Mechanical Advantage: 2:1 or 3:1

[@LittleDreamsz]

The simplest explanation ever after 3 years of working in the jungle! I finally understood. Much appreciated!

[@bfflorida2311]

Finally someone displays example, who understands physics and has experience on this subject .👏👏👏

[@walterwadlow9438]

By far, the clearest explanation of mechanical advantage and its relationship to frame of reference. Thank you!

[@jeremylunning654]

I had to watch this a couple times to understand the concept. Good explanation

[@calendareofd]

I initially didn't believe this and thought changing my frame of reference just meant the other pulley became the moving pulley and so the system would still be a 2:1. BUT... if you calculate the distance the rope moves based on your frame of reference, it truly does become a 3:1 when the "load" does the work. Remember if the frame of reference is from a person standing on the ground below, then pulling down 2 cm of rope will raise the load up 1 cm. From that frame of reference it is a 2:1. HOWEVER, if you are the load and watch the pulled end of the rope, you will see 2 cm of rope go down as you (the load) go up 1 cm. That means the loads position travelled 3 cm in reference to the pulled end of the rope. If the load (you) applies the force, the mechanical advantage is 3:1.

[@the11eventhour]

There are a few people who 'get it' in this 'inane relativistic way' and make fun of the people who don't get it; or is it 'everyone' gets it in this relativistic way and there are a few people who are looking for the truth, and a few who are happy to live relativistically and make fun of others. All that needs to be said is that the man on the ground is adding extra weight into the system, making it harder. The beam (tree, etc.) has one fixed rope and one (static) pulley attached: the fixed rope (when the man on the ground is pulling) is pulling 50kg of 100kg bodyweight upwards, the static pulley must hold the other 50kg on one side and at least another 50kg from the man on the ground pulling on the other side. A total of 150kg for the beam to pull up. When the climber is pulling his own weight, it is spread across the fixed rope and the static pulley, which must be a maximum of 100kg compared with the 150kg+ before with the added weight of the man on the ground pulling. Divided by all the three ropes carrying his weight is 33.33kg the force he is pulling is at least 33.33kg on the free rope to hold himself from falling and ascend.

[@ericjane747]

Thank you. Learned something new from you again!

[@GregoryLieb]

Richard, your examples are perhaps somewhat misleading in an alpine setup. In the far left example (the one attached to your harness), for every 1 unit of force your hands apply, the left carabiner supports 1 unit and the right unit supports 2 units of force. With the other rigged examples the (sole) carabiner supports 3 units of force. Therefore, as is often the case in an alpine situation, if you are trying to lift your partner on the other end of the rope, the system you are tied into provides no mech advantage whereas the other examples provide 3 to 1 mech advantage.

[@mattd8411]

Good video buddy. Not sure why but I always get confused trying set these up. We had set one up the other day drag a lady out of a tight place. Thanks.

[@deadcatbounce3865]

Depending on how high the load Is the rope going down to the ground will have a decent amount of weight. Enough to assist the system for up.

[@usethings]

Aha! It seems so obvious when expressed this concisely: frame of reference is a great way to understand it. I would have taken the external frame, seeing the bottom as the moving pulley for 2:1!

[@JoBianco]

Here's my way of understanding this which may be wrong, I'll let you decide. IF mechanical advantage is the ratio of applied force to input force, then when the load is also doing the work, the applied force has a direct affect on the input force. You are "making yourself lighter" as you pull down. This wouldn't happen with someone on the ground. The ground person, the person applying the force does not "lessen the weight" of the input force. I put that in quotes because I recognize our weight doesn't actually change. What I don't understand is the amount of rope passing through. It seems to me the amount of rope passing through the system is the same whether I pull it or you pull it. It is always the same. It's the reference of the applied force that matters.

[@JoBianco]

@richard delaney, am I saying this correctly?

[@mikemccord8399]

The amount of rope going through the system changes because the location of the rope meter changes. In The scenario of the person on the ground pulling, the rope meter is stationary. So 2 units will be needed to pull through the meter to raise the load. If the person hanging on the rope is doing the hauling the rope meter is attached to them so the rope meter is now mobile moving towards the anchor. So three units of rope would be logged at that location. Does that make sense why the distance through the M/A changes based on who is doing the pulling?

[@JoBianco]

@@mikemccord8399 That's helpful, but could you define "rope meter" for me? I think I get it but I'm not sure what you mean with that term. Thanks

[@mikemccord8399]

@@JoBianco i’m just referring to whatever tool you use to measure the amount of rope pulled. A measuring device.

