Power plants and some propulsion systems are going to require heat radiators or the ship will glow red then melt (NO, for the millionth time you CANNOT get rid of the heat by turning it into electricity!).
There are only three ways of getting rid of heat: convection, conduction, and radiation; and the first two do not work at all in the vacuum of space. So the ship designer is stuck with heat radiators, or what NASA calls Active Thermal Control Systems
Functionally they are not too different from the radiator on your automobile. Pipes full of radiator fluid are coiled around the cylinder heads and engine block, sucking up the heat so the engine doesn't turn into molten lava. The hot radiator fluid is moved by the coolant pump, carrying the heat into the engine coolant radiator (that flat box on the automobile's nose with all the scalloped holes). In the radiator, the heat is removed from the radiator fluid by conduction with the wind. The cool radiator fluid travels into the engine and the cycle begins anew.
Actually, in spaceships the heat radiators get rid of heat by … well … radiating, instead of conduction. Different design because there is no wind in space. But you get the idea.
See Thermophotovoltaic Energy Conversion in Space Nuclear Reactor Power Systems and HIGH TRADER for details.
If you want to calculate this for yourself use the Stefan-Boltzmann law:
P = A * ε * σ * T4
A = P / (ε * σ * T4)
- P = the power of waste heat the radiator can get rid of (watts)
- σ = 5.670373×10-8 = Stefan-Boltzmann constant (W m-2K-4)
- ε = emissivity of radiator (theoretical maximum is 1.0 for a perfect black body, real world radiator will be less. Should be at least 0.8 or above to be worth-while)
- A = area of radiator (m2)
- T = temperature of radiator, this assumes temperature of space is zero degrees (degrees K)
- x4 = raise x to the fourth power, i.e, x * x * x * x
My source (Matthew DeBell) says that if P = 150 gigawatts, ε = 0.94, and T = 3000 K, A would be 34,941 m2. Actually it could be half that if you have a two-sided radiator, which would make the radiator 17,470 m2 (a square 132 meters on a side). Which is still freaking huge.
For estimating the mass of the radiator array, go here.
Ken Burnside says that if one examine the equation carefully one will notice that the radiator effectiveness goes up at the fourth power of the heat of the radiator. The higher the temperature, the lower the surface area can be, which lowers the required mass of radiator fins. This is why most radiator designs use liquid sodium or lithium (or things more exotic, still). 1600K radiators mean that you need a lot less mass than 273 K radiators.
Ken Burnside also noted that radiators are large, flimsy, and impossible to armor (except perhaps for the droplet radiator). A liability on a warship. However, Zane Mankowski (author of Children of a Dead Earth) makes a good case that heat radiators can indeed be armored. Mr. Mankowski says the thickness of the radiator material can be increased to provide armor-like protection for the working fluid tubes, with the price of reducing radiator efficiency.
Mr. Burnside has an entire essay about the problem of heat on combat spacecraft, entitled The Hot Equations: Thermodynamics and Military SF. Since thermodynamics is one of the most important (and most neglected in science fiction) factors in combat, the essay will repay careful study.
In the military the old bromide is that amateurs talk about battle tactics while professionals talk about logistics. In the real of spacecraft design, @AsteroidEnergy said "Amateurs discuss rockets, professionals discuss heat management."
But do realize that if the spacecraft does indeed have a nuclear propulsion system or something else dangerously radioactive, the radiators must be tapered to keep inside the radiation shadow shield. Or bad things happen.
I had initially thought that the heat from the life-system could be simply dumped by the same radiator system dealing with the multi-gigawatt waste heat from the propulsion system or power system. Richard Bell pointed out that I had not thought the problem through. Due to the difference in the temperatures of the waste heat from life-system and propulsion, unreasonably large amounts of energy will be required to get the low-level life-system heat into a radiator designed to handle high-level propulsion heat. The bottom line is that there will be two separate radiator systems.
Not only are you going to require two separate radiator systems, the one for the modest cooling required by the life-system is liable to have larger radiator surfaces than the one cooling the multi-gigawatt propulsion system. Radiator effectiveness goes up as the fourth power of the heat of the radiator, remember?
