the rope needs to be thick enough to be grasped without cutting into your fingers
no, it doesn't! For ascending, climb up with prusiks; make them from 4mm Spectra/Gemini cord, and then attach small webbing slings to them for your hands to hold. For descending, you would use an old-fashioned munter hitch or carabiner wrap. I have a similar "utility belt" that i made years ago out of seat belt webbing; it has an inside zipper that hides a diaper-seat climbing harness inside. 80 ft of 5-mil cord and a couple of biners fit into one of the outside pouches. I would take this skiing with me just in case i needed to self-evac out of a stuck ski lift. Which, in fact, i did need to do once, at Waterville Valley, when they suddenly had to close the lift down in high winds. I didnt feel like waiting for their evac team to get to me, and used my own stuff.
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no, it doesn't! For ascending, climb up with prusiks; make them from 4mm Spectra/Gemini cord, and then attach small webbing slings to them for your hands to hold. For descending, you would use an old-fashioned munter hitch or carabiner wrap. I have a similar "utility belt" that i made years ago out of seat belt webbing; it has an inside zipper that hides a diaper-seat climbing harness inside. 80 ft of 5-mil cord and a couple of biners fit into one of the outside pouches. I would take this skiing with me just in case i needed to self-evac out of a stuck ski lift. Which, in fact, i did need to do once, at Waterville Valley, when they suddenly had to close the lift down in high winds. I didnt feel like waiting for their evac team to get to me, and used my own stuff.