How to calculate mechanical advantage - Petzl Sweden

How to calculate mechanical advantage

A mechanical advantage haul system reduces the effort required to raise a load. The mechanical advantage obtained is based on the pulley effect.


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1. The pulley effect

If we consider a load suspended on a rope, the rope passing through a pulley above the user, with the user's hand holding the rope on the other side of the pulley; any force applied to one end of the rope is transmitted to the other end of the rope, or, in this case, to the end of the rope on the other side of the pulley.

If the load weighs 100 kg, it is clear that the user must hold 100 kg on their side to hold the load. The two rope strands each exert a pull of 100 kg, so the pulley supports 200 kg.

The pulley effect.

Note: this theory is valid for an ideal pulley of 100% efficiency, which does not exist in the real world.In reality, pulley efficiencies range from about 50 % to 98 %.To simplify calculations, this discussion is limited to ideal pulleys.

2. Calculating mechanical advantage in practice

The efficiency (E) of a haul system indicates the force multiplier factor that you can exert on the rope.For example, if you are able to pull 20 kg maximum on a rope with your bare hands, a 3:1 haul system will enable you to raise a 60 kg mass.This reduction is obtained by increasing the amount of rope to be pulled: to raise a mass 1 meter with a 3:1 system, 3 m of rope must be pulled.

The efficiency (E) of a haul system may be calculated by adding the effects of each pulley.

Start by drawing a simple diagram of the system, then show the pulling force F that the hand applies to the rope.

Transmit the force F along the rope by adding the effects of each pulley.

When multiple rope strands are attached to the load (double pulley, rope clamp...), add the forces exerted by each strand.

1:1 haul system

1:1 haul system - 1/3
1:1 haul system - 2/3
1:1 haul system - 3/3

2:1 haul system

2:1 haul system - 1/3
2:1 haul system - 2/3
2:1 haul system - 3/3

3:1 haul system

3:1 haul system - 1/4
3:1 haul system - 2/4
3:1 haul system - 3/4
3:1 haul system - 4/4

Note: the advantage of a 3:1 system is its ease of setup and that it can easily be converted to a complex system (7:1) with one additional pulley and some cord.

7:1 haul system - 1/3
7:1 haul system - 2/3
7:1 haul system - 3/3

4:1 haul system

4:1 haul system - 1/4
4:1 haul system - 2/4
4:1 haul system - 3/4
4:1 haul system - 4/4

5:1 haul system

5:1 haul system - 1/4
5:1 haul system - 2/4
5:1 haul system - 3/4
5:1 haul system - 4/4