What is the best engine type for linear acceleration?

Linear Acceleration: A form of transit in space flight where a spacecraft points toward a destination and accelerates for half of the distance it needs to travel, then decelerates for the other half, currently not viable due to the high amounts of DeltaV and fuel required.

I'm working on a Sci-fi universe where due to humanity's lack of gravity manipulation technologies (BS artificial gravity plaiting, anti-gravity, etc.) human ships are oriented like towers (Engine being like the foundation, decks being different floors) and use Linear acceleration to mimic the sensation of gravity in space. (yes I did get inspiration from the Expanse)

Qualities im looking for:

1. high fuel efficiency
2. capable of acceleration of 9.8 m/s^2 or higher for days to years at a time
3. the shorter the structure, the better (no kilometer-long metal structures, as flipping halfway for deceleration would cause high amounts of stress on the craft that could tear it in half)
4. Optional: cool as all heck
5. Also optional: doesn't involve super-hypothetical tech (Such as small artificial black holes)
6. Technology at this point is to where fusion reactors are possible to build and maintain for long periods of time and Mankind is close to antimatter technologies (synthesis, reactors, etc.) and basic FTL (akin to a warp drive) (FTL is used to jump between two points in space nearly instantly but is incredibly dangerous, thus traditional space travel is used for interplanetary distances and traveling to jump points)
7. The distances travel range from between Earth and the moon to Earth to the farthest parts of the Kuiper belt
8. The engine can be turned off and on a near infinite amount of times (a common problem with current rocket technology is that engines can be ignited and shut off only a set number of times)
9. RADIATION IS NOT A CONCERN FOR ME As long as it can be shielded against, as these engines are only used in space.
• Best under which metric?
– L.Dutch
Commented Nov 17, 2022 at 16:09
• Another metric that would be helpful o know would be distances you have in mind. Interplanetary or interstellar? Commented Nov 17, 2022 at 16:49
• Items 5 and 6 contradict each other. Commented Nov 17, 2022 at 17:20
• There's a big difference between an organization with a half a Billion dollar yearly budget, being able to trap 3 anti hydrogen for 1000 seconds, and a non-hypothetical antimatter drive. Commented Nov 17, 2022 at 17:49
• @redfrogcrab square-cube was probably referring to the "basic FTL" and "warp drive", which is very much not compatible with (5). Commented Nov 17, 2022 at 22:11

Scientifically realistic option: the nuclear salt water rocket

From the question I'm not sure if you are looking for a scientifically realistic answer, with not involving super hypothetical tech being optional and all. If not, there are plenty of fictional options, e.g. the Epstein drive from The Expanse. It's described as being fusion powered, but how the drive as a whole works is just handwaved, and not possible with currently known technology.

If you are looking for something scientifically realistic, an answer that's still missing here is the nuclear salt water rocket. Nothing like it has ever been tested, but the design is based on powering a rocket with a continuous nuclear reaction. According to the Wikipedia page,

The design and calculations discussed above are using 20 percent enriched uranium salts. However, it would be plausible to use another design which would be capable of achieving much higher exhaust velocities (4,725 km/s) and use a 30,000 tonne ice comet along with 7,500 tonnes of highly enriched uranium salts to propel a 300 tonne spacecraft up to 7.62% of the speed of light and potentially arrive at Alpha Centauri after a 60 year journey.

I haven't done the math on how this works out for linear acceleration in the solar system, but with the above I'd guess it is at least in the neighborhood.

edit:

A bit more sci-fi but in line with your technology level: the direct thrust fusion rocket

Reading your requirements again, having a somewhat serious proposal in the current scientific literature doesn't seem to be the tech level you're aiming at. If they have experimental antimatter and warp-like technologies, they probably also have direct thrust fusion rockets. A deuterium - helium-3 fusion rocket has an exhaust velocity just above 21,000 km/s* assuming 100% conversion efficiency. Using magnetic fields to confine the reaction and direct the reaction products shouldn't be a problem, and should help with the longevity of the engine. According to Scott Manley, the Expanse's Epstein drives would need an exhaust velocity of 10000 to 15000 km/s, so this is perfectly in the range. Scott discusses that an Epstein drive fueled by deuterium - helium-3 fusion would still emit part of the fusion energy as energetic neutrons and hard X-rays and that would be enough to melt the rocket, so you'll need some science-fictional technologies to improve the cooling and/or reduce these side conversions, but that doesn't seem more difficult than handling antimatter and FTL.

