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 Website to complete Table 1. Estimate values for data you are unable to locate in a reasonable amount of time. Click Boeing Website to access a partial list of 747 data. 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.

 

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	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 = ma_g = W. The acceleration due to gravity, a_g , 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?