Rigging Math
(Made
Simple)
A
Primer by
Delbert L.
Hall, Ph.D.
ETCP Certified
Rigger
ETCP
Recognized Trainer
Lesson 7:
Center of Gravity for two loads on a beam
It can be handy to know where the center of gravity is when you have two loads
on a beam. I use this equation when I want to rig a spreader bar
that lifts two loads (performers) of different weights, where the spreader bar
is lifted from a single point, and where I want the spreader bar to remain
horizontal. Here is a diagram of the problem:
You might want to think of this as a
teeter-totter. What is on one side
of the fulcrum (lifting point) must balance with the other side. The concept of finding the center of
gravity (the lifting point) for two loads on a beam is very simple: Load 1
times the Length of Side 1 must be equal to Load 2 times the Length of Side
2. Since the loads and the
distance between them (the ÒSpanÓ) are known, the objective is to determine the
lengths of Side 1 and Side 2.
The equations to solve this problem are:
Length of Side 1 = (Load 2 x Span) / total
load
Length
of Side 2 = (Load 1 x Span) / total load
or
Length
of Side 2 = Span – Length of Side 1
Example:
If the total span is 10 feet, and Load 1 is 150 lbs and Load 2 is 100 lbs,
where is the center of gravity (what are the lengths of Side 1 and Side 2)?
Length
of Side 1 = (Load 2 x Span) / total load
Length
of Side 1 = (100 x 10) / (150 + 100)
Length
of Side 1 = 1000 / 250
Length of
Side 1 = 4Õ
Length of Side 2 = (Load 1 x Span) / total load
Length
of Side 2 = (150 x 10 )/ (150 + 100)
Length
of Side 2 = 1500 / 250
Length of
Side 2 = 6Õ
or
Length of Side 2 = Span – Length of Side 1
Length
of Side 2 = 10 – 4
Length of
Side 2 = 6Õ
