
Determining
Center of Gravity (Level 2) 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 747400 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. Use the BACK key to return to this page.
All problems are expressed
in metric units.
 What is the length
of a Boeing 747400 domestic airplane?
Length = __________
 Let us suppose
that the approximate weight distribution (function) on a loaded 747400
domestic airplane is given by the equation,
w(x) = 700 sin(2px
/ L) + 42,850,
where x is the
distance measured from the nose of the airplane. Graph the weight
distribution.
 What is the total
weight W of the airplane?
 Use the equation,
to calculate the
center of gravity of the airplane. The integration is calculated for
x = 0 (nose) to Length (tail).
[ Hint:
Use integration by parts.]
cg = __________________
 Let us suppose
that the approximate weight distribution (function) on a loaded 747400
domestic airplane is given by the equation,
w(x) = 777 ( cos(2px
/ L) + sin(2px / L) ) + 42,850,
where x is the
distance measured from the nose of the airplane. Graph the weight
distribution.
 What is the total
weight W of the airplane?
 How does the weight
calculated in Problem 3 compare with the weight in Problem 6? Explain
why this is so.
Use the equation,
to calculate the
center of gravity of the airplane with the new weight distribution.
The integration is calculated for x = 0 (nose) to Length (tail). [
Hint: Use integration by parts.]
cg = _____________
 Did the center
of gravity move?
 If
so, did it move toward the airplane's nose or tail?
 If not, why
did it stay in the same position?
 If the airplane's
center of gravity moved significantly during flight, do you think the
pilot would notice it? Why or why not?