Small scale versions (where the heating is manageable, but thrust and exhaust velocity are much lower) of such direct thrust fusion drives are actually being researched. You just need to scale it up.

So at the tech level you seem to be targeting, something like Epstein drives are perfectly possible.

* Calculated by converting the energies of the reaction products (3.6 MeV for the alpha particle and 14.7 MeV for the proton) to their velocities and taking a weighted average. If you are able to (magnetically) split the alpha particle and proton streams and transfer energy from the protons to the alpha particles so they both have the same velocity, you can get an even higher average exhaust velocity. If you have technology to ensure neutrons are emitted in the right direction or can be redirected, deuterium-tritium fusion gives about the same exhaust velocities, but then you need to deal with neutron radiation in your rocket exhaust.

TL;DR: rockets are limited in many ways. You can have high thrust, or high efficiency, but trying to combine the two does not work well if you're constrained by real world materials and physics.

Don't use rockets to provide artificial gravity.

high fuel efficiency

With rockets, this means high exhaust velocity, and good ways to get stuff moving fast are nuclear reactions. These are doubly useful in that they provide the energy to their exhaust products, so your fuel and your reaction mass are the same thing, which makes the plumbing easier.

Fusion reactions have products shooting out at up to 10% of lightspeed. Antimatter annihilation has stuff coming out faster, but for complex reasons is doesn't end up being quite as good as you might think.

capable of acceleration of 9.8 m/s^2 or higher for days to years at a time

The former is very, very tricky. The latter is stupendously difficult.

The problem with rockets with very high exhaust velocities is that they tend to be low thrust. If you can scale them up (and not all designs scale up well), then you have the problem of them requiring huge amounts of power, and hence huge amounts of heat.

Really huge amounts of heat, and really huge amounts of power.

The thrust power of an engine is $$F_p = \frac{FV_e}{2}$$ where $$V_e$$ is exhaust velocity and $$F$$ is the thrust in newtons. A 1000 tonne spacecraft accelerating at one standard gravity has a thrust of 9.81MN. With an exhaust velocity of 5% of C, that means a thrust power of ~74 terawatts.

Super-high-power nuclear rockets are also notoriously inefficient. Antimatter rockets lose >30% of their power output to hard gamma radiation. Fusion rockets lose at least 25% of their yield to x-ray and neutron radiation. That means carrying around huge radiation shields, and vast heat radiators to stop them melting.

But lets get back to your "years at a time"!

That gives you two additional problems.

Firstly, accelerating for a year at 1G gives you a velocity of about 0.72c, (including relativistic corrections). That means every gram of space debris you hit has the energy equivalent of 9 kilotonnes of TNT. Think about how easy it is going to be to armor you ships against that sort of punishment.

Secondly, now we've established that both Newton and Einstein hate your ideas, Tsiolkovsky gets to join in too. The relativistic rocket equation says that a fusion drive with a 0.05c exhaust velocity needs a mass-ratio of >70 million... that means that each gram of dry mass of your rocket, you need 70 tonnes of fuel to run that rocket for a year.

You can use antimatter instead, which needs a mass ratio of merely 15, but that comes at a cost of a thrust power of 485TW, and to achieve that you're emitting hundreds more terawatts of pure gamma radiation which needs massive shields and even more huge heat radiators to stop them boiling away in an instant. Also, carrying around kilotonnes of pure antimatter has its own risks.

