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?

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