An aircraft with an empty weight of 1,500 pounds and an empty weight CG of +28.4 was altered by removing two 12-pound seats located at +68.5, adding 28 pounds at +73, installing a 30-pound seat at +70.5, and 25 pounds of radio at +85. What is the new empty weight CG?

• A. +28.4
• B. +29.0
• C. +30.30
• D. +32.0

Answer: (C)

The concept being used is how the center of gravity shifts with changes in weight and its location. The CG is the total weight moment divided by the total weight. Each modification adds or subtracts weight at a specific arm, changing the overall moment and thus the CG.

Start with the original empty weight and CG: 1,500 lb at +28.4.

Removing two seats weighing 24 lb at +68.5 reduces both weight and moment by 24 × 68.5 = 1,644.

• New weight: 1,500 − 24 = 1,476 lb

• New moment: 1,500 × 28.4 − 1,644 = 42,600 − 1,644 = 40,956

• CG ≈ 40,956 / 1,476 ≈ +27.75

Adding 28 lb at +73 increases weight and moment by 28 × 73 = 2,044.

• New weight: 1,476 + 28 = 1,504 lb

• New moment: 40,956 + 2,044 = 43,000

• CG ≈ 43,000 / 1,504 ≈ +28.59

Installing a 30 lb seat at +70.5 adds 30 × 70.5 = 2,115 to the moment (weight becomes 1,534 lb).

• New moment: 43,000 + 2,115 = 45,115

• CG ≈ 45,115 / 1,534 ≈ +29.41

Adding 25 lb of radio at +85 adds 25 × 85 = 2,125 to the moment (weight becomes 1,559 lb).

• New moment: 45,115 + 2,125 = 47,240

• CG ≈ 47,240 / 1,559 ≈ +30.30

New empty weight CG = +30.30.