# 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

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.

### The questions – on Pulley System Progressions?

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 behind Pulley Systems

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.

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.

### 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 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 – about Pulley System Progressions

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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