Bear in mind, fabric length is always longer than what the hammock will actually take up in distance (unless you hang it like a guitar string). The sag will shorten that distance by roughly 85%.
That said, it's not something worth thinking about. As mentioned, the tarp ridgeline is really what determines minimum distance. And I agree with everyone else, 14-15' is ideal - should work with any hammock, and any tarp.
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