Don’t worry, KC, I’ve been able to view TreeSpyder’s tree lessons (and I responded in some detail). I just have to click on the flash object and grant the permission for it to run in my browser each time I want to load it.
Your illustrations, TreeSpyder and KC, prepped me for this: https://www.youtube.com/watch?v=vM24klVyxFk (not my work; though I work with trees, others or the wind fell them or not as the case may be for me to clean up). I arrive at a 35:1 advantage in the video (assuming perfectly parallel stands, a single-point attachment to the tree, and no friction etc. etc.), not the author’s 45:1.
Very nice, pure power example.
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i think the single connect point on target would be easier to calc total effect.
The varied heights/lengths from ground pivot of the pull points on target tree MUST:
pull with different leverage (of which you have the higher compounding highest for greatest force)
pull at different speeds (reciprocal of force increase) so lower lines have less distance to pull
(forcing higher to pull first, lower to backup that pull?? not sure of elusive quantity here, but less than optimal and don’t think is as eye sees/decodes)
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Hard to see but i think:
Compound/top pull is 5x2x2x
Middle is 5x2x
Lowest is 5x
(sum 35)
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Devil’s Advocate:
Might try using single leg termination points as dual strategy to also present support against the higher compound pull/ at that higher position.
each single leg could offer bight to compound pull, with seams buried/buffered from direct forces on host mount/target tree
presenting 2 seamless eyes , 1 from either side of spar against compound red pulley pull
spaced from tree for more strength from sharper point/teepee,
flat teepee is leveraged harder grip/less support efficiency so raises tension closer to ceiling limit/less headroom to compensate
To get all from equal distant/equal speed and greatest leverage point
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This has some nice compounding, even midway floating pulley concept for more power but not right on load
all ends used even in multiple lines
more in linear, end to end.
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With human body as power source,
can embed system inside of system, to work 2 pulls from inner system to outer system
i think of using the yin and yang of the force produced against the target.
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http://mytreelessons.com/images/forceplay-of-different-recursive-human-efforts-against-loading
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Trying on your tree:
if try to similarly ‘embed’ both pulls of 1 5x jig to pull from both compounding ends into another larger 5x system
So that inner 5xOutput end is input into single input of outer 5x (25x total)
and the lower 4xOutput of inner pulls just before that point in outer system (so will give 4x3 to top =12x)
to sum 37x against loading POTENTIAL
Potential output degraded to actual by compounding of frictions, elasticities, pulls not pure inline/parallel and now lie frictions from system crossing
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Playing with Forces, compounding the maths that still prove true even around counter-intuitive turns like Ancient Chinese Windlass/Differential !
Spring Paradox
http://tsgphysics.mit.edu/pics/B%20Dynamics/B17/B17.jpg
Explanation.
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=B%2017&show=0
Calculations
VERY NICE!
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To me,
In series both springs are carrying full weight;
in parallel each carries half is where the twist here is…
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In ropes, 500# on single leg stretches further on impact than pulley setup against same load
pulley rig now has ~2x as much power, so it’s ceiling is encroached on less , leaving more ‘max headroom’ of clearance/capacity.
This gives less elastic dampening from the pulley setup
more shockload to rest of connected chain, testing knots, ropes, supports etc. more
The single/series leg stretches further, gives more elastic dampening/stretch
some days this buffering is what outruns/wins over the stronger 2:1 pulley setup.
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Elastic response is per loading percentage of capacity, and not a nice even increments of change
so can’t forecast that 250# gets half the elastic response of 500# nice and neat
So, 2x250# does equal the same single leg 500#, but former ( 2x250# )is stiffer/less elastic response ; than latter (1x500#).
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A very counter-intuitive constant companion!
Fave topic actually; but wasn’t sure if that totally re-solved math of pulls here tho when looked at this even many years ago(?).