Author Topic: Knot Forces  (Read 12653 times)

TheTreeSpyder

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Knot Forces
« on: August 18, 2008, 01:42:55 AM »
Knot forces are just a microcosm of rigging / rope forces.  This old pic from when ya had to make it all count, shows a parbuckle.  A parbuckle is oft listed as a knot.  The parbuckle gets anchored on 1 end, drawn around a rolling load (usually under then over) and controlled on the other end.  Then you can draw in / up more powerfully or extend / lower with more control.

As you can see, to move the load forward, you must pull 2' of line, to shorten each leg (around the load) 1' (that then advances the load 1').  Therefore, your are pulling 2x the distance as the load is moved, therefore 2x the power on the load (less friction and stretch losses).

But, then; the real target force to be moved is the center of gravity of the log, the log itself is just a 'weightless container', through which you can react unto the center of gravity.  So, with the center of gravity, as the center of the log; the radius from the center, itself becomes a leverage over moving the center of gravity.  So, a denser log of the same width would be harder to move, because it would give less leverage over the center of gravity (ie. being denser, would be smaller; offering less leverage over the center of gravity).  Just like a smaller gear around the same shaft would give less leverage.

So, now our mechanical advantage over the log in a parbuckle is the original 2x X half the diameter (radius); less inefficiencies (friction, stretch, bumpy ground etc.).

To me, knots are similar systems; maid with the same materials, under the same forces.
« Last Edit: August 18, 2008, 04:08:22 AM by TheTreeSpyder »

roo

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Re: Knot Forces
« Reply #1 on: August 18, 2008, 05:34:31 PM »
So, a denser log of the same width would be harder to move, because it would give less leverage over the center of gravity (ie. being denser, would be smaller; offering less leverage over the center of gravity). 

You may want to re-think this statement.  For example, does the mechanical advantage of a pulley system vary with the diameter of the pulleys?

The center of gravity of a uniform cylinder should be at 1/2 the diameter, regardless of density.
« Last Edit: August 18, 2008, 05:38:28 PM by roo »
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TheTreeSpyder

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Re: Knot Forces
« Reply #2 on: August 18, 2008, 08:57:52 PM »
drRoo; i've long enjoyed the vision of your site.

We do agree that the radius (half the diameter) would be the cg position of the massive log.  This, is really the force that you fight, the ropes, shape of the log, are just the tools that you can react unto the cg force with your forces.

To the pulley question..
The sheave of the pulley would take leverage over the axle, when turned by hand.  Loaded with line, the outer diameter of the line would be fairly the operative leverage over the axle i believe.  Thus, this factor can take leverage over the bearings or bushing, to calculate the total efficiency of the pulley.  But, as you say, not take leverage over the load that follows the pulley

But, here the rotation of the log is the load, and the leverage device in one. This is a different scenario from a pulley acting on a seperate load.  If, we had a gear on a heavy axle, and parbuckled it with the line somehow, the gear would help carry leverage the axle weight.  Rolling a load, allows one to use the shape to take leverage over said load.  Whenever we compound events, to be both load, tool and or effort; we must look for compounding forces, not seen when all event's positions are seperate from each other.

Just as, a larger wheelbarrow tire will make a wheelbarrow easier to push (but s-lightly harder to start/ initiate said roll), and it will serve up over a step easier.  Especially if you pull it up over the step, so that the vector of your upper effort to the lower, loaded axle is upward out of the 'hole' rather than pushing a vector of force into the ground (from initiating effort pushing from high to recieving lower axle).  Also, with the larger tire,the bearings will last longer, for they take less revolutions for the same travel.

It is all, kinda exactly the same but different; kinda like the rope mechanics idea in knots.


« Last Edit: August 18, 2008, 09:12:24 PM by TheTreeSpyder »

roo

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Re: Knot Forces
« Reply #3 on: August 18, 2008, 09:46:23 PM »

But, here the rotation of the log is the load, and the leverage device in one. This is a different scenario from a pulley acting on a seperate load. 

I think you may have noticed the effects of a large tire's rolling resistance over obstacles versus a small tire, and may be trying to attribute it to some change in mechanical advantage where none exists.

To simplify, imagine a parbuckle at a very steep angle approaching vertical.  Now, isn't that analogous to the center pulley setup, shown below?



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TheTreeSpyder

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Re: Knot Forces
« Reply #4 on: August 19, 2008, 12:06:43 AM »
The way i see it, the log takes ma over the cg, as the pulley takes ma over the axle.  both are center of the radius resistance.  Only that resistance is not the load for the pulley rotation, but is the load for the log.  To me the log is wieghtless shell, whose shape gives handles for an exterior force to meet the cg through.

If we have a gear to turn a shaft, will not a larger gear(on the same shaft) yield more power over the resistance of the shaft??

