An aircraft loaded weighs 4,954 pounds at a CG of +30.5 inches. The CG range is +32.0 to +42.1 inches. Ballast at +162 inches is used to bring the CG within range. What is the minimum ballast weight required?

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Multiple Choice

An aircraft loaded weighs 4,954 pounds at a CG of +30.5 inches. The CG range is +32.0 to +42.1 inches. Ballast at +162 inches is used to bring the CG within range. What is the minimum ballast weight required?

Explanation:
To move the CG into the allowable range, you add ballast at a distant arm so the overall CG shifts aft. The minimum ballast weight is found by setting the final CG to the forward limit (32.0 inches) and solving the CG equation. Let W = 4954 lb, initial CG = 30.5 in, ballast weight b at arm 162 in. Target CG X' = 32.0 in. (W*Xcg + b*Xballast) / (W + b) = 32 W*Xcg + b*Xballast = 32(W + b) b*(Xballast - 32) = W*(32 - Xcg) Plug in numbers: Xballast - 32 = 130, 32 - Xcg = 1.5, W*(32 - Xcg) = 4954*1.5 = 7431. b = 7431 / 130 = 57.1615 lb ≈ 57.16 pounds. So the minimum ballast weight is about 57.16 pounds.

To move the CG into the allowable range, you add ballast at a distant arm so the overall CG shifts aft. The minimum ballast weight is found by setting the final CG to the forward limit (32.0 inches) and solving the CG equation.

Let W = 4954 lb, initial CG = 30.5 in, ballast weight b at arm 162 in. Target CG X' = 32.0 in.

(WXcg + bXballast) / (W + b) = 32

WXcg + bXballast = 32(W + b)

b*(Xballast - 32) = W*(32 - Xcg)

Plug in numbers: Xballast - 32 = 130, 32 - Xcg = 1.5, W*(32 - Xcg) = 4954*1.5 = 7431.

b = 7431 / 130 = 57.1615 lb ≈ 57.16 pounds.

So the minimum ballast weight is about 57.16 pounds.

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