Understanding Mechanical Advantage

The ability to understand mechanical advantage is an essential part of technical rope rescue, crevasse rescue and climbing self-rescue.

The best way to begin an understanding of mechanical advantage is to understand how a toprope works. If a 150lb person is on one side of a rope, then a belayer has to provide at least 150lbs of force to keep the person from lowering to the ground.

In order to make it easier to understand, we should consider the 150lbs as a unit of one. So to stop a unit of one from lowering, then an individual must put an equal amount of force on the other side, essentially a unit of one. The weight of 150lbs is arbitrary. The important thing to remember is that we have to put a unit of force on the opposite side to keep the first unit from going down.

If there is one unit of force on one side, countering a unit of force on the other side, that means that there are two units of force on the anchor.

The man in the image is putting one unit of force on the right side to counter one unit of force 

on the left. There are two units of force on the anchor.

In this image, there are two units of force on the load, and one unit of force on the anchor.

The hand is putting one unit of force into the system, because the rope travels through a moving 

pulley, it exerts  two units of force on the load. This is a simple 2:1 hauling system.

To count out mechanical advantage, one should always start with the haul line and always start by counting it as a single unit. Traveling pulleys multiple mechanical advantage. 

In this image, the rope remains a unit of one all the way through to where the green prusik is 

attached. At the pulley with the prusik, there is a 2:1 mechanical advantage.

The two in the traveling pulley are added to the one that follows the rope.

This is a 3:1 simple system, commonly called a z-pulley system.

In this image, the haul line is a unit of one. The upper traveling pulley is a unit of two.

The unit of two travels on the lower line through the lower pulley, multiplying at the load.

As there are two lines, with the unit of two traveling through the pulley, this is a compound

4:1 mechanical advantage system. It's compound because one pulley is compounding the force

of the other pulley.

In this image, a 3:1 has been laid on top of a 2:1, creating a 6:1 compound system.

The haul line places a unit of two on the upper traveling pulley. The line then runs through 

to the prussik, adding an additional unit. So the system is 3:1 at the green prusik. The 3:1

is mirrored on the opposite side of the lower traveling pulley, creating a 6:1.

It's important to note that the idea behind mechanical advantage is that pulleys and changes in direction theoretically decrease the amount of force required to haul a load. However, friction from rock or snow can increase the load.

It's also important to note that for every increase in mechanical advantage, one will have to pull more rope to move a load. For example, n a 2:1 mechanical system, a rescuer has to pull two-feet of rope for every one foot the load moves; in a 6:1 mechanical system, a rescuer has to pull six-feet of rope for every one foot the load moves...

Following are some challenges for you. Try to count out the mechanical advantage and then look at the bottom of this blog to get the answers. To avoid looking at the answers before you're ready, don't scroll past the section that says, "Don't scroll down any lower until you want to see the answers!"  There are five mechanical advantage challenges:

1)

2)

3) 

4) 

5)

Understanding mechanical advantage is an important part of rescue. It is possible to memorize what certain systems look like, but there is great value in being able to count out a system...

Don't scroll down any lower until you want to see the answers!

1) 9:1 Compound

2) 9:1 Compound, Offset

3) 4:1 Simple

4) 5:1 Complex (Complex systems often have pulleys traveling toward one another.)

5) 27:1 Compound

--Jason D. Martin