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Analysis: Pulley Efficiency, Base Systems and Their Relationship
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By 20 kN
Administrator
From Hawaii
Dec 19, 2012
I wrote this article for a different website, a slacklining website, but I figured there is some information in here that may be interesting to some so here it goes.

Introduction

Every moving component in a slackline tensioning system provides some mechanical resistance by friction. Pulley axles provide friction at the sheave connection point. Ropes create friction when they are forced to bend over a sheave. Mechanical brakes such as a GriGri will create friction when the rope is run through it. There are two ways to overcome this friction and add tension to your line: use more efficient equipment and increase the mechanical advantage of your pulley system. We will compare and contrast individual pulleys and their effect on total system performance. We will also discuss the fundamentals of what limits a tensioning system’s performance and how to overcome these limitations.

Experimental Platform and Error Rate

The testing platform consists of a 110’ of Mantra MKII webbing terminated to a variable base system interchanged between a 5:1, 6:1 and a 7:1 throughout the test (I will let you know when I change it). I chose a longer line because short lines provide less repeatability in testing results. A line of this length is sufficiently long enough to allow for a repeatability value of +/-20lbf for short-term retests (60sec) and +/-10lbf for long-term retests (5min), which is good enough for our purposes. With the exception of the static rope versus dynamic rope testing platform, all tests are of the short-term retest category. The pulley efficiency segment of this study has a testing equipment and methods imposed inaccuracy rate of +/-2% with a repeatability value of +/-2% @ 300lbf. However, because of the unique nature of pulleys, the quoted error rate of the pulley efficiency test is only applicable to this unique platform. This means that a pulley that scored 85% in my test may score 90% in your specific application.

IMPORTANT: Except for the pulley efficiency test, I terminated every test when I reached 100lbf on the pull strand. Consequently, the load values expressed in this study may appear to be relatively low for the system I am using. If you are thinking they are low, you are correct. My standard 7:1 base with a GriGri can allow me to subject 2,500lbf to my slackline even though it only shows that I got to around 1,000lbf in this study. However, yanking on the line until it is as tight as I can get it will provide hugely inaccurate test results because “as tight as I can get it” is not a repeatable value. However, stopping at 100lbf is very repeatable and therefore will allow me to compare every test under an “apples to apples” scenario.
The following photos demonstrate the base testing platform and the method used to capture and create the testing data found in this study.














Basic Theory

Pulleys have two primary functions: to create (negative or positive) mechanical advantage and to redirect the travel of a rope. To calculate mechanical advantage we count the number of strands supporting the load. The key word here is supporting the load. If a strand is not directly holding the load, it is not counted toward mechanical advantage. If the pulley is not directly holding the load, it is redirecting the load, which puts it into the redirect use category. Also you can also calculate the mechanical advantage by comparing the stroke length of the load against the stroke length of the pull rope. In other words, if it takes 10 feet of rope from you pulling on your tensioning system to tension the slackline 1 foot, you have a mechanical advantage value of 10:1 (minus friction). When multiple pulley systems are stacked on each other in parallel they form a compound pulley system. When this happens we multiply the advantage of all systems for the final mechanical advantage value.

Below we see a 4:1 base system with a standard pulley and GriGri multiplier setup. The total mechanical advantage of this system is 12:1 because the multiplier and brake form a 3:1 (3x4=12).

Okay, enough high school mechanics let us move on.

Pulley Efficiency

Pulleys naturally create friction and provide resistance because the sheave of the pulley is in physical contact with the axle. Manufacturers have two main ways to combat this issue and increase the efficiency of the pulley: use a larger sheave and use low friction material, such as a ball bearing system, to connect the sheave to the axle. The idea behind using larger sheaves is the pulley will provide more local mechanical advantage to overcome the friction imposed at the axle. Think of trying to turn a big steering wheel versus a very little one.

Calculating pulley efficiency can be tricky because the efficiency of a pulley varies depending on the load. So I chose two loads value to test, 100lbf and 300lbf. Note that these values are the load subjected on the pull strand, so the load on the pulley is approximately double, so 200lbf and 600lbf. I chose these values because a standard 5:1 base longlining pulley system will see approximately 300lbf per strand when tensioned for a shorter longline (1,500lbf total tension). The 100lbf tension value represents a slackline (as opposed to a longline) where the total tension is approximately 500lbf.

Clearly pulleys with ball bearings are generally superior to pulleys with bushings. However, it seems a large sheave can make a larger bushing pulley comparable in efficiency to a midsize bearing pulley. I added a standard oval carabiner in the testing mix to compare primitive systems to systems that use a legitimate pulley system. The GriGri efficiency test will play a key role later.







