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Determining Center of Gravity (Level 1) Activity
If so instructed by your teacher, print out a worksheet page for these problems.


Open the slide called Determining Center of Gravity (with text) and read the explanation on how an airplane in flight will rotate about a point in the airplane called the center of gravity.

A Boeing 747-400 domestic airplane is soaring the friendly skies (shown below). Use data from the Boeing 747 Wikipedia Website to complete Table 1. Estimate values for data you are unable to locate in a reasonable amount of time. You willl have to select an engine to go on your aircraft. 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.

Image of Boeing 747 in flight 
 
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?

Related Pages:
Standards
Worksheet
Lesson Index
Aerodynamics Index

 

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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Thu, Jun 12 04:46:36 PM EDT 2014

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