RADS Theoretical Ratio

The definition of MA has been around for a long time and is expressed as a ratio of the load to the force required to lift the load, specifically:

MA = load : force to lift the load

E.g.
I lift 200 lbs with a 100 lb force, what's the mathematical, i.e. theoretical mechanical advantage? Well, by the definition it would be:

MA = 200 : 100 which reduces to 2:1. And notice it's completely independent of how the pulley system "looks"!

Let's apply the math and physics to the simple pulley system we've been discussing. In my video, how much weight am I lifting? It's 200 lbs. How much force does my arm have to exert? I think the only reasonable guesses would be either 100 lbs (2:1) or 200 lbs (1:1). If it's 200 lbs, I couldn't even start to lift myself. So that only leaves a force of 100 lbs and that's what the math and physics says it should be. I can generate a force of 100 lbs with one arm as seen in the video.

So how much load do I lift? 200 lbs. How much force do I exert? 100 lbs. So according to math and physics, what's the mechanical advantage?

It is:

200 lbs : 100 lbs which reduces (mathematically) to 2:1.

If I didn't have a 2:1 advantage I couldn't lift my weight with one arm. The effect of this is readily demonstratable. Have a climber demonstrate that he can lift his entire weight with one arm. Then have him hand the pull rope to somebody else and see if they can lift him. They probably can't. Even if they manage to it will be quite difficult. Why the difference? Mechanical advantage!

I can see how tempting it is to equate how a pulley system "looks" to mechanical advantage. E.g. the rope over the pulley attached to a climber on one end and pulled by the climber on the other end, "looks" like the familiar 1:1 redirect. And, in fact, to a ground referenced climber it would be - he'd have to pull with a force equal to the climber's weight. But to the climber, he only has to pull with half his weight because to him there is a mathematical and real 2:1 mechanical advantage.
 
[ QUOTE ]
Oh, you got me wrong I'm on your side with this since the 9th grade.

[/ QUOTE ]
I am so sorry treebing
blush.gif
, it's awful to get old and confused.
frown.gif
I saw your post right after mine and didn't bother to notice the little detail.
blush.gif


Wait a minute, here's what was confusing, you said,

[ QUOTE ]
"Nice video Ron, I can't imagine why you would want to call it a 2:1. But if that is how it makes sense to you and you only use ground references to explain things. Like its a 2:1 system but the climber is pulling...."

[/ QUOTE ]

It reads like that whole paragraph is addressed to me and I'm looking at this in an odd way???

LOL! I was puzzled though; we had just agreed completely from where you posted 'what the scale would read'.
 
What a great experience that was. Although they are all good, I particularly liked the statement in the first one that explains how much easier it is per pulley. Pretty definitive!
 
"Wait a minute, here's what was confusing, you said,

Quote:
"Nice video Ron, I can't imagine why you would want to call it a 2:1. But if that is how it makes sense to you and you only use ground references to explain things. Like its a 2:1 system but the climber is pulling...."



It reads like that whole paragraph is addressed to me and I'm looking at this in an odd way???
-----------------------------------------------------------'

I've always had trouble with the use of the word "you" when refferring to a universal "one"


That is one of my big gripes with the english language I think, Or at least my use of it because I say "you" when I'm not really talking about you at all but a more general abstract "one". This has led to confusions in the past for me, definitely a subject for another forum though.
 
[ QUOTE ]
...I've always had trouble with the use of the word "you" when refferring to a universal "one"


That is one of my big gripes with the english language I think, Or at least my use of it because I say "you" when I'm not really talking about you at all but a more general abstract "one". This has led to confusions in the past for me, definitely a subject for another forum though.

[/ QUOTE ]

"You" talkin' to me??? LOL!!!
 
[ QUOTE ]
...I argued the very same thing, i.e. the RADS is 2:1, the same way, did all the measurements, etc., but then two guys, one a physicst kept insisting the RADS was a 3:1 to the climber and a 2:1 to a ground referenced person. I finally realized the "work" won't balance out for a suspended climber as a 2:1, but it does as a 3:1.

And throughout my arguments, in the back of my mind, it was forever nagging me that in a RADS, when I pull myself up, there are three lines supporting my weight. I could not resolve how three lines supporting the load could produce a 2:1 ratio. Well, it couldn't. So I had to really study a pulley system where the pull line attached to the load and produces an extra support line. I finally saw the light thanks to a buddy and a physicst...

[/ QUOTE ]

Ron, I thought this was particularly well worded and clear, not dissimilar to your videos. The lack of further input on this thread does leave me curious.

Is there anyone out there still that does not understand or flat out disagrees with the above statement?


Dave
 
[ QUOTE ]
[ QUOTE ]
...I argued the very same thing, i.e. the RADS is 2:1, the same way, did all the measurements, etc., but then two guys, one a physicst kept insisting the RADS was a 3:1 to the climber and a 2:1 to a ground referenced person. I finally realized the "work" won't balance out for a suspended climber as a 2:1, but it does as a 3:1.

And throughout my arguments, in the back of my mind, it was forever nagging me that in a RADS, when I pull myself up, there are three lines supporting my weight. I could not resolve how three lines supporting the load could produce a 2:1 ratio. Well, it couldn't. So I had to really study a pulley system where the pull line attached to the load and produces an extra support line. I finally saw the light thanks to a buddy and a physicst...

[/ QUOTE ]

Ron, I thought this was particularly well worded and clear, not dissimilar to your videos. The lack of further input on this thread does leave me curious.

Is there anyone out there still that does not understand or flat out disagrees with the above statement?


Dave

[/ QUOTE ]

Personally speaking, I'm going to adopt Moss's term 'hybrid' to differentiate between climbing and rigging i.e. drt - hybrid 2:1. I still dont like the 2:1 description because of the rope travel thing in a traditional sense, but dont deny the reduced effort involved either. Thats as good as its gonna get from me Dave
grin.gif
 
I think adding another term hinders more than helps. We have DRT, DdRT, now hybrid DdRT which is the very same thing as DdRT - that just takes us further away from the issues. E.g. doesn’t a hybrid pulley system have exactly the same issues as a non-hybrid system? Yes, and what’s more, the issues are now clouded by a new name.

Plus, there is no such thing as a hybrid pulley system. It's either a 1:1, 2:1, 3:1, etc. AND what it is, depends on who/what the reference is.
 
[ QUOTE ]
I think adding another term hinders more than helps. We have DRT, DdRT, now hybrid DdRT which is the very same thing as DdRT

[/ QUOTE ]

sometimes its the little things. What is DdRT v DRT?

Ron I'm sorry you felt the need to write all that other stuff down in response to my post, you really didn't have to, but I appreciate your time in doing so.
 
[ QUOTE ]
...sometimes its the little things. What is DdRT v DRT?

Ron I'm sorry you felt the need to write all that other stuff down in response to my post, you really didn't have to, but I appreciate your time in doing so.

[/ QUOTE ]
Reg,

Hmmm, I'm not sure whether this is good or bad, but 'all that' wasn't in response to your post. Only the part about hybrid was in response to your post.

The rest was just something I felt that had been said indirectly, and I wanted to try to summarize, hopefully to clean some things up and say them more directly. I should have put the rest in a separate post, as I will now do.

Sorry for the confusion.
 
With no reference to any particular post(s) and just for reference, hopefully this will explain some of those ‘mathy’ and ‘theoretical’ issues that apply, and some things that have been referred to but not stated directly.

I’m going to start with a couple of simple definitions and then paraphrase some principles that are ALWAYS true. There aren’t many times we can use ALWAYS, but this is one of them.

Definitions:
MA (mechanical advantage) – Gaining some kind of advantage to help us do something. We tend to think of MA as reducing the force required to move something, but it is not limited to that. E.g. what’s the difference in a 2:1 MA and a 1:2 MA?

In a 2:1, we use a force of 1 to move a load of 2. E.g. 50 lb pull to lift 100 lbs. 1:2 means we use a force of 2 to move a load of 1, e.g. we pull with 100 lbs to lift 50 lbs. This is NOT due to friction. We can have a theoretical MA of 1:2 in a frictionless system. An ‘over-drive’ transmission is an example of this.

Force Multiplication – This is really the term we ought to be using. What we hope to gain via MA is to move a heavier load with a lighter force so we need to multiply our lighter force into a greater force. MA is a correct term, but can be imprecise. E.g. I’m going to gain MA by pulling down on a rope to lift a weight over trying to pull up on the rope to lift the weight. This not force multiplication, but because when I pull down (i.e. with a rope over a pulley), I can bring my entire weight to bear against the load. That’s a form of MA without force multiplication. I do gain an advantage in pulling, but it’s still a 1:1 MA – I can just pull harder one way than the other.

Principles of MA, or better, force multiplication:
How many times have we heard, “You don’t get something for nothing.” That’s certainly true of MA or force multiplication.

Principle:
If we have force multiplication, we must pull the rope through a proportionally longer distance than the load moves. This is always true; you simply cannot have one without the other. E.g. if we have a 6:1 we have to pull 6 times as much rope as the load moves. The same principle applies to other ratios. Here’s why:

Let’s say we have a typical 2:1 pulley system (i.e. not a DdRT type) and we need to lift 100 lbs. Since we have a 2:1, we only have to supply 50 lbs to lift 100 lbs. That’s force multiplication – we make our 50 lb force lift 100 lbs; sounds like we got something for nothing doesn’t it?

But, if we raise that 100 lbs one foot, we have done 100 lbs x 1 ft, or 100 ft-lbs of work. Now let’s look at the work done on the pull line. If we pull 50 lbs one foot, we’ve only put 50 ft-lbs into the system. That leads to the next principle that is ALWAYS true:

Principle:
The amount of work produced by a system can NEVER be more than the work put into the system.

Hence, in the above example, we have a problem. It appears that we put 50 ft-lbs in and got 100 ft-lbs out and according to the work principle that’s impossible! So what gives? Well, what gives is we have to pull that 50 lbs through two feet, not one foot. Then we have 50 lbs x 2 ft = 100 ft-lbs - the work in, equals the work out. Actually, in real systems, work out is always less than the work in due to friction, but this thread is about theoretical MA.