[@JoBianco]

@@mikemccord8399 Actually that was really helpful, thank you.

[@trimix69]

I would like to see this done with load cells on the anchor, the load and the haul line..... to verify the information

[@ratagoniajones5430]

Well... you probably know the "load", as you choose the load to test with, and it can be weighed. The load on the anchor is the "load" plus the load on the haul line - so if you instrument the haul line, you can know the load on the anchor.

[@wd1000]

Pretty expensive way to "verify." Since mech. advantage (simplified without losses) is: Force x distance (input) = Force x distance (output) you can just measure distance. Pull the line 3 feet. If the load end moves 1 foot the MA is 3:1. If it moves 1.5' MA is 2:1. There I just saved you a whole bunch of time and money.

[@phoenix21studios]

when you pull yourself you are pulling your own weight off of yourself, when the other people pull that isn't happening.

[@Darlhim89]

Great video Richard but I am a little confused. In the system you are hooked into, regardless of the frame of reference, the second pulley is never truly a moving pulley. It is always the one at the bottom in this setup that is going to move. Same goes for a prusik setup, but the distribution of force is still the same in any of the setups you show, as you stated. (I understand why they are all equal) What I don't understand is why does it make a difference who applies the force? If you apply 33 lbs of force with your own arms, why is it different than me standing next to you, applying 33lbs of force for you? The rope still moves in the same direction through the same system? Regardless of what you consider the load and the anchor, equal force should be applied and the lighter object should move when that force exceeds the weight. But I just can't wrap my head around why the person doing the pulling makes a difference if everything but who's muscle is being used is the same. Thanks.

[@RopeLab]

Think of it like looking out the window of a moving train. You see a parked car but, relative to your position on the train, it appears moving towards you. As for the 33lbs: If you are 100lbs and suspended, you apply 33lbs to move up as you are divided equally between 3 strands of rope. If you hand the rope to the person standing on the ground, they need to pull 50lbs as now only two strands are supporting your 100lbs.

[@zrig1]

It does mess with the head. I look at it as, how many lines are shortening between pulleys and load (only in a simple system mind you). A redirect that goes up through a pulley and back down to your harness ( 1:1 or counterbalance system) actually creates a 2:1 if you pull yourself up. I had to try it to prove the concept to myself. Went through this very discussion on a jeep winching video. I think what messes some of us up is most rescuers are not the load and haul team at the same time.

[@ianbrown_777]

I was just about to say something similar - I will! Might help to imagine how many feet of rope between the pulleys need to disaapper to bring the 2 pulleys together. If each of those 3 lengths are 1 foot long, then 3 feet need to disappear. Then, when both pulleys are finally together, how many feet of rope have passed through his hands? 3 is the answer (and he has moved 1 foot)

[@bennyjustus]

@@ianbrown_777 The answer is 2 feet. Take another look at it. I am talking about the first system btw.

[@bennyjustus]

@@RopeLab The same number of strands support the load no matter whose hands are on the rope!

[@Tobi-zd9zp]

Ok this explains a lot, if I set up a System as shown, it was very easy to lift my self up while beeing the load. On the over side, if I clipped my younger brother on to it and tryed to pull him up, while standing on the ground it felt much harder. I always explained it like,it's easier because I'm pulling with my weight and it's like a Pull-up movement. Your video is confusing in the first moment, but in the end it makes sense. So what happens, if I'm mirrorring the System, standig above the load, rope and one pully attached to the load?

[@Capnmax]

Great explanation! Thank you

[@alancrook1034]

M.A. has to take friction into account.

[@davidw4346]

Great, thanks.

[@VisinskiRadoviBeograd]

How interesting!

[@mikemccord8399]

It’s sad and comical the amount of grief this topic brings up. If I may, add one more point of view. If you can look at this scenario as if when the load Is doing the hauling, they then become the anchor and the anchor is considered the load, all should work out in your examples.

[@CanyoneeringUSA]

Awesome. So clear.

[@cihankuscu1774]

Yo

[@videoboy6380]

it is very helpful . one question : is it possible to set a super system that is 18:1 or even more advantage with more and more pulleys and the related device. I search over the youtube. no such demonstration is available. of course It is for fun but it means : if such super system is set. it means a 8 year old boy could pull a 4 wheel car.