Optional: cool as all heck

Cool is subjective. I like the 2014 Firefly design from Icarus Interstellar... its awkward to get free papers about it anymore, but Project Rho has a nice summary. It should give you a good idea of the scale of the heat radiators that fusion rockets need. It would have a thrust measured in centigees, and a payload of ~150 tonnes for many tens of thousands of tonnes of starship. It is a pretty realistic design.

and basic FTL (akin to a warp drive)

Just use that for long distance travel. Forget using rockets to provide gravity... physics just won't let you do it nearly as well as you'd like.

• To be fair, the problems with travelling at any substantial fraction of C (impacts, etc) are something you're really going to have to deal with regardless, because if you're going to get anywhere in any reasonable timescale, you're really going to need to go at a decent velocity anyway, no matter what technology or technique you use to reach that speed... It's not really a problem specific to this scenario, but applies to most scenarios that aren't going to take centuries to get anywhere useful. Commented Nov 17, 2022 at 23:16
• Re "Fusion reactions have products shooting out at up to 10% of lightspeed": Wikipedia and this page seem to have it "only" in the hundreds of km/s, which is two orders of magnitude lower. Commented Nov 18, 2022 at 10:37
• this drive would be used to cover interplanetary distances, with FTL doing the super long-distance interstellar travel Commented Nov 18, 2022 at 19:54
• @redfrogcrab that makes no sense at all. Why not keep firing up the FTL drive until you get to where you want to go? Commented Nov 19, 2022 at 8:31
• @Peter-ReinstateMonica I was very careful to state "reaction product", because the products of a fusion reaction do travel at that speed, and therefore represent an upper bound for the exhaust velocity and hence specific impulse of a fusion rocket. Current designs involve exhausts which are not pure fusion products, but include non-fusing material that is heated by the reaction. Commented Nov 19, 2022 at 8:33

Ion engines are the best

Ion propulsion is what is used on satellites. It's extremely fuel efficient, since you're just shooting out xenon at extreme speeds. You don't need massive tubes. It's easy to turn on and off. And you can scale it up a lot.

The main limitation for them today is power. We use solar power to power them, and solar power doesn't have that much power. With fusion you can power massive electromagnets that move ships at huge speeds.

If you want a larger explanation on this, this answer on space.stackexchange explains how the main limitation on them is the limited power solar energy provides, not other things.

• Ion engines definitely tick the "high fuel efficiency" box, but I'm not aware of any that, regardless of power source, come even close to being able to achieve more than a tiny fraction of 1G of thrust. Commented Nov 17, 2022 at 21:56
• @KerrAvon2055 maybe an ion engine could accelerate a solar panel only to 1G, however this is about space travel, payload matters.. F=M*a so a=F/M. The more mass, the more Xenon you need to emit. Actually, I wonder if there's enough light, when traveling between stars, to feed the solar panels. Commented Nov 17, 2022 at 22:31
• @Goodies my knowledge is probably way out of date, but when I was interested in such things the most efficient thrust-to-mass ion drive available was only producing about 0.001 G. That was just for moving the engine, not even considering reaction mass, power source, superstructure and payload. Even if there are now ion thrusters that are two orders of magnitude more efficient (are there?), if the engine can't accelerate itself at anything close to 1G then it definitely can't accelerate the entire craft it's attached to. Commented Nov 17, 2022 at 22:45
• Aha well @KerrAvon2055 I'm not an expert either, I just cited Isaac Newton. When the thruster power (for satellites ?) is that low,it would not be able to accelerate its own power source to 1G, you're right.. Commented Nov 17, 2022 at 22:54
• @Goodies "1G" is the acceleration, not the speed. You don't "accelerate to 1G", you accelerate at 1G. If your ion engine is only capable of 0.001G then that's it - it doesn't matter how long you run it for - it'll still be 0.001G. Commented Nov 18, 2022 at 1:42

If you're looking for a physics-compatible answer that doesn't require any extreme technologies, I'm afraid you're going to be disappointed. The tyranny of the rocket equation is functionally unassailable.

