Condensed Mayhem

[TheTreeSpyder]

From something i noticed playing and drawing forces, i present this seemingly puzzle, that i presented in Talking at HS about Arboriculture , that ran into more depth in Olde Pulling Strategy Thread .

This is meant to be a slippery load of 100#, hung from a single line, turned on the load a certain way. It asks what is the pressure at the turn.

 

[TheTreeSpyder]

i think that i have tried to show rigging applications of this helpful principal; that this illustrates.

This is the best description of why that came out in the discussions:

Originally posted by Tim Gardner
Ken are you trying to illustrate a reversed single whip where the pull is coming from the weight itself?

i think this is easiest solution of what i try to show is in this pic; the tension at the curve is 2x the load in this free hanging piece, because:

 

[Tim Gardner]

I believe the power would be 1/2x at the foam or crotch. If you look at a reversed single whip the leg that is pulled on only requires 1/2x the weight of the load to lift. If the load were applying 2x the weight on the pulley (foam or crotch) then it would require 2x the power to lift the load.

I posted this in the other thread but it goes here I guess.

 

[TheTreeSpyder]

Tim i think that anchor marked 1/2couldn't be to the load itself, it would have to be to a seperate anchor, then each seperate anchor would hold each 1/2 load; to match each other through pulley. Here, on a single leg, the line tension is 100/full load, for the load is borne on a single support. The weight of the load is the power for the system, like in rigging etc. i think.


The load divided by the amount of supports will give the line tension; both of the rest of the 2 examples are the same. If you grabbed a hold of the upsidedown slingshot and pulled down, you would pull down 2' for every 1' of foam compressed, as the support and the anchor line would both have to be shortened seperately to the equivalent of the decrease in foam height.

 

[glens]

Answers to questions asked in image:

A)&nbsp; The total load would be 100 pounds, so the <i>pressure</i> would be 100 pounds divided by the surface area of the rope in contact with it and bearing weight, and in our system of measurement, normalized to PSI.

B)&nbsp; The pressure is not affected until the wraps are so tight, in conjunction with friction between them and the vertical line, that the interface (between wraps and line) itself will carry the load in any way.&nbsp; Though it's possible, if nothing else, the wraps will prevent the load from rolling quite so much at the top towards us in the left image and away in the right (as it certainly would, being asymmetrically supported), so the total contact area of the weight with the line may differ somewhat, thus altering the pressure slightly.

C)&nbsp; No appreciable difference from "B" except to the extent the surface aids in the f(r)ictionial holding power of the interface.

 

[TheTreeSpyder]

My Spyder Sense was Tingling......

i really don't know why the travel of line to foam compression distance would not be the pruf;

Here is a run of pix of this setup with fish scales, showing the compounding effect that i have tried to express in the different threads like Leg on Load Description and Using Self Tightening Tourque etc.

It has been a long road sniffing these things out and naming them; to command them more purposefully. This puzzle was something that kept banging in my head that must be true; i have proposed it to many people over the years; and in spans of time let them convince me different.

i still say the power is easily there, and even furthermore usable to target, which also carries the promise that it could somehow be used against ya inadvertantly because you couldn't see the pattern. Costing possibly more than a stretched fish scale and an eye hook...

i guess i should have done the scale thing a while ago, but i have enjoyed the growth from the mental exercise of drawing it in my head too. And, when i sat down and really thought about it; i din't have to buy no scales!

Orrrrrrrrrrrrrrrr something like that!
:alien: :alien: :alien:

 

[glens]

Ken,

Thanks for buying the scales and setting up the demonstration.&nbsp; You've successfully proven the leverage available when lifting a load using a pulley.

Now you need to find a way to set it up to measure what you have in your upside-down, single-hung slingshot example.&nbsp; Your sketched example in that last image (and several previously) is <i>not</i> the same as what you're measuring with the ropes, pulley, weight, and rake handle in the photos.

I'll try to "sketch" up a little something for you to be able to see what I'm saying.&nbsp; Should have it between now and this time tomorrow, okay?

