Author Topic: fiddling with a Poldo tackle  (Read 17648 times)

struktor

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Re: fiddling with a Poldo tackle
« Reply #30 on: June 12, 2015, 08:04:20 PM »
Hint - static friction  :)

xarax

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Re: fiddling with a Poldo tackle
« Reply #31 on: June 12, 2015, 08:33:28 PM »
   Correct -  but, in your simplification, you have distributed the static friction evenly, in all the four zig-zag points... I believe that the static friction at the two mid-tackle pulleys / tips of the eyes of the loops / mid-zig-zag points, is considerably smaller than at the two end-tackle points - the tensile forces running through the lines there are larger. So, in my simplification, I have placed completely self-balanced mid-tackle pulleys, and unbalanced end-tackle pulleys.
   The role of counter-balancing those unevenly-loaded end-tackle pulleys, and the unevenly loaded lines passing from the two sides of them, is played by the static friction in those points - OR by the "counterbalancing loads", denoted by the purple arrows.
   I believe that, if one tries the Poldo Tackle with minimum friction = bearings in place of the end-tackle pulleys, he will see that the mechanism will not be "locked" by the static friction on the mid-tackle pulleys alone - but it will be locked, if he does the opposite. That will illustrate my point, that it is better to ignore static friction at the mid-tackle zig zag vertices, and concentrate our descriptive efforts in the static friction at the end-tackle zig zag vertices.
« Last Edit: June 13, 2015, 09:33:01 AM by xarax »
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struktor

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Re: fiddling with a Poldo tackle
« Reply #32 on: June 13, 2015, 08:47:32 AM »
My calculation :

xarax

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Re: fiddling with a Poldo tackle
« Reply #33 on: June 13, 2015, 10:36:59 AM »
   I do not understand your calculation...  :-[ :-[
   I see two end-tackle pulleys, the "higher" and the "lower", which, when their axle is loaded with P, due to static friction, they do not rotate freely. Therefore, the tension of the incoming line is reduced by 2T - so the (P/2)+T incoming tension becomes (P/2)-T out-going tension : {(P/2)+T}-2T = P/2-T. So far so good... :)
   Now, we suppose that the two mid-tackle pulleys have the same size and are made from the same material, so the static friction on their axle will have "similar", proportionally, effects. The problem is that the axles of those pulleys are loaded with a smaller load, the (P/2)+T. How much will the tension of the incoming lines in them be reduced ? If the tension of the incoming line is (P/2)-T, what should the tension of the out-going line become ?
   To have the whole tackle in equilibrium, this (P/2)-T should become 2T, as you show in your first sketch.   
   However, this means that the tension on the out-going line will be reduced by (P/2)-3T : {(P/2)-T} - {(P/2)-3T}=2T
   1. When the axles of the (end-tackle) pulleys are loaded by P, and the tension of the incoming lines is (P/2)+T, we have a reduction in the tension of the out-going lines equal to 2T.
   2. When the axles of the (mid-tackle) pulleys are loaded by (P/2)+T, and the tension of the incoming lines is (P/2)-T, we have a reduction in the tension of the out-going lines equal to (P/2)-3T.
    Am I missing some essential property of addition and subtraction here ?  :) :) Where is the catch ?
    I do not understand the supposed "similarity" / proportionality of the 1 and the 2 !   :-[ :-[
   
   ( Mind you that we are talking about static friction, so the difference in the speed the pulleys are revolving plays no role ).   
   
« Last Edit: June 13, 2015, 12:12:59 PM by xarax »
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struktor

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Re: fiddling with a Poldo tackle
« Reply #34 on: June 13, 2015, 09:52:23 PM »
Take a simple test  :)


My Experiment.

