# Scientifically accurate fuel for a small spaceship

I'm designing a small two-person spaceship for use in battles in space. It is set around the year 2100.

It would be around the size of a tank (approx. 50 tons).

It would need to be fast and easy to control, as it would go up against laser weapons and heat-seeking missiles (Star Wars style).

As it would stay within 1km of its mothership, it could be regularly refuelled during the battle; it would, however, need to be compact.

Staying at around 1G, it would need to be able to fly for, say, 5 minutes.

The pilots could withstand up to 8G's.

What scientifically-accurate fuel/engine could be used on the ship?

Batteries and liquid hydrogen.

Your ship uses as its engines a quartet of electric ion thrusters which fire hydrogen plasma (ionized hydrogen) at a significant fraction of the speed of light. Each thruster can rotate 360 degrees, though will not fire when pointing at the ship (that is bad for the ship and occupants). Combinations of thrusters confer immense maneuverability in 3 dimensions; for example two forward and two back allow the ship to spin 180 degrees in place.

Energy conferred increases as the square of velocity and so most of the impulse is because the hydrogen gets moving so fast. Hydrogen is light and cheap. This minimizes the ships mass and maximizes maneuverability. Liquid hydrogen is a doable deal. If you want weirder scifi they could store it as exotic hydrogen metal.

I like the idea that the accelerator tubes stay short when a lot of maneuverability is necessary, to reduce angular momentum. If the ship really needs to go fast the accelerators telescope out behind the ship to increase the length over which electromagnetic acceleration can happen. Also they get hot and glow.

The thrusters can serve as weapons; a supply of radon is kept on board for that purpose because it makes a better particle beam than hydrogen. Radon dumped in as propellant can also provide a burst of speed because the mass part of mv2 increases by 3 orders of magnitude.

• Lots of real world stuff on hydrogen storage. en.wikipedia.org/wiki/Hydrogen_storage – Willk Jul 31 at 23:08
• Liquid nitrogen also has the bonus feature of being very cold - can help ships mask their heat signatures and avoid heat-seeking missiles. – cyber101 Aug 1 at 7:14
• Liquid hydrogen on a spaceship is a very bad idea: it diffuses through everything, needs a lot of cooling to keep it liqude, makes metals fragile, and can combust in spaceship cabin. There is a reason why everybody using xenon fo ion thrusters now. But the idea is perfect. Evaporized aluminum (or even lithium, or just water) would do the job as well. – ksbes Aug 1 at 14:15
• As mentioned in this section of the wiki on ion drives, Electric thrusters tend to produce low thrust, which results in low acceleration. So, not good for a fighter that needs to accelerate fast in space battles. More on the tradeoff between thrust (good for acceleration) and specific impulse (higher effective exhaust velocity, which means less fuel needed for a given change in velocity, but it may take a long time to achieve that change) at projectrho.com/public_html/rocket/enginelist.php – Hypnosifl Aug 1 at 16:26
• @Willk In the year 2100? Aren't we the optimist :) – kingledion Aug 3 at 21:33

Beamed power might be of interest: since these fighters remain close to the mothership, the mothership could supply them with energy via laser or microwave beams that they converted back into electricity for use in weapons and propulsion. This would allow your fighters to be smaller and lighter because they didn't have to lug around a power source, but it would be a lot safer than using high energy density fuel. Of course, You'd have to have some justification for why the mother ship doesn't focus these beams to the point where they do damage to the enemy and just shoot them down directly.

Other options are the aforementioned metallic hydrogen - but beware, this us a super theoretical substance right now. We're pretty sure it exists under the tremendous pressures found inside gas giants, but there's really nothing to indicate that there's a metastable state that will allow it to keep its metallic state at lower pressures. Also, because it's got so much energy stored, it's fiendishly explosive, and because it's so dense it makes for an amazing implosion target when used in an inertial fusion reactor.

A substance that is (somewhat) less likely to blow up when you look at it funny, is Uranium Tetrabromide dissolved in water. You store this is thin tanks coated with a radiation dampener, then when you want to GOFAST you pump it into the reaction chamber where enough of the solution accumulates to start nuclear fission. You then ride the fury road to Valhalla, all shiny and chrome, upon your continuously detonating nuclear bomb.

