Pulley system progression

Pulley system progression – is it worth it in practice?

A pulley system progression is when you go from a small to a large mechanical advantage (MA). For example, from a 3:1s (s means simple) to 3:1sCD (CD means Change of Direction) to a 5:1s, to a 9:1c (c means compound).

Note: You need some prior knowledge of Pulley Systems to get the most of this article. You can download a free 10-page guide (Pulley Systems 101) here to get you started: overtheedge.training

Pulley Progression Simple to Compound
You start with a pulley system that, based on experience, is the appropriate mechanical advantage to make hauling efficient considering:
  • the load,
  • the number of haulers,
  • the distance to be hauled and,
  • friction.
For example, with efficient pulleys, a team of two could easily haul a 100kg load with an MA of 3:1s. You have a progression planned and can go from one pulley system to the next to increase (or decrease) MA. Below is a complex pulley system progression that integrates into the simple to compound progression above as needed.
Pulley Progression Complex

The questions?

These are the two questions I had regarding Pulley System Progressions:

  1. When you go from one pulley system to the next in a progression, is it worth it in practice, i.e. increase MA/decrease the force for the haulers? 
  2. Is there any pulley systems in the progression that stand out as more or less efficient than the others.

The theory

We used the T (tension) method to work out the MA assuming 100% efficient pulleys.

Here is an example of how to do this for a simple 3:1. Use the same method for any of the previous pulley systems.

3:1s using T-method 100% Pulleys

We also used the T method to work out the MA with 90%(0.9) efficient pulleys. Note: This 90% is very close to the Petzl Partner and Mini Pulleys manufacturers recorded efficiency at 91%.

Here is an example of how to do this for a simple 3:1, which now becomes a 2.71:1 with the additional friction created by the pulleys. Use the same method for any of the previous pulley systems.

2.71:1s using T-method 90% Pulleys

 

The testing equipment

  • Load cells: x2 – Rock Exotica/CMC Enforcers, accuracy: +/- 2%, records 0.02kN increments
  • Rope: 9.5mm Kordas Fina semi-static Type A (EN1891), 4.1% elongation, Breaking 26.3kN 
  • Pulley system pulleys: Petzl Mini and Petzl Partner (91% efficiency)
  • Redirect pulley: Rock Exotica Large Omni Block
  • Rope grabs: Petzl Tibloc, Petzl Basic
  • Load: rocks in an Aspiring 75litre PVC Bag
  • Premade 5:1 pulley system
  • One person applying force to the end of the pulley system – via a cowstail on a harness.

The setup

Testing setup

The method

  • All load cells were reset and checked reading 0.00 before the testing began and in between each test.
  •  With the premade 5:1 pulley system, we tested the force being applied on the end of the pulley system after the redirect pulley (0.92kN)
  • For the rest of the testing (as shown above), I walked back monitoring the load cell, reading both max and actual to make sure they were similar. 
  • The load was hauled off the the ground around 1m before stopping each test.

The results

The MA has been calculated using an excel spreadsheet and rounded to 2 decimal places at the end but not during the calculations.

  •  MA 100%: this means the Mechanical Advantage if there was no friction loss in each pulley – 100% efficient.
  • MA 90%: this means the Mechanical Advantage if there was 10% friction loss in each pulley – 90% efficient.
  • Haulers 100%: this means what the haulers have to pull if there was no friction loss in each pulley – 100% efficient.
  • Haulers 90%: this means what the haulers have to pull if there was 10% friction loss in each pulley – 90% efficient.
  •  Actual: means the ‘Actual’ force pulled when tested. Max force recorded. As the force on the end of the pulley system was 0.92kN, I multiplied by 1.087 to convert to 1kN.
  • Difference: means the difference between ‘Haulers 90%’ and ‘Actual.’

Conclusions

Answering  the two questions I had regarding Pulley System Progressions:

  1. When you go from one pulley system to the next in a progression, is it worth it in practice, i.e. increase MA/decrease the force for the haulers? 
  • Given the accuracy of the Enforcer and the test method, the ‘Actual’ results were close to the predicted 90% efficiency of the pulleys.
  • The results showed that you do get additional benefit by undertaking a progression with efficient pulleys.
  • As part of the system (the hauler), I could feel the amount of force change.

2. Is there any pulley systems in the progression that stand out as more or less efficient than the others.

  •  There is little difference between a 5:1cx and 5:1s despite one having 3 pulleys and the other 4.
    • The 5:1s (4 pulleys) has both travelling pulleys attached to the same rope grab, and therefore the MA (2x 2:1s) is effectively acting directly on the load.
    • The 5:1cx (3 pulleys) has one of the travelling pulleys MA (2:1s) going around a fixed pulley before acting on the load.
  •  Recommend you limit the use 3:1sCD as an option to pull in the opposite direction, e.g. downhill. In the test results, 0.48 (48%) of the load had to be applied by the haulers. Consider using the 5:1cx for pulling in the opposite direction.

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