Equipment:
Weight  2.1 kG  +  Dynamometer (kitchen scale)


Results:

For Lifting (up)

Weight   2.1 kG
Dynamometer   5 kG

Sum:
5 + 2.1 = 7.1  kG 

Friction force:
T1 = 7.1 / 2  -  2.1 = 1.4     kG
T1 = 5 - 7.1 / 2 = 1.4          kG



For Lowering (down)

Weight   2.1 kG
Dynamometer   1.5 kG

Sum:
1.5 + 2.1 = 3.6  kG

Friction force:
T2 = 3.6 / 2  - 1.5 = 0.3      kG
T2 = 2.1 - 3.6 / 2  = 0.3      kG

P.S.
This is not a Coulomb friction but capstan equation.
https://en.wikipedia.org/wiki/Capstan_equation
« Last Edit: June 13, 2015, 10:30:47 PM by struktor »

knotsaver

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Re: fiddling with a Poldo tackle
« Reply #35 on: June 13, 2015, 09:56:10 PM »
We can transform the original Poldo Tackle, into a "Stabilized Poldo tackle", by adding two "counterbalancing" F loads,
Why, in this "Stabilized Poldo tackle" , isn't the IMA 4:1 ?
I'm missing the point...
(I'm studying the static friction)

   
the self-locking feature ( I consider it the best feature of the tackle ! )

  This "locking" is not achieved with any ingenious trick!  :) ! It is due to friction

The ingenius trick is the use of friction! ;)

xarax

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Re: fiddling with a Poldo tackle
« Reply #36 on: June 13, 2015, 10:55:15 PM »
  Why, in this "Stabilized Poldo tackle", isn't the IMA 4:1 ?

   I am glad that you see you should calculate ( ideal ) mechanical advantages only in ( ideal ) stabilized systems / systems in    With the "kinematic" way you use, you have to find out how much the load moves, when the point P moves, just as you did. However, in the "Stabilized Poldo tackle", "the load" is NOT only the initial load any more ! It is the sum of the initial load equilibrium, where all the individual parts "do not move" = move with uniform, not accelerating speed, plus the "counterbalancing" loads, which play the same role as friction, and stabilize the mechanism. Therefore, you have to calculate how much the centre of mass of all loads is lifted - which changes your initial calculation. I had mentioned it in passing :

... in order to calculate the mechanical advantage, we have just to measure how much the centre of mass of the TOTAL load will move ( the to-be-lifted load, plus the counterbalancing loads ) when a point P from which we drag a line of the tackle moves.

   Static friction will not save you !  :) :) There is friction on the axles, between the parts made from rigid material(s) ( the axles and the disks of the pulleys ), and friction on the rims, between the parts made from rigid and the parts made from flexible material ( the pulleys and the segments off the rope )... Moreover, there is the perhaps not insignificant/negligible elongation of the parts made from the flexible material ( you do not use a chain !  :)), which you should also take account, because it changes the whole geometry - and the differences are not only between the lengths of the segments of the rope before the loading and after the loading, but also during the loading, during the expansion or contraction, because the lengths of the parallel segments, which are not equally tensioned, will not change proportionally to their lengths, and this will generate more friction on the rims, etc... In short, a "real" mess !  :)
    Why, on Earth, you need all that ? Just "see" my first sketch, with the "dynamic" calculation of the mechanical advantage of the original Poldo Tackle, where the ratio of the added forces F to the initial load is 1/4 + 1/4 = 1/2, so the mechanical advantage is a nice round 2 : 1.  :)
« Last Edit: June 14, 2015, 04:38:34 AM by xarax »
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xarax

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Re: fiddling with a Poldo tackle
« Reply #37 on: June 13, 2015, 11:27:27 PM »
    Struktor, I believe you are calling the cavalry !  :)  :)  You add more and more not-"ideal", "real" elements with friction ( the capstan equation... ), but in this way your whole description/explanation becomes less and less convincing !
    You have not explained on what exactly the difference between the tension of the incoming line and the tension of the out-going line you show in your sketch depends ! If it depends on both, the static friction between the axles of the pulleys, on the one hand, and the capstan effect, on the other, as you say now, you have to calculate them ! I want to see why in the one case the difference is 2T, and in the other it is P/2-3T - for starters ( because, as an analysis of a "real" system, you have only started to take into account the possibly dozens of parameters which may alter the whole picture...), I do not need to now the exact value of T !
   And, of course, I am not convinced in the hand-weaving arguments, "decorated" by those "experiments" !  :)  :)  Make a decent, as "ideal" as you can, Poldo Tackle, and measure the static friction on the axles of the pulleys in the two cases ( the more loaded end-tackle pulleys, and the less loaded mid-tackle pulleys ), which prevent them from rotating freely, and the capstan effect, also in the two cases ( when the incoming tension is P/2 -T, and when the incoming tension is P/2 +T ). We want to describe the mechanical advantage if an "ideal", stabilized Poldo tackle - we already KNOW that it is stable  :), we do not know why it is stable !   

