Rope strength
Depending on the size of tree and degree of lean , cordage with very high WLL may be required if it may potentially support the full bending moment applied by the tree .
It is straightforward to calculate the approximate guying force that would be required to fully support a hung-up tree , should the tree suddenly dislodge from its position . It is unlikely that this would be used in practice however : the strongest available cordage should almost always be selected . The process below is intended to support training and assist with acquisition of suitable cordage .
Weight of tree :
Where :
W = πd " × L × ρ × g × f
4
W is the weight of the tree , in newtons
d is the diameter of the tree just above the root flare , in metres
L is the length of the tree along its stem from the base of the stem to the tip , in metres
ρ is the density of the green timber , in kg / m 3 . Green
log weight densities are available , for example in MIS303 Tree Dismantling , however a representative density of 1000kg / m 3 can usually be used for Australian and New Zealand native timbers .
g is the acceleration due to gravity ( 9.81m / s 2 )
f is a form factor to allow for the reduction in stem diameter and the weight of branches and foliage . A form factor of 0.8 is normally used but will be insufficient for some mature trees with heavy , spreading branch structures . A form factor of 1 is recommended for this application .
Incorporating the values recommended above for f , g and ρ and calculating for π gives :
W = d " × L x 7,700
This simplified equation should only be used with awareness that some tree species or forms may vary significantly from the suggested average values .
Bending moment applied by weight of tree at base :
Where :
M = r 1 W sin∅ 1
M
W
r 1
∅ 1 is the bending moment ( torque ) that the tree would apply to a fulcrum at the base if that fulcrum were to support the full leverage of the tree , in Newton metres . is the weight of the tree , in newtons . ( Calculated above )
is the distance from the base of the tree to the approximate centre of gravity , in metres .
is the angle between the force ( acting vertically downward ) and the lever arm of the stem , in degrees .
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