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:

• Pulley Camp Tethys Pro (28 mm sheave)
• Pulley/carabiner Petzl Rollclip A
• Carabiner Petzl Attache, an old, thick one
• Carabiner Black Diamond Positron
• Carabiner Ocun Kestrel

and

• 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:

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!