[@ratagoniajones5430]

In theory perhaps. In practice, there are losses in each pulley. Even with high-quality pulleys, each added pulley adds loss so getting past about 5:1 or 6:1 is very difficult to achieve.

[@andtheallstars]

@@ratagoniajones5430 while your correct that there is friction in each pulley your incorrect in saying that that mechanical advantage is exceeded by the friction in a 5:1 or a 6:1. Even building a 9:1 with nothing more than caribiners used as the redirects (which introduces far more friction than any pulley) you still have a system with a ton of mechanical advantage which makes a single person hauling another single person dead vertical very easy.

[@ratagoniajones5430]

@@andtheallstars - do you have evidence of this? Alas, I am not in a position to provide evidence to support my claim.

[@bennyjustus]

That first example is a 2:1 system no matter who is holding the rope!

[@mikemccord8399]

Sorry but try to see why it isn’t a 2:1.

[@bennyjustus]

@@mikemccord8399 I should have deleted or edited my comment. it is absolutely 3:1. it took me a little while to realize this.

[@mapleknot3]

Thats complete nonsense. Only one pulley ever changes its position in space, it is therefore always a 2:1 w a cod. It doesn't matter who pulls, the system is the same.

[@matteswe]

So let´s say I climb a tree with DdRT-system. I am the load and I pull myself up i.e I pull twice the rope (one end with my hands, rope goes through a pulley and back to me which also pulls me up). 2 distances pulled with my rope pulls me 1 distance closer to the pulley. What kind of system is that?

[@mapleknot3]

@@matteswe if I understand you correctly, the climber (the load) is attached to leg A of the rope which goes up the stationary pulley (the anchor) and leg B of the rope comes back down to the climber and is connected w a friction device. If the load weighs 100kg, then leg A of the rope has 100kg on it. What's on one side of the pulley MUST be on the other side too. So leg B has 100kg on it. So if the climber pulls on leg B, then they are pulling 100kg. 1:1 system. For every 1m the climber pulls on leg B, leg A will rise 1m. (Maybe this is where 2 rope "movements" comes from. It's not rope "movement", it's how much rope is actually pulled). 1:1 system. Finally, there are no moving pulleys in this system. 1:1 system. An alternative is that some climbers use a slack control pulley at their waist. Now if you pull up towards the anchor w this pulley, you just created a 3:1.

[@matteswe]

@@mapleknot3 No if the load weighs 100 kg leg A has 50kg on it and the other 50kg. You are saying there is 100+100kg on each rope attached to the pulley but somehow there is only 100kg on the pulley itself?

[@mapleknot3]

@@matteswe If leg B of the rope is attached w a passive friction device, then leg A is the only leg supporting the load. If the load is 100kg, then leg A must be 100kg. Leg A must equal leg B. That puts 200kg at the anchor. This is a 1:1 system. Also, moving pulleys create mechanical advantage. There are no moving pulleys in this system. Therefore no MA. Try youtubing "mechanical engineering: 11/19, why are pulleys a mechanical advantage". Michelvanbiezen. "Calculating the mechanical advantage in a simple system". Rigging lab acaademy. All the best.

[@matteswe]

@@mapleknot3 Maybe we are not talking about the same thing but DdRT IS in fact a 2:1 system and what the video is showing, with one added pulley IS a 3:1 system. There is no point in arguing that because believe me, I am correct (not trying to be rude but I've done my research). Tell me how there can be 200kg load on the pulley? Are you serious? Would it be 1000kg if you add enough ropes? Where is the extra weight? Does the climber gain weight when you add ropes?

[@VisinskiRadoviBeograd]

It would be nice if Richard would be kind to explain this interesting situation, if two strands of rope are hanging from the ceiling pulled through the pulley, and a person on the ground clip himself to one end and grab the other end and starts to pull himself up: kzbin.info/www/bejne/f5rXdGaPeal9g5o

[@TheMadMagician87]

That is a compound pulley system. Due to the 60ft rope through the pulley (main climbing line), that is a 2:1 system when pulled on by the climber. The ascender is used as an isolation point, to attach another 3:1 system (that particular setup is commonly called a 'Zed' or ('Zee') rig or drag). In that scenario, the theoretical mechanical advantage is multiplied, so 3x2, producing a theoretical 6:1 mechanical advantage for the climber.

[@L0sGuys]

If you had actually done the experiment of measuring the amount of rope going through the system if you (as the load) are pulling vs someone else pulling, you would see that this claim is verifiably false. Simply changing where the force is coming from doesn’t change how much rope goes through the system. It’s 2:1 either way. The problem here is that you are conflating weight and force. It doesn’t matter what your mass is, so much as it matters how much force you exert on the system, and where that force is applied. Remember, for every action, there is an equal and opposite reaction. If you (again, as the load) exert X lbs of force pulling down on the end of the rope, you reduce the force you exert on the rope as the load by the same amount. Because this is a 2:1 system, the force you apply by pulling is multiplied by 2 (relative to the load), and will exceed the force you exert as the load when it exceeds 1/3 of the total force. So if you exert 100 units on the system as a dead weight (at the lower, moving pulley), by pulling down on the end of the rope with 1 unit, the load becomes 99 units. When you apply 33.3 units to pull, it exerts 66.6 units (remember, 2:1) units on the load. The load has now become 66.6 units (because by pulling down you are counteracting your body as the force by an equal amount) so as soon as you exert more pulling force, it becomes more than the force of the load, and you go up. While you body weight never changes, the force it exerts as the load changes as you pull.

[@RopeLab]

Hey Scott, thanks for taking the time to pen such a detailed response. I guess one question I would ask you to consider is this: You have a 4x4 with a winch mounted on the front. You run that winch out to a tree and then back to the front of your 4x4 and start pulling with the winch - and you (in your 4x4) start moving towards the tree. What is the MA here?

[@L0sGuys]

@@RopeLab I think I know where you're going with that question. After following it to it's logical conclusion, I'm prepared to eat a big slice of humble pie. In short, what I failed to factor in was the amount of rope left over in both examples once the load gets to the top and you can't pull any more. For those who (like me) had a hard time with the examples given in the video, consider this: Imagine the person in the system is 10' below the anchor. This would put 30' of rope in the system. If the person is pulling himself up, when he reaches the top, how much rope has he pulled? The answer is 30'. If a static person 10' below the anchor is pulling, once the person in the system gets to the top, how much rope has been pulled? The answer is 20', because there's still the 10' of rope going from the puller to the first pulley. There's the difference between your 2:1 and 3:1. Thanks for the reply Richard. Keep doing what you're doing.

[@RopeLab]

Thanks Scott. There are so many situations like this where I have had to change my thinking. It took me a while.

[@xanderbianchi1015]

@@RopeLab I respect you greatly, and am grateful for all of the knowledge you share with the rope rescue community. However, I believe that I can explain why you are misled in this discussion. This has been a recurring discussion between myself and another experienced practitioner, Kevin Koprek. Myself and a canyoning guru friend of mine were very convinced of the explanation you present in this video, but Kevin has finally got me to see it clearly. It’s always a 2:1 with a change of direction, regardless of who is pulling on it. The issue that causes so much confusion is that some of the usual methods of determining mechanical advantage don’t work when the load and the hauler are the same, but no one intuitively recognizes this. For example, the method of trying to measure the amount of rope moving through the haulers hand in each scenario. The separate hauler could imitate the “3 feet” of rope moving through the load/hauler combo scenario by simply walking forward 1 foot for every 3 feet of rope that passes through his hands, which would still mean only 2 feet of rope has actually passed through the change of direction pulley. The rope and the pulleys don’t know who is doing the hauling. As far as suspending the load between either 2 or 3 strands, I can explain that as well. It’s easy to follow your explanation that when the load and the hauler are the same, they need only exceed 1/3 of their body weight to get themselves to move - and therefore, one might conclude that it’s a 3:1 system. However, this is also an error. The pull strand vectors cancel. Indeed, you need only pull 1/3 of your body weight, but your body now effectively weighs 2/3 of its normal weight from the perspective of the pulley clipped to your harness (T-method easily determines this). The remaining output to input ratio is 2:1 (0.66:0.33). You can apply this same thought to your 4x4 winch example. When the load is the hauler, it must overcome only half of its weight, but at that point, the amount of tension on the fixed side is also only half. Output to input ratio yields 0.5:0.5, or 1:1. The only thing that can be conceded is that when you are both the load and the hauler in the setup in this video, it “feels” the same as if you were pulling on a 3:1 when you’re separately hauling a person who weighs as much as you.

[@brookejacinto8686]

@@xanderbianchi1015 This physics professor explains identical situation: kzbin.info/www/bejne/ponIkHZ4d9mnj6s

[@MrSingleJack]

Very nicely done, Richard. I'm afraid some of the inane are still not going to get it. :(