The University of Pennsylvania School of Engineering and Applied Science blogpost How to Design a Sail that Won’t Tear or Melt on an Interstellar Voyage links to two new Nano Letters papers:

These describe some really detailed and thorough research and make for some excellent reading!

The abstract of the billowing paper begins:

We argue that light sails that are rapidly accelerated to relativistic velocities by lasers must be significantly curved in order to reduce their mechanical stresses and avoid tears.

Generally people have assumed that solar sails will be nominally flat to maximize photon recoil.

Question: Why do "Relativistic Light Sails Need to Billow"? Why does this unexpected and significant curvature they propose reduce mechanical stresses and avoid tears in these molecularly-thin sails undergoing intense laser illumination and acceleration?


1 Answer 1


The Hoop stress is proportional to the radiation pressure but inversely proportional to the curvature of the sail. Allowing the sail to billow increases the curvature and reduces the tension in the sail material. There must be an interesting curvature-thickness tradeoff where sails with more billow have more area but can be made thinner.

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    $\begingroup$ @uhoh It's based on my own views of non-relativistic barrels of beer. I must admit I didn't look at the papers :-( I don't understand how 'relativistic' can be relevant to anything other than to shift the wavelength of the illumination - but it certainly makes the title sound more exciting! $\endgroup$
    – Roger Wood
    Commented Feb 25, 2022 at 19:45
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    $\begingroup$ Ah, see equation S59 in the supplement and its reference 25 Yes, spherical pressure vessel. $\endgroup$
    – uhoh
    Commented Feb 25, 2022 at 21:02
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    $\begingroup$ @uhoh Yes, the sphere formula appears in the Wikipedia article but in the section called "relation to internal pressure". That billowing paper is quite interesting . . . now I finally look at it :-) $\endgroup$
    – Roger Wood
    Commented Feb 26, 2022 at 0:49
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    $\begingroup$ @ uhoh and Roger Wood in addition to stresses in the main body of the sail the designers must also pay attention to the stresses and strains where the sail attaches to the craft. Billow (or loft) can also help with reducing stress concentration problems at attach points at sail perimeter, helping to reduce overall mass. $\endgroup$
    – BradV
    Commented Feb 26, 2022 at 19:50
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    $\begingroup$ @BradV maybe a rotating sail to keep it stable and fairly flat without needing any rigid members? Wonder what the stresses look like in a rotating solid disk? $\endgroup$
    – Roger Wood
    Commented Feb 26, 2022 at 21:34

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