TheTreeSpyder
Branched out member
- Location
- Florida>>> USA
The Loading on the green pulley will be 2x at a closed angle and control end anchored. This double whammy will then bend the horizontal line with gold pulley. At this closed bent line angle(bend thru green pulley), the ends of the line have leverage over the bend/pulley position; so the green pulley bend will have more loading force than initial line input force.
At 120degree bend, neither the bend nor the end(s) will have leverage over each other; and the loading on each end will equal each other and the loading on the bend too. So actually the loading at the bend is doubled; 1/2 of this doubleing carried at each end carried. Whereby, at closed/Zer0 angle; 1/2 the load is carried at each end(so pulley/bend position is 2x either end or 1x the sum of both).
But, once past 120 degrees; (nearer a flat line) instead of the end having leverage over the bend; the bend has leverage over the end(s). So, the bend by gold pulley in the horizontal line multiplys it's force to the horizontal line tension/ ends at vertical support spars. The precise amount depends on the angle of this bend in horizontal ine. The more horizontal the line to a vertical loading; the more perpendicular this support line is to the loading, thus the more leveraged. Therefore, per loading and impacting this will all change; subject to the loading (that is doubled by green pulley), the initial horizontal line tension and the flex of the supporting vertical spars.
This highly amplified force will then leverage said spars by their length from the ground (as pivot) X their stiffness(resistance to bend; no resistance to bend-no leveraging). So we have impact/loading X 2 (for the pulley) X leverage from line stiffness (initial tension that imparts stiffness/ resistance to bend for horizontal line) and angle of horizontal line to give horizontal line tension. Then this line tension passed on to each of the vertical spar supports.
Nature will allow some of this 'steam' to escape under the dynamic forces by vertical line, horizontal line and spar elasticities; to what formulae She can assess gives the most conservative/ minimal loading to the system. The static parts of the loading(s) will have to be borne by the ropes, pulley and spars and their leveraged angles of loading as pre-scribed without elastic/dynamic reliefs.
In short, the only loading transfer that is 1:1 (not altered); is single to single inline device loadings. The opposite of inline is not inline and therefore leveraged; the closer to 1 device/force being perpendicular to it's 'transferee'; the more leveraged exchange there is. A vertical spar with balanced load on top is inline 1:1 force; as is a rope with load hanging freely; because the force flow is inline down these devices columns from the loads.
Impacting, to pulley support, to horzontal line, to perpendicular support is stacking multipliers on each other. Only releifes are dynamic elasticities during dynamic loadings; and however the horizontal line and vertical spars can assimilate themselves to be more inline/ less leveraged to the transferring forces from 1 device to another.
Line angle leverage calculator, drawings and specs
Flash version; less dialogue but doesn't work in all browsers or 10th square down on Right. the Flash calculators are for each leg of line to bend; so are 1/2 the load at 1/2 the bend or bend of each leg from inline/vertical.
Though Mark's numbers sound high; the loading could go much higher; depending on the angles of the rope and wood devices to the loading inputs passed to each in turn of the chain of multipliers. Fortifying the spar columns not to bend by anchoring back against the horizontal line input would reduce the elastic relief, and maintian more perpndicular line (horizontal) to the doubling green pulley. Tightening the horizontal line, increases it's stiffness, therefore increasing it's leverage-ability/ will bend less to have higher multiplying factor at the given loading.
Orrrrrrrrrrr something like that
At 120degree bend, neither the bend nor the end(s) will have leverage over each other; and the loading on each end will equal each other and the loading on the bend too. So actually the loading at the bend is doubled; 1/2 of this doubleing carried at each end carried. Whereby, at closed/Zer0 angle; 1/2 the load is carried at each end(so pulley/bend position is 2x either end or 1x the sum of both).
But, once past 120 degrees; (nearer a flat line) instead of the end having leverage over the bend; the bend has leverage over the end(s). So, the bend by gold pulley in the horizontal line multiplys it's force to the horizontal line tension/ ends at vertical support spars. The precise amount depends on the angle of this bend in horizontal ine. The more horizontal the line to a vertical loading; the more perpendicular this support line is to the loading, thus the more leveraged. Therefore, per loading and impacting this will all change; subject to the loading (that is doubled by green pulley), the initial horizontal line tension and the flex of the supporting vertical spars.
This highly amplified force will then leverage said spars by their length from the ground (as pivot) X their stiffness(resistance to bend; no resistance to bend-no leveraging). So we have impact/loading X 2 (for the pulley) X leverage from line stiffness (initial tension that imparts stiffness/ resistance to bend for horizontal line) and angle of horizontal line to give horizontal line tension. Then this line tension passed on to each of the vertical spar supports.
Nature will allow some of this 'steam' to escape under the dynamic forces by vertical line, horizontal line and spar elasticities; to what formulae She can assess gives the most conservative/ minimal loading to the system. The static parts of the loading(s) will have to be borne by the ropes, pulley and spars and their leveraged angles of loading as pre-scribed without elastic/dynamic reliefs.
In short, the only loading transfer that is 1:1 (not altered); is single to single inline device loadings. The opposite of inline is not inline and therefore leveraged; the closer to 1 device/force being perpendicular to it's 'transferee'; the more leveraged exchange there is. A vertical spar with balanced load on top is inline 1:1 force; as is a rope with load hanging freely; because the force flow is inline down these devices columns from the loads.
Impacting, to pulley support, to horzontal line, to perpendicular support is stacking multipliers on each other. Only releifes are dynamic elasticities during dynamic loadings; and however the horizontal line and vertical spars can assimilate themselves to be more inline/ less leveraged to the transferring forces from 1 device to another.
Line angle leverage calculator, drawings and specs
Flash version; less dialogue but doesn't work in all browsers or 10th square down on Right. the Flash calculators are for each leg of line to bend; so are 1/2 the load at 1/2 the bend or bend of each leg from inline/vertical.
Though Mark's numbers sound high; the loading could go much higher; depending on the angles of the rope and wood devices to the loading inputs passed to each in turn of the chain of multipliers. Fortifying the spar columns not to bend by anchoring back against the horizontal line input would reduce the elastic relief, and maintian more perpndicular line (horizontal) to the doubling green pulley. Tightening the horizontal line, increases it's stiffness, therefore increasing it's leverage-ability/ will bend less to have higher multiplying factor at the given loading.
Orrrrrrrrrrr something like that
