this sort of comes from winter camping, but is a valuable summer concept. Refer to NASIDS - nonavolanche snow immersion death, where a skier or snowboarder with momentum gets buried head first under a tree in a tree well - a hole under a tree. 90% of victims cannot get them selves out and a rescue strap to help pull a buddy out - who isn't completely buried - is one partial solution. Also tree wells offer a potentially warm safe plce to spend a night in an emergency - if you can get out.

Theres been times when I got into a lot of trouble in the wilderness and a piece of rope saved my butt. I carried a 30 foot piece of 4mm rope and it did save my life fer sure. Other times I have also carried 80 feet of 5mm and it too saved my life. So why don't people carry a piece of rope instead of something less important?

If you go into a tree well on purpose use the rope to help get yourself out - tie the rope to something outside the hole and use it to pull upwards as you gently step up into the snow. Have another plan if the snow is too loose to get out - you will need your skis or snowshoes to be on.

Given a choice - I choose length over diameter but less than 4-5mm is worthless - 9mm better - like a piece of old climbing rope. So how many would add 8 ounces of rope if it meant they could do more dangerous of activity summer or winter?
Jim smile
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These are my own opinions based on wisdom earned through many wrong decisions. Your mileage may vary.