# How big should this starship's power system be?

I have a near future starship that weighs about 10,000 tons. I've determined that the ship needs a 500 megawatt fission reactor, but the problem is that even though nuclear fuel rods are obscenely small for thier power capacity, a whole power plant is generally not small at all. My original thought was to just copy the power systems from a naval ship or terrestrial power plant, but these reactors typically use external sources of water for cooling/steam... but in space, cooling is way less easy, and all water has to be internally stored. I image that this will make the size of the power system significantly bigger and heavier, but I don't know by how much.

To try to make things easier, the ship only needs to be able to operate for up to 20 days between resupply and refueling as opposed to naval nuclear ships that are expected to operate for many months at a time.

What I need to do is figure out how small (size and weight) a whole nuclear power system of this output could be if used in space. The best answer will be one that uses known technologies to minimize the size of the reactor while taking into account the limitations of operating in space.

Based on comments: If it is not doable in the mass allowed, then the next best answer would be one that demonstrates how close to doable one can come.

• I suspect (strongly) that your mass allowance doesn't permit a fission plant of that size. I'm assuming your measurement is 500MW (electrical) not 500MW (thermal), so you're required to have radiators that will be able to dissipate at least 500 MW of energy, and those would require the majority of your mass beyond that of the reactor itself right off the bat. A Nimitz-class aircraft carrier doesn't generate that much power, and it's nine times that mass and has the ocean as a heatsink. Commented Jan 29 at 18:03
• "Copy the power systems from a naval ship": An advanced S8G nuclear reactor as used on the American peacekeeping nuclear attack submarines weighs 2,750 tons for an output of 220 MW thermal, so maybe 130 MW electrical. And you want 500 MW... Now, the reactor has no need to be larger than what's used on a nuclear submarine, but the cooling system will have to be enormous; current radiator designs are able to reject about 350 W per square meter tops, and you need to reject how many hundreds of millions of watts you need to reject. Commented Jan 29 at 18:10
• @jdunlop I'm aware. I'm not 100% sure that it is doable, and if it not being doable is the answer, then that is fine. But HOW not doable would at least tell me how much I need to adjust my expectations. Commented Jan 29 at 18:23
• From @AlexP's comment, "10000 tons" would account for just the reactor if you wanted 500MW electrical. And then there's the radiators. And the rest of the ship. Commented Jan 29 at 19:07
• @jdunlop - Point of Order - the current Gerald R Ford class of Aircraft Carrier has 2 A1B reactors, with each rated at 700MW. The Nimitz class carriers run two A4W reactors, each rated at 550 MW - however, they split the power between electrical generation and propulsion which is skewing the figures a bit. Commented Jan 29 at 20:52

10,000 tons - so you are looking at the size of a modern attack submarine or destroyer. I'm going to use the submarine as our proxy.

The current Virginia class of SSN weigh around the 10,000 ton mark (I think block 5 are around this) - the official statistics for the S9G reactor (Submarine, 9th Gen produced by General Electric) reactor is:

~150 Tonnes for the Powerplant and ~210 MW

Now, given that this is the front-line SSN, the power output is probably higher. I don't know by how much and I'm not going to ask the question on the War Thunder forum to find out.

You'll note that 150 tonnes is a lot smaller than the ~2,700 tonnes listed by AlexP's comment - however to give clarity that's the total weight of the compartment, including all the shielding, propulsion equipment, etc.

IIRC - US submarines have a closed-loop nuclear reactor so that there's no radiation that goes out into the water from their powerplants.

In short - depending on how much you are willing to bend capabilities with your 'near future' - it's plausible to have a 500 MW nuclear reactor in a 10,000 tonne vessel. It would probably take up about an 8th of the mass of the vessel when all the ancillary items are included (this is because we've removed the propeller shaft/gearboxes).

