Mechanical Advantage in Rescue Systems
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By Michael Strong - illustrations by Ryan Ojerio - video by Dan Crowe and Michael Strong

Rescuers would be hard pressed to raise a team member to safety without the application of mechanical advantage.  A rescue system incorporating mechanical advantage multiplies the pulling force and makes it possible to raise a heavy load with less effort than might otherwise be required.  This is a boon to the rescue team short on pulling power.  Mechanical advantage is best expressed as a set of ratios:

ratio 1

This ratio expresses how many pounds of lift are derived per pound of pull.  With a 3:1 system, a climber weighing 180 lb. can be raised with 60 lb. of pull, at least in theory. In actuality, friction in the system reduces the efficiency of a 3:1 system to about 2:1 without rescue pulleys.  Even when pulleys are used, mechanical advantage is much less than its theoretical value.

The distance the climber is raised is proportional to the amount of rope pulled through any rescue system incorporating mechanical advantage.  For example, in a 3:1 system, three feet of rope is pulled through the system for every one foot of lift achieved.

The best rescue system is not necessarily the one which uses the greatest mechanical advantage.  There comes a point where the benefits gained from additional mechanical advantage are outweighed by the increase in the amount of rope that must be pulled through the system.  For this reason, rescuers seldom use anything more than a 6:1 system. 

It’s usually best to use the simplest system possible, to reduce the set-up time and minimize the amount of required equipment.  From a safety perspective, a simpler system is easier to assess and monitor.

1:1 SYSTEM

As the name implies, the 1:1 system provides no mechanical advantage.  Every pound of pull exerted lifts a pound of the climber’s weight, and for every foot of lift, a foot of rope is pulled through the system.  When any load is fully supported by a rope, it’s a 1:1. 

1 to 1 systemfigure of eight follow-through

As the above illustrations show,, in a 1:1 system the rope simply changes direction around a pulley or carabiner. It’s important to be able to quickly recognize changes of direction when estimating the amount of force applied to different components of the system (e.g. the anchor).  In both of these examples, the anchor must support the weight of the climber and the counterbalancing force applied by the rescuer.

C-PULLEY - 2:1 SYSTEM

The c-pulley is a 2:1 system.  It’s easily recognized, as one end of the rope is always anchored.  In a 2:1 system, the anchored strand supports half of the load, while the rescuers support the other half.

c pulley

C-PULLEY ON A C-PULLEY - 4:1 SYSTEM

A c-pulley can be added to another c-pulley, providing a 4:1 system. In this example, a second c-pulley is attached to the initial c-pulley.  Notice that the end of each c-pulley set- up is anchored. 

Let’s examine this system a little more closely.  Assume a 200 pound load is being lifted.  The pull strand of the initial c-pulley supports half of the load, or 100 pounds.  This means that 100 pounds is transferred to the second c-pulley system, with the anchored and pull strands each accepting half of the load (50 pounds).  Thus, 50 pounds of pull is required to lift 200 pounds.

c pulley on a c pulley c pulley on a c pulley 2

It’s important to know how much force is transferred to the anchor when hauling with any rescue system.  In the above 4:1 system only 50 pounds are required to lift a 200 pound climber.  Does this means that the difference (150 pounds) is transferred to the anchor?  Let’s answer this by looking at this system from another perspective, by calculating how much force is placed on the anchor via each of the anchored strands.  The anchor strand of the initial c-pulley supports half of the climber’s weight, or 100 pounds.  The anchor strand of the 2nd c-pulley also supports half of its load, or 50 pounds.  So, the answer is yes, with 50 pounds, the anchor supports the remaining 150 pounds!  Keep in mind, however, that these are theoretical values.  Friction intensifies the load on all points.

Z-PULLEY - 3:1 SYSTEM

The z-pulley is the most commonly used rescue system, combining a 1:1 and a 2:1 system.  It provides 3:1 theoretical mechanical advantage

water knot 1

The illustration below shows the theoretical forces at work in the system.  Notice that 70 pound of force is required to raise the 210 pound load.  As the figure shows, the z-pulley consists of two significant changes of direction.  At each of these changes of direction, forces are transferred:  first to the sliding pulley and its attachment to the haul prusik (F1 + F2 = F4 = 140 pound); second, to the fixed pulley and its attachment to the anchor (F2 + F3 = F5 = 140 pound).  Adding the forces applied along the entire length of the rope reveals the following:  the initial 70 pound of pull is transferred around both of the changes of direction and along the rope to the point where the haul prusik is attached to the rope.  At this point, the 70 pounds of pull couples with the 140 pounds of force transferred to the sliding pulley and haul prusik, resulting in 210 pounds of theoretical force applied to the load.

 

water knot 6

In order to maximize mechanical advantage, use pulleys and pull in as straight a line as possible.  In the absence of pulleys use two carabiners at each 180° bend in the rope.  Friction is much greater with only one carabiner.  If only one pulley is available, connect it to the haul prusik.  This is the location where pulling efforts are concentrated.  More rope also passes through the sliding pulley than around a pulley attached to the anchor.

Z-PULLEY WITH A RATCHET PRUSIK

When the climber is raised with a z-pulley, the sliding pulley and haul prusik are pulled closer to the anchor until a point is reached where pulling any further results in a potential loss in leverage.  The addition of a ratchet prusik to the anchor allows the climber to be supported while the sliding pulley is reset further down the rope.

z pulley with ratchet prusik
6:1 SYSTEM

A c-pulley can be added to a z-pulley to create a 6:1 pulley system.  In this case, the two systems are joined by tying a loop in the pull strand of the z-pulley, attaching a carabiner and pulley to this loop and clipping the c-pulley to this set-up.

The 2:1 system (in effect) doubles the amount of mechanical advantage applied by the z-pulley.  The main disadvantage of the 6:1 system is that six feet of rope must be pulled through the system for a single foot of lift.  A lone rescuer will, however, be less concerned with the amount of rope that must be pulled and more appreciative of the relative ease with which a climber can be raised from a crevasse.

It’s also possible to add a z-pulley to a c-pulley (rather than a c-pulley to a z-pulley). The system illustrated  on page 104 combines the two systems in this manner.
6 to 1 system
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