Now, let’s apply all this to a frictionless RADS; first the MA or force multiplication. When we pull on the down rope of a RADS, we have three strands of rope supporting our weight – two from the Grigri (an imaginary frictionless Grigri – of course you couldn’t rappel on a frictionless Grigri!), and one strand we’re pulling on. Make no mistake here, we are applying a lifting force on the down rope by pulling on it, so it is sharing the load. Since three strands share the load, each strand will have 1/3 the climber’s weight. Hence, we can lift our weight with a force of 1/3 our weight, so we have a 3:1 force multiplication, or more commonly stated, MA.

The two above principles have to apply – there are NO exceptions. So, from the first principle we see that if we have a 3:1 MA, we must pull 3 times as much rope as the load (us) moves up. That meets the requirement of the second principle. If a 150 lb climber lifts himself one foot using the down rope alone, he does 150 lbs * 1 ft = 150 ft-lbs of work at the output of the system. Since he only is pulling with 50 lbs on the down line, he has to pull that 50 lbs through 3 feet to make the work balance – 50 lbs * 3 ft = 150 ft-lbs.

So, since this has to be true, it is inescapable, on a RADS, the <u>climber</u> is going to have to pull 3 feet of rope to raise himself 1 foot. It is the climber alone that has to do all the work. Now it’s just a matter of deciding how and where to measure the amount of rope pulled. We cannot look at a ground reference for this measurement because the ground isn’t doing any work, nor any one ground referenced. If we measure how much rope goes by the climber, it will be 3 feet.

I hope that helps.
 
[ QUOTE ]
[ QUOTE ]
...sometimes its the little things. What is DdRT v DRT?

Ron I'm sorry you felt the need to write all that other stuff down in response to my post, you really didn't have to, but I appreciate your time in doing so.

[/ QUOTE ]
Reg,

Hmmm, I'm not sure whether this is good or bad, but 'all that' wasn't in response to your post. Only the part about hybrid was in response to your post.

The rest was just something I felt that had been said indirectly, and I wanted to try to summarize, hopefully to clean some things up and say them more directly. I should have put the rest in a separate post, as I will now do.

Sorry for the confusion.

[/ QUOTE ]

No confusion here Ron, and its all good rest assured.

I never said hybrid DDrt or DRT (still dont know what the differece is), but a hybrid 2:1 when refering to the traditional double rope climbing set-up....because of the difference between a climbing 2:1 lets say or a traditional hauling system. I feel the need to call it something out in the field working with young climbers, but without being too long winded about it.

The whole pulling/passing rope thing, how much trails on the ground v how much is actually pulled (not passed) which you suggest isn't really that significant....although the amount will obviously change as we add more pulleys into the system. I have no desire to get into any of this on a job so prefer to use a term such as 'hybrid' - 'where the load and lifting force are combined' as Dave said many moons ago. If you can think of a more fitting term that might help me out then I'm all ears?

I would appreciate you're thoughts on something related Ron....staying with the traditional double rope climbing system. I weigh about 154 and my climber lets say 170. He has his line over a limb and is ready to start is ascent from the ground. If I replace his hands with my own and strart hauling nothings going to happen right, meaning I cant raise him....because its a 1:1 right, and he's heavier than me.

But then I spread out his attachment points. e.g. I attach each end of the line at opposite ends to a stretcher and have him lie on it. One end of the line is terminated while the other runs through a cam, the cam is fixed to the stretcher....but still the same line over the same branch as before etc

Now if I pull down on the cam-end of the line the other end is going to raise to the equal amount right? then I push/lift the cam-end with a force to just over half the weight of the load (while holding the rope in place) up until the stretcher is level, and then the cam locks in place, thus raising the entire load by whatever that was. But essentially the same load/line/crotch etc that I didn't have a chance in hell of raising earlier. Would you classify that technique as a 2:1 system?
 
Reg,

Ahhhh, what I'm reading finally registered.
blush.gif
Is this what you have in mind?

Regsstretcherexample-1.jpg


If so, I can analyze it; but it's complicated because it isn't a parallel rope system and some trig has to be used to calculate the theoretical MA. I just want to be sure I have the right configuration.

However, if this were a parallel rope system as shown in the figure below, it would be a 3:1.

regsexampleno2.jpg


However, all three configurations would have a balance problem. The stretcher likely wouldn't stay level.
 
I might be out of bounds here, but I think I understand what you're demonstrating in the diagram. I'm just wondering if the bottom of the left leg of line and the cam should be attached next to each other, in the center, or even to the same point? (Side by each?
grin.gif
)
 
You're quick! I was working on that as you typed. Check out my modified post.

And bear in mind, I'm not sure that's what Reg is meaning, but I think it is. We'll see.
 
I think the one on the lower left would most exemplify the concept, because the highest MA comes out of the line being redirected 180 degrees. And to be TOTALLY exact, I think you'd even have to connect the lower left leg to a thimble on the top of the cam. (Again, I think is close enough to understand).

Eric
 
You must log in or register to reply here.

New threads New posts

Back
Top Bottom