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I posted this in Space SE, but someone suggested I also post it here. So here it is!

I am wondering what type of engine would most likely be available in the next 80 that can constantly accelerate a spacecraft at 1G. Preferably, it could accelerate it for 4 weeks.

The engine could be fission, fusion or ion. If there's another one, please do mention it!

My biggest gripe is the fuel mass requirements. If we use the rocket equation below: $$ {\Delta} v = I_{sp}g_0ln{\frac{m_0}{m_f}} $$ we can calculate the fuel mass requirement for a rocket with an isp of 900, acceleration of 1g (9.80665 ms-2), dry mass (aka $m_f$) of 120 metric tonnes (or 120,000 kg) and a ${\Delta}v$ of 23724247.68 ms-1 (or about 7.91% of the speed of light), calculated with ${\Delta}v = a{\times}t = 9.80665 {\times}(4{\times}7{\times}24{\times}3600) = 23724247.68 ms^{-1}$.

Rearranging the equation for $m_0$, we get: $$ m_0 = m_f {\times}e^{\frac{{\Delta}v}{I_{sp}g_0}} $$ Plugging in the values we got above, we get this huge number: $$ m_0 = 120000 {\times}e^{\frac{23724247.68}{900 {\times} 9.80665}} = 120000 {\times} e^{2688} $$

Anyone who knows something about exponents knows that $e^{2688}$ is a huge number. This means that the fuel mass requirements for an engine with an isp of 900 (I used a theoretical number for a nuclear thermal engine) for a craft constantly accelerating at 1G for 4 weeks is astronomical (pun slightly intended).

I know that a more efficient engine (e.g. one with an isp of 1,000,000, which gives $m_0 = 120000 {\times} e^{2.4192} = 120000 {\times} 11.2368... = 1348423.947$ kg) would be far better.

I know in The Expanse, the engines are fusion, but:

  1. I don't know if we'd have fusion tech like that within the next 80 years
  2. what fuel would an engine like that need?

So, would fission, fusion or ion engines be better, and which would be able to produce the thrust needed for 1G of constant acceleration for 4 weeks? Also, would these engines' fuel mass requirements be calculated with the rocket equation?

Thank you all for your time!

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    $\begingroup$ From what I've seen, the Epstein drive in The Expanse is a fantasy torch drive -- it has higher performance than even a pure fusion rocket with .12c exhaust velocity. $\endgroup$
    – Zeiss Ikon
    Jan 30 at 18:38
  • $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Jan 30 at 18:39
  • $\begingroup$ The rocket equation does not give fuel mass requirements. It gives propellant (also known as reaction mass) requirements. The reaction mass can be something inert; for example, ion engines use a noble gas, such as xenon or argon. $\endgroup$
    – AlexP
    Jan 30 at 18:40
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    $\begingroup$ "80 years" is an arbitrary and unclear future timeframe — for all we know we might hit a singularity in 2050 and the superintelligent AI will figure out antimatter beam propulsion in the decades thereafter. My crude sketch of an answer would be to use a laser lightsail to speed up and a magsail to slow down, bypassing the rocket equation both ways. But the problem with asking questions about what'll be available in nearly a century is that it is very hard to make informed guesses. $\endgroup$
    – parasoup
    Jan 30 at 19:17
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    $\begingroup$ 99.9% of all human inventions and discoveries were made in the last 150 years with a nearly exponential pace- and that's excluding the almost inevitable near-future breakthroughs in AI. 80 years, being half that period and post-AI, is enough time to guarantee that the answer to your question is factually, "none that we know of." Thanks to AI, we might again enter a golden age of Science Fiction where imagination becomes more important than the science the story is built on. $\endgroup$
    – JBH
    Jan 31 at 1:08

2 Answers 2

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The actual requirements of your engine

First, let's enumerate the actual requirements for your engine.

  • The engine needs to be able to produce 1 g for four weeks (equivalent to 23,732,352 m/s of delta-v, which is an insane amount I might add but one I will nevertheless consider). This does not mean that the general rocket equation applies; since the 1 g will be maintained for the full four weeks, as fuel is expelled, the engine must throttle down in order to keep 1 g from turning into 1.5, 2, or 10 g and accidentally turn the payload into space.

    • This also adds another requirement implicitly: the engine must be able to throttle. The issue with things like solid rocket boosters (and, unless you size the warheads very carefully, nuclear pulse propulsion) is that the engine has only two states: on and off. As the mass of the ship changes, the acceleration will change as well, and unless the engine can account for this change, the ship might not arrive at its destination in one piece.
  • The engine needs to be accessible in under 80 years ideally, meaning that we can't use such outlandish technology such as antimatter propulsion or enormous mirror-focused lasers produced by reflecting all the light of a star onto solar sails. Things like nuclear pulse propulsion and fusion propulsion (given the recent advances in fusion and the fact that most technology we know today was invented in the last century or so) are on the table.

  • Lastly, although this wasn't originally stated, we may add that the engine has to actually have a high enough efficiency to get the 23,732 km/s dv with a reasonable amount of fuel. Nobody likes an engine whose fuel tanks' volumes are measured in cubic lightyears.

Now we may consider our options.

Nuclear thermal propulsion

As you calculated in your question, an NTR engine isn't going to work. With specific impulses capping out around 900 seconds in modern times, an improvement of a couple hundred seconds that we can expect to get out of the tech isn't going to change the fact that they're not efficient enough for our purposes.