You noted that having too many radiators distributed about an axis causes them to radiate into each other. It all boils down to what's known as a face factor, essentially how much of the radiation released by a surface is intercepted by another one. For two plates of equal length separated by an angle alpha (α), the face factor is:
F = 1 - sin(α/2)
So you can see right off the bat that for 2 radiators opposite each other, α = 180°, α/2 = 90° and the face factor is 0, no interception. But go up:
Multiple Radiator Panels # Face
Emit Efficiency 1 0.000000000 1.00000000 1.000000000 2 0.000000000 2.00000000 1.000000000 3 0.133974596 2.598076211 0.866025404 4 0.292893219 2.828427125 0.707106781 5 0.412214748 2.938926261 0.587785252 6 0.500000000 3.000000000 0.500000000 7 0.566116261 3.037186174 0.433883739 8 0.617316568 3.061467459 0.382683432 9 0.657979857 3.078181290 0.342020143 10 0.690983006 3.090169944 0.309016994 11 0.718267443 3.099058125 0.281732557 12 0.741180955 3.105828541 0.258819045
- # number of radiators spaced around the ship's long axis
- Face Factor how much heat radiation from a radiator is wastefully intercepted by another radiator
- Emit how much heat is effectively radiated by the total radiator array, in units of single radiator panels
- Efficiency how efficient is this array at getting rid of heat, single panel = 1.00 or 100%
The second column is face factor, the third column is how much is emitted relative to a single surface, and the last is "efficiency", how much every individual panel is emitting relative to a single unlimited surface (efficiency is just 1 - F = sin(α/2), which is itself the face factor for the surface relative to its unobstructed surroundings). As you can see, it falls off very very quickly; the third radiator is only 60% as effective (goes up from 2.00 to 2.60), and the fourth adds to this only marginally (goes up from 2.60 to 2.80). Unless there really isn't room to simply stretch out the panels, it just doesn't seem worth it to pack more than 3 about an axis, and even 3 might be a stretch.
Neat thing is, using the face factor you can figure out the efficiency of radiators in weird geometries. My textbook has face factors for cylinders, enclosed spaces and plates of unequal size, if you so desire, which is to say I could tell you how much is going into your spaceship, or out an open dock.
Another neat side effect of face factors is that you can make a radiator more efficient per given mass by poking holes right through it, since the inner surface of the hole radiates at least partly out into its surroundings (the rest radiates back into itself, but that isn't really a problem). This reduces efficiency per unit area (though interestingly not by much for giant holes), and the panel is significantly weaker as a result (even more than you'd think, since the hole provides an area of stress concentration — it can reach multiples what it would normally there), but for very small holes that are very close together, you can get efficiencies per mass that are many times higher than they would be for a straight panel.
Take this arrangement: a square grid of side L, with a hole in the center of each square and one on each vertex, each hole being of radius 0.35L so that the holes at the vertices are nearly touching that in the middle. Say, for L varying from 0.1 to 1, 10 and 100 times thickness, relative mass efficiency goes up 4.342, 4.010, 1.828 and 1.094 times(by the way, because the relative size of the hole is the same, you need 4.660 times the area of panelling to get the same mass as a continuous radiator).
(ed note: the above was orginally erroneously writen as 1.199, 2.204, 4.184 and 4.609 times)
You can force even more holes into there if they're arranged hexagonally; take a hexagon of side L, with a hole at the center and one each vertex, you can reach a radius of up to 0.5L. Now, for L varying again from 0.1 to 1, 10 and 100 times the thickness, relative mass efficiency goes up 10.741, 9.610, 2.763 and 1.193 times over (in this case, you need 10.74 times the area of panelling to get the same mass as a continuous radiator)!
(ed note: the above was orginally erroneously writen as 1.486, 5.035, 9.816 and 10.644 times)
Given that "every gram counts", it's almost certainly worth the fragility. You could probably thicken the panels somewhat to make up for it and hit a sweetspot
With certain kinds of rocket engines, you can cheat and avoid the need for heat radiators (and their ugly penalty weight). The dodge is called "open-cycle cooling", where the waste heat is carried away by the exhaust plume. In effect, the exhaust is their radiator, made out of rocket plasma instead of metal.
But it only works on certain kinds of engines.
Since the heat is carried by the rocket exhaust, you need plenty of exhaust. Which means each second of exhaust needs lots of propellant. Which means the engine needs a large propellant mass flow (called "ṁ" or "mdot"). This has consequences: raising the mdot will raise the thrust but drastically lower the exhaust velocity and specific impulse. Basically the engine will accelerate the spacecraft more quickly, but the gas mileage will fall into the toilet.
Some rocket engines (such as ion drives) have large exhaust velocities but low thrust. They cannot use open-cycle cooling because their ain't enough propellant in the exhaust plume to carry away all the heat.