Firstly you're going to need a lot of reaction mass. No matter how efficient and powerful your drive, you still need stuff to throw out the back to make you go forward. And the more reaction mass you carry the more you need to carry to accelerate the fuel mass along with the rest of the ship. This is a losing game.

We can flatten out the exponential curve a little by throwing more energy at the problem... right? Well, yeah, but there are limits here too. The more power you need to produce the bigger the reactor needs to be. And for fusion reactors (at least the ones we're working on now) that's an exponential growth in mass against a linear growth in power output. Not a problem for a Tokomak sitting under a mountain somewhere ground-side, but when you're trying to provide power to move a spaceship the reactor's mass is kind of a big deal. And of course you need a supply of deuterium and tritium (none of this protium trash) for the reactor, or maybe some enriched lithium for a breeder blanket to supply the tritium... and so on. A couple hundred tons of reactor is a pain to move around at the best of times. Getting it to produce enough power to lift itself at 1G, even ignoring the mass of the engines and various fuels, is simply bad SF for the foreseeable future.

Basically no matter how you look at this problem you'll find Physics standing there in a "Newton Rocks!" t-shirt, swinging a ruddy great club labelled "The Rocket Equation" around and grinning evilly. Or possibly doing an impression of Sylvester Stallone as Judge Dredd drawling that classic line: "I am the law!"

Because Physics can be a bit of a dick sometimes.

Still here? My, aren't we persistent. Or masochistic. Maybe both?

A lot of very smart people (no not me, actually smart people) have given this problem plenty of thought and come up with a few possible options. The best we've managed to come up with to date in terms of efficient, high power propulsion is the same thing engineers have been doing to tricky problem for centuries: blow s#!t up. If that doesn't work, blow s#!t up harder.

(Which, now I come to think about it, is already the foundation of rocketry.)

I present to you: the Orion nuclear pulse drive. This baby uses a series of nuclear (fission, not fusion) reactions as thrust. Sub-kiloton nuclear munitions are fired at about one per second, half of the explosion pushing against a pusher plate which transmits force through a series of shock absorbers to the body of the ship. With proper tuning you can get up to 4G pretty easily, and keep it up for a fairly long time.

Of course it's dirty as hell and you'll need quite a bit of shielding if you want to arrive at the outer planets with hair and germ cells intact. Never fear though, we have cleaner alternatives: Inertial Confined Fusion. Still blowing s#!t up, just with slightly cleaner fusion products and a greatly reduced "glow in the dark passengers" factor. Same basic idea, just using terrawatt XFEL or NDPG lasers (ask the NIF - they love this stuff) to touch off enriched deuterium/tritium ICF pellets. Might be lower yield per pellet, but you can fire them off more frequently... which gives a smoother ride, am I right? And since the resultant helium plasma has a charge we can use magnets to shape the exhaust, so it might even be more efficient and controllable. And it's a hell of a lot lighter than a Tokomak too.

Take that Bussard! Your ramjets might have the range, but we have more "blowing s#!t up" per ton than you'll ever have!

• Surprised that Nuclear Salt Water Rockets hasn't been proposed yet. Orion drive is a clever idea, but hella dirty and the fuel itself is complex to make Commented Nov 18, 2022 at 20:03
• Plus, I see a problem with the whole "turning around" part with the Orion drive Commented Nov 18, 2022 at 20:06
• @redfrogcrab, turning an Orion-drive ship around is no problem: shut off the engine, flip the ship end-for-end, and start the engine back up.
– Mark
Commented Nov 19, 2022 at 3:32
• @redfrogcrab You can do a powered skew flip in pretty much any rocket-like device, so I tend to overlook those bits. Or you can go unpowered for a few minutes to do an unpowered end-over like Mark mentions :P Commented Nov 21, 2022 at 6:48

Paraphrasing Elon Musk: The best mass is no mass; the best motor is no motor.

The only viable option for interstellar travel are tiny, very light probes driven by a ground-based laser shining at their light sails. Colonization of exoplanets is done by RNA/DNA only (like it happened with Earth, back then).

