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+5,000 = 0, and the lever is balanced. [Figure 2-3] The forces
that try to rotate it clockwise have the same magnitude as
those that try to rotate it counterclockwise.
Figure 2-1. Relationships between the algebraic signs of
weights, arms, and moments.
The Law of the Lever
All weight and balance problems are based on the physical
law of the lever. This law states that a lever is balanced when
the weight on one side of the fulcrum multiplied by its arm
is equal to the weight on the opposite side multiplied by its
arm. In other words, the lever is balanced when the algebraic
sum of the moments about the fulcrum is zero. [Figure
2-2] This is the condition in which the positive moments
(those that try to rotate the lever clockwise) are equal to the
negative moments (those that try to rotate it counterclockwise).
Figure 2-2. The lever is balanced when the algebraic sum of the
moments is zero.
Figure 2-3. When a lever is in balance, the sum of the
moments is zero.
Determining the CG
One of the easiest ways to understand weight and balance
is to consider a board with weights placed at various
locations. We can determine the CG of the board and observe
the way the CG changes as the weights are moved.
The CG of a board like the one in Figure 2-4 may be determined
by using these four steps:
1. Measure the arm of each weight in inches from a datum.
2. Multiply each arm by its weight in pounds to determine
the moment in pound-inches of each weight.
3. Determine the total of all the weights and of all the
moments. Disregard the weight of the board.
4. Divide the total moment by the total weight to determine
the CG in inches from the datum.
Fulcrum: The point about which a
lever balances.
Moment: A force that causes or tries
to cause an object to rotate.
The Physical Law of the Lever
A lever is balanced when the algebraic sum of the moments about its
fulcrum is equal to zero.
2–3
To prove this is the correct CG, move the datum to a location
110 inches to the right of the original datum and determine
the arm of each weight from this new datum, as in Figure
2-6. Then make a new chart similar to the one in Figure 2-
7. If the CG is correct, the sum of the moments will be zero.
Figure 2-4. Determining the center of gravity from a datum
located off the board.
In Figure 2-4, the board has three weights, and the datum is
located 50 inches to the left of the CG of weight A. Determine
the CG by making a chart like the one in Figure 2-5.
Figure 2-5. Determining the CG of a board with three weights
and the datum located off the board.
As noted in Figure 2-5, “A” weighs 100 pounds and is
50 inches from the datum; “B” weighs 100 pounds and is 90
inches from the datum; “C” weighs 200 pounds and is
150 inches from the datum. Thus the total of the three weights is
400 pounds, and the total moment is 44,000 lb-in.
Determine the CG by dividing the total moment by the
total weight.
Figure 2-6. Arms from the datum assigned to the CG.
The new arm of weight A is 110 – 50 = 60 inches, and since
this weight is to the left of the datum, its arm is negative, or
–60 inches. The new arm of weight B is 110 – 90 = 20 inches,
and it is also to the left of the datum, so it is –20; the new
arm of weight C is 150 – 110 = 40 inches. It is to the right of
the datum and is therefore positive.
Figure 2-7. The board balances at a point 110 inches to the
right of the original datum. The board is balanced when the sum
of the moments is zero.
The location of the datum used for determining the arms of
the weights is not important; it can be anywhere. But all of
the measurements must be made from the same datum
location.
2– 4
Determining the CG of an airplane is done in the same way
as determining the CG of the board in the example on the
previous page. [Figure 2-8] Prepare the airplane for weighing
(as explained in Chapter 3) and place it on three scales. All
tare weight, 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 of the wheels is entered into a chart like
the one in Figure 2-9. The arms of the weighing points are
specified in the TCDS for the airplane in terms of stations,
which are distances in inches from 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
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