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(as explained in Chapter 3) and place it on three scales. All
tare weight, that is, the weight of any chocks or devices
used to hold the aircraft on the scales, is subtracted from
the scale reading, and the net weight from each wheel
weigh point is entered on the chart like the one in Figure
2-9. The arms of the weighing points are specified in the
Type Certificate Data Sheet (TCDS) for the airplane in
terms of stations, which are distances in inches from the
datum. Tare weight also includes items used to level the
aircraft.
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.
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.
Shifting the CG
One common weight and balance problem involves
moving passengers from one seat to another or shifting
baggage or cargo from one compartment to another to
move the CG to a desired location. This also can be
visualized by using a board 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]
2–
Figure 2-10. Moving the CG of a board by shifting the weights. This
is the original configuration.
Figure 2-11. Shifting the CG of a board by moving one of the
weights. This is the original condition of the board.
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
in-lb, so the moment of weight B will have to be -5,000 lbin
in order for the board to balance. [Figure 2-12]
Figure 2-12. Determining the combined moment of weights A and C.
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.
Figure 2-13. Placement of weight B to cause the board to balance
about its center.
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:
This 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:
Solution by Formula
This same problem can also be solved by using this basic
equation:
Rearrange this formula to determine the distance weight B
must be shifted:
2–
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.
If the 200-pound weight B is shifted from station 80 to station
25, the CG will move from station 72 to station 50.
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
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Aircraft Weight and Balance Handbook(10)