For more details check out the Atomic Rockets website, and the Engine List pages in particular.

• The uranium tetrabromide sounds interesting, thanks. Also, I'll have a look at the website you mentioned :D – Finn E Aug 1 at 14:14

1G for an hour is an astonishing amount of fuel for a space vehicle. It doesn't sound like much for an air breather, but space vehicles have to hold onto their own reaction mass.

9.8m/s^2 for 3600 seconds is 35km/s of delta-V, which is how rockets measure these capabilities. 35km/s is a lot. That's almost enough to escape Earth's gravity well and head into the sun (which, ironically, is 2-3x harder to reach than Pluto). Here's what we used to get the Parker Solar Probe there:

The probe itself had a mass of 685kg (1,510 lbs). It took the mighty Delta-IV with an upper stage, weighing in at 733,000 kg (1,616,000 lb) to lift it there. Scaling that down to 100,000lbs, you can have a payload (pilot, weapons, life support, etc.) of around 93lbs.

Welcome to the tyranny of the rocket equation. You have to take everything with you. This results in an exponential increase in fuel mass needed as your delta-V budget goes up linearly. If you want to fly for 24hours at 1 Gee before refueling, that's the kind of budget you need.

We can save on this by using ion thrusters rather than chemical rockets. Ion thrusters have a higher Specific Impulse, but there's a catch. They have very small thrusts. The highest thrust experimental thruster to date clocks in at around 88N. That's enough to accelerate about 9kg of mass at 1G. Of course, the thruster itself is substantially more massive than 9kg.

So what you need is a sudden leap in ion thruster technology to gain several order of mangnitude of thurst-to-weight ratio. That's the direction Willik went with his answer, and its pretty much the best you'll be able to do. Just call them "{adjective} ion thrusters" and don't explain anything more than that.

This is why we find that most star-wars and star-trek style worlds simply invent their own technology. Trying to adapt our reality to those styles of worlds is fraught with difficulty. Better to have warp drives and inertial dampers.

• Thanks, I realised just now that it wouldn't need to constantly accelerate - I've changed the time in question to just 5 minutes – Finn E Aug 2 at 19:21

# Nuclear Rocket is the only solution within ~100 years...

### Chemical rockets do not work

Chemical rockets do not work because of the rocket equation. You have to carry your own fuel, so you need a very high effective exhaust velocity. See this table, here. Thrust is based on conservation of momentum ($$mv$$) between you and your fuel. If your $$v$$ is low, you need a lot of fuel to thrust; if you carry a lot of fuel, you need even more fuel to overcome the inertia of that fuel. Other answers cover the rocket equation in detail. The bottom line is, you need $$v$$ to be as high as possible to move.

### Electro-magnetic thrusters do not work

Other answers discuss the possibility of an ion engine. There are many variants using various electrostatic or magnetic (or electro-magnetic, or magneto-plasma-dynamic, etc) principle to fire high energy particles out as your source of thrust. Where the impulse of a chemical rocket might be 200 s; an electric thruster can easily hit 2,000 s, maybe as high as 20,000 s.

Unfortunately, the drawback here is the ratio of thrust to power is very high. You need to generate electric power, and then use that electricity to generate an electrostatic or magnetic (or both) field. Both these conversion processes have significant losses. For example, the VASMIR--possibly the most advanced magnetic thruster created thus far--as a power ratio of about 40 kW/N. An F-15 (25 tons, about the size you are talking about) generates about 140 kN at max power; that requires 5.6 GW of electric power; about the energy output of the world's largest coal and nuclear plants. Obviously, those plants aren't going to fit on a fighter.

### Which leaves a nuclear rocket

The only working idea is to use a nuclear rocket. This uses a nuclear reaction and magnetic field to blow fission or fusion products out the back of the rocket. The concept works best with fission fragments, as these have high mass and a strong positive electrical charge (electrons are stripped into plasma; fusion fragments are thus atomic nuclei).

While these rockets do have a relatively high power demand for maintaining a magnetic field, the impulse of the particles generated is much higher; as much as 1,000,000 s; with fission fragments ejecting at greater than 0.01$$c$$. Thus, the power to thrust ratio is much better than with electromagnetic thrusters.

