Anyone ever break a NEW 3/4" whoopie?

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Spike-it, the tensile strength of 5/8 Stable Braid is 15,600. Safe working load(SWL) is 4:1, I think, or 3,900. A 3,000 lb piece will put 6,000 lbs on your sling. If you used two slings, and assuming the load was evenly distributed, you're probably OK as long as shock load was minimal. But you still came close to the limit. Are you sure about the estimated weight? a 26" log averages about 200lbs. per foot!!!
 
with the oak limb there was no slings involved except for the ports wraps. i used crotch's for the bull ropes. i not too sure on estmating the weight. it was a red oak limb, the tips were hung up in phone and cable lines plus over a niehbors shed and pool. so i set it up to be butt heavy so i could lower the butt and cut piece's off to suck it back into the yard of the tree. using your formula the limb was probably heavier than i estmated. there was a good 20 feet of wood before it branched out. looks like i might pick up a few 7/8 slings and a 3/4 bull rope.
 
i only use the whoopie on the Porty(to snug it low as possible, so when using 5/1 pretightening, can take longer sweeps), so i too visualized it like that; had to back up and re-read original post after MM's post! I use heavier stuff on pulley redirect in tree; sometimes grabing both legs of it. It is a 4" doubled, sewn eye to eye sling.

In drawing might be a lil less pull on control line because of angle of it, it would only have 100# pull on veritcal control line; less per angle(thereby lessening the anchor load by lessening the control line pull, the only alterable part of single anchor load), next thing would be to let it run to lessen anchor load, share anchors or put pulley on load (2/1), but that would still be 1.5x Load on non-frictional redirect with zero impact; but also enable more pre-tightening. But the math of load + control line pull will equal Overhead Anchor Load still stands.

Also sling will have about 2.5x the strength in basket or round turn basket(for grip; sometimes called double basket) than choker lacing. That could have made the diffrence right there! (Calculating choker at 80% of straight leg (sling stretched out), and basket formations at 2x that of straight leg sling).

Even with a GRCS taking 1T of pretightenning it would take a lil bit to totally rule out impacting especially rigging under load rather than above it. That would be where we have groundies pulling over top of load, forcing beefier hinge to hand off to rig with less impact; as hinge delivered slower and gradually supporting part of load through the hinge's range.

With a 1T or 2K load, just 1' of drop/stretch would put 2T, 4K load just on load side of pulley, of course brake force on opposite side would have to match that. At 8" (3/4 of 1')of drop/stretch with 2000# load that would put 3500 # of force on just the load side of pulley, matched by braking force, would be 7000# on 3400#SWL choker/pulley/anchor set.
 

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