Illustrated Guide Chapter 1: Heat and Radiators - sswelm/KSPInterstellar GitHub Wiki
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#Chapter 1: Heat and Radiators
##The physics: Radiator performance
###Heat in space
Space itself is cold. The electromagnetic background radiation from deep space corresponds to a temperature of 3 kelvin, barely above absolute zero.
But despite the cold background, heat is a constant concern in spacecraft design. Every process that uses or converts energy - every electrical system, every life support system, and every crew member - adds heat to the spacecraft around it. The light of the Sun in Earth orbit is direct, with no atmosphere to filter it, delivering more energy to where it lands than in Earth's harshest deserts.
On Earth, machines that need to dispose of large amounts of heat typically transfer it to nearby air or water. In space, neither air nor water is an option. A spacecraft that needs to reject heat can either jettison hot material or rely on radiation.
###Black body radiation
All matter at any temperature above absolute zero radiates some of its heat energy as electromagnetic radiation. The spectrum or "color" of the radiation and the rate of energy transfer depend on the temperature of the radiating surface. The 3-kelvin cosmic background radiation is dominated by microwave frequencies, room temperature is strongest in the infrared, and visible light becomes noticeable around 700 K.
The simplest form of the governing equations is for a surface that absorbs all incoming photons without reflecting or scattering any energy. The same properties imply that the photons that such an ideal absorber radiates can depart the surface without scattering or interference. In discussions of thermal radiation, the term "black body" refers not merely to a body that looks black to the eye, but to such an ideal absorber and radiator.
As you may expect if you've encountered ideal objects in any other area of science, there is no perfect physical realization of a black body. Every real-world surface deviates from the ideal to a greater or lesser extent. Many are "grey bodies": surfaces that radiate a sufficiently uniform fraction of a black body's output in a similar spectrum across the temperature and wavelength ranges of interest.
The amount of energy that leaves a surface by radiation is given by the Stefan-Boltzmann law. When the Interstellar radiators' in-game descriptions refer to the "Stefan-Boltzkerman law", this is what they're referencing. The law is commonly written as
P = AεσT^4
where P is the power transferred in watts, A is the radiating surface area, and T is the temperature in kelvin. ε, the emissivity of the surface, is the fraction of a black body's radiation that the surface emits. σ is a proportionality constant with a value of 5.67 × 10^-8 watts per square meter per kelvin to the fourth power.
The best known materials have emissivities in the neighborhood of 99.6 percent. Economical spacecraft radiators today range from 90 to 98 percent.
##Heat in Interstellar
Interstellar represents heat energy that needs to be radiated with the WasteHeat resource. One in-game unit of WasteHeat represents one megajoule of energy.
There are two sources of WasteHeat that Interstellar tracks: solar panels, and generators, receivers, and reactors. I will discuss the game rules for solar panels here, and those for other systems when I cover the systems. Radioisotope thermoelectric generators have their own radiators built into the finned case. They don't contribute to WasteHeat for Interstellar's purposes.
Solar panels produce waste heat equal to half their ElectricCharge output. For conversions between KSP and real-world unites, 1 EC represents one kilojoule of energy (1 EC/second = 1 kilowatt). A bank of panels producing two megawatts of electricity (2,000 EC/s) will produce 1 WasteHeat per second (1 megawatt of waste heat).
Retractable solar panels will retract if the WasteHeat bar fills. A probe that overheats and loses all of its panels is likely to lose power and become inert before it cools enough to redeploy panels. Other systems will become less efficient or fail entirely.
An inactive ship will slowly radiate heat from its structure, but to keep up with any heat-producing systems that need to remain active, it will need radiators. The performance of each radiator part in Interstellar is defined by two numbers: its radiating area in square meters, and its maximum temperature in kelvin. Your goal in designing a ship is to equip it with enough radiator area to radiate all of the waste heat that it produces at a temperature that is 1) less than the maximum temperature of any of its radiators, and 2) less than the maximum temperature of its thermal sources.
The following radiators are available:
| Part | Size | Area (m^2) | Max. temp | Mass |
|---|---|---|---|---|
| Radial Radiator | Small | 0.25 | 970 | 0.005 |
| Standard | 1 | 0.02 | ||
| Flat Radiator | 8 | 1,350 | 0.1 | |
| Inline Radiator | 62.5cm | 1.25 | 970 | 0.05 |
| 1.25m | 5 | 1,350 | 0.2 | |
| 2.5m | 20 | 0.8 | ||
| Heat Radiator (deployable) | Small | 100 | 1,350 | 0.2 |
| Standard | 400 | 0.8 | ||
| Huge | 1,600 | 3.2 | ||
| Large Flat Radiator | 2,500 | 1,350 | 5 | |
When you unlock the Experimental Electrics node of the technology tree, all radiators upgrade to a maximum temperature of 3,500 K.
The in-game info window for each radiator part indicates how much energy it will radiate at its pre-upgrade maximum temperature, how much energy it will radiate at its post-upgrade maximum temperature, and how much it will radiate at the listed temperatures.
For solar-powered probes, the Small Radial Radiator radiates just over 12.5 kilowatts at its maximum temperature. A pair of these with a total capacity of 25 kilowatts is enough for probes generating up to 50 KW of solar power: enough for practically any scientific probe and most RemoteTech relays.
Note that the power output of solar panels varies with the amount of sunlight they receive, and hence with their distance from the sun. In stock KSP, these variations are reduced to a level that rarely affects gameplay. Interstellar overrides the stock curve and makes solar panel output strictly inversely proportional to the square of your distance from the sun. At Moho's periapsis of 0.31 Kerbin AU, panels will generate ten times the power - and heat - that they do at Kerbin. At an 8.35 AU Eeloo apoapsis, solar panels are only 1.4% as powerful as they are at Kerbin. For any mission farther out than Duna or Dres, consider other types of power generation.
##Reading the thermal helper
This is a typical unmanned spacecraft for the stage of the game where deployable solar panels and radiators become available. It has four OX-4L solar panels, developing 2 KW each in optimal orientation in Kerbin orbit for a total power budget of 8 KW and a heat budget of 4 KW. This would be enough to power the Communotron 16 and four DTS-M1 antennas if I were using RemoteTech.
I press "I" to open the thermal helper. If you have blizzy78's Toolbar mod installed, a button for the thermal helper is also available there. This window lists the vessel's total heat production and radiator capacity and calculates the equilibrium temperature. If you will be operating away from Kerbin space, set the slider at the top of the window to your intended distance from the sun so solar panel effectiveness can be calculated.
Right now, estimated heat production is 4 KW (half of the solar panels' electrical output) as predicted. Thermal source temperature is N/A because the only WasteHeat sources are solar panels whose temperature is not tracked. Radiator maximum dissipation is zero because we haven't installed any radiators yet, and the estimated radiator temperatures are N/A for the same reason.
If I now add a pair of small radial radiators, the thermal helper updates to show their 25 KW capacity at maximum temperature, and estimates a temperature of 612.9 K at 4 KW.
The thermal helper has some additional features that are relevant if you equip your vessel with nuclear reactors. I'll return to cover these features once I've covered the reactors.