Glen

 

[glens]

Okay, here's the image:

<img src="http://www.arboristsite.com/attachment.php?postid=169731">

Glen

 

[TheTreeSpyder]

Mayhem in my mind, test setup. In my laced rigs, when using an arc-ed line on the load for an effect, i have to be carefull where i place the hitch more. The loss of power by the friction at the turn is made up by using the same friction for me, by sweating out a leveraged purchase of line from that position prior to cutting/loading. In this way the bend, position C's loading is high as possible, by still being the sum of both legs of line to it.

 

[Tim Gardner]

Ken, considering you did state zero friction where the rope runs through the crotch of your slingshot I see a pulley as an acceptable substitute in your test. It appears as though you have proven your argument true and mine, as well as many others, incorrect. Well done. I still plan on confirming your results myself because until I see it with my own eyes I do not believe the 2x is there. This is a good example that what a person believes and the truth can be two different things.

Dang it hurt to write that.

 

[glens]

I still don't believe it because what he's doing is different than what he's doing, if you catch my drift (he's essentially saying "look, 29 = 30").&nbsp; We do not have a situation where a load is being carried by two points separate from the load and sharing the burden.&nbsp; One of his points is the load itself <i>and the clevis of the "pulley" in his photograph should be firmly fastened to the broom handle</i> in order to rightfully simulate the actual condition present in his inverted "slingshot" sketch!&nbsp; He could then preset the lower scale anywhere between zero and the limit of the ropes/broomstick and it would hold that setting.

The reason leverage (beyond 1:1) exists in an <i>actual</i> pulley setup similar to this is because the take-up produces a fixed reduction in speed of load movement, relative to that take-up speed, when the load is shared between two points distinct from the load itself.&nbsp; Discounting relative rope movement due to initial slack takeup and stretch, the rate of load movement in the non-pullied "slingshot" (or any situation where a sole pulley is being used with one end of the rope fastened directly to the clevis itself, which is the equivalent) arrangement is a 1:1 ratio of rope movement to load movement with no load "sharing".

Ken's recent photographic example is interesting, but does not correlate to the original sketched situation!

Someone please explain why the questions in <i>my</i> "sketch" are not rhetorical.&nbsp; How does load help to carry itself?

Glen

 

[TheTreeSpyder]

Glens, what i'm saying is that the pattern of the convenant of the arc power is so prevalent, that it even exists where it seems impossible. The whole idea, was to see it even here in this exercise, so as to catch it's fleeting pattern in more rigs/possible rigs.

Originally posted by Tim Gardner
Dang it hurt to write that.

i know the feeling JP has been right more than once and that really goes hard wit'me!.... And Brian as well... Then there is that dang pesky Bombazz, Stumpie, SRT(SingleRopeTom),NE-RB etc.

If ya try this, watch out as the pulley becomes the pivot of the broomstick, and the hitch point equal to the load; as the hitch gets farther from the pivot point, it can gain more leverage than the load, especially with the slightest tilt; the force is that apparent. Without scales, just watching quietly on your loading positions, a climber's eyes should be able to see the double loading event on the pulley position i think. Especially when the attatchment points are in range to show the loading on them, like weaker line, bungee etc. Playing with power, care should be taken.

Once again i think this would be a good simple, child's game, to teach these things whilst still believeing in magic, and minds more open to the material. That is why i thought the conceptualization would be good for the HS talk by AxMan as an example of the understanding of powers of a bent line etc. And that immediate disbeleif that can be set aside; giving kinda a mesmerizing, mind opening introduction for the rest of the material of the tree lessons. The hook to grab, like any other advertising for a cause.

Originally posted by glens
How does load help to carry itself?

By setting the equal and opposite reactions to it's force.

 

[Tim Gardner]

Ken, to make sure that I am on the same “page” as you are, does my attached drawing accurately represent your test apparatus? If so, your results indicate that Scale B has 2 times the load that Scale A does. Right?

Assuming that your slingshot and test apparatus weigh the same, there is zero friction at the pulley and crotch, the radius of the pulley and crotch were the same, would the load at the pulley equal the load at the crotch of your slingshot? If it does then I think your test apparatus represents your slingshot.

