Re: Puzzle Shows Freely Available Rigging Force He
i too must reread you thoughts, but they are similar.
My main point was that in my view the forces on the stump (will be as anything else, collectively zero from the 'event') should be calculated per position, and center is a more neutral zone.
Position (A) under the lean is compressed region forming pivot of balanced pulls on either side. One side is the load side, an acitve force of weight, length and lean; a value of Z(force). As the pivot between CG pulling down and (C) fibers pulling down (each = Zforce when they are each multiplied by their leveraged factor from (A); so (A)=2Z; supports both loads of downpressure of load and support, as if (A) was the pulley between 2 legs of line, load and control legs, and inheritted both loads as a central pulley does.
On the other side of pivot point (A)(extreme) is (C); the support; passive/responsive force self adjusting to the load of the tree's Zforce even as it is pitching in wind etc. dynamically loading per split second.
Because Z must balance on the support side; Z also=(A) to (C)distance X holding power at (C). Or tree falls. For when it is out of balance, tree as anything else wanders discontent until it is balanced by support/equal and opposite reaction. Everything is in balance, because Nature demands that every act be in balance; or the act continues until balance is found. Or something like that....
Seeing as Nature will use the smallest amount of resources the easiest way, i think using leveraged length at (C) is used as multiplier to reduce force needed from fibers. My position (B) your = (O) as a position in the stump, and not stump as a whole; therefore more neutral to the event forces i think. If the tree where to be taken by saw, these stress points of ABC in stump would be replicated in pattern in the hinge, as it stands under same forces and positions as stump did. How the pattern is shown in hinge can be adjusted by how the hinge meets the pre-existing force pattern in the stump, but will be a smaller version of the stump forces from that angle that the hinge addresses the preexisting lean Zforce's direction, from the pre-exiting point of the stump. i stole the neutral fiber idea from Stumper, and formed it to this. Though i learned through hinging, find same values in standing tree.
So i looked at (O) as a point and not a stump i guess!
Thanx alot, especially for clear collection of simple formulaes, and another way to express balanced forces.