## Measurements on some climbing pulley systems

Because Sweden has very long, dark winters and there are only three television stations, I found myself one evening practicing rescue procedures on my backpack. It was stranded, unable to move by itself, on my living room floor, and the goal of the exercise was to get it to a position of safety half way up my doorframe, using standard climbing techniques and equipment. I first rigged a 3:1 ratchet pulley system, as described in Petzl's Tibloc instruction sheet, but found that it still needed a lot of effort to lift the pack. When I put spring balances in the system, I found that the force I needed to apply to the fast-moving (rescuer) end of the system was indeed almost as high as the force experienced at the slow-moving (victim) end, despite the theoretical 3:1 advantage. It seems that the friction in the system cancelled out a lot of the mechanical advantage. This led me to set up some other systems and measure just how much help they were. The results are summarised below.

Conditions :
The pack weighed 10kg, and the pulleys used were either the Petzl emergency pulley wheel mounted on an oval carabiner, or a naked 12mm diameter carabiner with no wheel. The rope used was an 11mm static. The force given in the table is that required to move the victim upwards. Less force was required to hold it still.
Measurements were made with and without Tiblocs used as ratchets, but their presence made no significant difference to the friction in a given system.
The angle that the rope makes over a wheeless carabiner pulley affected the forces a lot, so all where measured for a 180° loop over the carabiner, but the photographs were taken with a somewhat smaller angle for clarity.
Click on the links to see photographs of the setups.

 Victim weight = 10kgf
 Arrangement Rescue force Simple redirect (1:1) (diagram) Carabiner pulley 22kgf wheel pulley 16kgf 3:1 Pulley (diagram) Carabiner pulley 7kgf wheel pulley 6kgf 3:1 Pulley with redirect (diagram) Carabiner bottom pulley 14kgf wheel bottom pulley 12kgf wheel top pulley 9kgf 2:1 Pulley (diagram) Carabiner pulley 7kgf wheel pulley 6kgf 2:1 Pulley with redirect (diagram) Carabiner top pulley 12kgf wheel top pulley 10kgf

At the time of these experiments, I only had access to one simple wheel pulley, but I will update when I have more, and can thus do permutations.

Conclusions :
1) Using a pulley wheel instead of a naked carabiner saves a lot of energy, especially when it is placed in the system at a point where the rope is moving fastest.
2) The 3:1 pulley system described in the Petzl Tibloc manual gave less benefit than expected in terms of the force required to lift a victim, whilst requiring three times as much rope to be pulled at that force. With a redirect, it was of no benefit at all. A 2:1 pulley can be much easier to set up in some circumstances, and gives almost as much benefit.
3) Redirection costs a lot of energy.

Mark Harris 26 Feb 2001

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