Nuclear pulse propulsion

Nuclear pulse propulsion is a mechanism by which you use controlled runaway nuclear reactions to expel the fissile material from your ship at extremely high speeds (detonating nukes behind your ship to push you forward), giving a very high exhaust velocity of up to 31 km/s and therefore a specific impulse of around 3160 s. This is definitely not a huge improvement over 900 due to the tyranny of the rocket equation, but it's an improvement nonetheless. Still, according to the rearranged rocket equation you kindly provided, the fuel mass you'd have to carry with you exceeds 9 * 10^307, which is where my calculator just calls it infinity. That value is around 250 orders of magnitude greater than the mass of the Universe, so good luck getting enough fuel for that. Plus, that's just to burn the whole way; keeping a 1 g acceleration will be even harder since most burns start very low-g and only become high-g towards the end. Plus, you can't throttle them - did I mention that? Nukes don't have a "detonation strength" dial. Either you are planning out your journey start to finish and marking nukes so that they always produce the correct amount of thrust, or you're going to have issues.

Is this even possible?

Let's consider some weird ideal engine that expels propellant at the speed of light. Or maybe just 1 cm/s slower, so that we don't make the relativists angry. This engine will have a specific impulse of almost 3,000,000,000 seconds. And, according to the rearranged rocket equation, it actually works (so this is possible)! And with only 9 tons of fuel.

So it's possible, what's the lower bound?

Let's say that you're okay with having 99% of your initial mass being fuel (much worse than the already-awful Daedalus spacecraft). We're now trucking around with 12,000 tons of fuel. As it turns out, if your specific impulse is around 993,880 seconds (equivalent to 0.03c exhaust velocity - for the record, the Parker Solar Probe, the fastest spacecraft ever launched, reaches only 0.000589c), you can manage the required delta-v by making your ship around 99% fuel. Yay?

The issue

This technology is definitely not going to happen in 80 years. The most efficient possible rockets we've ever built have specific impulses around 1,500 - a far cry from the required 993,880. Exhaust velocities at such high fractions of c would require something like a fusion reactor pumping hydrogen plasma out constantly. Even then, that magnetic propulsion system would face serious challenges; it would require a decent advance in fusion, which maybe we could achieve in 80 years, but moreover the reactor would almost certainly be so massive that it would outweigh the benefits: the best nuclear reactor we have weighs 23,000 tons, which is almost double the amount of fuel we're carrying, and that's not accounting for the huge systems required to put it into space and to allow it to expel plasma as propellant. Even if we somehow miniaturized it to 0.1% of the weight it is currently, magically stuck it on our spacecraft (which are at this point a few hydrogen spheres with a little box on one end), and allowed it to expel fusion plasma as propellant, it would weigh as much as our payload and we'd need to carry about 2.7 times as much fuel.

Then, of course, there's the thrust problem. Producing enough thrust to maintain 1 g requires a force of about 1.1 giganewtons - which is much higher than any current engine could possibly produce. And applying that force over so long a time is sure to cause structural instability in the ship, or worse, just break it apart.

So, to answer, given that modern (or even near-future) technology can't even come close to the possible requirements, I'm just going to say that this isn't possible.

But that's not fun!

Yeah, you're right. So, I'll give you this: antimatter propulsion. It sounds silly and all, but it may actually have the required specific impulse to have a lower fuel mass and high enough thrust to make it work. Maybe SpaceX is working on the basics right now, and in 2060 they perfect it and by 2100 we have working antimatter rockets. They would be extremely expensive and dangerous, but it's all I can think of that would come close to working.

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    $\begingroup$ Thank you for your brilliant answer! Yeah, it doesn't sound like 1G is 100% plausible. To be honest, if my calculations are correct (I didn't take into account orbital mechanics because, well, I don't know much about them to be honest), at 0.1 ms-2, you can get to Jupiter (at its current distance, which is about 741.5 million km according to NASA's Eyes) in about 63 days, including an acceleration and deceleration burn (you accelerate halfway there, flip the craft, and then decelerate the other half). $\endgroup$
    – Tom
    Jan 31 at 9:59
  • $\begingroup$ Also, if my calculations are correct, you'd only need an isp of approximately 258828.3295 seconds. This considers that: 1. the craft weighs 120000 kg dry mass, has 12000 kg propellant, and accelerates at 0.1 ms-2 for 4 weeks. I believe fission fragment engines might reach that level of efficiency, but I don't know if their thrust is enough. $\endgroup$
    – Tom
    Jan 31 at 10:00
  • $\begingroup$ Thanks for doing the math. I was considering proposing a nuclear salt water rocket but an isp of 6000 or so is apparently not high enough $\endgroup$
    – lijat
    Jan 31 at 10:34
  • $\begingroup$ @lijat Yeah, to be honest, fusion seems to be the most likely option. However, I have just looked up fission fragment engines. If you have an engine with about 4600 N of thrust (converted and rounded down from the figure from a NASA report) and an isp of 32000 s (again, from a NASA report, not rounded this time), you can accelerate a craft at approx. 0.035 ms-2. This can get you to Jupiter (at a distance of 741.7 million km) in about 151 days (not taking into account orbital mechanics). This means we'd have to accelerate for about 151 days to get Jupiter. $\endgroup$
    – Tom
    Jan 31 at 11:57
  • $\begingroup$ Taking this into account, we'd need about 391082 kg of propellent (if the dry mass is 120000 kg). This means the ship itself will be only about 23.5% of the total mass, but it is more plausible. $\endgroup$
    – Tom
    Jan 31 at 11:58
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It’s conceivable that a Starwisp might achieve that kind of number within eighty years, a very tiny spacecraft (orders of magnitude too small for human passengers, but size wasn’t included in your requirements) with a large sail, propelled by beamed electromagnetic radiation of some kind. Not having to carry your fuel makes a huge difference, and is the only even remotely plausible way to get the performance you need.

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