[3e] Statting a spaceship radiator

[GURPS Fox]

Originally Posted by Anthony

Yes and no. The problem with a high temperature radiator is that you need to get your heat to the radiator, which requires power (and additional heat production) if the radiator is hotter than the system it's intended to cool. If you want a 2,000K radiator... all your heat-producing components need to be able to run at 2,000K. There are a few components that really can operate at that kind of temperature, but most machinery really cannot (a 2,000K sodium cooled reactor will probably explode violently if you look at it funny).

It depends on whether you're willing to use things like Graphine/Carbon Nanotubes/metamaterials in their construction.

Originally Posted by Verjigorm

Couldn't we use different radiators for different systems though? Like, if our fusion engine produces a 1500k worth of heat to dispose of, we run it on some dedicated radiators, while our habs and their associated stuff use lower temperature radiators. Which probably gives us a really big set of radiators for our habs, and a much smaller one for our drive system.

This is what is done in Children of a Dead Earth. You need a radiator for any non-kinetic/VLS/engine component. They all have different heat pump outputs (for example, habitats consistently have the lowest heat dissipation requirements due to only needing kilowatts of heat to be dissipated while reactors -especially player-designed reactors- tend to require higher heat dissipation requirements. In contrast, lasers tend to be in the middle).

[Anthony]

Originally Posted by GURPS Fox

It depends on whether you're willing to use things like Graphine/Carbon Nanotubes/metamaterials in their construction.

It depends on whether you're willing to use materials that we know actually exist and work as required, or if you're speculating wildly on materials. Carbon compounds can absolutely do a lot of things, but they aren't universally useful for all purposes -- for example, they tend to be brittle with nasty failure modes (and 2,000K sodium has a vapor pressure of 80 atmospheres...), and they simply aren't a replacement for metals in electrical applications. Also, even if your reactor core runs at 2,000K -- that probably means 1,000K radiators.

[GURPS Fox]

Originally Posted by Anthony

It depends on whether you're willing to use materials that we know actually exist and work as required, or if you're speculating wildly on materials. Carbon compounds can absolutely do a lot of things, but they aren't universally useful for all purposes -- for example, they tend to be brittle with nasty failure modes (and 2,000K sodium has a vapor pressure of 80 atmospheres...), and they simply aren't a replacement for metals in electrical applications. Also, even if your reactor core runs at 2,000K -- that probably means 1,000K radiators.

Oh boy, this is a lot harder than it looks... even with 'crash course into radiator design' that Children of a Dead Earth gives me.

However, with the RAW of THS's radiator construction rules, we're probably looking at a ratio of between 15.66kW:1sf and 32.3kW:1sf, depending on the tech level.

[Anthony]

Originally Posted by GURPS Fox

However, with the RAW of THS's radiator construction rules, we're probably looking at a ratio of between 15.66kW:1sf and 32.3kW:1sf, depending on the tech level.

In general the power emission is the black body constant (5.67e-8W/m^2/K^4) times area times temperature^4, so at 1,000K you get 56.7 kW/m^2 or 5.26 kW/ft^2. However, the total heat output of a reactor is generally somewhere around 2x the electrical power output, and the things you're using the power for also produce heat, so that's about 2 kW/sf, which is a reasonable TL 10 value, the TL 9 value is probably more like 1 kW/sf.

[GURPS Fox]

Originally Posted by Anthony

In general the power emission is the black body constant (5.67e-8W/m^2/K^4) times area times temperature^4, so at 1,000K you get 56.7 kW/m^2 or 5.26 kW/ft^2. However, the total heat output of a reactor is generally somewhere around 2x the electrical power output, and the things you're using the power for also produce heat, so that's about 2 kW/sf, which is a reasonable TL 10 value, the TL 9 value is probably more like 1 kW/sf.