Rope Choice and Brake Efficiency

Most slackliners use static rope in their base system. There is good reason to use static rope; it will make the line easier to tension. However, does using dynamic rope actually decrease the efficiency of your pulley system? Note that the function of this test is NOT to determine the maximum amount tension you can obtain by yourself. The function of this test is to compare the system’s total efficiency when using static and dynamic rope. The idea is that smaller ropes bend easier than thicker ropes and therefore will produce less friction when forced to bend around a sheave. I performed this test performed on a 7:1 base system; the exact system shown in the photos at the beginning of this study.







As you can see, dynamic rope does not appear to reduce the efficiency of the pulley system. However, it WILL make the line harder to tension because it will absorb some force when you yank on the line. So for that reason and a few others, use static rope if you can.

The secondary function of this chart is to show the differences between using a GriGri or other mechanical brake (ID, Eddy, ect) and using a compound pulley for a brake (MPD, Pro-Traxion, ect).
Using a compound pulley such as an MPD will have a HUGE effect on your ability to tension your line. Switching from a GriGri to a Pro-Traxion yielded a 20% gain in system efficiency, and the line was much easier to tension. This is because the brake functions as a pulley in your base multiplier system. Remember before how I mentioned that compound pulley systems are multiplied to calculate total mechanical advantage? Well, let us create an example. We know that the efficiency of the GriGri is about 50% at 300lbf and the efficiency of the SMC 2” (my multiplier) is about 91%. That gives a multiplier system efficiency of about 70.5%. That means our “3:1” multiplier is actually more like 2.12:1. We multiply that into a 5:1 base system, and we get 10.6:1. Next let us compare that value to a compound brake pulley system. With the Pro-Traxion we have a multiplier system efficiency of 91%. That makes our “3:1” a 2.73:1. We multiply that into the 5:1 base, and we get a total of 13.65:1. So 10.6:1 or 13.65:1. Of course the real-world values will be lower because I did not account for the friction of the base system, but you get the concept.

Total System Efficiency

In this test I will compare three base systems against three pull methods: 5:1, 6:1, 7:1 and no multiplier, multiplier with GriGri, and multiplier with Pro-Traxion. On the below graph you can see the total force subjected to the slackline as compared on the primary chart axis with the actual mechanical advantage as listed on the secondary axis. The theoretical mechanical advantage is listed below the test name. As you can see there is a direct correlation with the number of pulleys in a system and the efficiency of the system. Adding more pulleys will gain more mechanical advantage, but it will also decrease the efficiency of the system. Accordingly, I would not recommend creating a base system larger than 9:1 otherwise you are mostly just wasting your money buying more pulleys that won’t add much to the system.



On this graph you can see the efficiency values of each system.



Again, this test was terminated once I reached 100lbf on the pull strand. The actual system efficiency will likely be slightly higher at greater tensions.

Brake Choice

In this final test I want to place additional emphasis on the importance of efficiennt multiplier equipment. In this test I examined four options: a base 5:1 with no multiplier, a 5:1 with a true 2:1 multiplier with no brake, a standard 5:1 base with a GriGri, and a standard 5:1 with a Pro-Traxion brake.



If you are keen you may notice that adding a 2:1 multiplier actually more than doubled the force I could subject to the line (295lbf vs 649), which should be impossible in theory because I am only doubling the mechanical advantage. This illustrates how the pulley efficiency test shown earlier transfers over to the real world. As you will recall almost every pulley I tested was more efficient at 300lbf than 100. The addition of the 2:1 multiplier increased the tension on the pulleys, which increased their efficiency.

Conclusion

Static ropes will increase your ability to pull a line tight, but they do not appear to increase the base efficiency of the system when compared to dynamic rope, at least not directly. Pulleys are less efficient at lower tensions than at higher tensions. Using an efficient multiplier and brake is critical to maximizing your tensioning system’s performance. Upgrading to an MPD or other compound pulley should yield a fairly large increase in efficiency, at least 20%.

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By amarius
Dec 19, 2012
Cool study
Coming from somewhat scientific background I am more comfortable with breaking down system efficiency to each individual element - if you setup consists of 3 pulleys I would attempt to evaluate efficiency of one and look at how that correlates with the overall efficiency, and you did evaluate efficiency of separate elements but I could not figure out how to combine them.
You claim +/- 2% error on measurement - this sounds like instrument error? How about statistical variances of measurements? - you did take more than 3?

I did not spent a whole lot of time contemplating your argument regarding low loads being less efficient than high loads - perhaps different levels of deformation of rope under different loads have something to do with it? - higher deformation, more surface area, more frictional losses.


Would be interesting to see if anything changes if you change thickness of tensioning rope.

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By Superclimber
Dec 19, 2012
My head caved in.

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By Jim Titt
From Germany
Dec 19, 2012
amarius wrote:
I did not spent a whole lot of time contemplating your argument regarding low loads being less efficient than high loads - perhaps different levels of deformation of rope under different loads have something to do with it? - higher deformation, more surface area, more frictional losses.


