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Weight and Balance Handbook

FAA-H-8083-1B Version 2016
All Library Documents FAA Source

Chapter 2

Weight and Balance Theory

Figure 2-4. Finding balance point with datum located off the lever.
Figure 2-4. Finding balance point with datum located off the lever.

As noted in Figure 2-4, 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. The total of the weights is 400 pounds, and the total moment is 44,000 lb-in.

Determine the balance point by dividing the total moment by the total weight. A balance point is equal to the CG and can be mathematically written as:

CG = total moment / total weight

To prove this is the correct balance, 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. [Figure 2-5] Then, make a new chart similar to the one in Figure 2-6, in which the sum of the moments is zero.

Figure 2-5. Locating balance point.
Figure 2-5. Locating balance point.
Figure 2-6. Proving balance point with three weights is correct.
Figure 2-6. Proving balance point with three weights is correct.

The new arm of weight A is 60 inches (the difference between 110 and 50), 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 20 inches (110 – 90), and it is also to the left of the datum, so it is –20; the new arm of weight C is 40 inches (150 – 110). It is to the right of the datum and is therefore positive.

The lever 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 may be in various locations, but all of the measurements must be made from the same datum location.

The procedure for finding the balance point is the same anywhere the datum is located. In Figure 2-7, the datum is located at C. Weight A has an arm of –100 inches (negative because it is to the left) of the datum and weight B has an arm of –60 inches from the datum. The table in Figure 2-8 is used to determine the new balance point.

Figure 2-7. Locating balance point with datum at C.
Figure 2-7. Locating balance point with datum at C.
Figure 2-8. Determining new balance point.
Figure 2-8. Determining new balance point.

To verify that this is the correct balance point, move the datum 40 inches to the left of the original datum and determine the arm of each weight from this new datum as in Figure 2-9.

Figure 2-9. Locating balance point with datum left of original.
Figure 2-9. Locating balance point with datum left of original.

The new arm for weight A would be –100 + 40 = –60; for weight B, –60 + 40 = –20; and point C, is +40. The lever is balanced and the balance point is correct when the sum of the moments is zero. [Figure 2-10]

Figure 2-10. Proving the new balance point is correct.
Figure 2-10. Proving the new balance point is correct.

Shifting the Balance Point or CG

One common weight and balance problem involves moving or shifting weight from one point to another in order to move the balance point or CG to a desired location. This can be demonstrated by using a lever with three weights to work out the problem.

Solution by Chart

As the lever is loaded in Figure 2-11, it balances at a point 72 inches from the CG of weight A.