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Determining Center of Gravity (Level 1) Worksheet

A Boeing 747-400 domestic airplane is soaring the friendly skies (shown below). Use data from the Boeing 747 Wikipedia Website (http://en.wikipedia.org/wiki/Boeing_747) to complete Table 1. Estimate values for data you are unable to locate in a reasonable amount of time. You should be able to find the length of the airplane (for the reference distances requested), the mass of the engine, and the fuel capacity. The distances in Table 1 should be measured from a reference line that starts at the nose (front) of the 747. Use the BACK key to return to this page.

Problem 1 will guide you in the calculation to find the mass of the fuel.

All problems are expressed in metric units. 

  
Mass (kg)
Distance from Reference Line (m)

  
payload

  

  
d1
engine

  

  
d2
wings

  

  
d3
fuselage

  

  
d4
fuel

  

  
d5
vertical tail

  

  
d6
horizontal tail

  

  
d7
Table 1 : Airplane component masses and distances from reference line
 
  1. What is the fuel capacity of the 747?

    Fuel capacity = Volume of fuel = ______________

     

     

  2. Assuming the density of an average jet fuel is 0.75 g/ml, use the density equation,
    density = mass / volume,

    to calculate the mass of the fuel. (Hint: You must convert from liters to milliliters.)

     

    Mass of fuel = ______________

    Record this value for the mass of the fuel in Table 1.

     

      

  3. In Table 2, record the weights of the components (parts) listed in Table 1.

    (Hint: Remember, F = mag = W. The acceleration due to gravity, ag , is 9.8 m/s2.)

      
    Mass (kg)
    Weight (N)

      
    payload

      

      
    w1
    engine

      

      
    w2
    wings

      

      
    w3
    fuselage

      

      
    w4
    fuel

      

      
    w5
    vertical tail

      

      
    w6
    horizontal tail

      

      
    w7
     Table 2 : Airplane component weights

     

  4. What does n equal?

    [Hint: The number n is the number of quantities being added together.]

    n = _________ 

     

     

  5. What are the values for i?

    i = _________________________

     

     

  6. What is the total weight W of the airplane?

     

  7. What is the value of the sum of the component weights times their distances from the reference line (see the equation below)?

     

  8. Using your answers from Problems 6 and 7, calculate the center of gravity.

     

  9. After a long flight, the amount of fuel left in the tanks is 20% of the initial amount. What is the mass and weight of the fuel that is left? Record your answers in Table 3.

      
    Mass (kg)
    Weight (N)
    Remaining Fuel

      

      
    Table 3 : Remaining Fuel Data

     

  10. Recalculate the airplane's center of gravity with the reduced fuel weight.

     

     

  11. Did the center of gravity change?

     

    1. If yes, by how many meters did the center of gravity move?

       

    2. If yes, did the center of gravity move toward or away from the nose of the airplane?

       

    3. Do you think the pilot would notice such a change in the center of gravity while flying? Why?