# For how much and for how long would a "Closed Cycle Nuclear Thermal Rocket Engine" generate thrust for a floating ship?

• Context/TLDR:

The "Closed Cycle Nuclear Thermal Rocket Engine" is just a big nuclear steam engine that in this specific case, uses the (non radioactive) water steam to stay in air, at the height of the clouds, from which it captures the water to refuel its engines (assuming the clouds have enough water for that.

So, allowing for floating steam ships in a way.

• Explanation:

A Thermal Nuclear Powered Rocket is basically a open nuclear reactor, where the coolant is heated by the enormous temperatures inside the reactor and expelled at absurd speeds (basically, a very dangerous steam engine).

Needless to say, this is a really dangerous way of propelling something on earth because of radioactive contamination, however, it is very safe to use once in space (because the atoms of the coolant are ejected so fast that they escape the solar system).

The solution would be to make a "closed cycle" system, where the coolant of the reactor would be used to heat a secondary coolant/propellant that would be expelled.

The only thing I could find relative to this was the "Nuclear Lightbulb", in which its nuclear core would heat up to 22.000 ºC and would heat the outer coolant/propellant with its hard ultraviolet emissions (thus, the nickname "lightbulb"). It is theorised to achieve a specific impulse (Isp) range from 1500 to 3000 seconds (15-20 kN·s/kg).

However, I would like to know about the possibility of using the closed cycle with something more akin to the ARE (Aircraft Reactor Experiment), which (I think) would be easier to to build calculate how much and for how long it would generate thrust with only the "steam" of the water of the clouds.

(Illustration of how the ARE works)

So, for how much and for how much and for how long this steam engine be able to lift a metal ship?

The first type of floating ship that I think of would be the "Sevastopol", from the game "Highfleet" since it has all the information necessary (in the link). But in that universe, they use pressurised methane. Of course, this is just an example, if you want to calculate something else of your choice, like a modern cruiser ship, I can't see a problem.

• You wouldn't want to use steam. 'Just' directly use air. Are you dead-set on steam in particular?
– TLW
May 8, 2022 at 22:48
• @TLW , yes, the nuclear powered turbine type in which directly used air to cool/propel itself was abandoned for spilling radioactive air (fallout). May 9, 2022 at 11:15
• I meant as a secondary 'coolant' for a VHTR molten-salt reactor or something equally insane.
– TLW
May 10, 2022 at 2:54
• This thing will be heavy. CG in the back of the plane must be compensated for. The reactor, and the bottom of the plane has to be made shock proof. Just imagine a belly landing with it. There's going to be heat which could damage the condenser outlet. Result will be no cooling reaching the reactor ! May 19, 2022 at 16:08
• Worth noting that when a reactor was flown on an aircraft, it didn't produce nearly enough power to keep itself in the air. With the exception of something like a nuclear ramjet (which has the fallout problem you mentioned and doesn't have to worry about the weight of shielding), a fission-powered aircraft is a complete non-starter, let alone a nuclear steam rocket. May 19, 2022 at 17:08

Not with Modern Reactors

Kori Nuclear Power Station, South Korea

This guy has a bunch of reactors. The biggest one has output of 1400MW. Construction started in 2009 and they turned it on in 2019. So this is state-of-the-art.

General figures suggest nuclear reactors weigh 1000-2000 tonnes. This is a big one so it might be heavier. Let's say it weighs 1500 tonnes.

Let's be generous and say the aircraft weighs 2000 tonnes. That's 1500 tonnes of reactor and another 500 tonnes of engine and bulkhead and fuselage. I imagine this is unrealistic since an aircraft with 3/4 of its mass concentrated in one place will be hard to control.

Putting that aside for the moment, how much energy is needed to get a two kilotonne block of metal into the air?

It seems about 180MW is needed to get a 747 into the air and those bad boys weight about 200 tonnes. Your nuclear sky fortress weighs 10 seven-four-sevens. So it takes 1800MW to get off the ground. This is more than the reactor output. That's a problem.

This of course assumes modern reactors. However that is the only context in which the question has an objective answer.

This is your world. So if nuclear sky fortresses is what you want, then nuclear sky fortresses is what you get. Simply declare their nuclear reactors are much lighter than real land-based reactors.

