AOE 3104 Homework #7 Solutions
Problem 1.
Wind tunnel tests yield the following data for lift coefficient and pitch moment coefficient
about the half chord line of a given wing:
¯
α
(deg)
C
L
C
m
1
/
2
4.0
0.257
0.149
2.0
0.030
0.084
0.0
0.194
0.062
2.0
0.210
0.020
4.0
0.540
0.033
6.0
0.752
0.066
Using the software of your choice (e.g., Matlab or Excel), determine
C
L
(¯
α
) and
C
m
1
/
2
(¯
α
) using a linear
least squares fit. Plot the data and the curve fits. Determine
h
ac
and
C
m
ac
.
4
2
0
2
4
6
8
10
0.5
0
0.5
1
1.5
C
L
4
2
0
2
4
6
8
10
0.2
0.1
0
0.1
0.2
α
(deg)
C
m
Figure 1: Least squares fits for
C
L
(¯
α
) and
C
m
(¯
α
) versus ¯
α
.
Solution.
Using Matlab’s
polyfit
and
polyval
functions, one may obtain the plots shown in Figure 1.
The data fits suggest that
C
L
(¯
α
)
=
0
.
136 + 0
.
093 ¯
α
(1)
C
m
1
/
2
(¯
α
)
=
0
.
0582

0
.
0197 ¯
α.
(2)
The neutral point can be found by differentiating the identity
C
m
1
/
2
=
C
m
ac
+
C
L
(
h
1
/
2

h
ac
)
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with respect to ¯
α
and solving for
h
ac
:
h
ac
=
h
1
/
2

1
C
L
α
parenleftbigg
∂C
m
1
/
2
∂
¯
α
parenrightbigg
=
1
2


0
.
0197
0
.
093
≈
0
.
711
The easiest way to find
C
m
ac
is to solve (1) for ¯
α
0
L
and substitute into (2). Doing so gives
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 Fall '09
 Aerodynamics, Airfoil, Angle of attack, CMAC, equilibrium flight

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