Mmmmmmmm, i think.............
as a static load hanging SRT(no bouncing etc.) on Overhead Anchor (OA?), ; i believe there would be 2x load with pulley (line draped, no friction) on OA, when controlled at ground. For, your weight would be powering 2 equivalent lines of pull on the OA (vertical pulls), with the pulley on the OA. as the control line would have to match the pull of the load to keep load raised, when there is no friction helping. Both these equivalent pulls pull on OA.
Then, load on OA would be equal to load, if just anchored totally above on OA, no control line pulling on the OA. Just a single overhead line terminating at OA (bowlined etc. to OA), only holds that load.
But, draping over a limb on OA, would be between the two numbers (load and 2x load), depending on the friction given by the 'frictional redirect' (non-pulley redirect) of the limb.
So that simply the load on the OA would be the sum of all lines pulling(typically load and control lines), which would be less on the control side with friction(no pulley), or other upper anchors bearing the load. But the friction of the redirect (anything that changes direction of rope movement i think, frictional or pulley -assume 0 friction for pulley) + the pull of the load on 1 side+ the pull of the control line on the other side will be 2x load .
But a tree climber's typical DDRT, would only equal the climber's weight(load), for all lines terminate at OA and climber, no pull comes from below climber, as the control line doubles as a load line, the OA would only carry the climber's load, pulley or not! But yet it is a 2/1 - friction when elevating yourself by pulling on 1 of the lines holding you.
So, {Load}={Single line terminating on OA}={DDRT on any OA(friction or pulley)} < {draped line's OA pull (load+control line pulls)} < {2xload}={same draped line (load line pull + control line pull)+ friction(that lessens the control line pull)}={pulley controlled load (no friction+load+tension on control line to keep load up; thereby matching load on its own}
So, more overhead friction, puts less pull on OA, by taking the load off the control line pulling on the anchor (replacing it with equivalent load carrying friction), and control lines at a slant, take progressively more load of an OA. Same in rigging loads. So if i am using a self tightenning rig, i will use overhead friction a lot to lessen anchor pull, while having less rope to stretch, thereby self setting quicker and positively for a machine without play in the works!
i don't mean to be picky, and i hope that is easy enuff to understand, for it is all around and i use it all the time for informed decisions, or just to exercise their creation, and beleive i got it write enuf to pass on!
