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Radiators Calculator


Waste heat accumulates quickly. An average adult produces 100 Joules of it every second, just doing nothing. Computer banks, nuclear reactors, laser weapons, etc. all add much more.

In space, this is a big problem. There is essentially no medium present to conduct or convect away waste heat. Only heat radiation is relevant. Therefore, spacecraft must have radiators: devices designed to radiate heat.

This calculator simulates the properties of several kinds of radiators. An answer of NaN means that no solution is possible for the requested quantity. A negative power means that the radiator is actually absorbing energy from its environment (this is possible if the radiator is somehow colder than space).

Calculator (Panel Radiator)

This kind of radiator is just a panel that is (evenly) hot. This is most-easily done by piping hot liquid through small channels in the panel. The liquid transfers heat to the panel, which radiates it away, providing the cooling effect. As seen on the space shuttle and ISS! Simple and effective.

The radiation to and from space is via the Stefan–Boltzmann Law:

\[ \Phi_e = A_d \cdot \epsilon \cdot \sigma_{sb} \cdot T^4 \]

Specifically, the radiant power \(\Phi_e\) is related to the radiating (or absorbing) surface area \(A_d\), the emissivity/absorptivity \(\epsilon\) (a material property), and the absolute temperature \(T\), in kelvins. The \(\sigma_{sb} \approx 5.670373 \times 10^{-8} \cdot \text{W} \cdot \text{m}^{-2} \cdot \text{K}^{-4}\) is a (derived; see link for details) constant.

Quantity Value Solve For
Surface Area: (one side)
(both sides)
Temperatures: (radiator panel)
(space radiative; typical: CMBR 2.72548 K)

Power Radiator Dissipates:

Calculator (Droplet Radiator)

This kind of radiator just shoots droplets of a hot liquid directly into space and catches them some time later, after they've cooled off (and possibly, solidified). One advantage is that there's no giant fin to be damaged by space debris or bad guys. One disadvantage is that it's much-less efficient (although by leveraging the heats of fusion/vaporization (energy associated with phase change), one can make it less-inefficient, and also reduce engineering costs; see here).

Quantity Value
Droplet Size: (emission diameter; typical: 100μm–200μm)
(emission radius; typical: 50μm–100μm)
Region of Droplets: (region area)
(droplets' centers' avg. separation)
(droplet mutual occlusion factor (typical: 0.001))
(time of flight)
(avg. number of droplets)
(mass of droplets)
(mass flow rate)
(volume of droplets)
(volumetric flow rate)
Droplet Material:
Standard materials Custom material (no phase change!) Custom material (phase change(s))
(coming soon?) (emissivity) (emissivity)
(SHC[note]) (SHC (solid))
(SHC (liquid))
(melting point)
(boiling point)
(heat of fusion)
(heat of vaporization)
(density) (density)
[note]Specific heat capacity (SHC). Typical metals: 0.1–0.4 kJ kg⁻¹ K⁻¹.
Temperatures and Energy: (droplets' start temperature[note])
(droplets' end temperature)
(per-droplet energy loss per flight)
[note]If using standard or custom phase-changing material and this is equal to the material's melting point or boiling point,
the droplet's thermal energy is assumed to be on the hot side of the phase transition. Cannot be greater than boiling point,
as gaseous droplets do not make sense.
Power Radiator Dissipates:

Note: The formulae required for this are unavoidably numerically unstable with respect to time of droplet flight. Hence, values for this should be set to reasonable values (e.g., your particles probably oughtn't to travel faster than the speed of light). An arbitrary-precision library has been used to get you more-accurate results.

Note: This calculator does not support solving for any input parameter. The formulae for this calculator are ludicrously complex, but this could in theory be managed with numerical solvers (as they are for other calculators). However, the larger problem is that there's no good way to interact with it. E.g. when I change the time of flight, both the end temperature and the power need to change.

Droplet Radiator Analysis


Part of the formula for liquid droplet radiator surface area comes from Eric Rozier's calculator (now defunct, but on archive.org). Note that the surface area is erroneously reported as being in MW (it's actually in kW), the temperature of space is not accounted for, and the droplet temperature is assumed constant. His discussion can be found quoted here.

Thanks to Mario Fernández Palos and James Du for helpful comments.