I get confused when I look at these fancy diagrams with ropes running in all different directions. How can I figure out what the real mechanical advantage is of a given system?
You're right, things can be difficult to figure out! At one level, you could say it doesn't really matter. If the 3:1 isn't working, you can add or multiply a 2:1 on top of this, and hopefully the resulting 5:1 or 6:1 gets the job done. The number doesn't really matter in the end.
But, since you asked the question . . . Remember our discussion simple, compound, and complex systems from this post? (Go read it now if you have not seen it.)
The answer of “what’s my MA” varies depending on which one of these systems you’re using.
For a simple system, we calculate the MA by counting how many strands of rope are going to and from the movable pulley(s) on the load or load strands. And, always remember, any pulley or carabiner that’s fixed on the anchor only changes the direction of pull, and does not create mechanical advantage. Let's look at a few examples.
Alse, 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.).
There’s 1 strand of rope coming from the load. So, 1:1 simple system (no mechanical advantage gained).
There’s 2 strands of rope going to and from the load. So, 2:1 simple system. (Rope end attached to anchor, even number MA of 2.)
There’s 3 strands of rope going to and from the loaded strand. So, 3:1 simple system. (Rope end attached to load, odd number MA of 3.)
For a COMPOUND pulley system, the hauling systems are MULTIPLIED together.
For example, this is a 2:1 on top of a 3:1, so multiplied we get a 6:1.
For a COMPLEX pulley system, the hauling systems are ADDED together.
For example, the image on the right shows complex system. The 2:1 on top of a 3:1 added together gives a 5:1.
For more on simple, compound and complex pulley systems, see post “The 3 kinds of pulley systems”.
There‘s also a more math oriented way to calculate your MA. It’s called the “T-system”. You can read more about it here.