P.S. Moreover, sorry, but I do not buy this "capstan effect" thing ! The line goes through the tip of the eye, where it is squeezed by three sides, with different forces : the stiffness of the rope, the amount of "flattening" of the cross sections of the two segments in the area of their contact, even the length of the eyelegs of the loop, and the size of the eyeknot itself ( because the two legs may not be parallel : a line passes much more freely from a wider tip, especially if the rope is stiff ...) are additional factors which aare not taken into account, and which do not have any relation with the calculations of the capstan effect !
« Last Edit: June 13, 2015, 11:41:52 PM by xarax »
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xarax

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The double-line Poldo tackle ( retraced Poldo tackle ).
« Reply #38 on: June 14, 2015, 04:34:28 AM »
   I believe that the title, alone, of this post, should had been enough !  :)  ( We will never understand why we had not understood the whole thing this way right from the very first minute - but, from my personal experience with knots, that is happening too often, so I guess we should better learn to live with it !  :) )
   The double line / retraced Poldo tackle is made from one unknotted closed line : no ends - and no need for any end-of-line loops. It is one loop by itself !  :)
   Obviously, when it is maximally extended, it has 4 parallel segments, and when it is maximally contracted, it has 6 parallel segments. Therefore, if the ropelength of the line is, say, 24L, the length of the tackle goes from 6L to 4L ( so that 4 parallel segments x 6L each = 6 parallel segments x 4L each = 24L ). ( To calculate the mechanical advantage, we should also specify which line(s) we grab. and to which direction we pull it/them ).
   Now, I like to imagine that THIS was the original Poldo tackle:)  :)  Poldo was just playing with a multi-folded closed loop between the fingers of his two hands, and he saw that, this way, he could easily expand and contract it, without removing any sub-loop from any finger - the rest is history. Of course, the idea to use, in those parts of the tackle he could do this, one line instead of two, was clever, too - but I think it was more straightforward...The truly ingenious idea was the multi-folded single loop ( where the single line traces this "endless" zig zag path ), which expands and contracts this way.
« Last Edit: June 14, 2015, 04:37:01 AM by xarax »
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Dan_Lehman

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Re: fiddling with a Poldo tackle
« Reply #39 on: June 14, 2015, 05:55:32 AM »
X, S, & K,
thank you for your patient persistence.
The realization of the not-quite-stable state
of an *untouched* Poldo tackle shook me into
seeing that the simple re-direction pulley (IMA 1:1)
requires much more than the "F" X indicates for
PT stability, so there must be something there.

But it is complex, and we really should have some
simply got actual forces of the structure in use
--for, after all, actual use is the point of a practical knot
or knot structure, not colorful diagrams and equations!

I've found the article about various such structures
--the obvious pulley systems and some of the more
sophisticated ones (Spanish burton & versatackle)--
by Charles Warner, in km023:13-15 (1988-Spring).
He tested systems both in pure rope and with "krabs"
for sheaves --the former showing worse friction.  He
used 11kg weight to be lifted, and measured the
force to raise the weight with a calibrated spring.

His important initial remark is worth echoing:
Quote
From time to time one sees in the knotting literature
(including Knotting Matters) note on rope tackles.  I wonder
if all the authors have ever desperately wanted to shift
a heavy weight and only had a length of rope to help.
Whenever I have had the experience, I have been most
impressed by the enormous friction in all the systems
I have used.  This friction is due not only to one rope
rubbing over the other, but also, and usually most
importantly, the rapid transfer of the sharp 180-degree
bend along the length of the rope.

For the Poldo tackle, he attaches his haul line
to pull downwards on the upper end of the "Z" part.
(Let's call the length that runs through the internal
sheaves "the Z part", in distinction from the rest of
the structure, which runs from end sheaves to the
"axel" --X's term-- or sheave-body (not through but
to) of the internal sheaves.  I.e., Warner loads just
one of the two points indicated by Xarax, to haul
downwards on the structure (as he does for all
of his tested structures --and, yes, which adds
one gratuitous-to-mech.advantage sheave of
friction ; but, yes, is going to be a common need
for lifting (but avoidable if one were just pulling
something horizontally, or hauling upwards/downwards)).

