What's the mechanical advantage? It's relative!
The illustrations in this article, used with permission, come from the excellent website RopeLab, run by Australian rigging expert Richard Delaney. RopeLab has a ton of great material for anyone who wants to dive into ropes, rigging, and mechanical advantage, check it out! There's a fair amount of quality free information, but getting an annual subscription unlocks the entire website. You can also connect with Richard on Instagram and his YouTube channel, where he has loads of concise, informative videos.
These diagrams come from a Ropelab online mechanical advantage quiz, which you can find here.
Okay, clever rope wizards and mechanical advantage fans. Here are some questions and diagrams that might leave you scratching your noggin.
A standard principle in mechanical advantage systems is that any change of direction that's on the anchor only serves as a redirect, and does not add mechanical advantage. Well . . . that's true most of the time, but not when the “load is also doing the lifting.”
The mechanical advantage of the system depends not just on the rigging. It depends on who is doing the pulling - a person who’s “in the system” or a person who’s out of it. Let's look at a few examples.
1 - This image shows someone standing on the ground attempting to raise their partner. What’s the Ideal Mechanical Advantage of this system (ignoring friction)?
image: https://www.ropelab.com.au/ropelab-quiz-1-mechanical-advantage/
Answer: It's a 1:1 mechanical advantage. The person on the ground is pulling the weight of the person hanging from the rope 1:1 through a redirect. No mechanical advantage is gained. The person on the ground needs to pull 1 meter of rope to lift their partner 1 meter, so it's a 1:1.
2 - This image shows a person attempting to raise themself by pulling down on the rope. What’s the Ideal Mechanical Advantage of this system (ignoring friction)?
image: https://www.ropelab.com.au/ropelab-quiz-1-mechanical-advantage/
Answer: Exact same rigging as before, but this time the person hanging from the rope is doing the lifting. This time, the mechanical advantage is 2:1! For the climber to go up 1 meter, they need to pull 2 meters of rope through their hand, so the mechanical advantage is 2:1.
Richard Delaney, from the YouTube video link at the bottom of this page: “Mechanical advantage is technically the ratio of the applied force to the input force.” There are two strands of rope holding the climber’s weight. If the climber weighs 100, that means each strand is holding 50. If the climber pulls down on the rope with a force slightly more than 50, they will start to move up. This means the applied force is 100, and the input force is 50, so therefore we have a 2:1.
Does this leave you scratching your head? It did for me when I first saw it! Next time you see a sport climber after a fall, pulling down on the belay rope to lift themselves back up to their high point, this is how they’re doing it, with a 2:1.
3 - Let's take this idea a step further. This image shows someone attempting to raise their partner by pulling down on the rope. What’s the Ideal Mechanical Advantage (ignoring friction) of this system?
image: https://www.ropelab.com.au/ropelab-quiz-1-mechanical-advantage/
Answer: 2:1, with a redirect through a second anchor point. There are two rope strands supporting the climber’s weight, so it's a 2:1.
4 - This image shows a person attempting to raise themself by pulling down on the yellow rope. What’s the Ideal Mechanical Advantage (ignoring friction) of this system?
image: https://www.ropelab.com.au/ropelab-quiz-1-mechanical-advantage/
Answer: 3:1. Just as in example #2, if the person pulling on the rope is the same as the load, the mechanical advantage increases, even though the rigging is exactly the same. In this case, there are three rope strands supporting the climber’s weight. For the climber to move up 1 meter, 3 meters of rope needs to be pulled, so the mechanical advantage is 3:1.
Back to Richard’s explanation of the ratio of input force to applied force: We have THREE strands of rope holding the climber’s weight. If the climber weighs 100, that means each strand is holding 33. If the climber pulls down on the rope with a force slightly more than 33, they will start to move up. This means the applied force is 100, and the input force is 34, so therefore we have a 3:1.
Isn't that interesting? The mechanical advantage of the system depends not just on the rigging, but on where the pulling force is coming from.
Here’s a climbing application of this principle.
Below is a screen grab from a video featuring IFMGA Guide Jeff Ward ascending out of a crevasse. He's using this 3:1 mechanical advantage system to help him climb the rope. I have an entire article on this clever ascending system, read it here.
Here's the set up. This works way better than the traditional “go up the rope with two prusiks” method.
Here's another way to think about it, in a horizontal plane.
You're out 4x4 wheeling in your truck, and you get stuck. You take the winch cable from the front of your truck, put it around a tree anchor, and then bring it back and connect it to your truck. You turn on the winch and slowly pull yourself out. What is the mechanical advantage?
If you clip the end of the winch cable to the tree, you would have a 1:1. But if you attach it back to the truck, you create a 2:1, because the load (truck) is also doing the pulling.
image: https://www.ropelab.com.au/ropelab-quiz-1-mechanical-advantage/
