Interesting post- I am no math wiz, however, in my line of work we suspend tons of equipment over peoples head. We use wire rope, shackles, & spansets to go around steel building supports to "fly" this equipment. Any rigger that wrapped a piece of wire rope around a beam multiple times would be fired immediately. We use one loop with the wire rope/beam cushioned with a burlap bag to prevent wear.
As to the size of the webbing- it seems the sewing on the loop of a 1/2" piece would have less load rating versus a 1" piece. The rigging is only as strong as it's weakest link.
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That has been another big concern for me on this. I've had double stitched X box sewn patterns fail on me on 1" straps, so I've gone to using bar tacks. I usually space them about 1/8" apart and do one stitch per 200 pounds of desired strength, I've never had one of these fail. With a half width strap I may go with one par for every 100 pounds.As to the size of the webbing- it seems the sewing on the loop of a 1/2" piece would have less load rating versus a 1" piece. The rigging is only as strong as it's weakest link.
But for arguments sake lets say that the friction is also a product of the surface area of the strap. Less width would be less surface area, so more of the weight would get transferred around the strap(s) on a thinner strap wouldn't it?Wrap the webbing only 180 degrees around the trunk and have someone (or yourself if you like pain) sit in the hammock. Unless it is a really big tree you won't be able to win the tug of war.
Now wrap it another 360 degrees even without overlapping the wraps and sit down. You will be very close to supporting your own weight if you can't already.
This just shows that the tension transferred from the strap to the bark of the tree fairly quickly, so the extra wrap does little for you.
I haven't tried that experiment yet, but what I have generally assumed until I really started thinking about this was the greatest pressure would actually probably be on the back of the tree, not the sides or front (nearest hammock).So the strap is putting a lot of tension (compression on the bark) very early so you want to have as much width of strap to distribute it as much as possible as soon as possible.
With each turn around the winch/tree the load is going down. The distribution of load is something that can be determined using calculus, a skill I no longer possess.
The ring I've described transfers the load first to the one turn of 550 that is in direct line with the load. As that one stretches the two wraps on either side begin to take up load, and so on ...
50' of cord would wrap a 9.5" dia. tree 20 times with a back-side strap width of 3".
Only one cord could hold a man if the tree was 15.9' in dia.
The advantage then of a very long cord strap played through a ring is the range of application.
The disadvantage is spending 30 minutes building it.