Technical Rescue Physics Question

1. Jan 9, 2014

cavertevans

Hi all! I am hoping your combined brains can help me with a problem in analyzing a technical rope rescue system I have been using for a few years. Here is the scenario:
There is a patient on one end of a rope. This rope runs up and over a pulley and back down to the ground where a rescuer is located (next to the patient). The rescuer tethers themselves to the patient; this creates a loop from the patient up to the pulley, down to the rescuer, and over to the patient. The rescuer then climbs the rope. As they climb the loop gets smaller and pulls both the patient and the rescuer up. (For this analysis assume no friction, a massless rope, and everything is occurring in free space.)
The system has a theoretical mechanical advantage of 2:1 where the load is both the patient and the rescuer. All of this is agreed upon in the rescue community. However, what is disagreed upon is if this should be classified as a counterbalance, or a haul system.
The rational for saying it is a counterbalance is that one mass (person) balances out the other (in part). So there must be some counterbalance going on. The opposite argument is that since both the patient and the rescuer are part of a single load, it is just a haul system. In other words, it can not be a counterbalance if the single load is holding itself up.
Personally I think the system is dynamic and can't be treated like there is one load. So I think there is a counterbalance at work, however, I would like clarity of thought and sound arguments to sway me because I'm literally hanging my life off this system! Any and all help would be greatly appreciated!

2. Jan 9, 2014

Simon Bridge

Welcome to PF;
It looks like it shares aspects of both - no reason you cannot combine the action of two machines - but I am having trouble visualizing it.

Can you show me a diagram, or a video of the technique in use?
Does the technique have a technical name I can look up?

Also - what are the stakes?
Why does it matter whether it is a counterbalance or haul system - those are just labels?
Why does it need to be one or the other?

3. Jan 9, 2014

Staff: Mentor

Welcome to the PF.

I agree that a diagram is needed to be of much help here. Also, I don't see the source of a 2:1 pulley mechanical advantage in your description (but I could be missing it). For a 2:1 mechanical advantage, you would need 3 rope lengths and 2 pulleys, I believe. You have to arrange it so that the rope gets pulled down 2x as far as the masses move up...

4. Jan 9, 2014

Staff: Mentor

5. Jan 10, 2014

jbriggs444

Nice drawing, but not matching the scenario that I hear being described.

As I understand the scenario, there is a single pully overhead. The hauler has one end of the rope in his hands. It is looped over the pully and the other end is tied to the hauler and to the patient so that they are tethered together.

The if the hauler pulls down 1 meter of rope, he will have lifed himself 1 meter upwards. That means that he will have pulled a net of 2 meters of rope past himself while lifting the combined load 1 meter. That is a 2 to 1 mechanical advantage.

As I understand the question, we are being asked what to call this system, "counterbalance" or "haul".

To me, a "counterbalance" system would put a passive load on the opposite side of the pulley from the payload. Depending on how well matched the counter-balance is, one can then apply an arbitrarily small effort to move the load. A "haul" system would be one in which you use the effort to pull a lot of rope with a little force so that the payload is moved a smaller distance with a greater force.

This system [as I understand it] is a hybrid. It is a counter-balance system which operates backwards, putting the passive load on the same side of the pully with the payload, thereby making things worse combined with a haul system that provides a 2 to 1 mechanical advantage.

If the rescuer weighed exactly as much as the patent then the net advantage would be one to one -- the rescuer would be doing the equivalent of a dead lift of the patient.