 

[TheTreeSpyder]

That is fair, only i tried to stay more in line with the stick.

i think per loading, with no pulley, a slick line prusik alone or with metal should suffice for pulley position in all slik line example.

In your pic, instead of foam under the line, lets put a bungee as the pulley mount. The load will dorp 2x as faar as the pulley moves?

Or soemthing like that
:alien:

 

[glens]

"Or soemthing like that"?&nbsp; More like "Or nothing like that"!&nbsp; You're certainly proving <i>something</i> but it's decidedly not what you're claiming it is.

Why can't you guys see that's not the same thing as if "Scale B" (a spring!) were replaced with an immovable link?&nbsp; So long as the pulley can move relative to the two points in the manner which it's attached to the stick allows, you will obtain the results you're so excited about.&nbsp; But as soon as you replace the spring with a solid link, you'll have exactly the same result as if you'd simply passed the rope around the sheave and tied it to itself.&nbsp; It's like you're comparing a compound bow to a recurve bow or something.&nbsp; I wish I could figure out a way to get you to understand that you're proclaiming bad science!&nbsp; I like you guys but this is getting a little exasperating.

How does your test setup differ from your inverted slingshot example?&nbsp; In the test setup you're freeing up the pulley to movement and working it against a spring, the only purpose and use of which is to indicate the force on that spring.&nbsp; Force which does not exist otherwise and only appears for non-usable reasons in this academic(?) exercise.

You say you must be very careful with your hitch locations in the test setup due to the instability.&nbsp; Is that same care required when the lower scale is replaced by a fixed link?&nbsp; Try it and report back.

Glen

 

[Tim Gardner]

So, as long as the pulley does not move then the amount of pull (or whatever the proper term is) on its connecting link will equal the pull on the portion of the rope supporting the test setup? Once the pulley has stopped moving the force applied to it is reduced by half?

 

[TheTreeSpyder]

i guess i can try that, but i don't think that the force comes or goes cuz it knows if ya got a scale; i think more logically there is force or there is not.

 

[Stumper]

No Ken, I think Glen has pinpointed the reason for your results-The spring scale allows the pulley to move creating a "runner" which give a 2/1 because both legs get to bear the load. If you anchor the pulley and the rope to the object being lifted then the tag line MUST bear the whole thing. Even with the spring scale creating a little run for the pulley I'm surprised that you get a 2/1 to show up with it all tied to the host line. As a matter of curiosity-did you weigh the apparatus? I wonder if the results were accurate in the test.:angel:

 

[glens]

I just passed a bunch of pertinent gas in the "Leg on Load" thread.&nbsp; See it if you haven't already.&nbsp; My head hurts and it hasn't had enough Bitburger.

Glen

 

[TheTreeSpyder]

Being as there is no friction between the support and the hitchpoint, it is as if one leg loaded the same. Bending that leg around a frictinoless pulley, maintains the pressure in both now shorter legs. At zero degrees/parallel no deflection of force, the pulley must carry the full force of both legs.

Done just with the throwline as mounts on broomstick, or even as the pulley if slick line is to be used for support too; expereinced eyes and fingers should both see extra tension at the arched position.

The first picture in the pix with fish scales was to verify scales read about the same; by hooking them in series and placing the weight of the broomstick and 066 powerhead assembly to be tested as the weight to test scales set to same accuracy. That is why the pointer is in the same position there as in positions A + B during the test.

The reason some of the posts applying this go back a couple of years is that i have been playing with and witnessing this effect for years.

If rigged in Leg on Load configuration (as puzzle), Nature does not care whether the puzzle is planted into the ground upside down like a regular "Y" and tension the line to 100#, whether you turn puzzle 90 degrees, tie rope to tree and pull load till line tensions to 100#, or if you turn puzzle another 90 and hang from line and the puzzles own weight tensions the line to 100# etc. Nature just commands that if the line is tensioned to 100#, the arc in puzzle is loaded 2x. The secret is there is no secret, all the examples are the same; 'exaclty the same but different'

The loaded arc of less than 120 degrees must carry more than the line tension, every time. For the same reason that accidents happen, physics takes no holidays and can be conjured up instantly by how the rope calls it. We can't stop it, might as well use it.