how to fall back leaners

I just rrad through all of it, and what a great discussion it was, as long as " The World's greatest treeman ( With bucket access, of course)" kept his nose out of it.
The rest of us managed to keep civil and agree that we are all different when it comes to falling trees.
 
I seemed to read in Burnham's thread reference that you net gain by shifting hinge location towards the back. There was reference to 5 or 10 degrees as maximum trunk lean angle to tackle.

On a 50 foot tree at 5 degrees the top is over center by 0.087 x 50 = 4.3 feet. Placing the CofG at less than half height due to trunk taper, 20 feet x 0.087 = 1.7 feet. If the trunk diameter was 3.4 feet at the base the CofG would be right on the edge. A 50 ft tree might more likely have a 2 foot diameter trunk at its base so its CofG weight would all be overhanging. At 10 degrees it would be 3.4 feet offset, so really overhanging.

So shifting the offset to the CofG by a few or 6" is quite less significant as a proportion of 1.7 or 3.4 feet, vs shifting 6" in the realm of half trunk diameter (1 ft) where it could cause a 30% lessening of hinge fiber tension as a loose approximation on a 2 ft diameter at base trunk.

If these number aren't messed up, they suggest you gain more from lessening your chance of tension snapping the hinge while wedging. It seems to come from operating as a (smaller) proportion of CofG shift vs operating as a (larger) proportion of trunk base diameter.

Allowing for loose accuracy I think the math is generally right.

? Any thoughts or observations or corrections?
 
No numbers version:

The CofG offset from centered x weight of the tree is a torque. The wedge/jack at the edge of the trunk x distance from the wedge/jack to the hinge is the equal, opposing torque.

(Big) Wedge/jack force is opposed by pull force on the hinge fibers. Big wedge/jack force is what causes hinge failures and spectacular youtube back leaner failure videos.

Figuring out how/why of avoiding hinge failures. On back leaners. By favourably choosing hinge location. Hinge closer to wedges intensifies both pull force on hinge and crush force on wedge face. Increasing chance of failure.

Hope that helped? :)

I have to say the other discussion thread was very good. Learned a lot about techniques from it. Makes you think about crushing wood fibers if you lose a leaner backwards. Psi on the wedge face, punky wood and all that stuff. Hate that feeling of wedging punky wood. Happened to me once on a big dead poplar.

edit - I left out the vs gaining by reducing the initial CofG offset via choice of hinge location in this no numbers version, which is the second half of the analysis, and is a one liner. On a vertical tree it's the Reg over-center cut to drop spar chunks effect that wins. On a significant leaner the Reg over center cut doesn't win you very much compared to rapidly ramping up the tension on the hinge (chance for hinge failure).
 
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If one rope isn't enough... use two... if you're still not sure, use three. set them high, use separate ground anchors.. for side leaners or side weight you can cut the notch just shy of 1/2 diameter, so the hinge is as wide as possible, gut the hinge if needed. Pull with the equipment. Keep it simple
 
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