When using pulley systems, mechanical advantage is expressed as the ratio of the amount of output force to the amount of input force. For example, a ‘3:1’ system has three times the amount of output force as the input force. If a person pulls with 10 units of force, this system will apply 30 units of force to the load. This allows a person to lift a load much greater than would be able to be lifted without the help of the system. This is the mechanical advantage.
Rope rescue, rope access, and rigging textbooks commonly show various pulley configurations and label them by the corresponding mechanical advantage. It is common to see 3:1, 5:1, 9:1, 4:1 and other systems presented. The numbers shown are the ‘Ideal Mechanical Advantage’. They show what the mechanical advantage would be in a perfect system with no inefficiencies introduced by outside forces such as friction.
When rope is pulled through a pulley, some of the pulling force is lost due to these inefficiencies. The amount of force NOT lost to these forces can be expressed as ‘Pulley Efficiency’. Pulley efficiency is dependent on a number of factors including pulley construction, rope construction, and the rope diameter in comparison with pulley sheave diameter. Some of these inefficiencies are from design decisions by the manufacturer and some are from decisions made by how the pulley is used by the end user. These inefficiencies can be minimized but can never be completely removed from a system.
We performed tests in order to determine the pulley efficiency of a number of rope rescue and rope access pulleys. Tests were performed using an approximately 50 kilogram weight and the input and output force was measured to determine the approximate efficiency of the pulley. The first round of test were performed using Teufelberger 10.5mm Platinum PES/PA. Additional tests were performed with Teufelberger 8mm Sirius Reep Cord and Teufelberger 3mm T-12 Technora Hollow Braid. The results of these tests were recorded as follows:
|Model||Sheave Diameter||Platinum 10.5mm||Reep Cord 8mm||T-12 3mm|
|DMM Revolver||0.4 in||77%|
|Climbing Technology RollNLock||0.9 in||69%||74%||79%|
|DMM Pinto||0.8 in||70%|
|CTOMS Prodigy||0.8 in||83%|
|Climbing Technology Orbiter M||0.7 in||72%|
|Edelrid Spoc||0.8 in||77%||87%||91%|
|Rock Exotica Double 6||0.9 in||86%||92%|
|DMM Revolver Rig||1.0 in||80%||86%|
|Petzl Micro Traxion||1.1 in||82%||87%||95%|
|Climbing Technology Uplock||1.0 in||87%|
|ARS Magnapulley||1.0 in||82%||88%|
|DMM Rigger||1.1 in||82%|
|Rock Exotica Omni-Block 1.1||1.1 in||84%||89%||94%|
|Rock Exotica Omni-Block 1.5||1.5 in||89%||92%|
|DMM Impact XS||2.0 in||89%|
|Rock Exotica Kootenay||2.2 in||89%|
|Climbing Technology Orbiter S||1.5 in||90%|
|Rock Exotica Omni-Block 2.0||2.0 in||92%||94%||98%|
|Rock Exotica Omni-Block 2.6||2.6 in||94%|
|Rock Exotica Omni-Block 4.5||4.5 in||95%|
The term ‘Actual Mechanical Advantage’ is used to express the mechanical advantage of a system including inefficiencies. By including the pulley efficiency into the mechanical advantage calculation, the true mechanical advantage of the system becomes clearer.
The following shows a few different combinations of pulleys from our previous tests and how the efficiency effects the mechanical advantage of various systems when using Teufelberger 10.5mm Platinum PES/PA.
|Climbing Technology Orbiter M||72%||1.72||2.24||2.61||2.88||5.01|
|DMM Revolver Rig||80%||1.80||2.44||2.95||3.36||5.95|
|Rock Exotica Omni-Block 1.1||84%||1.84||2.55||3.14||3.64||6.48|
|Rock Exotica Omni-Block 1.5||89%||1.89||2.68||3.39||4.01||7.19|
|Climbing Technology Orbiter S||90%||1.90||2.71||3.44||4.10||7.34|
|Rock Exotica Omni-Block 2.0||92%||1.92||2.77||3.55||4.26||7.65|
|Rock Exotica Omni-Block 2.6||94%||1.94||2.82||3.65||4.43||7.97|
When different pulleys are combined together to create mechanical advantage systems the order of the pulleys is important. The following chart shows 3:1 pulley systems created with two different models of pulleys. The pulley along the horizontal axis is the first pulley encountered in the system (closest to the pulling force) and the pulley on the vertical axis is the second pulley in the system (closest to the load).
|Carabiner||Pinto||Orbiter M||Revolver Rig||Omni 1.1||Omni 1.5||Orbiter S||Omni 2.0||Omni 2.6|
The effect of the rope on the efficiency of the system becomes clear when a smaller diameter rope such as Teufelberger 8mm Sirius Reep Cord is used. The following chart also shows a 3:1 system using Teufelberger 8mm Sirius Reep Cord:
|RollNlock||Revolver Rig||Edelrid Spoc||ARS Magna||Omni 1.1||Omni 1.5||Omni 2.0|
The true actual mechanical advantage is dependent on a large number of outside forces so even if the pulley efficiency is known we can still only get an approximate mechanical advantage number without performing tests on the entire complete mechanical advantage system itself. Even without measuring the entire mechanical advantage as a complete system, it becomes clear that the numbers shown in a textbook for ideal mechanical advantage can be very unrealistic in practice.