake loose etc, especially if firmly embedded in the casing? Commented Jul 17 at 15:49
• Padding is typically not an issue; when we talk about force loading limits, we're not talking about objects flying around inside the capsule, we're just talking about things breaking due to their own weight. Commented Jul 17 at 16:19
• Like on material molecular structures level? Or, if you have a gameboy as a unit internal components will break off? Commented Jul 17 at 17:35
• Meaning internal and external components can bend or break from the stresses. If you put satellite into a launch system that subjects it to 50 G forces, all sorts of antennas, solar arrays, batteries, even circuit boards and wiring, can become too heavy for their mountings to support, or just bend under the force and become damaged. You can design around that, but it's a significant limitation on the kinds of things you can launch. Commented Jul 17 at 18:14
• Understood. I think the main use would be in getting material to construct fab facilities in space, then it would be significantly easier to expand space infrastructure and build things directly in space. Commented Jul 18 at 17:57

Centripetal acceleration, $$a_c$$ is

$$a_c={v^2 \over r}$$

If 'r' is the radius of the planet, and 'v' is orbital velocity, then '$$a_c$$' will be 1G. If you travel in a circle with a radius of $$0.5 \times r$$ but maintain 'v' you'll end up with 2 G's of acceleration. If your payload and passengers can withstand 10 Gs, then the circle's radius will be $$r_{planet} \over 10$$, or 637.8 km and it's circumference will be ~4000km.

At 10 G's, you can accelerate in a straight line up to orbital velocity in a lot less distance than 4000km. $$t={v \over a} = {7800 \over {10 \times 9.8}} ~= 80sec$$ $$d = 0.5at^2 = (0.5)(10 \times 9.8)*(80^2) = 310408m ~= 310 km$$

So, it makes more sense to accelerate in a straight line if your goal is orbital speeds and you want to keep the g-forces in the "human-rated" range.

• I don't really want to keep the g-forces in survivable ranges, just to reduce construction requirements of the overall system by reaching some maximum in a loop. I'll think over the maths provided. Commented Jul 17 at 17:34
• If you don't care about G-forces, just accelerate hard in a straight line @FellahWithNoMentalModelsHere
– JCRM
Commented Jul 17 at 18:29
• @JCRM If we aren't worried about keeping the g-forces under control, then I think we can assume the track is already accelerating at maximum capacity and we're now looking for ways to reduce the accelerator footprint by having the cargo reuse part of the track. That's why particle accelerators are in a ring and not just a line that pushes harder. Commented Jul 17 at 19:27
• @DarthPseudonym That bit about particle colliders is not really true. There are linear accelerators and colliders. The reason for circular colliders is not to reuse the accelerator, but to reuse the particles - most of them pass each other without colliding and would be a huge waste of energy. Linear colliders could also do this but it is much more complicated. For a mass driver, the consideration is if can you apply more force to revolve a mass around the track than you can push forwards with. That may be true e.g. if power cannot be delivered fast enough to accelerate straight. Commented Jul 19 at 16:16
• @Morphit The LHC takes almost half an hour to get the particle stream up to the desired operational speed. Even the old SPS that now serves as the "preaccelerator" for LHC takes a few seconds to get to its maximum energy, which represents thousands of laps around the 7 km track. Commented Jul 19 at 17:49