Part 1: Hoisting in rock climbing rope systems

As climbers/mountaineers, we have a few options to hoist a climber, stuck person, or victim of an accident. This article also describes how to count the mechanical advantage of those rope systems.

Part 2 will look at the benefits of different systems, and the actual mechanical advantage as opposed to the ideal one.

The most simple and probably the most common use of hoisting in rock climbing, is a leader using a 3 to 1 hoist to assist their second through a hard move. I've had to do this in practise where my client couldn't make the 5a move because of wet holds, in real life on a multipitch crag with a traversing pitch this wasn't as easy as practising somewhere in a near ideal situation. But, although awkward the system was the same, just with much more friction. Using this 2 part article, we can look at how best to reduce the friction of a system, and possibly increase the mechanical advantage if the situation allows for it.

3 to 1 hoist:
As mentioned above, a 3 : 1 is the easiest and most simple way to hoist a struggling second. There are a few key safety points to bear in mind. Importantly, if the belay device is not auto-locking, there must be a clutch prussic placed in front of the belay device. (When dropping a loop of slack down to the climber and back to the belayer, if that loop is accidentally not secured, there is a potential to fall the full length of that slack rope.) The procedure: 1 Tie off the belay device if it is not auto-locking (best to back it up with a hitch even if it is). 2 Next (if the belay isn't auto-locking) tie the French prussic in front of the belay device, secured to something in the belay rigging behind it. 3 Drop a loop of rope to the climber with a carabiner/revolver/pulley on it. 4 The climber attaches the carabiner to the belay loop on their harness. 5 Tighten the ropes and make sure the french clutch prussic is tight and ready to bite. 6 Release (untie-off) the belay plate, and take that slack out of the system. 7 Climber pulls on the rope coming down towards them, and the belayer pulls on the rope coming upwards towards them. 8 Once ready to resume normal belaying, the belayer must hold the dead rope coming out of the belay device again. The loop of the rope to the climber can be unclipped from their harness, and retrieved. Then the clutch prussic can be removed.

How to count the mechanical advantage (MA):
Start by assuming that the climber is offering no help in hauling. The belayer's upward pull is the only acting input force in the system. If we represent the belayer's effort with '1 unit' of force. We can then work out the units being applied to the carabiners, prussics and the force on the belay itself. Adding up these units will tell us the ideal (without friction loss) MA of the system.
Because 1 unit is applied to the rope in front of the carabiner attached to the climber, that same force must be on the rope on the otherside of the carabiner too. The total force on that carabiner/prussic, is therefore 2 units.
The original 1 unit is on the rope in front of the belay device, and therefore must be on the otherside of the belay device too, leaving a total force of 2 units on the belay setup itself.
The orignial unit is still in tact above the prussic attaching the climber to the loop of rope. We add this 1 unit above the carabiner to the 2 units on the carabiner from the other loop of rope, making 3 units in total.
That's 3 units output force as a result of 1 unit applied input. And hence a 3 : 1 system.

Counting other MA systems:
Here is the same methodology applied to slightly more difficult hoists.

Exercises for yourselves:
Work out the MA of these systems, email/facebook me and I'll give the answers.