Potential 21x from a 5xRig and a 3xRig

TheTreeSpyder

Participating member
Location
Florida>>> USA
21xfrom a 5xRig and a 3xRig

By insetting the 3xRig (and not just piggy backing it on end of 5xRig) we can tap into the Equal and Opposite forces of the 3xRig that are promised, and use those forces to add more advantage.

Now if the person pulling, insets themself inside of the 3xRig the same way(so that we can not only get the effort of their pull, but also make use of the Equal and Opposite of that effort, then multiply it inside of the 3xRig, to then compound that multiplication into the 5xRig...), so that the 3xRig then pulls on the 5xRig as shown hear; (s)he can generate 21xBodyweight + 32xEffort. For a 100# person with an added 50# arm pull, this can give a potential of 21x100 + 32x50=3700.
 

tomthetreeman

Participating member
Location
Rhode Island
I'm beginning to think that Treespyder is a former astronaut or something. I have to read his posts slooowly to absorb what he's saying! Forward thinking for sure! Thanks, TS!

-Tom
 

Tom Dunlap

Here from the beginning
Administrator
In rope pulling tests for high angle rope rescue teams they've found that a person can put about 80% of their body weight into rope pulling on a horizontal rope. It would seem that the more vertical the rope the more efficient the pull would be until the puller lifted themselves off the ground. Then, it's time to get out the nail gun and stick them to the ground.

There is a time when the internal friction of compound MA start to experience diminishing returns.

Great graphics!!!
 

TheTreeSpyder

Participating member
Location
Florida>>> USA
Thanx, the flashVid is updated to show the 3700# potential i mentioned.

Yes, these are potentials, there will all ways and always be a friction loss, that in itself will be compounded too in series through the system to build to it's own law of "Diminishing Marginal Returns". In fact to that point, knudeKnoggin states that a zRig of rope on rope, has enough friction to allow only about half of the 3x Potential.

Now, we have that 80% no. for bodyweight into horizontal pulls that is popular(legs are 20%?). But, in the theory that anything that stands against ye, can work for ya- What if we kept legs real straight and tight, and leaned back on this lever pinching rope low to us? Would this conceivably give leverage to compensate for the 20% loss?

And of course there is impacting to add force. This is also where the 2 part force recognition helps (of bodyweight force and effort force. For, we can impact both together, or hold things pretty steady with 1 input (bodyweight for example) then impact with effort suddenly.
 
Location
Maine
Checking the math...

[ QUOTE ]
By insetting the 3xRig (and not just piggy backing it on end of 5xRig) we can tap into the Equal and Opposite forces of the 3xRig that are promised, and use those forces to add more advantage.

[/ QUOTE ]

Wow! Congratulations Spydie on the terrific graphics! And the idea of connecting one pulley system across two legs of another to enhance the mechanical advantage is very intriguing.

When I work out the numbers, however, I come out with something a bit different. For example, in your example combining a 3:1 across a 5:1, you calculate a final MA of 21. When I do it, I come out with a MA of 26. The root of the problem is that in this configuration both ends of the 3:1 move and this makes a difference.

Consider first the simpler case of a 3:1 connected to the end of a 5:1. Assume the 3:1 rig is 2 feet long and made with extremely tiny pulleys. This means we can pull fully 6 feet of rope out of the 3:1 before it closes up completely. In doing so, the upper pulley of the 3:1, which is attached to the load (the 5:1), moves 2 feet. Since the pulling force has to move 6 feet in order to make the load move 2 feet, we are getting 3:1 MA out of the system. Even though you can often use convenient shortcuts like counting lines to figure the MA, in some cases like your cool system of crossed rigs this doesn't work. Figuring the distances moved by the pulling force and load force always works.

Applying this same analysis to your example of crossed rigs can be done as follows. Assume again a 2-ft long 3:1 made with tiny pulleys. It contains 6 feet of rope. When we pull out all of it, the 3:1 closes completely. Since the two tiny pulleys are now side-by-side, the lower pulley has risen one foot and the upper pulley has descended one foot. But since one foot of rope has passed through the upper pulley of the 5:1, that pulley has descended 1/5 foot (.2 feet). How far has the pulling force traveled? Well, it would have been 6 feet if the upper tiny pulley had descended 2 feet to be even with the lower pulley, the standard 3:1 configuration. But it is .8 feet higher than that, so the net pulling distance is 5.2 feet. How far did the load move? The load is attached to the upper 5:1 pulley, and that moved, as we saw, exactly .2 feet.

The ratio 5.2/.2, or 26, is the MA of the whole system. Do you agree?

Someone may protest that real systems don't use microscopic pulleys, and I agree. They are there just to make visualizing the problem easier; the size of the pulleys has no effect on MA.
 
Location
Ohio
Re: Checking the math...

At what point would you get slippage from the prusik rope grab?

Speaking from a high angle standpoint (if my memory serves me) tandem 3 wrap prusiks (8mm) on 1/2" static kernmantle will slip at around 1000 pounds.

But that slippage is a good thing compared to desheathing a rope at around 1500 lbs like a mechanical rope grab will.
 
