I'm reading up on pulleys, and the more advanced articles talk about three different kinds, simple, compound, and complex. What do these terms mean, and which one should I use?
Now, this is heading into slightly more advanced territory, but if you’ve read this far you hopefully still have an interest in slightly esoteric things like this. :-) As to which one to use, there’s not a quick and easy answer.
The one potential issue with the compound and complex systems is that you usually have to reset the pulleys more often as they “collapse” (or, are pulled into each other) when you pull. If you have a large working area, like the top of a crevasse, this is probably not a big deal. If you have a tiny working area, such as a hanging rock belay, then it might be more of a problem.
If you want to geek out on this, look at the YouTube video links at the bottom of the page on compound pulleys and start playing around on your living room floor. That's really the single best way to learn this. You can do it with some parachute cord and a few carabiners, you don't need pulleys or a even a real climbing rope.
1 - Simple system
When you pull the rope, the pulley(s) move in the same direction and the same speed toward the anchor.
As the blue rope is pulled, the pulley on the green prusik moves toward the anchor at a constant speed. There are three strands of rope going to and from the load and load strand, so this means it's a 3:1 MA. This is also known as a “Z drag”, because the shape of the rope is a “Z”. (It’s actually a backwards “Z”, but close enough . . .)
In a simple pulley system, when the rope end terminates and is attached at the anchor, then the MA will result in an even number (e.g. 2:1, 4:1, 6:1, etc.). When the rope end terminates and is attached at the load, then the resulting TMA will be an odd number (e.g. 3:1, 5:1, etc.).
Below, in the 3:1, we see the rope end attaches to the load, therefore we have an odd number, 3:1.
A 3:1 simple system.
2 - Compound system
When you pull the rope, the pulleys move in the same direction, but at different speeds toward the anchor.
This can be created by building a 3:1 Z drag, and then adding a 2:1 onto the strand you’re pulling. With a compound system, the mechanical advantage of each separate pulling system is multiplied.
Below, we see a 3:1 on the red rope, and a 2:1 on the gray rope. Together, the two systems are multiplied to get a 6:1. Note that the red rope will move the load 1 foot for every 3 feet of rope you pull, while the gray rope moves upwards 1 foot for every 2 feet of rope you pull. Therefore, the gray rope will reach the anchor point before the red rope, meaning you need to reset the system more often.
Note - If you have 3:1 set up, and and need more pull, making a compound at 6:1, as we see below, is often a great idea. An example would be crevasse rescue on a two person team, when one person on top may have to do all the pulling. If you have a lot of friction from the rope running through the snow, and/or your partner in the crevasse is not able to assist you, the 3:1 is probably not going to work. Then, the 6:1 is going to be your best friend. The second rope, shown on the left in gray, does not have to be a second climbing rope. You could untie a cordelette and use that, or the tail end of the main rescue rope. Adding the 2:1 only requires one additional pulley and carabiner. Sweet!
Note: For a compound pulley system, you can add the very Crafty Rope Trick (CRT) of building a second anchor that’s farther away. This can allow you to completely collapse the 3 to 1 system before the 2 to 1 system collapses, which means you need to reset the system less often. Granted, this trick is probably more appropriate for professional riggers or maybe search and rescue teams, and not so much for climbers, but it’s still a pretty cool trick.
A 6:1 compound system.
3 - Complex system
When you pull the rope, you have pulleys that move TOWARD each other. Complex MA systems are okay, but a simple or compound system is usually a better choice, because they are generally easier to rig and understand.
Below we have a 3:1 simple system on the left (the plain vanilla Z drag that hopefully you know well by now). But on the right, with the addition of a prusik and pulley, you turn it into a 5:1. And, in the real world, this is actually a pretty handy trick. You get an extra 2:1 MA without any friction-inducing, efficiency-robbing redirect through the anchor.
This is now a complex 5:1 system. When the yellow rope is pulled, both pulleys move toward one another. When the red and brown pulleys touch (aka “collapse”), you need to reset the system. Probably not a problem if you have a large area to work in, but if you are on a tiny rock ledge, the pulleys collapsing toward each other is going to be a hassle.
Compare this with the compound 6:1 diagram just above. With the 6:1, you get a little more MA, plus avoiding the collapsing pulley problem, so that's why the complex system is not usually the top choice.
A 3:1 simple system (left) and a 5:1 complex system (right).
Here’s a nice video that show the difference between simple and compound pulley systems.