• I take no issue with any suppositions. However I must point out that compactness of design is not a necessity, in that shielding isn't necessary. It's possible to only the barest of gossamer like structure is needed to keep the reactor far enough away from the living area for safe operation. So big in this instance may not mean weight but the volume of the superstructure along with the not insignificant size of whatever method of heat dispersal. Commented Jan 29 at 19:59
• I would also point out that submarines are probably a better model for spacecraft than aircraft carriers, by virtue of being designed as a giant reverse pressure vessel with even greater space-efficiency which is intended to operate under a specialist crew without logistic support for long periods. Commented Jan 29 at 21:42
• @TheDemonLord Water is opaque to most infrared wavelengths, and those that do go through water don't carry very far. So dumping waste heat into the water does not significantly compromise your stealth. Commented Jan 29 at 22:52
• @KEY_ABRADE I wholly agree. since there's no water in space (citation required) the electrical output of the reactor is unlikely to be the fuel for the engines. That means that the wholly-contained submarine better models space than the access-to-air surface ships. Further, subs in combat mode must be completely self-contained - like a space ship in any mode. +1
– JBH
Commented Jan 29 at 23:36
• "I'm not going to ask the question on the War Thunder forum" - for which the mods are duly grateful. They've had enough top secret (and above) information leak out of there to last them a lifetime. Commented Jan 30 at 4:11

I think @TheDemonLord covers the power requirements well, but I feel like OP's question is specifically concerned with heat rejection, and I thought I would put in my 2 cents on that.

You'd need a large set of radiators, but that might not be a problem.

That much power doesn't make sense unless you're using something like an Ion Engine to generate thrust. So I'll assume that 95% of the 500MW are being ejected out the back of the ship as highly energetic ions. You need to reject 25MW of waste heat.

Radiators on existing satellites reject about 100-350 Watts per square meter. Let's use 250 as a middle ground. So we need 25,000,000 / 250 = 100,000 square meters of radiator.

Abstracting the ship as a cylinder 100 meters long and 10 meters in diameter - which is slightly smaller than modern submarines - you get just under 7,000 square meters of surface area. This is about 7% of the area that we need.

At about 12kg per square meter of radiator, you're looking at just over 1,000 tons of radiator. Which is about 10% of your ship's mass, so large, but not prohibitively large.

## Black Body Equation to the Rescue

The rate at which your radiators reject heat is a function of their temperature. Higher the temperature, the more heat is rejected per unit area.

So if you concentrate your waste heat (using basic heat pump / air conditioning / refrigeration tech) you can raise the temperature of the water you put through your radiators, and increase the amount of energy radiated per unit area.

At the 350 W/m^2 upper limit of "normal" quoted above, your radiator weighs ~800 tons. At 500 W/m^s you're down to ~500 tons.

• An ideal heat pump pumping 300K to 600K will double the heat radiated. However the radiators will be 16 times more efficient! So 1/8th the area needed. Even less-than-ideal heat pumps will still be used to save radiator mass. Commented Jan 31 at 6:05
• Using ejection mass to carry away a significant amount of the heat is a good starting point. As for using a heat-pump, obviously this takes an investment of power (and heat) to run the compressor. How would I determine how hot I should try to compress the radiator fluid to before the compression itself becomes more expensive than the benefit, or will it always take away more heat than I add to the system, and I should just be looking at material tolerances? Commented Jan 31 at 14:16
• @Nosajimiki - using ejection mass to carry away heat is required by physics. To move, you're "pushing" on something (in hard science, expanding gas or high energy ions, in soft science, the fabric of spacetime or something). That transfers energy to whatever you're pushing on. My submarine used something like ~90% of it's power to turn the propeller, which pushed against the ocean to generate thrust. So our waste heat rejection requirements were also a fraction of rated power. I'm just assuming that the distribution of power is similar for the spaceship. Commented Jan 31 at 15:44
• @Nosajimiki - "How many heat pumps?" might be an interesting question in it's own right. It's probably an engineering tradeoff between radiator weight, and number of stages of heat pumps. "Given X square meters of radiator area, how hot do I need my radiators to get in order to radiate away 25MW? Given that, how many stages of heat pump do I need to get my working fluid that hot if the ship's interior is maintained at STP?" Commented Jan 31 at 15:52

If you're after compact size, and 'relatively' cool self-contained reactor, with minimal shielding required, and increased safety margins, look no further than Lead Fast Reactors.

Similar reactors were used in the Alfa Class Soviet Submarines (although they used Lead-Bismuth) - utilised because of their large power output compared to their physical size. By compacting the size of the reactor, Alfa Class submarines were able to propel to extremely fast speeds, even outrunning torpedoes.