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and others negative. To simplify weight and balance
computations, most modern helicopters, like airplanes,
have the datum located at the nose of the aircraft or a
specified distance ahead of it.
A moment is a force that tries to cause rotation, and is the
product of the arm, in inches, and the weight, in pounds.
Moments are generally expressed in pound-inches (lb-in)
and may be either positive or negative. Figure 2-1 shows
the way the algebraic sign of a moment is derived. Positive
moments cause an airplane to nose up, while negative
moments cause it to nose down.
Figure 2-1. Relationships between the algebraic signs of weight,
arms, and moments.
The Law of the Lever
The 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 counter-clockwise).
2–
Figure 2-2. The lever is balanced when the algebraic sum of the
moments is zero.
Consider these facts about the lever in Figure 2-2: The
100-pound weight A is located 50 inches to the left of the
fulcrum (the datum, in this instance), and it has a moment
of 100 X-50 = -5,000 in-lb. The 200-pound weight B
is located 25 inches to the right of the fulcrum, and its
moment is 200 x +25 = +5000 in-lb. The sum of the
moment is -5000 + 5000 = 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 2-3. 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 the
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 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.
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.
To prove this is the correct CG, move the datum to
a location 110 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.
2–
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.
Determining the CG of an airplane is done in the same
way as determining the CG of the board in the previous
example. [Figure 2-8] Prepare the airplane for weighing
　
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