# Calculators

## Stellar Radiation Calculator

Written: 2002-03-30

This form will calculate the radiation absorbed by a starship of arbitrary size, at arbitrary altitude above a star of arbitrary size and luminosity. The input parameters are:

1. Stellar Luminosity, relative to our Sun.
2. Stellar Diameter, in kilometres.
3. Size of ship, in square metres. This is the projected area, ie- its "profile area". In the case of a GCS viewed from the side, this is roughly 40,000. Note that if you use an ellipsoid shield bubble instead of tbe ship's hull, and assume that it is 100% opaque to stellar radiation throughout its entire cross-section regardless of incident angle (despite onscreen evidence of only partial opacity at best), you can use 100,000 instead (and of course, if you're a delusional trekkie fanatic, you can use an arbitrarily large number such as 470,000 in order to exaggerate your figures).
4. Altitude of ship, in kilometres.
5. Area multiplier, ie- the difference between the ship's total facing area and its projected area. In the case of a sphere, this would be 2. In the case of a cube, it would be 1 (its facing side will absorb 100% of the radiation, and the other 5 sides will not), unless it points a corner at the star, in which case it would be 1.5. In the case of an ISD pointing at the star, it would be roughly 6½. In the case of a GCS with its side facing the star, it would be roughly 2 (note that I am neglecting thermal conduction to non-facing areas of the hull in order to be conservative).
6. Hull surface emissivity (if you don't know what this is, look it up). This ranges from near-zero to 1 for a perfect blackbody radiator. It's very low for highly polished, "shiny" metal surfaces (~0.05), but it can range as high as 0.7 for rough, oxidized metal, and more than 0.9 for certain graphites, as well as water and human skin.
7. Hull surface reflectivity (ie- albedo). This ranges from 0 for a perfect blackbody to 1 for a theoretically perfect mirror. In order to generate absorption limits, this value is traditionally set to 0. However, this is not realistically the case. For example, the albedo of snow is nearly 1. In general, reflectivity and emissivity are inversely correlated.

The calculated values are:

1. Intensity of stellar radiation, in MW/m².
2. Stellar radiation absorption for the ship, in watts and also in megatons per hour.
3. The equilibrium temperature in K (ie- the temperature at which the hull can dump heat as quickly as the star pours it in), assuming isothermal conditions on the facing side.
4. The "solar sail" radiation pressure (ie- the pressure applied to the ship by stellar radiation), in bars, assuming that the ship is completely opaque (obviously). This figure has a lower limit (for absorption) and an upper limit (for perfect 180 degree reflection).
5. The "solar sail" radiation force (ie- the radiation pressure multiplied by the profile area), in Newtons. Divide this by the mass of your ship in order to determine its acceleration due to radiation pressure.

The defaults are for an ISD pointing toward our Sun, at an altitude of 300,000 km. The default emissivity and albedo are 1 and 0.

## Input Values

 Stellar Luminosity Stellar Radius (km) Profile area of ship (m²) Altitude of ship (km) Area multiplier Hull surface emissivity Hull surface reflectivity (albedo)

## Calculated Values

 Radiation intensity (MW/m²) Max radiation absorption(Watts) Equilibrium temperature (K) Max radiation absorption(megatons per hour) Radiation pressure LL (bars) Radiation force LL (N) Radiation pressure UL (bars) Radiation force UL (N)

Note: If you want to use the planet Earth as the "ship" in this form, use an altitude of 1.5E8 km, a profile area of 1.275E14 m², an area multiplier near 4 (because the Earth's rotation allows it to dissipate absorbed heat over its entire area), emissivity of roughly 0.61, and albedo of roughly 0.33 (these figures are caused by the atmosphere, which both reflects incoming radiation and retains outgoing radiation through the greenhouse effect). Note that you'll get an equilibrium temperature of 284K (~11 degrees C), although the realistic temperature varies with latitude because the Earth's surface is not an isotherm.

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