Warner's results for the PT are the worst except for
the simple 1:1 redirection (in rope/krab measurements,
19/15kg vs 23/18kg to raise 11kg).

But one thing I cannot make sense of is Warner's statement
that "Although stated to hold a weight without anchoring,
I did not find this in my conditions." --I can only think that
there's some misunderstanding of this statement or what
he did : for, surely, with the terrible MA tested, this would
be a structure that happily didn't move at all, absent the
(considerable) effort needed to make it move!!

NOW, with the insights given above,
I have taken X's (K's (S's)) indication to attach haul lines
for proper effect to the by-the-anchor-sheaves ends of
the "Z" part, pulling resp. up/downwards as indicated.
NB:  one cannot simply pull X distance from the sheave
for each end-of-this-Z-part, as the top sheave is fixed
in position (the anchor) and the lower one moves
in raising the weight --if one moves the haul lines joined
together, the distance between bottom and the
attached-to-it line will be half that of the other.

>>> With a 10# barbell weight, I found that 10#
attached to joined-together haul lines didn't move
the weight (and this is my slippery structure that DOES
move, with weight alone, slowly expanding the reach)
Adding a 2.5# weight will raise the weight, slowly,
slightly (adding 5# got a quick movement to raise ...).

NB : The re-directional sheave that I used for converting
the upwards pull to downwards --and going downwards,
it was joined to the other haul line so I would weight
a single part and move the two of them in unison--,
was an actual, wide-diameter cheap clothesline(?)
pulley --not high-grade yachting gear, but well
more efficient than a 'biner or another cut-off plastic
bottle neck (used in the system)!

(I would like to see results using substantial materials
--e.g, 8mm rope and decent pulleys, and 50-100# weight!?)

 - - - - - - -

Consider : the Poldo tackle is presented without any
good indication of how to work/use it --i.p., where to
haul, how to haul.  Other MA systems have an obvious
haul line (though their workings might be sophisticated!).
That's part of the problem.  It is also obvious from static
analysis, that the maximum possible movement is not
much --1/3 of the span.

And that's something I'd like to hear Knotsaver explain,
for his using it.  After all, that was part of the OP, that
this structure had proven useful to him (or that he so
believes !).  And I surmise that his use of it is in
the worse condition --rope-through-rope-sheaves.


--dl*
====
« Last Edit: June 14, 2015, 06:18:23 AM by Dan_Lehman »

xarax

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retraced Poldo tackle tied with-a-bight
« Reply #40 on: June 14, 2015, 06:54:41 AM »
   Retraced Poldo tackle tied with-a-bight.
   Just follow the zig zag path of the original Poldo tackle, and tuck the tip of the bight/retracing double line once more, through the "lower" or the "higher" anchor.
   It can be tied in 5 seconds, even by me !  :) ( Alan Lee would need 2...) Climbers who have slippery slings, are kindly requested to try it.
   Of course, with so many contact points, there is no "real" mechanical advantage left ! However, it may be useful to shorten a bridged distance from 6L to 4L. I do not know if ir can be adjusted under load, when it is "tied" on Dynnema...
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xarax

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Re: fiddling with a Poldo tackle
« Reply #41 on: June 14, 2015, 07:16:22 AM »
  much more than the "F" X indicates for PT stability.
  But it is complex,

  Noope. To be stabilized, it requires exactly F + F ( where F=1/4 of the load ) - and it is simple ! Do the math ! ( simple arithmetic...)

  not colourful diagrams and equations !

  Nooo... We need sheets of knotting liter-ature:)   

 
Warner loads just one of the two points indicated by Xarax, to haul downwards on the structure

  His tackle will accelerate in no time !  :) Simple Galilean / Newtonian mechanics, which is almost half a millennium old ! The (vector) sum of ALL forces ( initial and "stabilizing" loads ) should be ZERO ! Elementary !

the Poldo tackle is presented without any good indication of how to work/use it --i.p., where to haul, how to haul.  Other MA systems have an obvious haul line (though their workings might be sophisticated!).
That's part of the problem.  It is also obvious from static analysis, that the maximum possible movement is not much --1/3 of the span.

