An aircraft loaded weighs 4954 lbs at a CG of +30.5 inches. The CG range is +32.0 inches to +42.1 inches. Find the minimum ballast weight needed to bring the CG within range. The ballast arm is +162 inches.

• A. +57.16 pounds
• B. −57.16 pounds
• C. +42.0 pounds
• D. +60.0 pounds

Answer: (A)

The key idea is to use moments to shift the center of gravity (CG) and set the new CG to the nearest acceptable limit. CG is found from total moment divided by total weight: CG = (existing weight × existing CG + ballast weight × ballast arm) / (existing weight + ballast weight). You want the minimum ballast so that CG is at the lower limit of +32.0 inches.

Current moment = 4954 × 30.5 = 151,097 in-lb.

With ballast Wb at an arm of 162 inches, the new CG should satisfy:

(151,097 + 162·Wb) / (4954 + Wb) = 32.

Solve:

151,097 + 162Wb = 32(4954 + Wb) = 158,528 + 32Wb

130Wb = 7,431

Wb ≈ 57.16 lb.

So the minimum ballast needed is about 57.2 pounds. The ballast at the given arm shifts the CG from 30.5 to the lower limit of 32.0, bringing the aircraft within the allowed range.