Questions: The following alteration was performed on an aircraft; a model F engine weighing 175 pounds was replaced by a model Z engine weighing 185 pounds at a -62.00 inch station. The aircraft weight and balance records show the previous empty weight to be 998 pounds and an empty weight CG of 13.48 inches. What is the new empty weight CG?

The following alteration was performed on an aircraft; a model F engine weighing 175 pounds was replaced by a model Z engine weighing 185 pounds at a -62.00 inch station. The aircraft weight and balance records show the previous empty weight to be 998 pounds and an empty weight CG of 13.48 inches. What is the new empty weight CG?

Transcript text: The following alteration was performed on an aircraft; a model $F$ engine weighing 175 pounds was replaced by a model $Z$ engine weighing 185 pounds at a -62.00 inch station. The aircraft weight and balance records show the previous empty weight to be 998 pounds and an empty weight CG of 13.48 inches. What is the new empty weight CG?

Solution

Solution Steps

Step 1: Understand the Problem

We need to find the new empty weight center of gravity (CG) of the aircraft after replacing the engine. The initial conditions are:

Previous empty weight: 998 pounds
Previous empty weight CG: 13.48 inches
Weight of model $ F $ engine: 175 pounds
Weight of model $ Z $ engine: 185 pounds
Location of engine station: -62.00 inches

Step 2: Calculate the Initial Moment

The moment is calculated as the product of weight and CG. The initial moment of the aircraft is: \[ \text{Initial Moment} = \text{Previous Empty Weight} \times \text{Previous Empty Weight CG} = 998 \, \text{lbs} \times 13.48 \, \text{in} = 13445.04 \, \text{lb-in} \]

Step 3: Calculate the Change in Moment Due to Engine Replacement

The change in moment due to replacing the engine is calculated by the difference in weight of the engines multiplied by the station location: \[ \text{Change in Moment} = (\text{Weight of Model } Z - \text{Weight of Model } F) \times \text{Station Location} \] \[ = (185 \, \text{lbs} - 175 \, \text{lbs}) \times (-62.00 \, \text{in}) = 10 \, \text{lbs} \times (-62.00 \, \text{in}) = -620 \, \text{lb-in} \]

Step 4: Calculate the New Moment

The new moment is the sum of the initial moment and the change in moment: \[ \text{New Moment} = \text{Initial Moment} + \text{Change in Moment} = 13445.04 \, \text{lb-in} - 620 \, \text{lb-in} = 12825.04 \, \text{lb-in} \]

Step 5: Calculate the New Empty Weight

The new empty weight is the sum of the previous empty weight and the change in engine weight: \[ \text{New Empty Weight} = \text{Previous Empty Weight} + (\text{Weight of Model } Z - \text{Weight of Model } F) = 998 \, \text{lbs} + 10 \, \text{lbs} = 1008 \, \text{lbs} \]

Step 6: Calculate the New Empty Weight CG

The new empty weight CG is calculated by dividing the new moment by the new empty weight: \[ \text{New Empty Weight CG} = \frac{\text{New Moment}}{\text{New Empty Weight}} = \frac{12825.04 \, \text{lb-in}}{1008 \, \text{lbs}} \approx 12.7231 \, \text{in} \]