   Aha ! THAT was your problem !  :) :) :)
   As everybody knows, all pictures show ( as well as the B&W or "colourful" / "decorative" diagrams in this thread  :) ), the Poldo tackle is meant to be attached from the axle of the "higher" pulley ( or from the tips of the corresponding "higher" bights, if we do not use pulleys ), and the load is meant to be attached to the axle of the "lower" pulley ( or from the tips of the "lower" bights ). ALL diagrams in this thread indicate that !
    "1/3 is not much", if and only if the span of the tackle is small ! For a tackle of a span, say, 1.50 meter in its maximum extension, the movement is 0.50 m., which may be useful in securing heavy objects, for example. ( Because I do not believe that the advantage of this tackle is its 2:1 "ideal" mechanical advantage ( which, if we do not use pulleys but loops, becomes negligible...). As knotsaver said, the most interesting feature of this tackle is that it is an adjustable, self-"locking" binder.   

   We have NOT tried to explain/predict the "real" situation, which is very complex, as I had mentioned in my reply to struktor. The task was to calculate the "ideal" MA - however, MA can only be calculated for mechanical systems in equilibrium, which are NOT accelerating ! We "stabilized:" the original Poldo tackle, and then the calculation of the MA of THIS system was a piece of cake !

   My dear Dan Lehman, I am sorry to inform you that, regarding elementary mechanics, at least, your Nobel Prize is stamped with the "bon pour l orienrt" mark !  :) :) :)

    P.S.
    I post again my "colourful" diagram, in the hope that it might be of some help... It is very simple - one has just to remember that the forces are "transported" to the pulleys through the tensioned lines, and that ALL forces, acting on each "free-floating " part of the mechanism / on each pulley, should cancel each other : their (vector) sum should be zero.
   The small arrows represent force F, the longer ones force 2F, and the fat (green) ones, the forces applied on the tackle by the action of the initial load and by the reaction at the high anchor point - represent force 4F. One can easily see how they cancel in each and every part of the mechanism, and on the whole mechanism ! ( so nothing starts to accelerate ! )
   To expand or contract the mechanism, in the "ideal" case, one need not apply any other force ! ! The "ideal" mechanical advantage can only be calculated in this "idea" case, where there is a perfect equilibrium of forces. In the "real" case, however, it can not, because of friction ( which stabilizes the mechanism, but not just so ! there may be HUFGE friction forces, which will require a HUGE amount of additional F forces in order to put the mechanism in motion ).
« Last Edit: June 14, 2015, 12:09:55 PM by xarax »
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xarax

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Retraced Poldo tackle
« Reply #42 on: June 14, 2015, 03:50:49 PM »
  In this double-line / retraced Poldo tackle, we can push or pull the two mid-tackle vertices of the endless zig zag path of the line ( = the tips of the eyes of the loops, in the original tackle ), back and forth - both of them at the same time, or any one of them each time. It is amusing to watch how the tackle expands or contracts - because it is difficult to see how each individual line moves when it slides through the double-line tip af a bight, so all we can do is just to pull the strings, and enjoy the overall spectacle :)
   I believe that it will still be possible to contract it under loading if it is tied on Dyneema, but I am not sure about it. Too many contact areas, of too many lines... However, as a self-locking adjustable binder, it is great !
   ( See the attached picture, for a detail view, when the "lower" zig zag / U turn point has moved upwards a little bit. Do not pay any attention to the bend - I had not a sling, and I do not know how to splice this braided nylon rope... For people who do not understand how the tackle is loaded, I have to say that it is not raining, so the umbrella is closed, and it is hanged by the lower U-turn of the tackle. However, I could well had turned it upside down - or hang the tackle itself from the handle of the umbrella, when it will start raining.  :) )
   Now, there is yet another problem of nomenclature here ! How can we call a knot like this, which can be tied with-a-bight, on/within a closed loop, a sling ?  :) Some proper alphabet soup pieces would be much welcomed... :)
« Last Edit: June 14, 2015, 03:58:45 PM by xarax »
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Dan_Lehman

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Re: fiddling with a Poldo tackle
« Reply #43 on: June 14, 2015, 05:44:27 PM »
Warner loads just one of the two points indicated by Xarax, to haul downwards on the structure

  His tackle will accelerate in no time !  :) Simple Galilean / Newtonian mechanics, which is almost half a millennium old ! The (vector) sum of ALL forces ( initial and "stabilizing" loads ) should be ZERO ! Elementary !
Somehow you manage to read poorly : his tackle
took considerably more force to raise the weight than
most other systems --only the 1:1 re-direction was worse.

