INTERNATIONAL AND SPECIALIZED TRANSPORT
■
DECEMBER 2013
THE KNOWLEDGE
37
STEP 3
We now need to divide the object into
smaller “sub-objects” for which we can
easily determine the CoG. See
Figure 2
and
Figure 3
. There is no science behind
choosing these smaller objects. Anything
will do, as long as the total object is
covered, obviously nothing should be
forgotten or left out. In this example I have
chosen;
1.) a triangle (a 3 x 3 m square cut in half)
2.) a square (3 x 3 m). Note that this box
includes a void
3.) a rectangle (1 x 2 m). This is the void of
the square mentioned above at 2.
STEP 4
Of each of these sub-objects the CoG
should be determined and expressed
in co-ordinates. See
figures 4
and
5
. By
drawing assist lines (in red) from one
corner to the opposite one the CoG can
be found for squares and rectangles. By
drawing (assist) lines from one corner to
the centre of the opposite side the CoG
can be found for triangles. This CoG is
found at the intersection of these assist
lines. The result is as follows:
CoG 1.
(+1.0, +1.0)
CoG 2.
(-1.5, +1.5)
CoG 3.
(-2.5, +2.0)
Simplification
Earlier I stated that the CoG is determined
by the weight and location (co-ordinates)
of each of the individual components.
Here is a hint to make the calculations
easier. For two-dimensional objects, like
the one in this example, the area of the
object is proportional with its weight.
When the area is twice as large, the weight
also doubles.
For three-dimensional objects the
volume of the object is proportional
with its weight. These hints allow you
to calculate CoG without knowing the
object’s weight or what it is made of.
The formula to calculate the CoG is
CoG = ∑D
*
W
∑W
In words it reads that the location
of the CoG can be found by summing
(
∑
) the multiplication of the distance
by the weight (area) and divide it by the
summation of all the weights (areas).
Since this is a two-dimensional object,
this calculation should be performed in
x-direction as well as y-direction. For a
three-dimensional object it should also be
performed in the z-direction.
In x-direction the formula can be
rewritten as
CoG
x
= ∑D
x
*
W
∑W
Similarly for the y-direction
CoG
y
= ∑D
y
*
W
∑W
In numbers;
The CoG can be found at the
co-ordinates (-0.35, 1.13), see
figure 6
.
NOTE:
When performing such calculation
on a more frequent basis and experience
is gained, some of the above steps can be
combined to speed up the process.
CoG calculations and, more important,
the reliability of
an accurate CoG,
can become a very
important property.
The transport in the
photograph illustrates
this. The CoG is marked
almost at the top of the
white board that covers
the intake. It is above
the light post at the left
of the transport.
■
FIGURE 4
FIGURE 5
2 m
1 m
1 m 1.5 m
2.5 m
y
y
x
x
FIGURE 6
2 m
0.35
1.13
1 m
1 m
2 m
3 m
y
y(pos)
y(neg)
x(neg)
x(pos)
x
1.5 m
2
3
1
OBJECT
X- CO-ORDINATE
Y- CO-ORDINATE
WEIGHT/AREA
1
+1.0
+1.0
(3 * 3) / 2 = 4.5
2
-1.5
+1.5
(3 * 3) = 9
3
-2.5
+2.0
(1 * 2) = 2 (**)
(**) As object 3 is actually a void, the weight (area) needs to be entered as a negative value in
the formula in Step 6.
STEP 5
Arrange all the numbers in order to perform the CoG calculation.
CoG
x
=
(+1,0
*
4.5) +(-1.5
*
9) + (-2.5
*
-2)
=
-4
=
-0.35
(4.5+9-2)
11.5
CoG
y
=
(+1,0
*
4.5) +(-1.5
*
9) + (+2.0
*
-2)
=
13
=
1.13
(4.5+9-2)
11.5
STEP 6
NOTE:
Every effort is made to ensure the
accuracy of the contents of these articles. If
you find any mistakes, a brief notification and
explanation would be appreciated.
