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...that type of rope does not handle dynamic shock loading as well as a polyester rope would. In the event of a bridge failure you would end up falling a little distance before your fall would be arrested by your back up rope...
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It is true Spectra and similar ropes will have negligible stretch and thus negligible energy absorption. But the same short backup rope made of polyester will also have negligible stretch simply because it is so short. There may be plenty of other reasons to prefer one over the other, but stretchiness would be down near the bottom of my list. I use Dyneema tethers on my ascenders because they are very small, tidy, cut-resistant, and no knots are involved. But in the case of a fall, they would not absorb as much energy as an equal-length tether of polyester. The vanishingly small disadvantage in energy absorption is easily outweighed, for me, by the advantages I listed.