# Pulley Systems

#### Pulley systems are used to provide us with a mechanical advantage, where the amount of input effort is multiplied to exert greater forces on a load.

They are typically used for hauling and lifting loads but can also be used to apply tension within a system such as in a Tensioned Line or Tyrolean. This page explains the basic principles of pulley systems and how they work, for information on how to use them in hauling see the hauling systems page.

Force is an influence that has both magnitude and direction, it is usually given in the dynamic unit of Newtons (N). For ease of explanation we have used kilograms on this page. Additionally, the examples on this page do not take into account the effects of angular vector forces or the coefficients of friction.

## The 1:1 Redirect

In the illustration to the right we have a rope attached to a load weighing 100kg. The rope has been passed through a pulley which is attached to an anchor point and returns back down to ground level.

The amount of effort required to lift the load in this situation is 100kg so we have not formed any mechanical advantage. This system has a ratio of 1:1, additionally for every metre of rope that the user pulls through the system the load will be raised by a metre.

All this system does is change the direction of where the effort needs to be put in, instead of pulling the rope in an upwards direction it can now be pulled downwards which is usually more efficient. This is commonly referred to as a directional or redirect pulley.

In this situation the directional or redirect pulley and its anchor point will actually be feeling double the weight of the load, as there is the loads weight on one side and an effort of 100kg needs to be applied on the other side to raise the load.

## The 2:1 Pulley System

If we take a 1:1 system and turn it upside down it will result in a 2:1 mechanical advantage. Instead of the pulley being attached to an anchor it is now attached to the load (pulley A).

On one side of pulley A the rope has been attached to a fixed anchor point, the rope on the other side of pulley A has been sent back down to the ground via a redirect pulley (pulley B) where the user applies the effort to lift the load.

As the load is being supported by two sections of rope (via pulley A), each rope will bear half of the loads weight or 50kg in this example. Pulley A is being subject to the full weight of the load (100kg).

The directional or redirect pulley (pulley B) supports half of the weight of the load (50kg) on one side but an effort of 50kg is being applied on the other side to raise the load, so pulley B and its anchor are actually being loaded with 100kg.

## The 3:1 Pulley System

Here we have a 3:1 mechanical advantage. First one end of the rope is attached directly to the load, this is then passed around an anchored pulley (pulley B) and returns back to the load where it is passed through pulley A which has been fixed to the load.

This forms the 3:1 mechanical advantage, finally the rope is redirected by pulley C back down to the user who applies an effort of 30kg to raise the 90kg load.

An easy way to calculate the ratio of a pulley system is to count the amount of lines that apply effort on the load. In this system there are three ropes that exert effort on to a load of 90kg, so each rope is supporting 1/3 of the loads weight (30kg). Pulleys B & C and their anchors are subject to 60kg each.

## The 4:1 Pulley System

This pulley system provides a 4:1 mechanical advantage. The user is required to apply a force of 25kg to raise this 100kg load, for every 4 metres of rope that the user pulls through the pulley system the load will only be raised by 1 metre.

If we count the amount of ropes that are actually supporting or applying effort on the load, and then divide the loads weight equally between them we should easily be able to calculate the overall mechanical advantage of the pulley system.

In this scenario there are four sections of rope supporting and applying effort to the load. So the loads weight (100kg), divided by the amount of supporting sections of rope (4), should result in each rope supporting one quarter (25kg) of the loads total weight. The rope is then returned to the user via a redirect (pulley D) who applies 25kg of effort to raise the 100kg load.

## The 5:1 Pulley System

With this 5:1 pulley system the user is required to apply an effort of only 20kg to lift the 100kg load. Notice that when the end of the rope is attached directly to the load this usually results in a mechanical advantage with an odd ratio.

When the end of the rope is attached to a fixed anchor point this will normally result in a mechanical advantage with an even ratio.

## The 6:1 Pulley System

As we continue to apply more pulleys to the system then the mechanical advantage ratio increases. In this system some of the pulleys that have been used are double pulleys.

A double pulley has two pulley wheels usually of the same diameter housed inside a single block, the two pulley wheels are able to move independently of each other. By using a double or multiple pulley block we are able to condense the pulley system making it more manageable.

## Disadvantages of Conventional Pulley Systems

This conventional 3:1 pulley system has been assembled to raise a load weighing 90kg which needs to be lifted over a height of 50m.

Due to the way that the system has been created we would need at least 150m just to form the 3:1 mechanical advantage, plus an additional 50m to redirect the rope down towards the user who will apply the effort at ground level so all in all this system will require at least 200m of rope!

It is possible to redesign the pulley system making it more compact and manageable while using less rope. To see how this can be done then have a look at the hauling systems page.