• yeah but that's kinda lame Commented Nov 18, 2022 at 17:37
• @redfrogcrab I know, I'm skirting your actual question. But to my defense: It solves at least two big questions with one stroke: The Fermi paradox (they were here!) and the origin of life. The Fermi paradox is, if you want, solved in a paradoxical way: We don't see U.F.O.s because indeed, conventional interstellar travel with manned, large craft is impossible -- but Earth has been visited nonetheless, in an unconventional fashion. Commented Nov 19, 2022 at 13:10
• Look up the Kare Sailbeam concept. It uses smaller lasers to shoot sails near lightspeed at a spacecraft, which uses them to propel itself forwards. Commented Nov 21, 2022 at 13:50
• @TheDyingOfLight Interesting! Would be nice if somebody started shooting sails at you from the destination though once you are half-way ;-). Commented Nov 21, 2022 at 15:39
• The paper is worth looking at. You use the magnetic sail you used to capture the sails as a drag brake against the interstellar medium and solar wind to slow down. Interestingly, this is the deceleration you get out of that scales with your velocity. So, it doesn't really matter if you moved at 0.1c or 0.7c. Commented Nov 22, 2022 at 10:50

Dry Nano-Particle Field Extraction Thrusters

Nano-Particle Field Extraction Thrusters are to date the most powerful electric propulsion systems invented being hundreds of times stronger than traditional ion engines... but they are still a long way from being as optimized as they could be or achieving 1G of thrust.

They work in principle similar to an ion engine, but instead of noble gases, they use carbon based nano particles. Because of the unique conductive properties of carbon latices, and the ability to shape them however you need them to best meet your goals, you can use carbon nano-particles to achieve far greater thrust than ionized gasses, but more importantly, because there are infinite possible shapes to a carbon nano-particle, you can easily handwave in "better shapes" as an excuse for why your NPFETs produce more thrust than modern ones.

That said, there are a few engineering hurdles in the design of modern NPFETs that we already know that we can improve on by solving specific problems. The biggest is the Wet-NPFET problem. Carbon nano-particles are a solid, not a fluid; so, getting them to the charging pad is difficult. The primary solution for this is to mix them with a liquid, but then the liquid adds wasted fuel mass and tends to build up on the charging pad significantly reducing its efficiency. It also aligns the nanoparticles randomly whereas a solid fuel could align them with the charging pad taking better advantage of shape optimization. In theory, a Dry-NPFET thruster will produce much more force, but there is very little published experimental data on such designs because there are no published mechanisms for feeding one... the good news is that you don't have to delve very deep into science fiction to come up with a solution for this.

Graphene is an incredibly strong 2-dimensional crystal that can in theory be processed into sheets that are only 1 or 2 atoms thick, but tough enough to hold several pounds of weight. If your ship were have a sort of high-speed graphene printer, it could have a graphite fuel tank that is used to print a continuous sheet of graphene interlaced with the sort of carbon nanoparticles you need. You could then feed this sheet over the charging pad like a cassette tape repelling the heavier, weakly bonded nanoparticles harder than the graphene causing them to be ripped from the sheet and expelled as a super high velocity reaction mass. If you build your charging pads in pairs (one positive and one negative), you could then feed the waste graphene strips into each other to neutralize their now significant electrostatic charge. The strips can then be reloaded with new nano particles or recycled into new strips if damaged.

Rock plasma rocket.

This very long and awesome rocket collects rocks and asteroids. Junk from the crew can also be put in the hopper as well as waste material and whatever else you have. It is fuel efficient because this stuff is fuel only for the rock plasma rocket.

You have fusion power. You use the fusion power to heat the trash to plasma. Plasma is charged particles. You use your fusion power magnets to accelerate the charged particles out the back. You can add various things to the hopper to color your plasma different colors if you want.

You are very long; yes very long indeed. Some say too long but you will remind these folks that it is not how long your ship is, but what you do with it. There will be no flipping; nay. You move like the graceful dancer you are, slowly pirouetting about your great length such that forces balance and all remains well despite your extreme to the point of impracticality longness. Your ship may groan a little with the strain. That is still ok.

