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Determining
Center of Gravity (Level 2) Answers
 What is the length
of a Boeing 747400 domestic airplane?
Length = 70.7
m
 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.
A
sine wave oscillating for one period at the Y = 42, 850 level. The
amplitude of the oscillation is small compared to the constant Y term
of 42,850.
 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.]
 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.
A
sinusoidal curve oscillating for one period at the level of 42,850.
The amplitude of the oscillation is minute compared to the height
of the function.
 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.]
(a)
They
are equal because the contributions to the integral by the sine and
cosine average to zero.
(b)
= 35.15m
 Did
the
center of gravity move?
 If
so, did it move toward the airplane's nose or tail?
Yes.
(a) Toward the nose.
 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?
 Yes.
The airplane would begin to rotate about the cg because the plane would
no longer be properly trimmed.

Related Pages:
Standards
Activity
Worksheet
Lesson Index
Aerodynamics Index


