Questions: An aircraft with an empty weight of 2,100 pounds and an empty weight CG +32.5 was altered as follows: - two 18 -pound passenger seats located at +73 were removed; structural modifications were made at +77 increasing weight by 17 pounds; a seat and safety belt weighing 25 pounds were installed at +74.5 ; and Radio equipment weighing 35 pounds was installed at +95 . What is the new empty weight CG?

Solution Steps

The initial moment is calculated by multiplying the empty weight of the aircraft by the initial center of gravity (CG) arm.

\[ \text{Initial Moment} = \text{Empty Weight} \times \text{Initial CG} = 2100 \, \text{lbs} \times 32.5 = 68250 \, \text{lb-in} \]

1. Remove Two Seats:

   • Weight removed: \(2 \times 18 = 36 \, \text{lbs}\)
   • Arm: \(+73\)
   • Moment change: \(36 \, \text{lbs} \times 73 = 2628 \, \text{lb-in}\)

2. Structural Modifications:

   • Weight added: \(17 \, \text{lbs}\)
   • Arm: \(+77\)
   • Moment change: \(17 \, \text{lbs} \times 77 = 1309 \, \text{lb-in}\)

3. Install Seat and Safety Belt:

   • Weight added: \(25 \, \text{lbs}\)
   • Arm: \(+74.5\)
   • Moment change: \(25 \, \text{lbs} \times 74.5 = 1862.5 \, \text{lb-in}\)

4. Install Radio Equipment:

   • Weight added: \(35 \, \text{lbs}\)
   • Arm: \(+95\)
   • Moment change: \(35 \, \text{lbs} \times 95 = 3325 \, \text{lb-in}\)

1. New Total Weight: \[ \text{New Total Weight} = 2100 - 36 + 17 + 25 + 35 = 2141 \, \text{lbs} \]

2. New Total Moment: \[ \text{New Total Moment} = 68250 - 2628 + 1309 + 1862.5 + 3325 = 72318.5 \, \text{lb-in} \]

The new empty weight CG is calculated by dividing the new total moment by the new total weight.

\[ \text{New CG} = \frac{\text{New Total Moment}}{\text{New Total Weight}} = \frac{72318.5}{2141} \approx 33.78 \]

Final Answer