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Pulleys and different line materials

Tuomas Pöysti 2020

We already know that pulley efficiency strongly and undoubtedly depends on sheave diameter. It is easy to guess that it is not only sheave diameter, tough, but relation between sheave diameter and line thickness.

This is something I have done some empirical studies with. The “pulleys” where:


  • 11 mm EN 1891 rope (Petzl Grillon)
  • About 10,5 mm EN 892 rope (of unknown brand, sorry)
  • Half rope, Beal Cobra II 8,6 mm
  • Petzl PUR’Anneau as a loop
  • Wild Country 10 mm dyneema sling, as a loop
  • The same as tape
  • Ocun O-sling (16 mm nylon, flat) as a loop
  • Black Diamond Nylon Runner 16 mm (tubular) as a loop
  • Nylon accessory cord, Mammut, 6 mm
  • Dyneema cord, Beal 5,5 mm

These were mostly picked as something that really could be used in emergency pulley systems, that is, mountaineering materials, lightweight carabiners and such. Positrons are there for a specific reason: I have only one “fat” Attache, and I wanted to test the friction of a typical two carabiner toprope anchor.

The results are below, sorted in efficiency order. Some average deviations between repeated tests were a bit high, they are highlighted in the table. “Small wiregate” means Ocun Kestrel.

Some remarks

Two carabiners is clearly worse than two. The difference was about 13 %-points. According to the capstan equation, there should not be any difference. I think this is a noteworthy detail, since it suggests that even in case of a carabiner as a “pulley”, there’s something else going on than just surface friction.

Also, the thicker the material, the more there is friction in general – even with carabiners.

Dynamic rope seemed to do way better than semistatic, and nylon cord had a bit less friction than a little thinner dyneema cord. These differences could of course be explained by actual surface friction properties, but at least in case of the ropes, it sounds unlikely.

There’s a clear difference between tape and sling (or two tapes, of course). This image explains it to some extent:

The worst combination of this set

Probably for this exact reason wider 16mm slings did generally worse than 10mm slings. It does not make any difference how carefully the sling is piled in the beginning.

There’s a distinct gap between actual pulleys and carabiners, but on the other hand the step from Tethys+cord to Tethys+rope is bigger than from Tethys+rope to carabiner+tape.

In general, cord seems to be the most efficient companion to both actual pulleys and carabiners.

Two carabiners and the capstan equation

As said earlier, the capstan equation does not explain the significant difference between one and two carabiners. The angle and even contact area remains the same, no matter how far away the two 90º turns are from each other:

Also, if one already is a believer in the rope’s internal friction, it would be tempting to count this situation as a larger bend radius, and thus expect less friction. I’m all the time more interested in the hypothesis of bend radius changes.

This hypothesis suggests that two consecutive 90º deviations is less efficient than one 180º deviation. The idea is that the energy is lost every time that the rope’s bend radius changes. In case of two 90º turns there are four changes (marked as dashed lines in the picture), whereas one 180º turn consists of two changes (straight-curved-straight).

I’m happy to have something to study in the future!

2 replies on “Pulleys and different line materials”

Thank you for taking the time to perform these pulley experiments! Your work seems very rigorous and you have a lot nice equipment!

Optimising the efficiency of big-wall climbing pulley systems is a matter of obsession among a section of the rock climbing community. Just try googling ‘2:1 hauling ratchet forum’ and check the number of pages of replies in those threads..

A few years ago people loved massive pulleys the most for hauling on El Cap, but now people seem to be settling down to much smaller pulleys and the “Chongo 2:1 hauling ratchet”. It surprises me that such small sheave-diameter pulleys (eg Petzl Partner, or RE Omniblock 1.1) are settling as favourites.. It seems to go against the previously accepted maxim of bigger is better.

I have a suspicion that the use of 5-6mm “zed-cord” in the hauling ratchet setup is offsetting the smaller sheave size in this setup. It would be very interesting if you could design some experiments to directly test this. I am curious to know whether there would be any significant efficiency increase with a bigger top pulley (you have a couple of nice ones!). It would be an elegant curiousity that by down-scaling cord diameter, smaller, lighter pulleys are actually hitting top performance.

Best wishes, Steve

Hi Steve!

Thanks for the comment. It is really nice to see someone actually reads my stuff and even finds it interesting!

So, a 2:1 with a redirect test – I’m sure I could do that! I typically tend to think this kind of applications do not need to be tested separately, since they can be quite reliably calculated using the “raw” information from simple pulley tests.

The calculated MA of a 2:1 with a redirect is P1 + P1P2, where P1 is the efficiency of the lower pulley and P2 is the efficiency of the pulley closer to the hauler.

For a combination of 6 mm cord and two rollclips, using the data from this test, we get MA 0.91 + 0.91*0.91 = 1.73.

I’m not quite sure what the old standard has been, but Google shows me some pictures of a 3:1 with a redirect. That would have a calculated MA P3 + P2P3 + P1P2P3, where P3 is closest to hauler and so on. To achieve MA 1.73 using three similar pulleys, each should have efficiency 0.75. This is quite close to what one should expect from a rollclip and an 11 mm EN 1891 rope.

This quick (I should go to my daytime job) and dirty calculation shows the beauty of external pulley systems, and I’m happy bigwall climbers have found it, too! By changing from rope to cord, it is possible to do the job of a 3:1 with a 2:1.

I actually once got interested about this and tried if a small emergency lift of a heavy load (to unload a knot) is possible using minimal gear, if the benefits of external pulley systems with thin lines are exploited. This is in Finnish, but I guess the pictures are enough to tell the most important:

The actual pulley system is just an upside down “fool’s tackle” or “mezzo poldo”, a 3:1 with a redirect. The Microtraxion is just for progress capture. I was able to lift a 115 kg load, 1,44 times my weight using a piece of cord, two carabiners and a prusik loop. It took about a minute to unload the knot, but of course this is not efficient enough for longer hauls. Just a nice extreme case.

Of course the calculated values should not be taken as the final truth. It would be nice to do the tests and hopefully validate the calculations! I’m afraid I don’t have three pieces of any single pulley type, though… We’ll see what I can do about that when the season is over and it’s time for the nerdy lab stuff 🙂


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