Where would the CG of an aircraft be located if Weight A is 175 pounds at 135 inches aft of datum, Weight B is 135 pounds at 115 inches aft of datum, and Weight C is 75 pounds at 85 inches aft of datum?

Where would the CG of an aircraft be located if Weight A is 175 pounds at 135 inches aft of datum, Weight B is 135 pounds at 115 inches aft of datum, and Weight C is 75 pounds at 85 inches aft of datum?

• A. 114.56 inches
• B. 118.24 inches
• C. 120.63 inches
• D. 122.00 inches

Answer: (B)

To determine the center of gravity (CG) of the aircraft given the weights and their respective distances from the datum, the following formula is used: \[ CG = \frac{(W_A \cdot D_A) + (W_B \cdot D_B) + (W_C \cdot D_C)}{(W_A + W_B + W_C)} \] Where \( W \) represents the weight, and \( D \) is the distance from the datum. In this case: - Weight A is 175 pounds at 135 inches. - Weight B is 135 pounds at 115 inches. - Weight C is 75 pounds at 85 inches. First, calculate the moments of each weight: - Moment A = 175 lbs * 135 in = 23,625 lb-in - Moment B = 135 lbs * 115 in = 15,525 lb-in - Moment C = 75 lbs * 85 in = 6,375 lb-in Next, sum the moments: \[ Total\ Moment = 23,625 + 15,525 + 6,375 = 45,525 \text{ lb-in} \] Now, calculate the total weight

To determine the center of gravity (CG) of the aircraft given the weights and their respective distances from the datum, the following formula is used:

[

CG = \frac{(W_A \cdot D_A) + (W_B \cdot D_B) + (W_C \cdot D_C)}{(W_A + W_B + W_C)}

]

Where ( W ) represents the weight, and ( D ) is the distance from the datum.

In this case:

• Weight A is 175 pounds at 135 inches.

• Weight B is 135 pounds at 115 inches.

• Weight C is 75 pounds at 85 inches.

First, calculate the moments of each weight:

• Moment A = 175 lbs * 135 in = 23,625 lb-in

• Moment B = 135 lbs * 115 in = 15,525 lb-in

• Moment C = 75 lbs * 85 in = 6,375 lb-in

Next, sum the moments:

[

Total\ Moment = 23,625 + 15,525 + 6,375 = 45,525 \text{ lb-in}

]

Now, calculate the total weight