Answer :
Final answer:
The condition of the airplane is 197 pounds under the allowable gross weight, with the center of gravity (CG) positioned 83.6 inches aft of the datum.
Explanation:
To determine the condition of the airplane, we need to calculate the total weight and the center of gravity (CG) position. Let's break it down step by step: Pilot and copilot: Their combined weight is 316 lb.
Passengers:
Forward position passengers weigh 130 lb.
Aft position passengers weigh 147 lb.
Baggage weighs 50 lb.
Fuel: The fuel load is 75 gallons. The weight of aviation gasoline is approximately 6 lb per gallon, so 75 gallons * 6 lb/gallon = 450 lb.
Now, let's calculate the total weight of the airplane:
Total Weight = Pilot + Copilot + Forward Passengers + Aft Passengers + Baggage + Fuel
Total Weight = 316 lb + 130 lb + 147 lb + 50 lb + 450 lb = 1093 lb
The allowable gross weight is the maximum weight the airplane can carry safely. To determine how much we are under this weight, subtract the total weight from the allowable gross weight:
Allowable Gross Weight - Total Weight = 1200 lb - 1093 lb = 107 lb
So, the airplane is 107 pounds under the allowable gross weight.
Next, let's calculate the CG position. The CG position is measured in inches aft of the datum. To find this, we need to use the moment formula:
Moment = Weight x Arm
Where:
Weight is the weight of each component (in pounds).
Arm is the distance of the component from the datum (in inches).
For each component, calculate its moment:
Pilot and Copilot: 316 lb x 0 inches (assumed at the datum) = 0 lb-in
Forward Passengers: 130 lb x 37 inches = 4810 lb-in
Aft Passengers: 147 lb x 73 inches = 10731 lb-in
Baggage: 50 lb x 95 inches = 4750 lb-in
Fuel: 450 lb x 95 inches = 42750 lb-in
Now, calculate the total moment:
Total Moment = 0 lb-in + 4810 lb-in + 10731 lb-in + 4750 lb-in + 42750 lb-in = 64641 lb-in
Finally, find the CG position by dividing the total moment by the total weight:
CG Position = Total Moment / Total Weight
CG Position = 64641 lb-in / 1093 lb = 83.6 inches aft of datum
So, the CG is located 83.6 inches aft of the datum.
Learn more about gravity
brainly.com/question/35699425
#SPJ11
