Rigging
Math
(Made
Simple)
A
Primer by
Delbert
L.
Hall, Ph.D.
ETCP
Certified
Rigger
ETCP
Recognized Trainer
Lesson
2: Resultant Forces
Understanding
Resultant Forces
Let
me begin this lesson by discussing
pulleys. Everyone knows that a pulley is used to change the
direction of
a rope or cable. What is less understood is what
load is exerted on
a pulley and beam that the pulley is attached to when a load that is
attached
to the rope or cable that runs through the pulley is
lifted. The
term Òresultant forceÓ is commonly used to refer to the load on the
pulley and
its supporting beam. It should be understood that the
load/force on the
beam is seldom equal to the load being lifted. This force can
be a
fraction of the load being lifted, or as great as twice the load being
lifted.
The determining factor is how much the rope or cable bends around the
sheave of
the pulley as it changes direction.
The
equation for computing the resultant force is: Resultant
Force = Load 
DonÕt
let this formula scare or confuse you.
This equation can be broken into two parts: The
first part is the
load being lifted, and the second part, the scary and confusing part,
is the
multiplying factor (MF). The
MF is the sine of the angle divided by the sign of half the angle as
shown by the
formula: 
.
This MF that is based on the
angle of the rope/cable going to the sheave compared to the angle of
rope/cable
after it as exited the sheave.
Below are some examples of ÒAnglesÓ in order to help you
understand them
better.
So,
using this equation, letÕs work though a
problem.
Example:
What is the resultant force on a beam when load being lifted is 200 lbs
and the
angle of the cable is 90 degrees?
First,
letÕs compute the multiplying factor.
[ON/C]
90 [SIN] [Ö] 45 [SIN]
[=]
(1.41)
Note: Since I could calculate 90/2 in my
head (45), I did.
Now,
I multiply the MF (the result of my last calculation) by the Load.
[X]
200 [=] (282.84) lbs.
Note: Since I wanted to use the result of my last calculation in this
one, I
did not press the [ON/C] to clear that result.
Using
the same Load, try different angles. You will discover that
the greater
the angle - the lower the MF, and the smaller the angle - the greater
the
MF.
One
more thing: Do NOT confuse the Resultant Force with the load on the
rope/cable. If the load
being lifted is 200 lbs,
that is the load on the rope/cable, even if the Resultant Force on a
pulley and
supporting beam is different.
