Calculating the required rating of a guying system ; worked example ( continued )
The team leader uses the formula previously provided to check the required rating to support the hung-up tree should it become dislodged from the other tree during rescue operations :
Where :
F = r 1 × sin∅ 1 r 2 × sin∅ 2
× d 2 × l × 7 , 700
r 1 is the distance from the base of the tree to the approximate centre of gravity , 20m
∅ 1 is the angle between the force ( acting vertically downward ) and the lever arm of the stem , 30 °
r 2 is the distance from the base of the tree to the attachment point of the guy line , 30m
∅ 2 is the angle between the guy line and the lever arm of the stem , 30 °. d is the diameter of the tree just above the root flare , 1.6m
L is the length of the tree along its stem from the base of the stem to the tip , 40m
F =
20 × sin30 30 × sin30 × 1 . 62 × 40 × 7 , 700
F = 525,653 N
F ≈ 526 kN ..
It is anticipated that rescue teams may find this number alarming . 53 tonnes is beyond the capacity of most rescue cordage , even when multiple legs are used .
The calculation includes a significant safety factor and assumes that no support is provided by the tree ’ s remaining root system . In practice a significantly lower amount of support may be required . In fact , if 526kN of force was applied as pre-tension the tree would almost certainly stand back up .
Improving the rope angle by finding an anchor point further back or setting the top anchor higher in the tree ( e . g . by moving the guy lines higher before cutting the arborist free ) would also immediately reduce the rating requirement for the guy lines .
The best possible solution in this scenario would be to install a directional pulley in the rear pine tree . With an angle of 60 ° at the failed tree the revised rope rating requirement would be reduced to 303kN .
© Arboriculture Australia 2022 - 211 -