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majid_sabet


Sep 22, 2009, 1:58 PM
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calculating friction over the edge
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So let say you are pulling a 100 KG pig off the wall and for every 1 KG of weight on a true vertical situation, you are actually required 1 KG of force but then you get to the top, find a tree and redirect your pull and begin hauling where you are no longer on a true vertical and got this 75 degree edge.

Obviously, the type of rope, type of rock , the surface area, the load itself and .....whatever effect the friction amount which directly effects your pulling force but is there way to calculate this ?

can we just use a 0.5 efficiency as a rule of thumb meaning for 1 KG of pig load, we are using 1.5 KG of hauling force ?


hafilax


Sep 22, 2009, 2:21 PM
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I'm afraid to ask, but a diagram might clear things up (no tires please).


trenchdigger


Sep 22, 2009, 2:31 PM
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http://www.jrre.org/att_frict.pdf


majid_sabet


Sep 22, 2009, 2:46 PM
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That is exactly what I was looking for amigo

Thanks


wjca


Sep 22, 2009, 2:53 PM
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hafilax wrote:
I'm afraid to ask, but a diagram might clear things up (no tires please).

Be careful what you ask for, you just might get it.


adatesman


Sep 22, 2009, 2:54 PM
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trenchdigger


Sep 22, 2009, 3:22 PM
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adatesman wrote:
Excellent link, Trenchdigger!

BTW, I've kicked this thread over to The Lab...

-a.

Yah, nice paper, eh? I dug that one up a while back when I was building a spreadsheet to compare multi-loop anchor strength to wrap-3 pull-2 (or others). Some interesting conclusions were that wrap-2 pull-1 anchors were generally weaker than the two-loop option, a 3-loop is just about as strong as a wrap-3 pull-2, and that you can significantly weaken a multi-loop anchor point by beginning with the loops of uneven size (especially with the knotted loop smaller than the rest).


petsfed


Sep 22, 2009, 3:32 PM
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majid_sabet wrote:
So let say you are pulling a 100 KG pig off the wall and for every 1 KG of weight on a true vertical situation, you are actually required 1 KG of force but then you get to the top, find a tree and redirect your pull and begin hauling where you are no longer on a true vertical and got this 75 degree edge.

Obviously, the type of rope, type of rock , the surface area, the load itself and .....whatever effect the friction amount which directly effects your pulling force but is there way to calculate this ?

can we just use a 0.5 efficiency as a rule of thumb meaning for 1 KG of pig load, we are using 1.5 KG of hauling force ?

Can we use measures of force when we talk about force, and not measures of mass? It confuses the physicists.

I've always used u as the coefficient of static friction, where the speed is low enough that friction is pretty linear with force. That's how I was taught.

Similarly, most people are taught that the efficiency n is some number less than one that indicates the fraction of work put in that actually does work in the system.

So an n of .9 means that 90% of your input energy goes into moving the pig up the wall, and 10% is lost to heat, friction, spelling errors, and masturbating.


trenchdigger


Sep 22, 2009, 4:03 PM
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petsfed wrote:
Can we use measures of force when we talk about force, and not measures of mass? It confuses the physicists.

I've always used u as the coefficient of static friction, where the speed is low enough that friction is pretty linear with force. That's how I was taught.
Well if we're going to be anal, it should be "ĩ" not "u". And kinetic (moving) friction would be and static .

"... friction linear with force."? Not sure what you mean by that. Friction isforce. Do you mean linear with normal force maybe? Then yes... they are directly proportional. The coefficient of friction (as generalized by Coulomb's model) is not linear with velocity, it is a step function with one value at v=0 and another, generally smaller value for non-zero velocity. The coefficient of friction of a material will generally vary, sometimes dramatically with temperature, speed, etc.


petsfed


Sep 22, 2009, 5:00 PM
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trenchdigger wrote:
petsfed wrote:
Can we use measures of force when we talk about force, and not measures of mass? It confuses the physicists.

I've always used u as the coefficient of static friction, where the speed is low enough that friction is pretty linear with force. That's how I was taught.
Well if we're going to be anal, it should be "ĩ" not "u". And kinetic (moving) friction would be [image]http://upload.wikimedia.org/math/3/a/d/3ad4fa5a7787192d8cbb5f69d33d05cc.png[/image] and static [image]http://upload.wikimedia.org/math/a/6/4/a643b93335c0aaf422a24480e3435257.png[/image].

"... friction linear with force."? Not sure what you mean by that. Friction isforce. Do you mean linear with normal force maybe? Then yes... they are directly proportional. The coefficient of friction (as generalized by Coulomb's model) is not linear with velocity, it is a step function with one value at v=0 and another, generally smaller value for non-zero velocity. The coefficient of friction of a material will generally vary, sometimes dramatically with temperature, speed, etc.