6. Jan 10, 2014

cavertevans

Thank you all for your thoughts! To clarify the system I just attached a written description of the system as well as some diagrams that should clarify what I am talking about. Figure 1 is the most relevant. The other figures have multiple systems stacked together, so they are more complicated.
The system is called the Diminishing Loop Counterbalance, and it is primarily used in cave rescue for small party rescues with few people and little gear. It certainly is not perfect, but it can get the job done if you do not have many resources!
jbriggs444: Your analysis of the 2:1 system is mine as well. Since the work is a function of distance the load is elevated, the mechanical advantage is calculated by the number of times the climber has to climb the length of the pitch. In this case it would be two. With that said, the climber still has to pull their own mass up plus/or minus half the difference in the masses between the two people.
Simon: Your question about nomenclature is a good one. Why does it matter? It really doesn't. The rescue community is just like the academic community, sometimes we disagree and argue about things that ultimately do not really matter. Professionally I am a paleontologist and at most of the meetings I attend people argue about things that really do not matter too. Personally I would just like to make sure I am not fibbing to my students when I teach them the system. Professionally, it doesn't matter. The system works and it is safe.
Again, thank you all for your help! And let me know if that document is insufficient in answering your questions! If need be I can build it in my office and take some pictures, so if the figures are not enough, I'd be happy to make some more visuals! Thanks again!

Attached Files:

• The Diminishing Loop Counterbalance-Paper.pdf
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7. Jan 10, 2014

CWatters

Seems easy enough to understand how it works. If there is no friction in the pulley their total weight MUST be equally distributed either side of the pulley or the pulley would rotate until it was.

Imagine if both people were replaced with a section of thicker/heavier rope. At all times it would look like this (see attached). The tension in the rope would be half the combined mass and that's what has to be overcome to shorten the loop.

It doesn't matter if one person is heavier than the other - their combined centre of mass will move until it's below the pulley.

Haul system or counterbalance? I believe that's a false dichotomy.

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• rope.png
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8. Jan 10, 2014

Simon Bridge

Oh I see it now - you could almost think of it in two stages ...

1. rescuer climbs the rope a bit and stops.
2. rescuers weight pulls the patient up, rescuer falls a bit
... repeat.

The key is that the length of rope gets shorter at each stage so they cannot fall lower than the patient - otherwise the rescuer would just stay at the bottom. This will be why the rescuer is attached to the patient.

9. Jan 11, 2014

CWatters

Good description Simon.

It's quite interesting to consider what happens if the rescuer is a lot heavier or lighter than the patient. Who gets to the top first? It's not always the rescuer (although the difference is probably marginal).

10. Jan 11, 2014

Simon Bridge

You could probably see the effect if the pulley is very sticky - so a quick rescuer can climb a bit ahead of the patient before the patient starts to move. [1]

The difference in arrival times will depend on the length of rope attaching the two people (and the climb rate etc).

Looking at the videos of the technique, it looks like the patient would almost always arrive first.
The instructors seem to be telling people to make the connecting rope long enough for one to sit below the other... usually the rescuer below the patient. But cavertevans can tell us from personal experience...

Figuring - if the rescuer is a lot lighter than the patient then the effect is that the rescuer climbs ahead and hauls the patient up a bit, then patient and rescuer fall to the bottom of the, shorter, loop. Rinse and repeat.

In both descriptions, leave out the gap in the steps and the effect is simultaneous - when you are doing it, it must feel like magic.

-----------------------

[1] ... then the patient overtakes the rescuer - catching the rescuers knees, hip, ribs, and chin with the sides of the stretcher on the way past. Boudica's stretcher had knives - ladies first!

Last edited: Jan 11, 2014
11. Jan 11, 2014

cavertevans

All good points. When the rescuer is lighter than the patient they end up on top, and when they are heavier they end up hanging below the patient. So tether length is important! Regardless of the length you can just grab the patients rope and pull them up and down pretty easily, so moving them around when you get to the top is pretty trivial. And yes, it does feel like magic! You can climb and it feels like you have hardly any weight on you and magically the patient just goes right up with you! While the system is in operation, assuming you have a halfway decent pulley, the rescuer propels themselves up, and during that motion they only go half way up and the patient moves up simultaneously. So most of the time it feels like one motion rather than standing, having the system adjust, then standing again. This is partially why the confusion as to what to call this thing... Anyway, it sounds like it is a combination of a haul and a counterbalance, and I should not try to over simplify it by categorizing it as one or the other. Which helps!

12. Jan 12, 2014

CWatters

That's what I would expect. Their mass should be carried equally by the ropes either side of the pulley. If the patient is heavier then part of his weight must be supported by both ropes. That can only happen if he is lower then the rescuer. Something like this (ignore the angles on my bad drawing). So whoever is lighter gets to the top first..

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