Having your radiators tactically protected from enemy fire by the armor shape of your space warship is nice, but having a regular one or double-sided radiators is still a vulnerability. Other concepts such as liquid droplet and electrostatic radiators seem to be too complex and require much more power. I was thinking of radiators similar to that of the graphite spikes that are seen on the fusion torch cages in Attack Vector: Tactical. They would stick out of the body of the warship at an angle that allows them to be blocked from oncoming fire from by the frontal armor. They would have a radiating surface wrap around the entire circumference with working fluid pipes running through the interior. How feasible is this? What are your ideas for their design (approximates for length, diameter, and materials)? How would I calculate how much heat they would dissipate? Assume it is about 1-2GW of waste heat from a 200MW nuclear reactor.

Strategically drawn red circle pointing out the radiator spikes on a warship from AV: T

• Earthly power plants have an overall yield of about 30%. Dumping 1 GW out of 1.2 GW is about half that yield. – L.Dutch - Reinstate Monica Apr 18 at 7:01
• See Thermal radiation/Radiative power. Apply a scientific calculator to compute what area you need based on the temperature. – Adrian Colomitchi Apr 18 at 8:50
• Just FYI, the spikes on that design are 'secondary' radiators meant to get rid of a minor amount of waste heat involved in the magnetic containment of the fusion drive. The main radiators are a conventional type, retracted in combat. Here's the same class, with radiators extended: projectrho.com/public_html/rocket/images/basicdesign/… – Catgut Apr 18 at 20:34

The equation for radiant power is $$P = \epsilon \sigma A T^4$$ Graphite starts to sublimate at 3,700 degrees Kelvin. Let's assume there's no factor of safety, but a typical one for aerospace is 1.5, which would bring the design operating temperature down to 2,500 Kelvin.

Unfortunately, as others pointed out, your heat pump is the limiting factor at a much lower radiator temperature of 600 degrees Kelvin.

$$\epsilon$$ is our emissivity from 0 to 1. Let's assume it's an ideal radiator at 1.

$$\sigma$$ is a constant $$5.67 \times 10^{-8}$$.

Assuming you had some futuristic better-than-perfect heat pump, and could utilize the radiators fully to their material limit, to radiate 2 GW, then, you need 188 square meters of radiator at failure (the rods start vaporizing) or 903 square meters at the factor of safety.

More realistically, with a maximum temperature of 600 degrees Kelvin at the radiators, you need 56 thousand square meters of radiator to radiate the same 2 gigawatts.

For those rods to be effective, they can't be radiating back into your hull. So, about half the radiating arc of cylinders shielded from fire by the front of the hull is unavailable. You also don't want the hive pictured because the radiators would be interfering with each other. If you have two sets of 4 offset from one another vertically down the hull, they'd each need to be 225 square meters. Easily doable with 100 meter spikes about 2 meters in diameter.

For a more realistic forest with a 600 K limit at the radiator, the same configuration would need to 13.4 meters in diameter.

• Ah, but you cannot bring the temperature of the coolant anywhere near 2,500 K. You are pumping heat uphill; even if you use an ideal heat pump you still want a coefficient of performance greater than 1, otherwise you expend more energy pumping it than you pump into the coolant. Assuming you want to keep the interior of the spacecraft at around 300 K, you won't be able to increase the temperature of the coolant above 600 K or some 330° C. OK, you are rejecting the heat of a cool side of a thermal power plant, say at 100° C; but still, you'll be limited to maybe 700 K or 430° C. – AlexP Apr 18 at 17:47
• @AlexP Didn't think about that. My assumptions: Graphite has an emissivity of .70-.98, so I'll assume it is around 0.90 and the radiating surface area is at 3000K. In another comment, I actually said the radiating area should be 188 m² at a 2-meter diameter and 20-meter length. Plugging that into P = A ⋅ ϵ⋅ σ ⋅*T⁴*, it seems that this would radiate 777MW. Get two of those on top and bottom, you get 1554MW or 1.55GW (minus some if they are angeled). – zertofi Apr 18 at 18:04
• @zertofi: Unfortunately, one cannot escape the tyranny of Monsieur Sadi Carnot. There is no way to bring the coolant to such a high temperature. (If the coefficient of performance of the heat pump drops below 1, you expend more than 1 joule for each joule of heat you pump into the coolant; and you cannot do this, because the difference will then accumulate as heat, defeating the purpose of the cooling system.) – AlexP Apr 18 at 18:55
• @AlexP So am I better off using some type of droplet or standard radiator? – zertofi Apr 18 at 19:07
• @b.Lorenz Yes, of course, habitat needs radiators, even the high power electronics need mini radiators (such as the laser generator). The cylindrical radiators would be for reactor use only. – zertofi Apr 19 at 15:59