# ... but not with people onboard

So we have the perfect engine, capable of outstanding thrust with a minimal power source. Unfortunately, you do have the issue of the nuclear bomb going off right behind the cockpit. While magnetic fields can reasonably contain charged particles, they cannot do anything about gamma radiation or neutrons, both of which will be produced in abundance.

Unfortunately for any squishy biological, gammas and neutrons will quickly extinguish any life forms within ~20 meters of such a powerful reaction. If you want these fighters, they will have to be piloted by AI, or remote operators.

Or, instead of fighters, they could be torpedos, which is the hard-sci-fi practical way of doing it...

• Thanks - I may end up using the torpedos and AI piloting idea – Finn E Aug 2 at 19:29
• When you say "nuclear rocket" do you just mean the type that uses actual fission products for thrust as in the fission-fragment rocket, or would you include nuclear-thermal rockets that just use a nuclear reactor to heat a working fluid that is shot out for thrust. It may be that the latter would produce less radiation than the former, so it might be possible to adequately shield people in the cockpit with a layer of lead or something, especially if the rocket had a long stretched-out shape so the cockpit was far from the reactor. – Hypnosifl Aug 2 at 20:41
• @Hypnosifl "Nuclear rocket" is a any group that uses the high energy products of a nuclear reaction (fission or fusion) to generate thrust. So fission fragment, nuclear-thermal, nuclear salt-water, gas core reactor, etc. – kingledion Aug 3 at 21:32
• Are you saying they all produce similar levels of radiation, even if some actually expel radioactive material as exhaust while in others the radioactive material is confined inside a nuclear reactor which can be shielded? Also you say there is a 'nuclear bomb going off right behind the cockpit', but in a reactor the rate of the chain reaction is controlled whereas in a bomb the chain reaction happens in a quick burst, wouldn't that make a difference? – Hypnosifl Aug 3 at 21:56
• @Hypnosifl Whether or not the charged atomic nuclei are controlled, the danger come from gamma radiation and neutrons; both fission and fusion reactors create these. Since neither of those have electric charge, they can't be controlled or directed away from a pilot (with known technology). Unless you can afford the mass of dozens (possibly hundreds) of tons of shielding, any nuclear reactor will kill a pilot with acute radiation poisoning in minutes – kingledion Aug 5 at 12:12

I am assuming you are not proposing some unknown method of thrust. Are you sure you need to thrust at 1 g for an hour? The rocket equation has something to say about this.

The rocket equation tells you how much change in velocity you can get from a given rocket for a given change in mass. The rocket design gives you the specific impulse (that's the $$I_{sp}$$ factor). Then by pushing mass out the back you make the rocket go forward. The mass you lose as reaction mass means you start with mass $$m_f$$, and finish with mass $$m_o$$. And $$g_o$$ is one Earth gravity.

If you use the specific impulse of a space shuttle solid booster (about 250 seconds), then the rocket equation tells you that to accelerate for 1 hour at 1 g requires about 1.7 million times the mass in fuel as you have in ship.

If you use liquid oxygen-liquid hydrogen you can get a specific impulse of about 450 seconds, which means you need about 3000 times the mass of fuel as ship. Still seems unreasonable.

If you could get an ion thruster (specific impulse about 3000 seconds) to thrust you at 1 g, then you'd need about 1.3 times mass fuel as ship. But ion thrusters produce very small thrusts. And a ship with a fuel tank larger than it is still seems pretty clunky.

In other words, maybe you don't need to be thrusting for that entire hour? It is space, after all. If you don't thrust you just "follow your nose" in whatever orbit you happen to be in. If all you really need is a few minutes of maneuvering during actual combat then liquid oxygen-liquid hydrogen might cover it.