Other engines (such as solid-core nuclear thermal rockets) have relatively low exhaust velocities but high thrust. They work splendidly with open-cycle cooling. So as a general rule, most NERVA type engines do not have heat radiators. If they do, this is because they are bimodal NTRs, and the radiator is only used when there is no rocket exhaust (when it is generating electricity instead of thrust).
What color will the radiators glow? A practical one will only glow dull red. You can use the Blackbody Spectrum Viewer to see what temperature corresponds to what color. If it was glowing white hot, the temperature would be around 6000 Kelvin. This would be difficult for a solid radiator, since even diamond melts at 4300 degrees K.
Here is some scary math about radiators from Dr. Tony Valle and Ray Robinson, along with some interesting conclusion. Remember that according to the radiator equation the hotter temperature the radiator is run at, the more waste heat it can dispose of.
Use the "Life Support" radiator data for life support and other low-waste-heat management. Use all the others for high-waste-heat management, such as fission/fusion reactors and weapons-grade lasers.
In each radiators Specific Area data table will be listed Heat Cap., Mass, and Op. Temp.
Heat Cap.: heat capacity in kWth/m2. This is how many kilowatts of waste heat each square meter of radiator can get rid of. Multiply the surface area of the entire radiator by the heat capacity to find the total amount of heat the radiator array can handle. kWth means "kilowatts of thermal energy" (i.e., waste heat) as opposed to kWe which means "kilowatts of electricity".
Mass: specific area mass of the radiator in kg/m2. This is the mass of each square meter of radiator in kilograms. Multiply the surface area of the entire radiator by the specific area mass to find the total mass of the radiator array.
Op. Temp.: the operating temperature of the radiator. You probably won't need this unless you want to fool around with the Stefan-Boltzmann equation. The higher the operating temperature, the higher the heat capacity. Which means the value listed for the heat capacity is only valid if the radiator operates at this temperature.
Use the "Specific Area" values in the tables to calculate the radiator mass.
- Decide how many kilowatts of waste heat the radiator will have to handle (from the engine, the power reactor, the laser cannon, etc.)
- Select which radiator type to use, and examine its Specific Area table.
- Divide the total waste head in kilowatts by the Heat Cap. entry of the table to get the square meters of radiator area required.
- Multiply the radiator area by the Mass entry to get the total mass of the radiator required.
or in other words:
radiatorMass = (wasteHeat / specificAreaHeat) * specificAreaMass
- radiatorMass = mass of radiator array (kg)
- wasteHeat = amount of waste heat to dispose of (kWth)
- specificAreaHeat = Heat Cap. from radiator table (kWth/m2)
- specificAreaMass = Mass from radiator table (kg/m2)
Note that Step 3 calculates the radiation surface of the radiator. If the radiator is layered flat on the ship's hull, the radiation surface is the same as the physical radiator size. However, if the radiator is attached edge on so it extends out as a fin or a wing, the physical radiator size will be one-half the radiation surface. This is because you can use both sides of the physical fin as radiator surface. Yes, even a liquid droplet radiator. This might not apply for some of the stranger radiator designs, but details are scarce.
Having said that, things are complicated for liquid drop radiators. The radiation surface is the surface area of the droplets. Figuring out the physical radiator size is compilcated, you can find the equations here. There is also Eric Rozier's online calculator.
Note, in the illustrations from the High Frontier game, it uses very strange game-specific terms. Each "mass unit" is equal to 40 tonnes, each thermometer is one "therm" and represents the radiator dealing with 120 megawatts of thermal waste heat (120,000 kWth). When a specific area value was missing I uesd the therm, mass points, and radiator area on the cards to calculate.
Here is a table of the various radiator types. Their area and mass has been calculated as if they were sized to handle 250 megawatts of waste heat.
The table is sorted by array mass, so the better ones are at the top. At least if you want the lowest mass radiator. If the radiation area was an issue you'd probably prefer a Mo/Li Heat Pipe instead.
