Let's start simple.
I don't know about you, but when I start looking at diagrams of complicated pulley systems and 5:1 rescue setups, my eyes get crossed and my brain starts to fog. Good news is, we don’t need to analyze a 5:1. At least not right now. Let’s break this down by starting at the beginning and then working up to a simple MA system, so you can really see how this works.
The basic 1:1 pull
Sticky the Climber needs to lift a 100 lb. load up to her ledge. She ties a rope onto the load, and starts pulling. To even budge it off the ground, she needs to pull up with 100 pounds of effort. She pulls 1 foot of rope, and the load rises 1 foot. She has no mechanical advantage or progress capturing, so her arms get tired pretty fast!
In this case, it's probably not a good system. But in other situations, it might work just fine. Got a crevasse rescue with five people on top ready to pull? Great! Put prusiks on the rope for everybody, have them clip in, and start pulling with their legs and bodyweight (not their arms). Probably no need for anything fancier than this.
Sticky thinks, “Hmm, how about I put a sling and a carabiner on that stout tree branch, and run the rope through the carabiner? That way, I can pull DOWN with my bodyweight instead of lifting UP with my arms, and I won't get so tired. That should be easier!”
The 1:1 pull with a redirect carabiner (load at rest)
Does Sticky gain any MA with this setup? No. She changed the direction of pull, but because the direction change is on the fixed anchor, she did not gain any MA. She is still pulling a 1:1, just like before, just with the rope now moving down instead of up. She pulls 1 foot of rope, and the load rises 1 foot. This carabiner in the tree is called a “redirect”, because it, umm, redirects your direction of pull.
Does she get an easier pull? Maybe. She can now use gravity and pull down using bodyweight rather than lifting up with her muscles. Pulling down is always easier than pulling up! But the redirect adds a lot of friction. By running the rope through a carabiner, which is only about 50% efficient, she'll have to pull down with 200 pounds to move the 100 pound load.
Note: The “200 pound” load on the anchor label in the diagram above is the load at rest. The load on the anchor will increase to about 300 pounds as soon as Sticky starts to pull, because she has to overcome the friction from the carabiner. Not so good!
Which is better, 100 pounds lifting straight up, using your arm muscles, or 200 pounds, pulling down, using your bodyweight? There's really no right answer. It depends on how far you need to move the load, your weight, and your strength. (Personally, I'll take 200 pounds with the redirect pulling down, thank you very much.)
Does she need a bomber anchor for the redirect? Yes! Notice that each strand of the rope is holding 100 pounds, so that means that the pulley high up in the tree is holding a load of 200 pounds with the load at rest. The redirect doubles the weight of the load and adds it to the anchor. When Sticky starts hauling, the load increases on the anchor even more, because she has to overcome all the friction in the system.
This is known as the “pulley effect”, and it's definitely something to consider when climbing. (For example, at the belay to bring up your second, you might be tempted to put in a single piece of gear above your head, and run the belay strand through that. If your second takes a fall on this piece, you have a pulley effect, essentially doubling the load on that single piece of gear. That could be a problem, and that's one of the main reasons why this belay technique has fallen out of favor.)
And, the friction in the system, which is always present in the real world, means the force on the anchor will be greater than 200 pounds. More on this below.
The 1:1 pull with a redirect carabiner and progress capture prusik
Sticky thinks, “Well, it is easier pulling down with my bodyweight, but if I ever let go, this load is going to zing all the way to the ground again. How about I put a prusik on the load strand so I can take a rest?”
Excellent idea! This is known as a progress capture, or ratchet. It allows the load to move up, but whenever Sticky wants to let go and rest, the prusik keeps the load from sliding back down. (If you want to get fancy, you could use a progress capturing pulley here, such as Petzl Traxion.)
Note: This is the same basic setup big wall climbers use when hauling small to moderate loads - a 1:1 pull with a progress capture. They use their bodyweight, not arms, to move the haulbag(s).
The 2:1 pull
Sticky says to herself, “OK, time to start working smart instead of working hard!” She anchors one end of the rope to the tree, puts a pulley on the 100 lb. load, runs the rope through the pulley, and starts hauling. Now she’s getting somewhere!
Does Sticky gain any MA with this setup? YES! She is now pulling with a 2:1 mechanical advantage. Look how the load is distributed on the rope. 50 pounds goes to the tree, and 50 pounds goes to her. So, if she pulls with 50 pounds of force, the load will rise! She has to pull 2 feet of rope to move the load 1 foot.
Does she get an easier pull? Well, it depends how you look at it. In theory, she only has to pull with 50 pounds of force to move the load, which is good. But, she needs to pull twice as much rope, which is not so good. In the end, she's doing the same amount of “work”. Would you rather lift 100 pounds 10 times, or 50 pounds 20 times? In the end you’ve still moved 1,000 total pounds, it's all the same.
How’s she doing for efficiency? Great! By using a quality pulley on the load, she can lift the load with much less effort. Way better than the carabiner with a 1:1 redirect.
The 2:1 pull with redirect and ratchet prusik
Sticky thinks, “Well, this is definitely easier to pull, but my arms are still getting tired. I'd rather use my bodyweight, and not lose what I’ve already pulled. Let's put a pulley in the tree, and a prusik on the load strand.”
Now we're getting somewhere. She’s lifting with 2:1 MA, used pulleys at both changes of direction to minimize friction, and added a ratchet prusik so she can take a break whenever she needs to without dropping the load. This is pretty much a perfect set up!
This, right here, is the foundation of mechanical advantage systems. All the fancy stuff in the rock or crevasse rescue books that makes you go cross-eyed? It's all just adding and stacking additional redirects and pulleys in different variations on top of pretty much what we just saw. (And no, I'm not going to show 101 flavors of pulley setups, because you can easily find them in a crevasse rescue book or Google image search.)
Now, the above diagrams might appear to be overly simplistic. But if we break them down, we can learn some important principles that apply to every kind of MA pulley system.
Changing the direction of pull at the anchor does NOT add mechanical advantage.
Changing the direction of pull at the load (or the load strand) DOES add mechanical advantage.
Even if a change of direction at the anchor does add friction, it might make your pull easier, depending on your own personal strength, body weight, and the weight of the load you need to move.
Try to minimize friction at every change of direction by using a pulley rather than a carabiner whenever possible.
A change of direction at the anchor introduces the pulley effect, taking the load weight and doubling it at that anchor point. (If you’re hauling, the force on the anchor is even more, due to friction.) Be sure your anchor can handle this.
Adding a progress capture / ratchet means your load will not slide back down if you stop pulling.
In the end, the “work” you do is the same with an MA system. You move the same amount of weight over the same distance. So, in a sense it's not necessarily “easier” to move the load all the way up, you just get to pull less weight on each stroke.