Forces are vectors, since they have a definite size and direction.
The direction of a vector determines which way a force is
acting. Since a rope can only support a load along its length,
the rope indicates which way the force is acting. If we turn a
rope through a pulley, the force is now acting in two directions?
the direction of each leg of the rope. The resulting force
on the pulley now depends on these two component forces and
the angle the rope enters the pulley. These two component
forces create a single force that would cause the pulley to move
toward the middle of this angle if it were free to move, much
in the way a bow and arrow works .
Why is this important in tree rigging? Well, if we can manage
to direct the force exerted on the block to act along the
length of a tree leader, as opposed to across the grain horizontally,
we utilize the natural columnar strength of the tree, which
can give us a greater working load limit. Everyone should understand
how a 2-inch diameter limb is much easier to break if
we step on its middle instead of standing it upright and stepping
on it end to end. It would be nearly impossible to break.
We can mimic this in the tree by incorporating more than one
block into our rigging.
In order to calculate the load on a block, we need to determine
two things: the load on the rigging line and a
block-loading factor. This loading factor is determined by the
angle by which the rope is deflected by the block. The angle
that we are referring to is not the angle between the two legs of
rope, but the angle between an imaginary line drawn straight
through the block from the load, and the leg of rope entering
the block from the friction device.
The greater the angle created by the block, the greater the
resultant force placed on that block. For example, a block that
turns a rope 180 degrees will see a load equal to twice that of
the load on the rope itself. Conversely, a line that enters the
block at 0 degrees or runs straight through the block would
create a resultant force of zero on that block. In the middle of
the road, we have a 90-degree angle. The block-loading factor
of a right angle would be 1.41 times the weight of the load.
How can this be useful in our day-to-day operations? We
can create lesser pulley angles on smaller rigging points or
structurally compromised parts of the tree and use a second
pulley to create a larger angle at a more beneficial spot to support
more of the load. This can be very useful when dealing
with co-dominant stems and other structural flaws. The rigging
line itself can act as a temporary cabling system to lace the
stems together.
Angle of Deflection Load Multiplier
30 o .52 x Load (L)
45 o .76 x (L)
60 o 1.00 x (L)
75 o 1.22 x (L)
* 90 o 1.41 x (L)
105 o 1.59 x (L)
120 o 1.73 x (L)
135 o 1.85 x (L)
150 o 1.93 x (L)
160 o 1.97 x (L)
180 o 2.00 x (L)
* Example: 90 o Rope
angle with 500 lb. load = 705 lbf. on Block
RESULTANT FORCE
ON BLOCK...