That is the characteristic of sintered bronze impregnated bearings (Oilite is the best known make), they start to release the lubricant at high pressures which is why they are used for low-speed, high load applications.

And for general information for 20kN, the bit the rope runs on is the pulley or sheave, the bits each side that hold it all together are the cheeks and the entire object is called a block. Put a rope through and it and the two combined are a tackle. Correct terminology is everything, except perhaps for slackliners trying to make tight lines!

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By brenta
From Boulder, CO
Dec 20, 2012
Cima Margherita and Cima Tosa in the Dolomiti di B...
If the loads shown are those actually measured by the cell attached to the post when 100 lbf are applied to the free end of the rope, then the problem with the analysis is that the tension in the slackline is actually higher by 100 lbf than the force measured--assuming that you are pulling towards the post, which is, to first approximation, what is seen in the pictures.

The effect of underestimating the tension in the slackline is to underestimate the actual mechanical advantage by 1: proportionally more so for the systems with lower advantage.

That would explain why the efficiency of the simple systems is lower than the efficiency of some of the most complex systems (which have higher losses). It would also explain the large apparent increase in efficiency of the complex systems built on the 5:1 base system: 2*(295+100) > 649+100.

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By 20 kN
Administrator
From Hawaii
Dec 20, 2012
You claim +/- 2% error on measurement - this sounds like instrument error? How about statistical variances of measurements? - you did take more than 3?

I did not spent a whole lot of time contemplating your argument regarding low loads being less efficient than high loads - perhaps different levels of deformation of rope under different loads have something to do with it? - higher deformation, more surface area, more frictional losses. Would be interesting to see if anything changes if you change thickness of tensioning rope.


The +/-2% value came from the resolution of my second load cell indicator, which is in 2 lb increments. So in the case of the 100 lbf efficiency test, the force I was subjecting the pull strand could have ranged from 100 - 101.9 lbf. I do not know how the indicator handles sub-digit readings. It might just round them down or up, but I suspect that it does not round at all and will not display the next higher increment until the actual threshold of the next increment is reached (i.e. 102 lbf). The actual accuracy of the equipment is pretty spot on, especially for the small range I was using. The official non-linearity specification of the cell is .85 lb maximum, but I have been able to resolve accurately down to .2 lb increments at low loads and a low scan rate with proper filtering.

There was some statistical variance, generally 2-4% including instrument error; although for the higher-end pulleys it was less. However, I did not account for that in the data because I wanted to display the actual efficiency achieved in the test as opposed to an average. I tried to mention this when I said "However, because of the unique nature of pulleys, the quoted error rate of the pulley efficiency test is only applicable to this unique platform. This means that a pulley that scored 85% in my test may score 90% in your specific application." I could create a new graph with the averaged numbers, but it would not be that much different. In that portion of the test, what I really wanted to point out was the differences between the pulleys in the chart. In reality, the actual efficiency of any pulley is going to be unique to the exact situation it is being used in because a number of factors affect the efficiency.

As far as the rope bends go. I specifically tested that in the low-stretch rope versus dynamic rope test. The dynamic rope was a heavily used 10.3mm (actually more like 12mm now) rope and I compared it to a new 9mm low-stretch rope. As the charts show, there was no observable difference between the two, although physics seems to imply thinner ropes should bend easier and thus be more efficient. I suspect that one of the major reasons why I did not see much of a change between the two ropes is because the sheaves on the main pulleys are 2 3/8" which are large enough to handle a 9mm or 10.3mm rope.

If the loads shown are those actually measured by the cell attached to the post when 100 lbf are applied to the free end of the rope, then the problem with the analysis is that the tension in the slackline is actually higher by 100 lbf than the force measured--assuming that you are pulling towards the post, which is, to first approximation, what is seen in the pictures.

The effect of underestimating the tension in the slackline is to underestimate the actual mechanical advantage by 1: proportionally more so for the systems with lower advantage.

That would explain why the efficiency of the simple systems is lower than the efficiency of some of the most complex systems (which have higher losses). It would also explain the large apparent increase in efficiency of the complex systems built on the 5:1 base system: 2*(295+100) > 649+100.


That is a very keen observation, I did not catch that, thank you. I will retest this tomorrow adjust for the error. Fortunately the baseline was always 100 lbf, so I envision all I need to do is add 100 lbf to all of the values. But I will test your hypothesis tomorrow to verify.

That is the characteristic of sintered bronze impregnated bearings (Oilite is the best known make), they start to release the lubricant at high pressures which is why they are used for low-speed, high load applications.

And for general information for 20kN, the bit the rope runs on is the pulley or sheave, the bits each side that hold it all together are the cheeks and the entire object is called a block. Put a rope through and it and the two combined are a tackle. Correct terminology is everything, except perhaps for slackliners trying to make tight lines!


