Tree rescue manual | Page 118

On the previous page , the images showed an example of simple mechanical advantage , where a rope is loaded at one end and anchored or loaded at the other , to create an increased force at the top anchor point .

In practical applications , the two sides of the rope rarely run parallel unless a mechanical advantage system is being deliberately constructed . To understand and work with variable rope angles , we need to introduce the concept of a force as a vector , including both magnitude and direction .

Two simple ‘ rules of thumb ’ are used in this manual to quickly assess the net force applied to an anchor where a loaded rope changes direction at that anchor .

3 : The angle rule

The direction of the net force applied by a loaded rope passing over a point bisects the angle made by the rope at the point .

In other words , the net force applied to the anchor will be halfway between the two arms of the rope .

Note that this rule ignores the effects of friction at the point – this can alter both the magnitude and direction of the resultant force vector . The rule is still useful though , as it can give a useful ‘ rule of thumb ’ for designing systems that include redirects on branch ends or other weaker parts of the tree ’ s structure , particularly where those systems will be used for dynamic rigging or for both lifting and lowering .

4 : The force rule

The wider the angle made by a loaded rope passing over a point , the less force the rope applies to that point .

Angle

Net force on anchor ( rounded to nearest 0.01 )

This simple rule , when combined with the rule above , can be used to design both mechanical advantage systems and complex structures such as suspension bridges .

The table on the right provides the approximate net force magnitude for various rope angles over a perfectly efficient pulley :

120 ° 1 x load on rope

180 ° 0 load applied

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