I played a bit fast and loose with terminology there, didn't I?

I should've clarified. Resistance is typically a higher order term, but for the low speed case across a solid, resistance is well approximated by the coefficient times the normal force.


adatesman


Sep 22, 2009, 5:09 PM
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majid_sabet


Sep 22, 2009, 7:38 PM
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adatesman wrote:
trenchdigger wrote:
...to compare multi-loop anchor strength to wrap-3 pull-2 (or others).

Wrap-3 pull-2? Never heard the term, but assume it is obvious once you know what it is?

Nevermind... Apparently I need to reread FotH again as I'm forgetting things:
[image]http://mazamas.org/images/uploads/wrap3_thumb.jpg[/image]

let me make it clear




JimTitt


Sep 23, 2009, 11:08 AM
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While Attaways work is interesting it doesnīt tell the whole story, in fact slightly less than half. In the examples he uses the friction effect is the lesser one, the rope bending force being higher.
The frictionless abseil device on my desk is living proof!

Also you should note he uses an abitrary figure for the coefficient of friction.
The static coefficient for nylon varies (decreases) with pressure in a not-quite linear way. The dynamic coefficient varies wildly with velocity (by a factor of 4 or 5) at the speeds we are using and great care has to be used in applying this.

In answer to the OP: the best thing is make a few set-ups and test them. Simple rope/krab pulley system efficiencies have been done by the slackliners.
Jim


snoboy


Sep 23, 2009, 12:14 PM
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Life On a Line has a pretty extensive discussion of friction...

T. Moyer has a brief presentation on rescue physics with some discussion of friction at http://www.xmission.com/~tmoyer/testing/


(This post was edited by snoboy on Sep 24, 2009, 12:28 PM)


adatesman


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majid_sabet


Sep 23, 2009, 12:40 PM
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Alright, this thing got little bigger than I thought which encouraged me to add more ingredients to the original topic and that is " Amonton’s law" and whether this law is also a key factor in my original question.

Amonton’s law from Wiki

Amonton's Law of Friction is a very simple concept, first logged on the books in the late 17th century by Guilliame Amonton. (Incidentally, it was first discovered by Leonardo da Vinci, but never popularised until later.) It states, simply put, that the amount of force needed to overcome friction between two surfaces only depends on the types of surfaces being pushed together and the amount of force pressing them together. The actual surface of contact between the two surfaces is not related to the friction force at all; large, small, whatever, you have a two types of surfaces (expressed in a coefficient) and the amount of force between the two. Size Doesn't Matter.
This law was proven and proven again and again in experiments and taught up until the 1930s in physics classes. But then, people came to their senses.
Chances are, the surface you are considering, any surface, in fact, is not perfectly flat. There are many millions of imperfections, crags, teeth and ridges, all smaller than the eye can see or the skin can feel. And when two surfaces come into contact, these tiny geographies will not match up correctly. The mountains on one side will not fit into the valleys on the other. The actual surface of contact is much smaller than what you may think. So the force needed to overcome friction is indeed proportional to the contact area - measured accurately.
This does not erase the usefulness of Amonton's Law. The equation still stands, even though the explanation behind it does not. Any engineer involved in studies of storm and stress (structural engineers, seismologists, etc.) has used Amonton's Law to quickly and accurately approximate friction forces.
Amonton's Law has also been shown to break down in various nanometric scenarios, such as when two surfaces get close enough so that molecular interactions and atomic forces come into play, sometimes attracting the two surfaces together and creating what's known as 'negative load'.


trenchdigger


Sep 23, 2009, 1:57 PM
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JimTitt wrote:
While Attaways work is interesting it doesnīt tell the whole story, in fact slightly less than half. In the examples he uses the friction effect is the lesser one, the rope bending force being higher.
The frictionless abseil device on my desk is living proof!

Also you should note he uses an abitrary figure for the coefficient of friction.
The static coefficient for nylon varies (decreases) with pressure in a not-quite linear way. The dynamic coefficient varies wildly with velocity (by a factor of 4 or 5) at the speeds we are using and great care has to be used in applying this.

In answer to the OP: the best thing is make a few set-ups and test them. Simple rope/krab pulley system efficiencies have been done by the slackliners.
Jim

While I would agree that other factors are involved in generating resistance in a system involving a rope running over a rock edge, I would argue that the majority of that resistance is going to be due to nylon-on-rock friction and NOT due to rope bending force. The radii of the bends involved will not be small enough to generate significant rope bending forces relative to the forces generated by nylon rubbing on rough rock. Where are you getting your figures that state the coefficient of dynamic friction varies by a factor of 4 or 5 at the speeds we're talking about (let's say <2m/s)?

I believe you when you say there's more to this story, but your statistics seem a bit out of whack.


JimTitt


Sep 24, 2009, 12:59 AM
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Amontonīs law is still a useful approximation for some things but it is nescessary to know the coefficient of friction, sadly this does vary for any two pairs of materials depending on quite a few factors.
The header on nearly all tables of friction coefficients have a note to the effect that the values given are a generalisation and should be confirmed experimentally.

Unfortunately the various ASTM tests are designed for industrial applications and usually are not suitable for our purposes.

For materials like metals and rock the variation isnīt so drastic but a lot of materials behave in a different way, polymers being particularly difficult. At higher pressures and speeds they are better considered as semi-fluids, the reasons for this are shockingly complicated and not yet fully understood.

If you take a quick look at http://www.jrre.org/mechanics.pdf (which incidentally is exactly what you wanted to know in your original post but I forgot about it) you see that the experimental results vary considerably from the predicted ones. Fortunately for Mannings purposes which was rescue hauling over rock edges the predicted values where generally the highest giving a reasonable safety margin for real-life situations.
The deviation between theoretical and experimental results are down to applying an incorrect coefficient, even though Manning spent a lot of time and effort experimentally verifying it on various surfaces.

That the coefficient varies a lot is quite clear, for nylon/aluminium Manning obtained by testing 0.7 whereas Attaway uses 0.25, other sources give 0.16. All these are correct and a lot of other values as well!

On a practical level this has serious implications. Take for example Attaways figure of 8 analysis which gives a holding power of 10:1 to 15:1 (and you can verify this experimentally at your local cliff). Set up a free hanging abseil with a free-hanging 50m rope weighing 5kg, according to his figures a climber of 50 to 75kg can let go of the rope and will not plummet to his death. Using Mannings coefficient the climber can weigh 140 to 210 kg before appearing in the accidents forum.
I think most of us will accept this is not the case!

In reply to Trenchdigger:
As you say, the radius of the edge will make a lot of difference but also so does the load, at what point the friction is greater than the bending effect is very hard to say, sadly because Manning didnīt consider the bending effect he didnīt include various radii in his tests.

There is peer reviewed research confirming that between 0 and 3m/s the coefficient of friction of nylon can have values varying between 0.7 and 0.1. I have also done experiments varying both pressure and velocity to confirm this.
When the current project I am working on is completed I will probably publish the results, until then you can either believe me or not.

Aric
A rack was the easiest way to make an abseil device and fit the rope in. In itīs final version I used two needle roller bearings one inside the other to get the bearing friction as low as practible but this put the radius up too much, by the end this one had 12 bars which was 48 bearings! 8mm OD bearings were great with 6 or 8 rollers needed depending on the rope but a totally useless and impractical device!
Sadly I havenīt any photos of this and I had to give the borrowed bearings back ( but Iīve got a frictionless belay plate somewhere which Iīll dig out.

Gotta do some real work now!

Jim


majid_sabet


Sep 24, 2009, 9:43 AM
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JimTitt wrote:
Amontonīs law is still a useful approximation for some things but it is nescessary to know the coefficient of friction, sadly this does vary for any two pairs of materials depending on quite a few factors.
The header on nearly all tables of friction coefficients have a note to the effect that the values given are a generalisation and should be confirmed experimentally.

Unfortunately the various ASTM tests are designed for industrial applications and usually are not suitable for our purposes.

For materials like metals and rock the variation isnīt so drastic but a lot of materials behave in a different way, polymers being particularly difficult. At higher pressures and speeds they are better considered as semi-fluids, the reasons for this are shockingly complicated and not yet fully understood.

If you take a quick look at http://www.jrre.org/mechanics.pdf (which incidentally is exactly what you wanted to know in your original post but I forgot about it) you see that the experimental results vary considerably from the predicted ones. Fortunately for Mannings purposes which was rescue hauling over rock edges the predicted values where generally the highest giving a reasonable safety margin for real-life situations.
The deviation between theoretical and experimental results are down to applying an incorrect coefficient, even though Manning spent a lot of time and effort experimentally verifying it on various surfaces.

That the coefficient varies a lot is quite clear, for nylon/aluminium Manning obtained by testing 0.7 whereas Attaway uses 0.25, other sources give 0.16. All these are correct and a lot of other values as well!

On a practical level this has serious implications. Take for example Attaways figure of 8 analysis which gives a holding power of 10:1 to 15:1 (and you can verify this experimentally at your local cliff).
In reply to:
Set up a free hanging abseil with a free-hanging 50m rope weighing 5kg, according to his figures a climber of 50 to 75kg can let go of the rope and will not plummet to his death. Using Mannings coefficient the climber can weigh 140 to 210 kg before appearing in the accidents forum.
I think most of us will accept this is not the case!

In reply to Trenchdigger:
As you say, the radius of the edge will make a lot of difference but also so does the load, at what point the friction is greater than the bending effect is very hard to say, sadly because Manning didnīt consider the bending effect he didnīt include various radii in his tests.

There is peer reviewed research confirming that between 0 and 3m/s the coefficient of friction of nylon can have values varying between 0.7 and 0.1. I have also done experiments varying both pressure and velocity to confirm this.
When the current project I am working on is completed I will probably publish the results, until then you can either believe me or not.

Aric
A rack was the easiest way to make an abseil device and fit the rope in. In itīs final version I used two needle roller bearings one inside the other to get the bearing friction as low as practible but this put the radius up too much, by the end this one had 12 bars which was 48 bearings! 8mm OD bearings were great with 6 or 8 rollers needed depending on the rope but a totally useless and impractical device!
Sadly I havenīt any photos of this and I had to give the borrowed bearings back ( but Iīve got a frictionless belay plate somewhere which Iīll dig out.

Gotta do some real work now!

Jim

I have done a 600 footer on a solid 11 m rope on a true vertical via fig 8 and I could not rap on my own. I had to feed force the rope in to 8 to rap however, once I was near the last 100 feet or so where, I began controlling the descent .


trenchdigger


Sep 24, 2009, 9:53 AM
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JimTitt wrote:
For materials like metals and rock the variation isnīt so drastic but a lot of materials behave in a different way, polymers being particularly difficult. At higher pressures and speeds they are better considered as semi-fluids, the reasons for this are shockingly complicated and not yet fully understood.
...
That the coefficient varies a lot is quite clear, for nylon/aluminium Manning obtained by testing 0.7 whereas Attaway uses 0.25, other sources give 0.16. All these are correct and a lot of other values as well!
...
There is peer reviewed research confirming that between 0 and 3m/s the coefficient of friction of nylon can have values varying between 0.7 and 0.1. I have also done experiments varying both pressure and velocity to confirm this.
When the current project I am working on is completed I will probably publish the results, until then you can either believe me or not.
...

Thanks for the reply, Jim! I'm not sure it's appropriate to compare rope-on-aluminum friction to rope-on-rock friction. The texture of the rock makes these situations very different. I think it's important to point that out. While I would agree there would be a large difference in the coefficients of static and dynamic friction, I still find it hard to believe that there can be a seven-fold difference in the coefficient of dynamic friction with velocities under 3m/s with all other variables kept constant. Where do your experiment results get published?


JimTitt


Sep 24, 2009, 10:38 AM
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Not sure I quite get the first bit! The texture of the rock has very little to do with how polymers react under load and also very little to do with the coefficient of friction. The link I gave above (which I forgot to "clicky" gives the coefficients Manning measured for various rock types and other materials.
Unfortunately he was concerned with the maximum loads when hauling so obtained static coefficients which is logical but it was a shame he didinīt do dynamic as well!

Iīll be giving a lecture on friction at the next BMC Technical conference (Nov 2010) but what gets included is a question of whether the information could be useful for commercial purposes-all the best information is secret until paid for!

Jim


trenchdigger


Sep 24, 2009, 11:31 AM
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JimTitt wrote:
Not sure I quite get the first bit! The texture of the rock has very little to do with how polymers react under load and also very little to do with the coefficient of friction.

I would beg to differ... "rough" friction is very different than "smooth" friction. With "rough" friction, other forces are contribute to the "friction" as rope fibers catch on the rock, etc. For example, "rough" friction with rope on rough rock will be partially dependent on the weave of the rope. For two ropes produced from the same polymer, one weave will exhibit different friction properties than another weave since one may result in more fibers catching on the rock features than others. True, these forces are not really "friction" per se, but in the experiments we're talking about, these forces get lumped into "friction" and consequently the calculated coefficient of friction.


JimTitt


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Unless the material is physically catching on the surface your rope and destroying it in the process then this is not the case.
This set of tested static coefficients of the following materials certainly donīt seem to display any noticeable `roughnessīeffect.

Nylon rope against:-
Sandstone 0.6-0.9
Limestone 0.5-0.9
Granite 0.5-0.9
Stainless steel 0.7
Galvanized steel 0.6
Aluminum 0.7


petsfed


Sep 24, 2009, 2:37 PM
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JimTitt wrote:
Unless the material is physically catching on the surface your rope and destroying it in the process then this is not the case.
This set of tested static coefficients of the following materials certainly donīt seem to display any noticeable `roughnessīeffect.

Nylon rope against:-
Sandstone 0.6-0.9
Limestone 0.5-0.9
Granite 0.5-0.9
Stainless steel 0.7
Galvanized steel 0.6
Aluminum 0.7

Point of order:
Are those numbers based on a prepared sample, or a real world example?

Really crystally granite or limestone will catch on rope a lot more than water polished granite or sandstone.


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