The life support radiator was included even though it was not intended to handle waste heat over 100 kilowatts or so.
|Radiator for 250,000 kilowatts waste heat|
|Marangoni Flow||293.04 kWth/m2||24.4 kg/m2||853 m2||20,816 kg|
|Electrostatic Membrane||51.3 kWth/m2||4.275 kg/m2||4,873 m2||20,833 kg|
|Hula-Hoop||300 kWth/m2||33 kg/m2||833 m2||27,500 kg|
|Buckytube Filament||293.03 kWth/m2||48.839 kg/m2||853 m2||41,667 kg|
|Curie Point||212.75 kWth/m2||35.459 kg/m2||1,175 m2||41,667 kg|
|Tin Droplet||38.49 kWth/m2||6.4154 kg/m2||6,495 m2||41,669 kg|
|Flux-Pinned Superthermal||76 kWth/m2||17 kg/m2||3,289 m2||55,921 kg|
|Attack Vector: Tactical||357 kWth/m2||100 kg/m2||700 m2||70,028 kg|
|Bubble Membrane||21.01 kWth/m2||7.00 kg/m2||11,899 m2||83,294 kg|
|Mo/Li Heat Pipe||453.54 kWth/m2||151.18 kg/m2||551 m2||83,333 kg|
|Microtube Array||102.6 kWth/m2||34.2 kg/m2||2,437 m2||83,333 kg|
|ETHER||212.75 kWth/m2||70.92 kg/m2||1,175 m2||83,337 kg|
|Ti/K Heat Pipe||150.22 kWth/m2||100.14 kg/m2||1,664 m2||166,656 kg|
|SS/NaK Pumped||90.83 kWth/m2||60.554 kg/m2||2,752 m2||166,669 kg|
|Salt-Cooled Reflux tube||75 kWth/m2||75 kg/m2||3,333 m2||250,000 kg|
|Life Support||0.19 kWth/m2||3.1 kg/m2||1,315,789 m2||4,078,947 kg|
|Heat Cap.||~0.19 kWth/m2|
|Op. Temp.||? K|
Technically you also need radiators to keep the life-system habitable. Human bodies produce an amazing amount of heat. Even so, the life-system radiator should be small enough to be placed over part of the hull, since life-support waste heat is quite tiny compared to nuclear reactor or gigawatt laser waste heat.
Use this radiator type for life-support and other modest waste heat management. Use the other radiators for gigantic waste-heat producers.
The life-system radiators on the Space Shuttle are inside the cargo bay doors, which is why the doors are always open while the shuttle is in space.
Troy Campbell pointed me at a fascinating NASA report about spacecraft design. In the sample design given in the report, the spacecraft habitat module carried six crew members, and needed life-system heat radiators capable of collecting and rejecting 15 kilowatts of heat (15 kW is the power consumption for all the systems included in the example habitat module). The radiator was one-sided (basically layered over the hull). It required a radiating surface area of 78 m2, had a mass of 243.8 kg, and a volume of 1.742 m3. It used 34.4 kg of propylene glycol/water coolant as a working fluid. In addition to the radiator proper, there was the internal and external plumbing. The Internal Temperature Control System (coldplates, heat exchangers, and plumbing located inside the habitat module) had a mass of 111 kg and a volume of 0.158 m3. The External Temperature Control System had a mass of 131 kg, a volume of 0.129 m3, and consumes 1.109 kilowatts.
What this boils down to is that the described system needs about 96 kilograms and 0.405 cubic meters of temperature regulating equipment per crew person. That's the total of the external radiator on the hull and the internal temperature control system.
Simple math tells me the radiator has a density of about 140 kg/m3, a specific area of 3.1 kg/m2 and needs a radiating surface area of about 5.2 m2 per per kilowatt of heat handled (1/5.2 = 0.19 kWth/m2). The entire system requires about 35 kg per kilowatt of heat handled, and 0.13 m3 per kilowatt of heat. But treat these numbers with suspicion, I am making the assumption that these things scale linearly.
Liquid Droplet Radiators use sprays of hot droplets instead of tubes filled with hot liquid in the radiator. This drastically reduces the mass of the radiator, which is always a good thing. A NASA report suggested that for 200 kW worth of waste heat you'd need a 3,500 kg heat pipe radiator, but you could manage the same thermal load with a smaller 500 kg liquid droplet radiator.
The droplet generator typically has 100,000 to 1,000,000 orifices with diameters of 50 to 20 μm. They are a bit more susceptible to damage than the components of more conventional radiators.
A drawback is that the spray is in free fall. This means if the radiator is operating and the ship starts accelerating, the spray will start missing the collector and precious radiator working fluid will be lost into space. Brookhaven National Laboratory has patented a way to magnetically focus the droplet stream. Using a large radiator it will allow the spacecraft to maneuver at acceleration of up to 0.001 g (0.00981 m/s2) which is barely an improvement. The acceleration can be increased but only if the single radiator is replaced by numerous smaller radiators. Which of course makes the sum of the radiators have a larger mass than the single large radiator. Oh, and Brookhaven's patent expired in 1994.
