AOE 3104
Aircraft Performance
Exam #2 Solutions
Problem 1. (35 points)
The installed sealevel power for a singleengine, propellerdriven aircraft is
P
A
= 80 hp. The nominal weight of the aircraft is
W
= 2500 lb and the planform area is
S
= 150 ft
2
.
The stall lift coefficient is
C
L
max
= 2
.
0. Flight testing has established the power required curve illustrated
below. Determine the following:
•
The minimum and maximum speed at sea level.
•
The parameters
C
D
0
and
K
(assuming a parabolic drag polar).
•
The maximum climb rate at sea level.
•
The absolute ceiling altitude.
40
60
80
100
120
140
160
180
200
220
240
30
35
40
45
50
55
60
65
70
75
80
Equivalent Airspeed, V
eq
(ft/s)
(Power Required)*
σ
1/2
(hp)
h
G
(kft)
σ
0
1.0000
5
0.8617
10
0.7386
15
0.6295
20
0.5332
25
0.4486
30
0.3747
35
0.3106
40
0.2471
45
0.1945
50
0.1531
Solution.
Part 1 (10 points)
The minimum and maximum speed are obtained by find the intersection of
power available and power required. Note, however, that the minimum speed, as determined in this way,
may be unattainable because the aircraft would stall. In that case, the stall speed is the minimum speed.
From the plot, we see that
V
min
≈
50 ft
/
s (?)
and
V
max
≈
230 ft
/
s
To check
V
min
, we compute
V
stall
=
radicalBigg
2
W
ρSC
L
max
≈
84 ft
/
s
>
50 ft
/
s
so
V
min
=
V
stall
and
V
max
≈
230 ft
/
s
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Part 2 (10 points)
We can find the minimum power, and the corresponding equivalent airspeed, directly
from the plot:
P
min
= (40 hp)(550 (lb ft
/
s)
/
(hp)) = 2200 lb ft
/
s
and
V
mp
≈
125 ft
/
s
We also know that
P
R
=
D
*
V
, so
P
min
=
D
mp
V
mp
=
C
D
mp
parenleftbigg
1
2
ρV
2
mp
S
parenrightbigg
V
mp
=
4
C
D
0
parenleftbigg
1
2
ρV
2
mp
S
parenrightbigg
V
mp
so
C
D
0
=
P
min
(
2
ρSV
3
mp
)
−
1
= 0
.
0158
We also know that
W
=
C
L
mp
parenleftbigg
1
2
ρV
2
mp
S
parenrightbigg
=
radicalbigg
3
C
D
0
K
parenleftbigg
1
2
ρV
2
mp
S
parenrightbigg
so
K
=
3
C
D
0
parenleftBig
2
W
ρV
2
mp
S
parenrightBig
2
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 Fall '09
 Aviation terminology, sea level, Airfoil, Stall, Angle of attack

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