Who knows -- it might be relatively easy to cut the weight of the Shin Kori-4 reactor by half. I imagine the engineers didn't bother trying, since their nuclear plant was designed as a building and not designed as an aircraft.

But in that case you have your answer. The plane can stay in the air as long as you want, depending on how light you decide the engines are.

• Also worth noting that the OP is talking about using a rocket engine to float, rather than using aerodynamics to provide lift, so your power requirements are even higher. May 19, 2022 at 18:20
• Your answer is off topic. First the 1400 MW output is electrical output, the thermal output is about double of that. A very heavy nuclear carrier need less than a tenth of that power. Second the example you made use low enriched fuel. The reactor in the OP would use HEU. So, if you decrease the size of the starting reactor, you decrease the size of the weight to lift and eventually you decrease the amount of required power. May 19, 2022 at 20:56
• @FluidCode The amount of power needed depends on how heavy the carrier is. May 19, 2022 at 22:01
• I think this is the answer ("not with modern tech unless you shrink things") and power requirements are definitely a function of the weight of the aircraft. I think what remains to be answered is how much nuclear fuel can be carried by the aircraft and for how long said fuel can power the reactor. These are also functions dependent on the design of the aircraft. Perhaps some sample numbers and calculations might paint a better picture of what might happen?
– stux
May 20, 2022 at 12:46
• @stux I think a reactor uses about 100 tonnes of fuel rods and they last a few years. That's half the weight of a 747 but it could stay in the air for years if fuel was your only concern (and we could actually build the damn thing). May 20, 2022 at 12:54

# Just use propellers

We can find out how much water we need to fight gravity by simply dividing gravitational acceleration by the specific impulse. Using your specific impulse of 20 kNs/kg for a closed nuclear thermal reactor, we arrive at 1.76/hr. That is, every hour, you need a mass of propellant equal to 1.76 times the mass of your aircraft. That's a lot. Granted, clouds have a lot of mass, but it would definitely be a logistical headache to collect it. And this doesn't even count the mass of the water stored on the ship, which would quickly snowball into an exponential rocket equation.

So if you're in air anyway, why not just use your onboard nuclear plant to power propellers? It's vastly more efficient in energy and propellant (in that it doesn't require any propellant), not to mention that the people aboard your flying ship will appreciate the ground not constantly rumbling like a magnitude-7 earthquake from your thrusters' vibrations.

Sorry, I can't comment because I only finally made an account.

How dead set are you on using a nuclear fission reactor? These have several issues which make them unideal for flight with fair amounts of gravity. Daron mentioned how a reactor is incredibly heavy. However, there also is the weight of uranium and of water. Turns out, water is also incredibly heavy, and you'd be using a lot of it for steam thrust.

While this may not be what you're looking for, it may help: Try a fusion reactor instead. While still large and heavy (and experimental irl, we can only make them work with tritium, a hydrogen isotope), the fuel is entirely different. It could intake air from the atmosphere and produce thrust through heat (stars have no problem burning oxygen, carbon, and nitrogen for fuel, and fusion is what they use). This eliminates the need for Uranium or similar metals and of water. Additionally, as hydrogen (probably from water vapor) is input into the reactor, it can output helium which further increases the buoyant force upon your aircraft.

Daron mentioned another major thing: the output of the reactor he presented was 400MW less than the energy required to lift it. A fusion reactor can theoretically produce 3 to 4 times as much energy as a fission reactor for each reaction (does for stars!), meaning one of similar weight would be able to lift itself, and some water if you so chose to use it for steam power.

Basically, if you just swapped your nuclear fission reactor for a fusion reactor, you could possibly achieve near infinite flight, using air as fuel and outputting hotter air with different elements present. Just be careful, as eventually the atoms will try to become carbon and iron, and then you're dusting everything under you in a nice layer of graphite and iron flakes. I suppose in this case, using it to heat water and just outputting that water would be more environmentally friendly.

TL;DR, using a fusion reactor instead of a fission reactor could possibly achieve your goals of flight for an infinite amount of time, or based on how much water you carried if you insist on using steam.

I know this doesn't work exactly with your requirements, but this is the best alternative I can think of that even could fly, as Daron described, a real nuclear reactor couldn't really lift itself at all, so your flight time would be null (no flight was achieved at all).