Late breaking news, the Curie point type of liquid drop radiator is relatively immune to ship acceleration.
Many liquid droplet designs are well suited for warships, since they do not utilze large fragile panels vulnerable to hostile weapons fire. If a rail gun round or laser bolt passes through a spray of working fluid, it will just make a bit of fluid miss the collector. If weapons fire passes through a conventional panel it will wreck it.
|temperature range||coolant type||example|
|250 K – 350 K||silicone oils|
|370 K – 650 K||liquid metal eutectics|
|500 K – 1000 K||liquid tin|
Rectangular LDRs have collectors the same width at the droplet generator. The droplet density remains constant across the flight path. It is a simpler more robust design than a Triangular LDR, and has a larger radiating surface (twice the surface area).
However the triangular LDR is lighter (40% less massive) due to its smaller collector. As previously mentioned, the rectangular LDR's collector is a long bar the exact same width as the droplet generator bar. By way of contrast the triangular LDR's collector is a small bucket, which has about 40% less mass than a corresponding rectangular LDR collector. But it has drawbacks.
Triangular LDRs have a tiny collector a fraction of the width of the droplet generator, unlike rectangular LDRs. The droplet density increases across the flight path. It is 40% less massive compared to a comparable Rectangular LDR due to the smaller collector, reduced mass is always a plus.
However it is a more complicated design with more failure points, and it has only half the surface area of a same sized Rectangular LDR. Because the radiating surface is a triangle instead of a rectangle.
For reasons that have not been made clear to me, Triangular LDR is currently the focus of much of the research and development. NASA likes them better than Rectangular LDRs. I guess in NASA's eyes lower mass trumps all other considerations.
So the equations are:
a = (0.5*b*h) / (16*r2) * 4*π*r2
a = (0.5*b*h) / (4*r2 + 4*r*q + q2) * 4*π*r2
- a = surface area of lithium droplets in radiator surface
- b = length of base of radiator triangle
- h = length of height of radiator triangle
- r = radius of indiviual droplet
- q = inter-droplet gap
Specific Area Heat Cap. ~38 kWth/m2 Mass 6.4 kg/m2 Op. Temp. 1030 K Emissivity 0.96
Tin droplet radiator
Atomization increases the surface area with which a fluid can lose heat. A hot working fluid sprayed into space as fine streams of sub-millimeter drops readily loses heat by radiation. The cooled droplets are recaptured and recycled back into the heat exchanger. If tin (Sn) is used as a working fluid, the kilos per power radiated is minimized, using a heat rejection temperature of 1030 K and a total power in the megawatt range (comparable to the game value of heat rejection of 120 MWth per therm). The low emissivity of liquid tin (0.043) is increased by mixing in carbon black, which distributes itself on the surface of the droplet. Evaporation losses are avoided by enclosing the radiator in a 1 μm plastic film, which transmits radiation in the 2 to 20 μm (IR) range. Such a film would continue to perform its function even if repeatedly punctured by micrometeoroids. The illustration shows a triangular liquid droplet geometry. The collector, located at the convergence point of the droplet sheet, employs centrifugal force to capture the droplets. The total specific area is 6.4 kg/m2.
K. Alan White, "Liquid Dropbt Radiator Devebpment Status," Lewis Research Center, 1987
There are certain magnetic materials that abruptly loose their magnetism if heated above a certain point. This is called the Curie Point for that material.
A team of scientists led by Mario D. Carelli used this property to create a species of liquid drop radiator.
Droplets or particles of magnetic material are used in the droplet radiator, heated above their Curie point so they lose their magnetism. They are sprayed in a stream, spreading out to maximize heat radiation. At some point they radiate enough heat to drop below the curie point and abruptly become magnetic. Whereupon they change course and make a bee-line for the magnetized droplet collector.
Just like the liquid droplet radiator, this design is relatively immune to meteor strikes and hostile weapons fire. Beyond NERVA points out another advantage. The Curie point radiator is somewhat immune to any maneuvering the spacecraft performs, which the LDR is not. The LDR drops move in a straight line to the collector, acceleration moves the position of the collector so the drops miss. But with the Curie point, the collector is magnetized, so the drops will automatically correct their course to enter the collector.
