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Analysis: pulley efficiency, base systems and their relationship.
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USnavy


Dec 19, 2012, 4:34 AM
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Analysis: pulley efficiency, base systems and their relationship.
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Click on the photos and graphs to enlarge them if you cannot read them.


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 complex 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 complex 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%.


(This post was edited by USnavy on Dec 20, 2012, 11:05 PM)


marc801


Dec 19, 2012, 7:24 AM
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Re: [USnavy] Analysis: pulley efficiency, base systems and their relationship. [In reply to]
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TL;DR

You need to put an abstract up front that explains your study in one sentence and gives an overview of the major results in 2-4 more sentences. IOW, start with your conclusions, then explain how you got there.


zxcvbnm


Dec 19, 2012, 3:42 PM
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Re: [USnavy] Analysis: pulley efficiency, base systems and their relationship. [In reply to]
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What kind of difference is their between static and kinetic friction in these systems?


USnavy


Dec 20, 2012, 4:20 AM
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Re: [zxcvbnm] Analysis: pulley efficiency, base systems and their relationship. [In reply to]
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zxcvbnm wrote:
What kind of difference is their between static and kinetic friction in these systems?
I have not tested this personally; however, others have. The study I saw showed that the pulleys were more efficient at slightly faster speeds of about 4FPS. I kept the rope travel speed fairly slow because that is most relevant to slacklining.


(This post was edited by USnavy on Dec 20, 2012, 4:21 AM)


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