## Component forces in pulley systems

#### How to use the calculator

This tool has been set up to allow users to calculate the mechanical advantage of a pulley system, while taking into account friction of its various components. It can be used to optimise your chosen system with auto-blocks and pulleys to help you decide where to use each component to increase efficiency and reduce load on weaker pieces.

The 'tension method' has been used to calculate the force on each component. Friction due to the system running over rock/snow and the load pulling over edges/crevasse lips has not been included in this tool - to approximate this friction component you can increase the load (which could easily more than double depending on edge/lip preparation).

1. Select your pulley system, auto-block and pulley efficiencies from the drop-down lists (or enter your own efficiencies as a decimal number eg. 50% is entered as 0.5).
2. Enter your load in kilograms and select which units you'd like the results to be displayed in.
3. Click 'Calculate'.

#### References and Notes

Frictionless system: To see the theoretical mechanical advantage and corresponding component loads, select frictionless auto-block and pulley options.

Angles: The angle of the load line and haul line on each pulley in the provided diagrams are treated as being at 180° to each other (they have been shown at different angles to each other in the diagrams for clarity).

Device efficiencies: The auto-block and pulley efficiencies provided in the calculator are real world efficiencies measured during a steady state lift from used devices (not brand new or from manufacturer's specifications). They can easily be substituted for your own measurements using the 'Other' efficiency options. Our tests showed that the efficiency for each tested device decreased as the rope diameter and its age/usage amount increased.

Reducing carabiner friction: Duplication of carabiners (ie. using 2 identical carabiners in one pulley location) was also tested. In each case, with a variety of carabiners, the amount of friction was always increased if a second carabiner was added - this was independant of the rope used for testing. To significantly reduce friction, proper pulleys are recommended.

© Elke Braun-Elwert, Alpine Recreation 2016

#### Pulley System Diagram -

Efficiency of pulley system: