Spin Stabilized Solar Sails
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Spin stabilized prevent the sail from collapsing by spinning.
If you took your rock and cloth and gave it a good spin, the cloth would lift up and pull out flat, defying the gravity that tries to collapse it.
In the same way, spinning a solar sail pulls it out flat.
Because the sail material itself is very lightweight, it is a good idea to reinforce it with some tension lines to carry most of the loads caused by spinning.
One nice effect is the sail will need very little heavy structure, because tension lines are a lot lighter than the booms used in