AOE 3104 Homework #3 Solutions
Problem 1.
An aircraft weighs 12
,
500 N and has a 20 m
2
wing area, an aspect ratio of 6 and efficiency
factor
e
= 0
.
9. If
C
D
0
= 0
.
02,
(a) Calculate the values of the minimum drag force
D
min
and the airspeed for minimum drag
V
md
at
standard sea level conditions.
(b) Assuming a constant sea level thrust
T
SL
= 5000 N, find the maximum speed
V
max
and minimum
speed
V
min
at sea level.
(c) Calculate the airspeed for minimum power
V
mp
at standard sea level conditions and the value of
minimum power required
P
req
,
min
.
Solution.
First, compute the induced drag parameter
K
=
1
πeAR
=
1
π
(0
.
9)(6)
= 0
.
0589
Because
D
=
W
D
L
=
W
C
D
C
L
in equilibrium, constantaltitude flight, the minimum drag force (at any altitude) is
D
min
=
W
C
D
md
C
L
md
=
W
2
C
D
0
radicalbig
C
D
0
/K
= 2
W
radicalbig
KC
D
0
= 858 N
and the speed for minimum drag at sea level is
V
md
=
radicalBigg
2
W
ρSC
L
md
=
radicalBigg
2
W
ρS
4
radicalbigg
C
D
0
K
= 41
.
9 m
/
s
Next, because this is a
constant thrust
aircraft, we may compute the minimum and maximum speed from
the quadratic equation
V
2
=
T
0
C
D
0
ρS
±
radicalBigg
parenleftbigg
T
0
C
D
0
ρS
parenrightbigg
2

4
KW
2
C
D
0
ρ
2
S
2
Given
T
0
= 5000 N, we compute
V
max
= 142 m
/
s
and
V
min
= 12
.
3 m
/
s
Of course, the value of
V
min
given above is only a
candidate
value for the minimum speed, It may be lower
than the stall speed of the aircraft, in which case, the given value of minimum speed may not be sustained
in equilibrium flight. However, the stall speed can not be computed from the information given; you were
not given
C
L
max
for this problem.
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 Fall '09
 Aerodynamics, Mach number, Airspeed, sea level

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