• This article says the submarine uses only 80 tonnes of water as coolant compared to the 1000ish tonnes of reactor. 80 tonnes is a lot but it is small compared to the dead weight of the engine. May 19, 2022 at 17:03
• How heavy are fusion reactors predicted to be? May 19, 2022 at 17:03
• Since fusion is new technology, I don't find a working fusion reactor any easier to believe than a lightweight fission reactor. Both require upgrades that don't currently exist. May 19, 2022 at 17:04
• "Using air for fuel" is also extremely hopeful, as modern fusion reactors only work with deuterium as fuel. May 19, 2022 at 17:05
• @Daron, I was thinking the ship used steam pressure directly and output steam like a real life power plant, meaning it would lose lots of water as steam escapes. As far as weight, current ones weigh around as much as fission reactors. As far as miniature fission reactors, "small" ones did exist and they blew up spectacularly, as it is very hard to control the fuel rods in such a small environment (corrosion is a death sentence). Because the fusion reactor COULD provide enough output to lift itself at the full size, there's no need for a miniature one, just add more the bigger the ship. May 19, 2022 at 17:32

NERVA TWR was 6 - https://en.m.wikipedia.org/wiki/NERVA

That was a working engine we can refer to for some specs.

Using water is not viable in the case of yours, clouds do have water, but per cubic meter of air - mass of air is way more than water it contains cloud or not. So a reactive mass it needs to use it the stuff which is there around.

So height limit will depend on density of air, and it will be, probably, few km's or something. It may jump higher but it does not mean it can hover higher.

So model your thing with typical jet engines with mods to them, it just that you do not need the fuel mass for them.

Do not model it after rocket engines, you have a different situation, as you do not need(if you use air around) high ISP, because lower it is, less energy it uses, more efficent it is and higher TWR it can have.

As steam punk plumes - you will have them being in clouds, after that reaftive mass cools down enough down there, so have them as much as you like it.

How long such engine can work, depends on mechanical system resources, but it can have continiuous operation time, indefinitly, if you shut down repair replace some engines, and supply nuclear fuel for it. So once you make everyone busy and tech is mature enough - it years - unitl the hull holds.

If not, but tech is mature enough, a 100 hours between maintanance periods, may be reasonable.(or less depends on tech maturity, or more, depends in complexity of organization of in air repair maitanance, up until decades in air, or if nanothech is there then until there is a fuel it will be in the air)

This would be rather difficult, though not completely impossible.

Water is a terrible rocket fuel in the context of rocket fuels. It's relatively high mass and volume make it rather hard to accelerate to very high speeds. The best specific impulse that you'll get out of steam is around 200 seconds, and that is at a temp of 500c. At 200 seconds to produce the 36000 tons of thrust needed to float the ship means you need to be throwing 180 tons of steam out the back every second. To heat that water to that temperature you'll need a reactor producing 37GW.

This is a rather extreme amount of power, basically requiring that you completely utilize all the energy from a kilo of uranium or thorium about every 35 minutes. (We'll make that 2 kg per hour.)

Now, if you want more power, all you need is denser and more active nuclear fuel. At some point it's so dense it becomes a nuke, but try not to go there. The other issue is temperature. The process of producing that much energy at once creates a lot of heat. The scale of your reactor will be the determiner of how hot the reactor will run, but we're talking temperatures that require handwaved materials to hold. It would also need a constant stream of removing waste and adding new nuclear fuel, since it would be burning through the stuff so fast.

Finally, capturing 180 tons of water per second is gonna be difficult... (That is about the rain of a square kilometer of London over an entire day. Not impossible, just difficult...)

The lifetime of a nuclear reactor depends on a number of factors, but will be in the months to years. In a normal power generating nuclear reactor, it is ~6 years.

This usage is likely much more intense, so 1-2 years is perfectly feasible and on the conservative.

The thrust generated is a function of how much air is entering the intakes and how hot the engines are. The faster you travel, the more air goes in and the more cooling the air provides.

Project Pluto used a similar thrust idea (air being passing over a hot reactor) and it needed around mach 3 to get enough air to maintain thrust and cool the reactor. That had a projected flight time in the months.