• I just realised that I didn't take into account the fact that I wouldn't need to constantly accelerate - I'll change the time in the question... hang on – Finn E Aug 2 at 19:16
• Would you be able to explain to me how the rocket equation works? – Finn E Aug 2 at 19:19
• @FinnE I added some text. – puppetsock reinstate Monica Aug 2 at 19:25
• Thanks, I think I get it now – Finn E Aug 2 at 19:31

As discussed on this projectrho.com page, for near-future rocket technologies there tends to be a tradeoff between thrust (which gives the force on the rocket, so you can divide by the rocket's mass at any given moment to get its acceleration) and specific impulse (which is just the effective exhaust velocity divided by an acceleration of 1 G, as mentioned here). According to the Tsiolkovsky rocket equation, if you want to know the total change in velocity $$\Delta v$$ a rocket can achieve if it fires continuously in a straight line until it burns all its fuel, this doesn't actually depend on the thrust, only on the effective exhaust velocity $$v_e$$ (or specific impulse $$I_{sp}$$) and on the ratio $$\frac{m_0}{m_f}$$ between the initial mass $$m_0$$ of the rocket including fuel at the beginning of the acceleration and the final mass $$m_f$$ remaining once all the fuel has been burned (i.e. the payload mass).

The Tsiolkovsky rocket equation is $$\Delta v = v_e \ln \frac{m_0}{m_f}$$, where $$\ln$$ is the natural logarithm function, and if you divide both sides by $$v_e$$ and take $$e$$ to the power of each side (see e (mathematical constant)), you get the equation $$\frac{m_0}{m_f} = e^{\frac{\Delta v}{v_e}}$$ (the natural logarithm function $$\ln (x)$$ is the inverse of $$e^x$$, so $$e^{\ln \frac{m_0}{m_f}} = \frac{m_0}{m_f}$$). So if you know the effective exhaust velocity of a type of rocket and the desired change in velocity $$\Delta v$$, this will tell you how many kg of fuel you're going to need for every kg of payload mass.

A 9.8 m/s^2 acceleration for an hour would give a change in velocity $$\Delta v$$ of about 36000 m/s, so for example if the effective exhaust velocity $$v_e$$ was 4400 m/s, about that of the space shuttle main engine, then you'd have an initial mass to payload mass ratio of $$e^{\frac{\Delta v}{v_e}} = e^{\frac{36000}{4400}} = 3575$$. That means if the initial mass when fully fueled is 50 metric tons or 50000 kg, the final mass when the fuel is burned would only be 50000 kg/3575 = 14 kg! No real or proposed chemical rocket has an effective exhaust velocity much greater than this, so you'll need to go with some other form of propulsion.

Others have suggested an ion drive, but while these do have a much higher exhaust velocity, the problem as mentioned on this NASA page is that "The trade-off for the high top speeds of ion thrusters is low thrust (or low acceleration)." If you scroll down to the "Drive Table" section of the projectrho.com page I linked earlier, it has a large variety of real and proposed future rocket designs, including many possible types of ion drives. As the wiki page mentions, 'Ion thrusters are categorized as either electrostatic or electromagnetic', so if you look in the 'Code' column of the projectrho table, ion drives can be identified by the code "ESTAT" or "EMAG". And the final column of the projectrho table is T/W, or the thrust-to-weight ratio for each type of engine, i.e. the thrust it produces divided by its weight in standard earth gravity (mass times 1 G), not including fuel mass or any additional structural mass like the payload. So, a T/W value of 1 would mean that if such a rocket was burning the last of its fuel, and was in space with no other mass attached, it would be accelerating at 1 G (as mentioned in the 'Rockets' section of the wiki page on the thrust-to-weight ratio, 'The thrust-to-weight ratio of an engine exceeds that of the whole launch vehicle but is nonetheless useful because it determines the maximum acceleration that any vehicle using that engine could theoretically achieve with minimum propellant and structure attached.') And if you look at the table, the T/W for all the engines labelled "ESTAT" or "EMAG" are much smaller than 1, meaning those ion drives couldn't accelerate at anything close to 1 G.