It seems that there is more to this issue than just the technology used in the bearing. First off, most of the pulley did not have bearings, only four did. Second, in every test except one, the test subject was less efficient at lower loads than higher loads. This includes the carabiner and the GriGri, neither of which are even pulleys in a conventional sense.

Thank you for the terminology advice. I am aware that a pulley, as used in this study, is actually a block. However, in slacklining, the term pulley is normally used to indicate the entire assembly, and the word sheave is used to indicate just the wheel. Also, most rock climbing pulley manufacturers call the entire assembly a pulley as well. If you look on SMC's, Petzl's or CMI's website, they all call the block a pulley. In fact, I dont think I have actually heard anyone from the climbing realm call a pulley a block, I have only heard that term in sailing. Admittedly, I did not know the plates on the side were called cheeks. That sounds like a sailing term as well. SMC and CMI call them sideplates. I pretty much listen to whatever SMC and CMI says as they are kind of the rock climbing, slacklining and possibly rescue industry de facto standard for pulleys.

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By Jim Titt
From Germany
Dec 20, 2012
From what you wrote I´d assumed all the pulleys had some come of bearing, whether it is a ball, roller or plain bearing. Oilite bearings are plain bearings or what you called a bushing.

You want to perpetuate the ignorance of slackliners and a rag-bag of miscellaneous foriegn companies in abusing the English language?

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By zoso
Dec 20, 2012
avatar
Just how long did you camp out in a public park trying to pull city light poles down?

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By 20 kN
Administrator
From Hawaii
Dec 20, 2012
Jim Titt wrote:
From what you wrote I´d assumed all the pulleys had some come of bearing, whether it is a ball, roller or plain bearing. Oilite bearings are plain bearings or what you called a bushing. You want to perpetuate the ignorance of slackliners and a rag-bag of miscellaneous foriegn companies in abusing the English language?

SMC and CMI are not foreign entities. SMC is out of Seattle and CMI is out of West Virgina. Like I said, CMI and especially SMC are the industry standard in America. Pretty much every fire department I know of uses SMC gear for rescue operations. They make some of the best pulleys, or as you call it blocks, in the world.

Yes, all the pulleys, or blocks as you wish, have a bushing or bearing except for the CAMP Andry which is just a sheave mounted directly onto an axle. Either way I am interested in knowing why all of my test subjects preformed poorly at low tensions. Your theory on the bushings may hold true for the pulleys that actually have bushings, but not all of the test subjects (e.g. GriGri, carabiner, ball-bearing pulleys) have bushings.

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By Jim Titt
From Germany
Dec 20, 2012
20 kN wrote:
SMC and CMI are not foreign entities. SMC is out of Seattle and CMI is out of West Virgina. Like I said, CMI and especially SMC are the industry standard in America. Pretty much every fire department I know of uses SMC gear for rescue operations. They make some of the best pulleys, or as you call it blocks, in the world. Yes, all the pulleys, or blocks as you wish, have a bushing or bearing except for the CAMP Andry which is just a sheave mounted directly onto an axle. Either way I am interested in knowing why all of my test subjects preformed poorly at low tensions. Your theory on the bushings may hold true for the pulleys that actually have bushings, but not all of the test subjects (e.g. GriGri, carabiner, ball-bearing pulleys) have bushings.


As an Englishman I´m glad you´ve comfirmed that they are foreign, both to me and the English language! From my time in the marine industry I doubt any of them make the "best" blocks in the world anyway, the usual standard is Harken or Lewmar for money-no-object racing yachts.
The answer to your problem lies in the bending force required in the rope which to a certain extent is a fixed amount so proportionally more at light load. At an infinitely light load for example it still takes force to bend the rope so the block would show 0% efficiency, you can demonstrate this experimentally by bending a steel bar in a U and trying to pull it through a block.

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By 20 kN
Administrator
From Hawaii
Dec 21, 2012
brenta wrote:
If the loads shown are those actually measured by the cell attached to the post when 100 lbf are applied to the free end of the rope, then the problem with the analysis is that the tension in the slackline is actually higher by 100 lbf than the force measured--assuming that you are pulling towards the post, which is, to first approximation, what is seen in the pictures. The effect of underestimating the tension in the slackline is to underestimate the actual mechanical advantage by 1: proportionally more so for the systems with lower advantage. That would explain why the efficiency of the simple systems is lower than the efficiency of some of the most complex systems (which have higher losses). It would also explain the large apparent increase in efficiency of the complex systems built on the 5:1 base system: 2*(295+100) > 649+100.

I updated the graphs to account for the error you mentioned. I used an entirely new data set with the load cell placed on the load instead of the anchor this time.

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