6:1 compound pulleys in the real world
Say you’ve built a 2:1 mechanical advantage (MA) system or 3:1 MA system, and it's not quite doing the job. You need some greater pulling force, so how do you do it? Here are two approaches that combine a 2:1 and a 3:1 to make a 6:1 MA system. If you find yourself in a one person rescue situation, a rig like this might be required.
Both of these examples are known as a compound pulley system. With a compound system, you have one simple system pulling on another simple system. The pulleys move in the same direction, but at different speeds, than the load.
In a compound system, the hauling systems are multiplied to get the final mechanical advantage. In both of these examples we have a 3:1 multiplied by a 2:1, so the resulting theoretical mechanical advantage is 6:1.
With a 6:1, you need to pull 6 feet/meters of rope in order to move the load 1 foot/meter.
Enough with the terminology and theory, let's see how to build these for real. If you want, go get your gear, lay it out on the floor and follow along. (Please don't pull heavy furniture around in your house, it's rough on the floor. =^)
Let’s start with a 3:1 system, then add a 2:1 on top of this to get a 6:1.
This is one of many different ways you can set this up, with various combinations of hardware, pulleys, rope grabs, etc. This has a Petzl Mini Traxion progress capture pulley at the anchor. You could use a regular pulley and prusik loop here as well.
Let's start with a basic 3:1 Z drag.
Step 1 - Clip some cord onto the anchor master point. Here it’s an untied cordelette. It could also be the far end of the rescue rope itself.
Step 2 - Tie a prusik in the hauling strand as shown and clip a carabiner and pulley (if you have one) to it. (If you don't have a second prusik loop, you could tie a clove hitch in the white rope. You would have to retie at every time you reset the system, but it works.)
Step 3 - Clip the cord into the pulley and pull.
That's it, a 2:1 on top of a 3:1, resulting in a 6:1 theoretical mechanical advantage.
Here’s a similar setup, but reversed. We're going to start with the 2:1 and add a 3:1 on top of it, resulting in a theoretical 6:1.
Again, this is one of many different ways you can set this up, with various combinations of hardware, pulleys, rope grabs, etc.
Let's start with the basic 2:1. Note that in this 2:1, the red Traxion progress capture pulley is on the load, rather than the anchor. This can be advantageous in certain rescue situations.
Step 1 - Clip a carabiner into the anchor master point, and clip the pulling rope to this carabiner. (This changes the direction of pull and does not add any mechanical advantage.)
Step 2 - Add a prusik to the pulling strand near the load.
Step 3 - Clip a carabiner (and a pulley if you have it) to the prusik.
Step 4 - Clip the haul rope to the pulley, and pull.
You’ve added a 3:1 on top of a 2:1, giving you a theoretical 6:1 system.
If you happen to have another pulley, add it to the redirect carabiner that's on the anchor. If you have only one pulley, it’s in the correct place; on the prusik that's closest to your pulling hand.
Finally, here is a great video by IFMGA Certified Guide Jeff Ward showing the 6:1 “Z on a C” System applied to crevasse rescue. (His rigging is slightly different than what I shared above and that he has the progress capture above with him and not down on the climber, but other than that the system is identical.)
