I would be very not keen at all on climbing with a static rope.
If you fall on a static rope all the force is transmitted directly to (a) the anchor and (b) you. This is a bad thing if there is any slack in the rope when you fall. The stretch of a dynamic rope (in general thinner rope = more stretch) soaks up that impact and spreads the force out so you don't get it all at once.
I have a 9.7 for rock climbing (not that I do much of that these days) and an 8mm for alpine use.
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