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Might it work if the stiffness of the strip is just right?
It's rather unlikely to form a circular arc of the desired radius. Assuming it's a physics problem rather than a serious engineering proposal, so ignoring any imposed loads from actually venturing outside a gravity free vacuum chamber, and equally assuming the fishing line is has zero flexural stiffness but infinite longitudinal stiffness and that the brake bridge end of the strip is perfectly rigidly constrained to be tangential to the tyre clearance arc, you just have to solve for the lowest energy configuration given a known length of the springy strip and the known coordinates of the fixed end of the fishing line. It's a large deformation cantilever problem but with the end load vector determined by the axis of the fishing line, which is well beyond my level of maths.
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gbj_tester
nick_h.
How's this for a full length but minimalist mudguard design, for a rim brake bike? A flat strip of carbon fibre, 30mm wide. It's stiff but it bends a little if you force it. It's attached to the brake bolt in the usual way. The stays are just fishing line. The lines are pulled tight so the strip bends to form the usual circular shape. The tension in the strip holds the lines taut. Might it work if the stiffness of the strip is just right?