Location
Maine
Nope, I\'m wrong!

[ QUOTE ]
...The ratio 5.2/.2, or 26, is the MA of the whole system. Do you agree?

[/ QUOTE ]

This is tricky, and in spite checking my work many times, I still managed to get it wrong! The correct answer, I believe, is 21, just as Spydie told us.

Spydie's diagrams are excellent, so I will just try to make the argument using plain old words. The analysis is tricky because almost everything in the diagram is moving. What we have is a standard 5:1 tackle and a standard 3:1 tackle, well-depicted in the diagrams. When they are connected end-to-end you get a simple multiplication of MA, namely 15:1. But Spydie has cross-connected them (SpyRigged?) and you can no longer simply multiply 5 X 3 to get the answer.

Let's assume, as in the diagrams, that the moving tackle and load are always at the top and we pull downward on the free rope end to make everything move. In a simple 5:1 if we pull downward one foot, the tackle will move 1/5 ft. Similarly, in the case of the simple 3:1 a 1-foot pull will move the tackle 1/3 foot.

Now let's SpyRig the 3:1 across the 5:1 as in the diagrams. Let's refer to the upper prusik connection as U and the lower prusic connection as L. The only free end in the system now belongs to the 3:1, and as we pull it everything will move, including the upper block of the 5:1 and the attached load. The distance moved by the free end divided by the distance moved by the load gives the mechanical advantage of the whole system.

Attacking this in reverse, assume we have pulled out enough rope to cause the 5:1 tackle to move .2 feet. Then U has moved 1 foot downward. But since the block itself moved downward .2 feet, only .8 feet of rope actually moved through the block from L to U. U moves down .8 feet from the block and L moves up .8 feet towards the block. They are now 1.6 feet closer together than before.

This means the 3:1 tackle is now 1.6 feet shorter. Since it consists of two lines connecting the pulleys plus the free pull line, the two lines have given up 1.6 feet each, or 3.2 feet in all. So we have pulled 3.2 feet plus the 1 foot that U itself has moved, or 4.2 feet in all. Divide that by the .2 feet moved by the load to get 21, the MA advantage of the whole system.
 
Re: Nope, I\'m wrong!

Welcome Ghillie!

And Kenny... Good work! But, you have the biners loaded the bad way.
tongue.gif
Was that a test for us?
pbj.gif
 

TheTreeSpyder

Participating member
Location
Florida>>> USA
Re: Nope, I\'m wrong!

It is kinda counter-intuitive until you are on the inside looking out!

One thing fer sure; as an accountant balances his debits and credits, algorithms by checksums; we should check our imagery / understandings so that the theories check out forward and backwards, by power differential analysis checking against distance differential.

Many lessons hear, can adjsut thru these positions like a transmission, going faster with lower power rig when loading is less etc.

Here are some rigs i put together; showing the old worlde solutions (that i have poured over for many moons): The Spanish Burtons 'Class' . The drawing (and other Flash items) is/are vectorized, so if you right click on the drawings and choose zoom (even a number of times in succession ); there will be more detail when getting a closer look, rather than like with a regular picture that give less detail and blur out eventually.

Also, for everything we find in 'flexible lever systems'; we should also find a comparable 'non-flexible lever system' (steel etc.). Then L-earn lessons from each to carry back over to the other. For, these things all at once very simple/ working on all the same rules and yet multi-dimensional. Many times it takes seeing them from all different angles to see all the facets of these jewels!

i plan to keep working on all this. Add things as we go along. One thing i need to include, is that if you are setting, pulling, tightening with a 5xRig yourself, and reach across as this theory has shown, you get your 5xBodyWeight + 8xEffort. So you can cinch up at what you can at 5x(5xBodyWeight + 5xEffort) at 1 speed, then switch to your 5xW + 8xE, which would be slower, but more powerful. A transmission for your effort input, just downshift into low (5xW + 8xE) like a 10 speed bike facing a hill. Or by what i show kids as '2speeding a screwdriver'; spin shaft for fast, low power. Many probably show or fall into that; but i hand it off purposefully calling it out as leverage, and making compairisons to bikes, levers, screws/ramps etc.

Another use of the bodyWeight + 2xEffort strategy(or harnessing the equal and opposite of your effort and putting it to work too), is a climber helping setting a rigging line, or just setting rigging to control themselves. Always tied in on lifeline as failsafe catcher, hang on control side of rig line, then reach out and pull up on load side of line. i think if you can move the branch up any, you can get a (Zer0 Friction) potential of bodyWeight + 2xEffort potential. Now, if you reach out further than hitchpoint on load, thus get more leverage (from that leg, then into the whole) on top of that. But, if you can't really 'impress' move load up with that; then go further up the rope and exert force to place that bodyWeight + 2xEffort on pre-stretching the line itself (which is also an optional 2nd step if you can 'impress' target/load. Better than that, keep Pantin on, and set your self to exert 2xEffort of legLift, rather than 2xEffort of armLift (in addition to bodyWeight).

krabs didn't turn out write.
 

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