Forces of Rope Arcs

[TreeSpyder]

Rope arcs happen inside of knots whar ya can't see'em. But, they also happen in rigging. Because a pulley has 2 legs of loaded line on it, it has a potential loading of 2x Load. But, because the sling/rope holding the pulley, only resists inline not perpendicular tensions, we only need to calculate the inline forces of the rope angle from the sling X 2 legs. This means that we take 2x Load X cosine of half the spread. And we are done.

 

This also explains a pulley with weight on a horizontal clothesline, or leveraging tighter by swigging or sweating purchases. For, this is the same math, in reverse, we are now just initiating force by the bend, not the end, into the system.

 

Thus; if we place 175 degree spread in angle box, we will see very little load on pulley; so pulley has leverage over the line at that angle. Thus, if we anchor leg and pull bend, we can incite those kind's of forces. The calculator crunches by radians, so calcs by hand in degrees all the way through might be slightly different. For code testers/breakers i allowed negative/floating load weights, but not angles< Zer0 nor > 180.

 

Numbers are assuming that preserving all forces, none lost to frictions elastic distance/stretch etc.

 

calcPulleyLoadings.swf

[Dean Lofthouse]

Whey hey, straight over the top of my head that one Spyder:001_tongue:

[TreeSpyder]

i keep trying to say it better; for it is how everything works.

 

2legs of pull place 2x Load at each pulley everytime. But not all of it pulls on the pulley, some pulls across the pulley to the other leg of line. So it is just a question of how much of the 2xLoad potential; pull on the pulley. The cosine scale is the Zer0 to 1 percentage type scaling we use. So can take Zer0 or all of full potential of forces(2x Load). So, 2x Load X Cosine; gives this percentage of the total force of 2 legs of line on the pulley.

 

We don't use sine, because that is across force. The 2 legs of line will center the sling between them with their across force, because the sling doesn't resist there sideways (sine of angle) forces. If the sling doesn't resist sideways force, it doesn't incur the forces. So half the spread is how far off the lines to self centering pulley are from the all important inline with the sling we must calculate from. So we take 2x Load X cosine of half the spread of legs of line to the pulley to get force on pulley.

[Ian150482]

Glad im not the only one Dean.

[Bundle 2]

Thats why the calculator is there for you...handy!!

I will admit that the maths only makes sense as it is explained....ask me to repeat it and I'd be stuffed!!!

Good post IMO

[Khriss]

The first rule of timber lowering club is 'Double your safety margin...'

The second rule of timber lowering club is 'DOUBLE YOUR SAFETY MARGIN !'

 

K ( Who burnt his 18mm pulley strop on the last lump he lowered -should have soaked it ?)

[j r hartly]

i thought the first rule of timber lowering club was, you dont talk about timber lowering club

[Dean Lofthouse]

i thought the first rule of timber lowering club was, you dont talk about timber lowering club

 

Wrong again, the first rule is don't talk about the don't talk rule of the timber lowering club

[munkymadman]

this is what happens to pupils who don't understand what the teacher's on about they just muck about in the back until the bell goes

[MasterBlaster]

They don't need no education, lol.