Ouch, that makes THS radiators super-science levels from what you're saying if we use the assumptions I've made:

Originally Posted by THS (3e) Book, Appendix A pg186-187

Required Radiator Area (RRA)
This is the area in ksf of radiators required. Add up the total requirement and record it; this statistic is used in space combat.

Fission drive, nuclear light bulb drive, or old fission power plant: 1 ksf per 8 spaces of drive or power plant.

Old fusion power plant or new fission power plant: 1 ksf per 4 spaces of power plant.

Fusion pulse drive (any), fusion torch drive (any), antimatter pulse drive (any), or new fusion power plant: 1 ksf per 2 spaces of drive or power plant.

Radiator Panels
Each radiator panel occupies 1 ksf. Radiator panels do not add mass or cost; this is included in the systems that require them. They only require unused surface area.

Radiator Wings
A vessel with insufficient surface area for radiator panels will usually need radiator wings. Subtract the area of any radiator panels from RRA to get the area of radiator wings required.

Radiator wings are mounted externally on lightweight structures parallel to the hull. A craft may have up to two wings; each wing’s area in ksf may not exceed (Spacecraft’s Longest Dimension)^2/1,000 ksf. Radiator wings are 4 tons and M$0.4 per ksf.

Radiator wings may be designed to fold up. Vessels intended to enter atmosphere may only have folding wings. Military spacecraft often have folding wings, as the radiators are vulnerable in combat. Folding wings are 0.5 space, 5 tons, and M$0.5 per ksf.

Select the dimensions of the radiator wings; they should not be longer than the craft. For instance, 4 ksf of radiator wings could be two wings, each of 2,000 square feet; a 2,000-sf wing might be 100’ ´ 20’.

If we keep to RAW, then THS's radiators are pretty potent, depending on the designers' assumptions.

Quick question: What is a radiator's radiance when the temperature is 1200K, 1500K, or 2000K, respectively? Because that could explain a lot.

[Verjigorm]

I believe this may be a useful source, though it's very, very dense. Our own Anthony Jackson is quoted quite frequently too, for what it's worth. Atomic Rockets. Winston suggests you design your radiator for 3/4s of the temperature of your heat source or do the scary maths.

Now, one cool thing is that at tl10, I think it's reasonable to assume room temperature super conductors. With those, you could create pretty powerful magnetic fields. If you then heat up an iron based solution to a certain point, it will lose it's magnetic properties and be expelled in a cloud into space. While in space, the iron dust will radiate away the heat really effectively, cooling enough to become magnetic and be caught in the magnetic field and recollected. You now have a really efficient radiator with a lot of extra neat things. Due to consisting of a diffuse cloud of iron dust in magnetic fields, it's rather resilient and rugged, so long as the magnets have power.

A related idea is to use a magnetic field to contain some sort of plasma in a "bubble". In space, this could be used as a mag-sail, and would also make communication(and identification) with the ship quite difficult, if not nearly impossible, without shaping the magnetic field to provide some sort of window(which is likely possible) in the plasma bubble. In an atmosphere, this plasma bubble could be used as a sort of air foil and thermal barrier for the ship. In either case, the bubble will tend to swell to the limits of it's magnetic field, so it's inherently "adjustable", and it will tend to capture charged particles.

Visually, I think this works out to ships having rather small "active" parts, and then the vast bulk of the ship being a sort of ephemeral latticework supporting magnetic fields for fusion rocket nozzles, plasma sails and radiators.

[Anthony]

Originally Posted by Verjigorm

I believe this may be a useful source, though it's very, very dense. Our own Anthony Jackson is quoted quite frequently too, for what it's worth. Atomic Rockets. Winston suggests you design your radiator for 3/4s of the temperature of your heat source or do the scary maths.

The scary maths have issues, which is why my numbers are considerably more conservative than his. If you assume a power plant operating at the Carnot limit, and all you care about is optimizing for minimum radiator area, you get the highest output with a 25% efficient power plant with a radiator temperature of 75% of the core temperature -- but typically neither of those statements is true (approaching the Carnot limit requires increasingly massive and complex reactor machinery, and fuel is generally not free).