Specific Area Heat Cap. ~300 kWth/m2 Mass 35 kg/m2 Op. Temp. 1200 K
A ferromagnetic material heated above its Curie point loses its magnetism. If molten droplets of such a substance are slung into space, they radiate heat and solidify. Once below their Curie temperature, they regain their magnetic properties and can be shepherded by a magnetic field into a collector and returned to the heat exchanger. A 120 MW system operating at 1200 K includes a 13 tonne magnetic heat exchanger and a rotating dust recovery electromagnet on a 25-meter boom, plus 7 tonnes of dust spread in a spiraling disk 27-meters in diameter (35 kg/m2). The usual medium is iron dust, which has a Curie point of 1043 K and is easily scavenged by magnetic beneficiation from regolith.
M.D. Carelli, 1989
Specific Area Heat Cap. 51 kWth/m2 Mass 4.3 kg/m2 Op. Temp. 1000 K Emissivity 0.85
Electrostatic membrane radiator
This heat-rejection concept, also called a liquid-sheet radiator, encloses radiating liquid within a transparent envelope. It consists of a spinning membrane disk inflated by low gas pressure, with electrostatically-driven coolant circulating on its interior surfaces. The liquid coolant is only 300 μm thick and has an optical emissivity of 0.85 at a temperature of 1000 K. An electric field is used to lower the pressure under the film of coolant, so that leakage through a puncture in the membrane wall is avoided. The membrane has a specific area of 4.3 kg/m2 and 51 kWth/m2.
Shlomo Pfeiffer of Grumman, 1989
Specific Area Heat Cap. 213 kWth/m2 Mass 71 kg/m2 Op. Temp. 1200 K
ETHER charged dust radiator
To avoid the evaporation losses suffered by radiators that use liquid droplets in space, dust radiators use solid dust particles instead. If the particles are electrostatically charged, as in an electrostatic thermal radiator (ETHER), they are confined by the field lines between a charged generator and its collector. If the spacecraft is charged opposite to the charge on the particles, they execute an elliptical orbit, radiating at 1200 K with a specific area of 71 kg/m2 and 213 kWth/m2. The dust particles are charged to 10-14 coulombs to inhibit neutralization from the solar wind.
Specific Area Heat Cap. ~469 kWth/m2 Mass 150 kg/m2 Op. Temp. 1450 K
Mo/Li heat pipe radiator
A heat pipe quickly transfers heat from one point to another. Inside the sealed pipe, at the hot interface a two-phase working fluid turns to vapor and the gas naturally flows and condenses on the cold interface. The liquid is moved by capillary action through a wick back to the hot interface to evaporate again and repeat the cycle. For high temperature applications, the working fluid is often lithium, the soft silver-white element that is the lightest known metal. Molybdenum heat pipes containing lithium can operate at the white-hot temperatures of 1450 K, and transfer heat energy at 240,000 kWth/m2, almost four times that of the surface of the sun. The specific area is 150 kg/m2.
David Poston, Institute for Space and Nuclear Power Studies at the University of New Mexico, 2000
Specific Area Heat Cap. ~153 kWth/m2 Mass 100 kg/m2 Op. Temp. 1100 K
Ti/K heat pipe radiator
A Rankine evaporation-condensation cycle heat pipe uses metal vapor as the coolant, which is liquefied as it passes through a heat exchanger connected to the radiator. A liquid metal near the liquid/vapor transition is able to radiate heat at a nearly constant temperature. The pipe is made from SiC-reinforced titanium (Ti) or superalloy operating at up to 1100 K, and the working fluid is potassium (K). The pipe is covered with a lightweight thermally-conductive carbon foam, which protects the pipe from space debris and transfers heat to the radiating fins. The total specific area is 100 kg/m2.
Specific Area Heat Cap. ~21 kWth/m2 Mass 7 kg/m2 Op. Temp. 800 K
Bubble membrane radiator
This high-temperature concept uses a spinning bubble-shaped membrane to reject waste heat. A two-phase working fluid (hot liquid or gas) is centrifugally pumped and sprayed on the interior surface of the bubble. The fluid wets the inner surface of the sphere and is driven in the form of a liquid film by centrifugal force to the equatorial periphery of the sphere. As the liquid flows along the inner surface of the envelope it loses heat by thermal radiation from the outer surface of the balloon. The use of membranes woven from space-produced carbon nanotubes and cermet fabrics offers a specific area of 7 kg/m2, radiating from one side at 800 K. Liquid metal pumps return the liquid out of the sphere through rotated shaft seals to its source.
