Projects like Breakthrough Starshot or LightSail investigate a concept of probe gaining momentum by reflecting laser beam by a light sail. Material used for such a sail has to be very thin to minimize mass and be able to reflect as much possible percentage of the laser light not to vaporize. (And ideally transmit the light it does not reflect instead of absorbing it).

What is a realistic specific reflected energy of materials that are available today for construction of the light sail? By specific reflected energy I mean maximum reflected power of the laser divided by the mass of the reflecting area of the sail. (Watts / m^2 for the reflected power divided by kg / m^2 for the mass, i.e. in watts / kg.)

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    $\begingroup$ Oh, I see, this is calculated at the maximum light intensity the film can tolerate without being destroyed. Cool! $\endgroup$ – uhoh Nov 28 '19 at 23:08
  • $\begingroup$ Mostly I have learnt that all the interesting papers on actual solar sail implementations are paywalled, but that the greater heat tolerance of aluminised kapton more than makes up for its greater weight than mylar. I could add my workings as an answer, if you liked, but they're not from actual rocket science sources. $\endgroup$ – Starfish Prime Nov 29 '19 at 14:37
  • $\begingroup$ I will be very happy to hear it, I have no idea even on the order of magnitude for the available materials. $\endgroup$ – Irigi Nov 29 '19 at 20:17

materials that are available today

That's a tough restriction. A very brief peek at some papers suggests that everyone is theorising about fancier thin film materials that don't exist yet, presumably because all the real-world alternatives are too heavy and heat-intolerant and their absorptance is too high. Solar sail people either don't care as much about absorptance, or the places where they do care are hidden behind paywalls so I couldn't see it.

Anyway, I threw together some figures myself. My assumption is that the maximum reflected flux is limited by the absorptance of the sail (which seems reasonable)... treating the sail as a black body, I declare the limit to be the point at which the absorbed flux equals the emitted flux at the point at which the structural component of the sail's fabric breaks down or melts. The reflected flux can then be calculated from that.

5 micron aluminised mylar is about 6.8g/m2. You'll want to paint the far side of the sail with something in increase its emissivity... apparently 5-20nm of chromium is a reasonable choice. I haven't found a weight for that particular sail material, but it'll probably be somewhere between 6.8 and 7g/m2. The reflectivity of the aluminium is apparently 0.88-0.9. The emissivity of the chromium side is apparently 0.63 to 0.73. I didn't have much luck finding the emissivity of the aluminium side... this old NASA report suggests about 0.3, though I'm not certain I'm comparing apples-to-apples there (especially given the absorptance figures I look at next). The melting point of mylar is about 527.15K. According to Stefan-Boltzmann, the black-body radiation from the sail at its melting point is somewhere between 4072W/m2 and 4510W/m2, depending on the emittance of the chromium side.

The NASA report gives an absorptance of aluminised mylar of 0.14 which seems a little high, and doesn't really tally well with the reflectivity figures I found. A more recent work on materials for eco resorts (google books link, may not work for everyone) gives a suspiciously round 0.1 which does tally better with the reflectivity figures above. If it turns out to be correct, that gives you a maximum flux of 40722-45100W/m2, for a specific reflected energy of 5.27-5.97MW/kg, depending on the actual reflectivity of the aluminium and emissivity of chromium.

Kapton/polyimide doesn't melt, but it does decompose at 520°C. Assuming a sail with the same copper and chromium layers as above, you get a maximum flux of 208967-231137W/m2 at that temperature. Kapton films weigh about 12g/m2, giving specific reflected energies of 15.3-17.3MW/kg, making that weight trade off worthwhile.

Take the figures above with a small pinch of salt (for a start, I wasn't using the emissivity of those materials for the black body emission peak at the given temperatures). Though the figures themselves may bit a bit dubious, the key take home message seems reasonable, and that is that the specific reflected energy is limited by the sail burning up and so scales in proportion to the material's absorptance and the fourth power of the material's thermal breakdown point.

Therefore, you are at best going to be able to increase your specific reflected energy by three orders of magnitude at most by using more refractory sail materials (before you reach the limits of normal matter), but absorptance can be reduced by perhaps ten orders of magnitude (according to Kare's sailbeam stuff) and so will give you much better bang for your buck.

I've not bothered working out any figures for these thin film and dielectric sails because no-one seems to have actually made and tested any of the stuff, and given the weirdness of thin film behaviour compared to bulk materials, I'm not sure how meaningful the results would be. FWIW, Kare's CVD diamond sails weigh less than a tenth of the mylar sail per unit area, and have an absorptance 1011 times lower, and the emissivity is about a thousand times lower, so the end result is probably about a billion times higher.


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