More Low Friction rings
In the first article of this series we gave results on using fairleads and showed how the added friction is not significant with low deflection angles. In this article we consider using low friction and other standard rings with high deflections and analyze how these can be used in systems to provide simple and inexpensive mechanical advantage. Again we used the digital scale shown on the right to make the measurements. This scale reads up to 220 pounds with 1/2 pound resolution. One nice things about the scale is that it has a peak hold function so the test can be made without constantly looking at the readout as the peak can be read at the end.
The test data below was made with 1/8 inch Amsteel and a number of different rings. There was a fair amount of variation in the readings particularly as the Amsteel set to the ring. For example, one set of measurements read 54.5, 53, 51, 51 in four readings and settled on 51. For this to happen, something has to change in the material of the line and what changed was the line flattened and took a set to the ring. Once that happened, the variation in the readings went away. I tried using different diameters of line but found the variation line to line was not explainable by diameter alone so did not draw conclusions about the effect of line diameter. The major conclusions would not change as we still learned a great deal using the 1/8 Amsteel.
The test bench used a 40 pound weight hung over the edge through a Garhauer block. Measurements were taken with the digital scale discussed in the introduction.
Five rings were tested. Four had round cross sections. Two were standard rings. One of these was a standard stainless steel ring made with a 9mm diameter wire. The other was a REI Omega Rappel Ring shown to the left. It was under $5 at REI but you can also get it from Amazon for a couple of dollars more.
The other two rings were Antal low friction rings. One the 20x14 and the other the 14x10. Both are very nice products and highly recommended although the $5 ring from REI works just as well. They are all light with the smaller Antal at 1/2 oz. The Omaga was 1.2 oz and the larger Antal 1.5 oz. and all much lighter than the 3 1/4 oz of the stainless steel ring. The diameters of the working surface ranged from 9mm for the SS ring to 22mm for the larger Antal. The Omega was 11mm and the smaller Antal 15mm.
As was stated above, four rings had round cross sections. The fifth had a cross section as shown in the picture on the left. This cross section seems very smooth but is not round and did not do nearly as well in the testing. Perhaps related to the line taking a set on the ring, the desirability of a round cross section is a huge deal. If you want to use Carabiners or anything else, make sure the cross section of the surface the ring will run over is round. Smooth does not cut it, it must be round for best friction and thus most mechanical advantage of any system you are going to build. I do not recommend this ring for this kind of use but the product is shown on the right for your amusement.
I would consider the differences between the various round rings noise. The average loss from a 90 degree bend was 24% and from a 180 degree bend 32%. Notice however that the loss from the SMC ring was much higher.
A Simple One Part System
The system above is a simple "2:1" system. To analyze what the mechanical advantage is consider the pulling force required to lift the 40 pound weight. We know the loss through the ring is 32% so the force you pull on the line is 1.32 times the force delivered to the other side of the line you are pulling on with the rest of the force lost in friction. Both these forces pull on the ring meaning that the load sees 2.32 times the force on the anchored ring. The pulling side is 1.32 times the anchored side so the mechanical advantage is 2.32 / 1.32 or 1.75:1, just under the 2:1 frictionless case. In the example above, the pull is 23# and the anchored side sees 23# / 1.32 or 17#. The total pull is then 23 + 17 = 40 pounds. (There is some rounding in this example).
To check this and to serve as another example I built the system above and measured the pull required to pull my 40 pound weight up. It was exactly 13 pounds just like the theory from the measurements would say. This "4:1" system is 3.1:1 which is just what you would expect from a cascaded system where the individual blocks are 1.76:1. Please note that there is a small loss in the Garhauer block (not shown) so that there is really 41 pounds required to lift the 40 pound weight.
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