Specific Area Heat Cap. ~300 kWth/m2 Mass ~100 kg/m2 Op. Temp. 1300 K
Buckytube filament radiator
Waste heat may be rejected by moving thousands of loops of thin (1 mm) flexible "Buckytubes" (carbon nanotubes), which radiate their thermal load prior to return to the heat exchanger. Cables constructed of Arm-chair type nanotubes are the strongest cables known, with design tensile strengths about 70% of the theoretical 100 GPa value. The moving filaments are heated by direct contact around a molybdenum drum filled with the heated working fluid, and then extended into space a distance of 70m by rotational inertia. Their speed is varied according to the temperature radiated (from 273 K to 1300 K). The loops are redundantly braided to prevent single point failures from micrometeoroids. Each element is heat treated at 3300 K to increase the thermal conductivity through graphitization to about 2500 W/mK.
Richard J, Flaherty, "Heat-transfer and Weight Aialysis Of a Moving-Belt Radiator System for Waste Rejection in Space", Lewis Research Center, Cleveland, Ohio, 1964.
Specific Area Heat Cap. 76 kWth/m2 Mass 17 kg/m2 Op. Temp. 928 K Emissivity 0.9
Flux-pinned superthermal radiator
Variable configuration radiators take advantage of the surprising physics of high-temperature flux-pinning superconductors. These materials resist being moved within magnetic fields, allowing stable formations of elements. No power or active feedback control is necessary. The radiating elements fly in a flux-pinned formation, not physically touching, but connected by superthermal ribbon. Superthermal compounds hypothetically conduct heat as effortlessly as superconducting materials conduct electricity. The radiating surfaces are graphite foams, which have both a high emissivity (0.9) and a high thermal conductivity (1950 W/m°K) if the heat conducts in a direction parallel to the crystal layers. Operating at 928K, the superthermal radiator has a specific area of 17 kg/m2 and 76 kWth/m2.
Dr. Mason Peck, 2005
Specific Area Heat Cap. 300 kWth/m2 Mass 33 kg/m2 Op. Temp. 1300 K
By imparting heat to twin washer-shaped disks by direct conduction, the Hula-Hoop radiator avoids the diseconomies of scale that plague fluid radiators. Furthermore, they are robust against micrometeoroid strikes and hostile attack. The two hoop are 100-meters in diameter. They are made of braided cermets coated with graphite, and lubricated in a heat exchanger with tungsten disulfide (WS2). Radiating at 1300 K, each has a specific area of 33 kg/m2 and 300 kWth/m2.
This design is a Philip Eklund original, published here for the frst time.
Specific Area Heat Cap. ~300 kWth/m2 Mass 24 kg/m2 Op. Temp. 1300 K
Marangoni flow radiator
In zero-g, a surface tension gradient can create a heat pump with no moving parts, or drive micro-refining processes. This phenomena, called Marangoni flow, moves fluid from an area of high surface tension to one of low surface tension. Bubbles operating at 1300 K have a specific area of 24 kg/m2.
G. Harry Stine, "The Third Industrial Revolution," 1979
Specific Area Heat Cap. ~104 kWth/m2 Mass 34 kg/m2 Op. Temp. 1000 K
Microtube array radiator
Nanofacturing techniques can fabricate large, parallel arrays of microtubes for high performance radiators. The radiating surface comprises a heavily-oxidized, metal alloy with a 100 nm film of corrosion resistant, refractory platinum alloy deposited on it. The working fluid is hydrogen, which has low pumping losses and the highest specific heat of all materials. This fluid is circulated at 0.1 to 1 MPa through the microtubes, and the heat radiates through the thin (0.2 mm) walls. This allows a specific area of 34 kg/m2, including the hydrogen. The rejection temperature for titanium alloy tubes is from 200 K up to 1000 K, if a high temperature barrier against hydrogen diffusion is used. High speed leak detection capability and isolating valves under independent microprocessor control provide puncture survivability.
F. David Doty, Gregory Hosford and Jonathan B. Spitzmesser, "The Microtube-Strip Heat Exchanger," 1990
Specific Area Heat Cap. ~75 kWth/m2 Mass 75 kg/m2 Op. Temp. 1100 K
Salt-cooled reflux tube radiator
In contrast to a heat pipe, that uses capillary action to return the working fluid, a reflux tube uses centrifugal acceleration. This design is more survivable than heat pipes, especially when overwrapped with a high-temperature carbon-carbon composite fabric. Unlike metals, the strength of these composites increases up to temperatures of ~2300K. However, they degrade when subjected to high radiation levels. The working fluid is molten fluoride salts, the only coolant (other than noble gases) compatible with carbon-based materials. Radiating at 1100 K, this radiator has a specific area of 75 kg/m2.