Your best bet for a near-future technology might be a nuclear thermal rocket, where the working fluid is heated by nuclear reactions rather than chemical ones before being expelled out the nozzle to create thrust. These types of rockets have codes beginning with "NTR" in the table. They would have the advantage of producing thrust in about the same range as a chemical rocket, but with significantly higher exhaust velocity, so less fuel needed to achieve a given $$\Delta v$$. And the technology isn't too advanced to be plausible in 2100, nuclear-thermal rockets were studied by NASA in the sixties, probably the main reason they never went forward was the danger associated with radioactive exhaust or the possibility of exploding in the atmosphere, but there would be much less danger if they could be constructed in space. One design that was studied was named DUMBO, the projectrho section on it here links to a NASA document here that gives more details. The table lists several variants of DUMBO, with DUMBO (H) having the highest exhaust velocity of 16,000 m/s. So, for a $$\Delta v$$ of 36000 m/s, you'd have an initial mass to payload mass ratio of $$e^{\frac{\Delta v}{v_e}} = e^{\frac{36000}{16000}} = 9.5$$. So if the initial mass when fully fueled is 50 metric tons, the final mass when all the fuel is burned can be about 5.3 metric tons. The engine itself is said to have a mass of about 5000 kg = 5 metric tons, so this doesn't leave a lot of mass for pilots and cockpit, but you could always boost the total mass to say 70 metric tons, in which case the final mass when the fuel is burned would be 7.4 metric tons so you'd have 2.4 metric tons left over after accounting for the engine mass. And this engine is said to have a thrust of 3500000 Newtons = 3500000 kg*m/s^2, so even with a fully fuelled mass of 70 metric tons = 70000 kg, the acceleration could be as high as 3500000/70000 = 50 m/s^2 or about 5.1 G, and as fuel is burned and the mass goes down, the maximum acceleration will increase.

One thing I'm not sure about here is that DUMBO (H) on the projectrho page presumably refers to a DUMBO drive using monatomic hydrogen as the working fluid (distinct from DUMBO (H2) elsewhere in the table), and it lists this with the code "NTR SOLID" meaning it's using nuclear fuel in solid form inside the reactor (as distinct from nuclear thermal drive designs using liquid or gaseous nuclear fuel, discussed here), but the "Propellants: Advantages and challenges" section on this page claims that "Unfortunately, solid fuel cannot reach the temperatures required to dissociate H2 into monatomic hydrogen." So it could be that the projectrho guy was incorrectly extrapolating the DUMBO design to see how it would perform with monatomic hydrogen even though it's not actually capable of using it. None of the other nuclear thermal rockets on the table seem to have combos of exhaust velocity and T/W that would work as well, but you could always modify the parameters of your ship to something that would still exceed the capabilities of chemical rockets but not need to accelerate for quite as long, say a ship capable of 1 G acceleration for 30 minutes for a $$\Delta v$$ of 17640 m/s. That way the DUMBO (H2) which has an effective exhaust velocity of 8093 m/s would be able to do it, since the initial mass to payload mass ratio would be about the same as in my previous calculation, $$e^{\frac{\Delta v}{v_e}} = e^{\frac{17640}{8093}} = 8.8$$ (meaning that if the initial mass when fueled is 70 metric tons then the final mass when the fuel is spent is about 70/8.8 = 8 metric tons) and the mass of the rocket engine is still 5 metric tons (leaving 3 extra tons for crew capsule and other non-engine structure that remain when fuel is depleted) and the thrust is exactly the same as in the previous calculation so it can still do about 5 G of acceleration when fully fueled.

• How would I calculate the amount of fuel needed for the ship to travel a certain distance? – Finn E Aug 2 at 21:01
• In space a ship can just accelerate up to some desired velocity and then turn its engines off and coast at that velocity indefinitely, so there's no limit to the distance you can travel. If you want to place some constraints on the engine you need some different type of desired figure like maximum acceleration, or distance traveled at some fixed rate of constant acceleration, or maximum velocity after burning all the fuel. – Hypnosifl Aug 2 at 21:10
• And the amount of fuel needed to reach the desired velocity? – Finn E Aug 2 at 21:15
• See the second paragraph of my answer, the rocket equation gives a relation between final velocity after burning all the fuel, the "effective exhaust velocity" for the type of rocket you're looking at (the values for different rockets can be found in the table on the projectrho page I linked to), and the ratio m_0/m_f, where m_0 is the initial mass of the rocket including fuel, and m_f is the final mass once all the fuel has been burned, so the total mass of the fuel alone would be (m_0 - m_f). – Hypnosifl Aug 2 at 21:18
• So what is I$_s$$_p$? – Finn E Aug 2 at 21:22