THS is generally 'technically doesn't violate known physics but implausibly optimistic'.

[GURPS Fox]

Originally Posted by Verjigorm

I believe this may be a useful source, though it's very, very dense. Our own Anthony Jackson is quoted quite frequently too, for what it's worth. Atomic Rockets. Winston suggests you design your radiator for 3/4s of the temperature of your heat source or do the scary maths.

Now, one cool thing is that at tl10, I think it's reasonable to assume room temperature super conductors. With those, you could create pretty powerful magnetic fields. If you then heat up an iron based solution to a certain point, it will lose it's magnetic properties and be expelled in a cloud into space. While in space, the iron dust will radiate away the heat really effectively, cooling enough to become magnetic and be caught in the magnetic field and recollected. You now have a really efficient radiator with a lot of extra neat things. Due to consisting of a diffuse cloud of iron dust in magnetic fields, it's rather resilient and rugged, so long as the magnets have power.

A related idea is to use a magnetic field to contain some sort of plasma in a "bubble". In space, this could be used as a mag-sail, and would also make communication(and identification) with the ship quite difficult, if not nearly impossible, without shaping the magnetic field to provide some sort of window(which is likely possible) in the plasma bubble. In an atmosphere, this plasma bubble could be used as a sort of air foil and thermal barrier for the ship. In either case, the bubble will tend to swell to the limits of it's magnetic field, so it's inherently "adjustable", and it will tend to capture charged particles.

Visually, I think this works out to ships having rather small "active" parts, and then the vast bulk of the ship being a sort of ephemeral latticework supporting magnetic fields for fusion rocket nozzles, plasma sails and radiators.

So, basically, stat a droplet radiator if I'm reading this right?

To be honest, some would say I'm ripping off Mass Effect radiator designs (though the idea of droplet radiators isn't Mass Effect; you know how the general populous perceives things).

[GURPS Fox]

Originally Posted by Anthony

The scary maths have issues, which is why my numbers are considerably more conservative than his. If you assume a power plant operating at the Carnot limit, and all you care about is optimizing for minimum radiator area, you get the highest output with a 25% efficient power plant with a radiator temperature of 75% of the core temperature -- but typically neither of those statements is true (approaching the Carnot limit requires increasingly massive and complex reactor machinery, and fuel is generally not free).

THS is generally 'technically doesn't violate known physics but implausibly optimistic'.

That's the funny thing about Children of a Dead Earth: all the numbers in the game are very conservative (the Dev made it clear that all the numbers were low-end, something that carried on with the Metamaterials Mod). However, given that it's made by a single person, it's understandable.

So, using the equation you gave me, P = A * ε * σ * T^4, I'm assuming 0.85 in this example because Atomic Rockets says anything less than 0.8 is a horrible radiator.

A= 32887.67616m^2 / 354000cf - based on THS's radiator area rules for a 708 Space septuplet (7) HePlaR rockets
ε = 0.00000005670373
σ = 0.85
T = 1500K

So, P = 32887.67616 * 0.00000005670373 * 0.85 * 1500^4, which goes to P = 32887.67616 * 0.00000005670373 * 0.85 * 5062500000000.

If I did the math correctly, then P = 0.0018648539093040768 * 4303125000000, ending with P = 4,303,125,000,000 (or 4.303125 PW).

... and I feel like I messed up somewhere here.

[Anthony]

Originally Posted by GURPS Fox

... and I feel like I messed up somewhere here.

I'm not sure where "A = 32887.67616m^2 / 354000cf " comes from -- I'm pretty sure A is just 32887m^2. Other than that, 4,303,125,000,000 is 4.3TW, not 4.3PW.

I will, however, observe that HEPlaR is not a THS term, and TNE HEPlaR is superscience.