Pulley Forces Grid Calc

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TheTreeSpyder

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http://mytreelessons.com/Flash/forces/forcesPulley_1.swf

Animated Calculator / toy for forces lifting/holding/lowering on pulley at various degrees/loads.
Grid shows Black supporting line tension, Red how much of that line tension is to support of pulley, and Blue percentage of line tension pulling across to other leg of line( for line tension not working on support of load).

Same math applies to hosting by by hook etc. So, if lifting a crate with angled slings, this would show the tension of the slings, and the potentially crushing force across the top of the crate etc.

Also, Sweating/Swigging lines tighter, same math, guy wires etc.

Biggest thing here is not exact numbers, but patterns of changes, impact of changes, at what points are what forces working for and against you, to what levels of trade off. At what points do you want to input pull on end of line and receive output at bend/pulley, and at what angles would that put you 'upside down' / getting less output than input, so would reverse strategy and pull at bend/pulley to get leveraged return at intersection of Black & Blue.

Glad to see y'all still rocking and rolling!
 
Nice work, Kenny! :thumbup:
Glad to see you're still rocking and rolling! :)
 
Thanks for that Kenny, really nice reference to have on hand.
Back in the day when I took ArborMaster Training's rigging courses we had a digital weight scale at our disposal for determining shock loads.
I could sure make use of that scale today if it was in my tool kit.
I do alot of guying now mostly anchored with my diesel pickup, alot of tension can be applied to a 3/4" stablebraid when being snugged up in 4X4 low range. But just how much tension do I have on that line?
 
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  • #9
Is prodigal some kind of fancy cussword?



HolmenTree
This works on right triangles, need at least 2 pieces of data to resolve.
(1 of them being a known force, other a force or angle).
So can't say from data given.

But; if that then presents opportunity to add data;
and wanting to play with to find out; must give all safety disclaimers, we are playing with / respecting forces here.
Also, must assume below that neither end of line (truck or target) gives or moved when (possibly hyper-) loading line as discussed.

Short Answer:
Without the calculator i would hang known load in center of lineTension (giving load 2 legs of support against gravity), and multiply loadHalf X tangent of (90- lineDeflection w/load on it).



Generally play with degree slider and numbers are just to reveal patterns to learn(l-earn) on graph;
but can use for specific static calcs too.




Tech-nicals :
Changing the degree, changes the geometry of support.
lineTension (BLACK) pulls less efficiently on RED (for load support) at 'flatter' / less inline angles (as more lineTension is pulling on BLUE)
Tangent = (far) sine / c(lo)sine or RED loadHalf / BLUE pull across;
LineTension = loadHalf / c(lo)sine ( loadHalf supported by enough c(lo)sine X lineTension, but looking for lineTension, so invert)
Proof > loadHalf = lineTension x c(lo)sine (of course loadHalf x c(lo)sine/ c(lo)sine = loadHalf ).

pull across= lineTension x (far)sine = pull across BLUE;
so shortcut is loadHalf x tangent... for tangent forces across (BLUE).
Proof (either way)> loadHalf (RED percentage of BLACK lineTension) squared + pull across (BLUE calculator output percentage of lineTensi) squared = BLACK actual lineTension.
 
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  • #10
If wanting to play with calculator to find out; playSafe!
Also, must assume below that neither end of line (truck or target) gives or moved when (possibly hyper-) loading line as discussed.

Short Answer:
Hang known weight in exact middle of lineTension / pull; enter known weight into calculator (calcs loadHalf for you).
Set slider to (90 - lineDeflection ); read the pull across BLUE # as output answer.


Techs:
Measure the lineDeflection; BUT
Enter the REVERSE angle (90- lineDeflection) as we are coming thru calculator at a lysdexic angle with BLUE as support NOT RED...;
See the RED lineTension as actual support for load in center of lineTension, you (i believe)
want the BLUE data, for how much of lineTension pulling on BLUE axis;
RED axis, each line is like a long lever, holding up half the known weight (placed in center of lineTension).

The calculator was made to support on opposite axis than you propose is all.
Calculator reference is from origin intersection of BLACK + RED, facing to intersection of RED + BLUE as assumed 0 degrees to support directly against gravity .
From calculator point of reference, calc RED as c(L)osine angle / percentage of BLACK and then
calc BLUE as the (FAR)sine / percentage of BLACK (actual lineTension).



Flood Warning:
In geometricianses terms, BLACK (actual lineTension) is the hypotenuse. BLACK line length not changing here, BLACK will fit vertically or horizontally (on it's wing/side of support) perfectly. RED/BLUE just show how much of BLACK line tension fores tensions on RED / BLUE. Geometry (just punch cosine or sine or tangent on windows calculator in sci. mode) X forces, instead of distances. BLACK as lineTension is largest line/force of triangle, c(lo)sine to find close/inline force, (far)sine to get across pulls (each as a part/percentage of lineTension as a potential on RED or BLUE axis, instead of BLACK as a potential length on RED or BLUE.)
Also, note that RED squared (load/2 lines) + BLUE squared (pull across on calculator, actual pull in your REVERSE scenario) = BLACK squared(actual lineTension).

Force wise; each RED leg supports half the needed force (load shown calc) using c(L0)sine (as inline support efficiency of lineTension) of deflection from needed support against gravity .
But also can generate sideways force, BLUE using (FAR)sine to show lineTension NOT PULLING ON RED to support load, but pull across(what you need ).
 
Don't be a stranger, Kenny...well, any stranger than you already are :P.

Real happy to read you again, old friend :D.
 
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