Oh, xenon. Xenon! Yes xenon is fine reaction mass for deep space probes out in interstellar space. Tiny probes where cargo area is at a premium. But the farthest that the Rock Plasma Rocket is going to go is the Kuiper Belt! That is right up the street! The planned routes for this rocket are liberally strewn with reaction mass free for the taking and there is plenty of space on board to store it because this rocket is seriously long.

• I think you're grossly overestimating how much mass will be available in the form of crew junk and (even in the asteroid belt) rocks and asteroids. Commented Nov 18, 2022 at 14:11
• @Chepner! The crew poo alone could be reaction mass! These are short trips because this is fast acceleration. Assume steady acceleration of 4.5 m/s2 - that gave me 64 days to go 75 billion km to Pluto. That is not long enough to make growing your own food worthwhile. They will bring all their food and go by blasting their dung out the rear. Of the ship. Commented Nov 19, 2022 at 0:21

Beamriders

A beamrider is a spacecraft using externally produced energy to accelerate. It is free of the limits of the rocket equation. I've seen proposals that could do 24h Earth-Mars transfers (with human-compatible accelerations), and aren't that sophisticated on the technical side. The basic idea is that you have the fuel come to the rocket. How do you do that?

• Sunlight- or Windsail: Those are the most well-known version; those concepts have been tried already. You use the sun's light or particle emissions to propel yourself, but this is rather slow. Check out sun-diver mission concepts to see the limits of this approach. All of the following approaches require magnetic fields as rocket nozzles. This gives you an interesting opportunity because the fields don't care if the plasma they reflect was created by the energy a distant beam station sent you or if you've just thrown a nuke out behind you. Look up Mini-Mag-Orion for the basic concept.
• Bomb Trail: Use Lighsails or Mass drivers to position fission, fusion, or antimatter bomblets in a long arc along the trajectory you want to travel along. The initial stages require actual bombs, but once you've reached about 100km/s of relative velocity, you can drop a small mass in the path both the bomblet and the fusion reaction will ignite itself.
• Particle or Macron Beams: Those are a tad hard to keep focussed, though options exist. Especially cold, laser-coupled particle beams could stay coherent over several AU. Particle velocities of those systems can be measured as significant fractions of c if the theology is advanced enough.
• Lasersail: Breakthrough Starshot is the best-popularised version of this concept. The fact that it is considered for interstellar missions illustrates the power level involved. You can use power satellites near the sun to generate the energy you need. However, lasersails suffer from a number of serious drawbacks. Titanic lasers, mirrors, and sails are needed. The solution:
• Sailbeam: Instead of dragging the vessel along with a light sail, you use small sails, which can get very fast quickly. Those sails are then vaporized by a shipboard laser or by colliding with a target mass. The plasma is then reflected in the magnetic sail.

Sailbeam is great for a number of other reasons as well. It requires less infrastructure than pure lasersails, and has a greater range, especially if relay stations are used. The system can be used for more than just spacecraft propulsion. It can be used to export solar energy from Mercury. The same magnetic reaction that drives the spaceships can be used on stations and planets as a magnetohydrodynamic generator. Incidentally, this allows you to move asteroids, and you could set up sail beam relay stations in the Kuiper and Oort regions if you have relativistic interstellar intentions.

Fusion is capable of 2 million seconds specific impulse. That is very efficient but you'll want to add additional propellent such as water or hydrogen. This separates fuel from propellent.

200 tons with 2 million isp at 40% efficiency uses 350 grams of deuterium and 350 kilograms of water in an hour at 1G constant acceleration. So days of constant 1G acceleration is possible. Years is not possible. First a single year gets you to light speed on paper and interstellar dust will rip your ship apart at much slower speed,let alone actual meteors the size of a golf ball that you can't see. Even if that were not a problem, you couldn't store enough propellent. The tyranny of the rocket equation sucks.