Charles W, Forsberg, Oak Ridge National Laboratory, Proceedings of the Space Nuclear Conference 2005, San Diego, California, June 5-9, 2005.
Specific Area Heat Cap. ~93 kWth/m2 Mass 61 kg/m2 Op. Temp. 970 K Emissivity 0.9
SS/NaK pumped loop radiator
A Rankine evaporation-condensation cycle exchanges heat using a liquid metal as a coolant, which is vaporized as it passes through a heat exchanger connected to the radiator. A liquid metal near the liquid/vapor transition is able to radiate heat at a nearly constant temperature. The usual medium is sodium (Na) or sodium-potassium (NaK), which has a saturation temperature of nearly 1200 K at 1.05 atm. The plumbing is stainless steel (SS) tubes operating at up to 970 K with an emissivity of 0.9. The tube wall is half a millimeter thick to guard against meteoroid-puncture, and each pipe is an independent element so that a single puncture does not cause overall system failure. Molecular beam cameras on long struts scan for meteoroid leaks, which are plugged with pop rivets installed by a tube crawler. Radiating at 970 K from both sides, this radiator has a specific area of 61 kg/m2, including fluid and heat exchanger.
J. Ca/ogeras, NASA/LaRC, 1990.
This fictional radiaor is from the tabletop wargame Attack Vector: Tactical, which is why the description talks about weird units like "power points" and "heat points."
Specific Area Heat Cap. 357 kWth/m2 Mass 100 kg/m2 Op. Temp. 1600 K Emissivity 0.9
(1 - 0.1)
Knowing that our reactors produce 62.5 MW as a base power unit, and using the proof at right, we get an efficiency of 4 J of waste heat per J of power generated. This tells us that wee need to radiate ~250 MW per point of power. The Stefan-Boltzman law states that the surface emits power at a rate of (1-A) * 5.67×108 Wm2 K4 * T4 where A is the albedo, and T the absolute temperature in Kelvins. With an albedo of 0.1, a temperature of 1600K, and 250 MW of output, we need 700 square meters of radiating surface. Extending as a fin, radiating from both sides, this is roughly 18 meters square. At roughly 0.3m thick, and flexible enough to be retracted and extended, we get something that's reasonably 70 tons, or a bit shy of 3 hull spaces. For the sake of game play, one hull space of radiators dissipates 100 MW, or 0.4 heat points.
A civilian (starship) reactor has a built in 16 meter by 16 meter radiator that dissipates its waste heat; this radiator is built into the hull of the ship. This is why civilian reactors require part of the hull of the ship to be unarmored.
Storing the heat before radiation requires a heat sink. A sodium heat sink is ~21.5 cubic meters of sodium, with a density of 0.968 tons per cubic meter. Sodium has a thermal capacity of 28.2 J/mole/K. A mole of sodium weighs 22.98 grams. One gram of sodium absorbs 2.82/22.98 = 1.22 J per K of heat increase. A heat sink of sodium weighs 20.82 tons, raising that mass by 1 K absorbs 25.4 MJ. Sodium melts at 372 K and vaporizes at 1252 K. Pressurized, it remains liquid to 1600 K, our radiator temperature. Assuming a working range of 1300K (room temperature to 1600 K), each heat sink stores 1300 * 25.4 MJ = 33.02 GJ, which is one heat point, assuming other inefficiencies.
Lithium's thermal capacity of 24.8 J/mole/K and molar weight of 6.94 allows 1 gram to absorb 3.57 J per K of heat increase, or 2.92× the heat capacity of sodium. By using 22 tons of lithium, we get triple the capacity of the sodium heat sink.
Water's thermal capacity is 4.186 J/gram/K, 3.426 times that of sodium. Room temperature to boiling is ~85 K, which limits its usefulness. Raising 1 ton of water by 85 K takes 355.88 MJ. One heat point is 33 GJ, and the amount of water needed to store one heat point is 33 GJ/350.88 MJ = 93 tons. Including the extra mass for plumbing, that's 5 hull spaces all told.
Vaporizing water takes 2256 J/g, 6.3× the energy needed to raise it by 85 K. Because the vaporization is not quite perfect, we treat it as 6 heat points removed when the heat sink is vented. The liquid metal heat sinks aren't vented, as vaporized metal would deposit on the sensors of the ship.