Similarily, if i wiegh 100# and you lift me through a pulley, there is 200# of load on pulley, and you have 1:1 power, so must exert 100# force.  But, close the system, so that i lift self, there is only 100# on system, and each leg has 50# of force on it, and thus i have a 2:1 advantage, and only exert 50# of force.  The similarity, is that the effort and the load are now one position, more of a closed system of compounded forces, that can be elusive to the eye, but can certainly be felt.

If we didn't have a rope, and were just rolling the log, would not a larger diameter shape give offer us leverage over the cg, to flip said log??  A peavey or cant hook is a device(peavy having 2 sharp points, cant hook having 1, to take more care of finished/squared cants) that we can hook on the log; for extra leverage to turn it, by extending the log's framework to a larger size; like if a solid branch was sticking out and we grabbed this extension as more leverage to flip the log.  If we could place a pulley on said branch; would we not get the pulley ma x the leverage of the shape (now extended by this arm)?  If we were needing to lift log as it traveled to load; would not ramps give another leveraged multiplier(to the string of multipliers) to the equation?

my Pulley Page shows how a Spanish Burton, climber self lift, mayhem puzzle etc. all have compounding forces in them beyond the usual, all by similar strategies.



« Last Edit: August 19, 2008, 01:53:53 AM by TheTreeSpyder »

DerekSmith

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Re: Knot Forces
« Reply #5 on: August 19, 2008, 10:58:54 AM »
Hi KC,

Since you led me to make a fool of myself on an earlier exercise you posted here, I am always wary about making comments to your posts which are at first sight counter intuitive. However, against my better judgement, I feel like jumping in anyway.

You have already made the mental simplification that the tree is a massless cylinder with all the mass collected at the centre of gravity (CG).  Could I for the sake of further simplification propose that we reduce the length of the log to just a slice and then take a plank from the slice going top to bottom - in other words, we now have a pole, stuck in the ground one end (friction of the log against the earth we assume prevents slipping so at any one point of contact, the contact is static), and with a rope tied around the top end (again we assume that the rope does not slip over the surface of the log).  In line with your previous assumption we will assume that the mass of the pole resides in its CG in the mid point of the pole.

Now if we pull on the rope and move the top of the pole forward by a foot, the the centre of the pole moves forward by 6"  :  mechanical advantage (MA)= 2.

Of course, no matter what length the pole is, the middle only moves forward by half the movement of the pulled end, so the MA is always 2 irrespective of the length or mass of the pole.

The reference to using a cant hook is I believe a change of circumstances because using it, you are changing the pulling radius while leaving the rolling radius unchanged.

So for a log of 2ft diameter (a pole 2ft long), pulling the top forward by a foot moves the CG sitting 1 ft above the ground forward by 6" (MA = 2).  However if I stick a 4ft cant pole onto the top of the log, the Cg is still only a foot above the floor, but the pulling point is now 6ft away from the ground.  Now, if I move the top of the cant pole forward by a foot, the CG only moves forward by 2",  so yes I have improved the MA to 6 but only because I made the pulling radius larger than the rolling radius.  In a log the CG always stays in the middle irrespective of the logs diameter, so the pulling radius and the rolling radius stay in constant ratio irrespective if density.

However, despite the amazing impact of this image of human ingenuity from a time gone by, for me there is another issue at question.  The real issue is that the Parbuckle is a rope device (machine) and not a knot, much like a hammock is a device made up using many knots but is not a knot itself, so the Parbuckle is a device made using virtually no knots (and indeed the load itself becoming part of the machine).

Although I think of knots as being 'rope machines', the important distinction for me is that in a knot, this machine bears upon itself to achieve its functionality.  Even in hitches where some 'third party component' is an essential part of the functioning structure, at some point the rope still bears upon itself to achieve the functionality of the knot.  Inevitably, such a description leaves out elements of importance to rope use such as the almost vital 'Round Turn' - I class the round turn and the Parbuckle as rope tools not rope knots.

roo

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Re: Knot Forces
« Reply #6 on: August 19, 2008, 04:47:46 PM »
The way i see it, the log takes ma over the cg, as the pulley takes ma over the axle.  both are center of the radius resistance.  Only that resistance is not the load for the pulley rotation, but is the load for the log.  To me the log is wieghtless shell, whose shape gives handles for an exterior force to meet the cg through.


Could you explain in other terms how you think the pulley being rolled up by the rope (see previous N=2 diagram) is different than a log or cylinder being rolled up by the rope?  I'm not understanding "radius resistance".
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TheTreeSpyder

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Re: Knot Forces
« Reply #7 on: August 20, 2008, 10:01:18 AM »
Sorry, i guess i missed something >:(!  The science i was applying, only works if the wheel carries the weight (sprung load) and not if the wheel is the weight (unsprung part of the load).  i've played with'em both doing this kind of thing.  Just as wheel weight on a car or bike is calculated seperately as sprung and unsprung load.

The parbuckle is great, and it still feels like something is missing to understanding it; to me.  i've all ways wondered why it was called a knot, or at least listed with them myself.