Quote
the Poldo tackle is presented without any good indication of how to work/use it --i.p., where to haul, how to haul.  Other MA systems have an obvious haul line (though their workings might be sophisticated!).
That's part of the problem.  It is also obvious from static analysis, that the maximum possible movement is not much --1/3 of the span.

   Aha ! THAT was your problem !  :) :) :)
   As everybody knows, all pictures show ( as well as the B&W or "colourful" /
"decorative" diagrams in this thread  :) ), the Poldo tackle is meant to be attached
from the axle of the "higher" pulley
( or from the tips of the corresponding "higher" bights,
if we do not use pulleys ), and the load is meant to be attached to the axle of the "lower" pulley
( or from the tips of the "lower" bights ). ALL diagrams in this thread indicate that !
//
   I post again my "colourful" diagram, in the hope that it might be of some help...
It is very simple
And it very simply has no " 'higher' pulley " [sic] but is
oriented for lateral/horizontal force.  Not only that, but
it has no hint of there being an "anchorage" side vs. a
"weight/load" side; no, it appears as though it might work
on both sides (not "higher"/"lower" things) moving,
which is another can of worms to address.  Thank you for
trying soooo hard to find the most innocuous thing "wrong"
in my post and going to silly extremes of mis-reading my
"literature" [sic], and misrepresenting even your own imagery.

Quote
"1/3 is not much", if and only if the span of the tackle is small ! For a tackle of a span, say, 1.50 meter in its maximum extension, the movement is 0.50 m., which may be useful in securing heavy objects, for example. ( Because I do not believe that the advantage of this tackle is its 2:1 "ideal" mechanical advantage ( which, if we do not use pulleys but loops, becomes negligible...). As knotsaver said, the most interesting feature of this tackle is that it is an adjustable, self-"locking" binder.   
It is hardly so interesting if this adjustability
covers an inadequate range, and requires
considerable and awkwardly applied force to
achieve any movement!  (My testing reported
in the above post is with a system that is found
to have uncommonly good movement, low
friction (plastic-bottle sheaves and a hard-slick
cord); now, what sort of practical application
does one have for this tensioner?  --gotta be
one in which one's available force is relatively
Paul-Bunyan-sized (overpowering to resistance)!

Quote
We have NOT tried to explain/predict the "real" situation, which is very complex,
as I had mentioned in my reply to Struktor.
Maybe this is results from this thread being in
Chit-Chat vs. Practical knotting?  Well, *I* have
tried to present the practical aspects of the PT.


--dl*
====

Dan_Lehman

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Re: fiddling with a Poldo tackle
« Reply #44 on: June 14, 2015, 06:02:38 PM »
NOW, with the insights given above,
I have taken X's (K's (S's)) indication to attach haul lines
for proper effect to the by-the-anchor-sheaves ends of
the "Z" part, pulling resp. up/downwards as indicated.
...
Today, I made some measurements : when loading
via a single haul line that joins the two above (pulling
upwards via a pulley redirection on the lower poing),
I see that the upper internal sheave has NO movement
--everything happens elsewhere--, and from a fully
extended length of 70cm the structure contracts only
to the point where the pulled-upwards internal sheave
abuts the top sheave (at which point the haul-line
attachment point for the other internal sheave's
"Z" part is abutting the lower internal sheave.
The length of it all, end-2-end, is now ~56cm
--where ~47cm would be the ideal full contraction.

(I have just loaded the system with more weight
and pressed upon that to get non-locking expansion,
and here, too, I see that the upper internal sheave
has no movement --it happens elsewhere.)

This means (as foreseen) that in order to achieve
some ideal (?) equal movement to the fully contracted
state, one must move faster the hauling of
the upper internal sheave's "Z" part, and so this cannot
be achieved with a haul line that joins the two.

In using my hands on this moderately weights (15# now)
system, I feel no obvious indication to change pressure
on either haul point, but need to do so in order to get
even contraction for maximum lift --varying force gets
one varied movements/non-movement (at internal
sheaves).


--dl*
====