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with three weights and then working out the problem the way
it is actually done on an airplane.
Solution by Chart
The CG of a board can be moved by shifting the weights as
demonstrated in Figure 2-10: As the board is loaded, it
balances at a point 72 inches from the CG of weight A.
[Figure 2-11]
To shift weight B so the board will balance about its center,
50 inches from the CG of weight A, first determine the arm
of weight B that will produce a moment that causes the total
moment of all three weights around this desired balance point
to be zero. The combined moment of weights A and C around
this new balance point is 5,000 lb-in, so the moment of weight
B will have to be –5,000 lb-in in order for the board to
balance. [Figure 2-12]
Figure 2-8. Determining the CG of an airplane whose datum
is ahead of the airplane.
Figure 2-9. Chart for determining the CG of an airplane
whose datum is ahead of the airplane.
Figure 2-10. Moving the CG of a board by shifting the
weights. This is the original configuration.
Figure 2-12. Determining the combined moment of weights A
and C.
The empty weight of this aircraft is 5,862 pounds. Its
EWCG, determined by dividing the total moment by the
total weight, is located at fuselage station 201.1. This is
201.1 inches behind the datum.
Figure 2-11. Shifting the CG of a board by moving one of the
weights. This is the original condition of the board.
Tare weight: The weight of any
chocks or devices used to hold the
aircraft on the scales. Tare weight is
subtracted from the scale reading, to
get the net weight of the aircraft.
Station (GAMA): A location along
the airplane fuselage usually given
in terms of distance from the
reference datum.
2–5
Determine the arm of weight B by dividing its moment,
–5,000 lb-in, by its weight of 200 pounds. Its arm is –25 inches.
To balance the board at its center, weight B will have to be
placed so its CG is 25 inches to the left of the center of the
board, as in Figure 2-13.
Solution by Formula
This same problem can also be solved by using this basic
equation:
Figure 2-13. Placement of weight B to cause the board to
balance about its center.
Rearrange this formula to determine the distance weight B
must be shifted:
The CG of the board in Figure 2-10 was 72 inches from the
datum. This CG can be shifted to the center of the board as
in Figure 2-13 by moving weight B. If the 200-pound weight
B is moved 55 inches to the left, the CG will shift from 72
inches to 50 inches, a distance of 22 inches. The sum of the
moments about the new CG will be zero. [Figure 2-14]
Figure 2-14. Proof that the board balances at its center. The
board is balanced when the sum of the moments is zero.
When the distance the weight is to be shifted is known, the
amount of weight to be shifted to move the CG to any location
can be determined by another arrangement of the basic
equation. Use the following arrangement of the formula to
determine the amount of weight that will have to be shifted
from station 80 to station 25, to move the CG from station
72 to station 50.
A Basic Weight and Balance Equation
This equation can be rearranged to find the distance a weight must
be shifted to give a desired change in the CG location:
The equation can also be rearranged to find the amount of weight to
shift to move the CG to a desired location:
It can also be rearranged to find the amount the CG is moved when
a given amount of weight is shifted:
Finally, this equation can be rearranged to find the total weight that
would allow shifting a given amount of weight to move the CG a given
distance:
? : This symbol, Delta, means a
change in something. ÐCG means a
change in the center of gravity
location.
If the 200-pound weight B is shifted from station 80 to
station 25, the CG will move from station 72 to station 50.
2– 6
A third arrangement of this basic equation may be used to
determine the amount the CG is shifted when a given amount
of weight is moved for a specified distance (as it was done
in Figure 2-10). Use this formula to determine the amount
the CG will be shifted when 200-pound weight B is moved
from +80 to +25.
Moving weight B from +80 to +25 will move the CG 22
inches, from its original location at +72 to its new location at
+50 as seen in Figure 2-13.
Shifting the Airplane CG
The same procedures for shifting the CG by moving weights
can be used to change the CG of an airplane by rearranging
passengers or baggage.
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