AOE 3104 Homework #4 Solutions
Problem 1.
A sailplane of mass 500 kg has an aspect ratio
AR
= 22 and a wingspan
b
= 15 m. The drag
parameter values are
C
D
0
= 0
.
01 and
K
= 0
.
015.
The glider is released at 3,000 m on a standard day.
Estimate the best range and best endurance in still air. State your assumptions clearly.
Solution.
The range in gliding flight is
R
= Δ
h
parenleftbigg
C
L
C
D
parenrightbigg
so maximum range occurs when
L/D
is maximum, i.e., for
C
L
=
C
L
md
=
radicalbigg
C
D
0
K
= 0
.
8165
and
C
D
=
C
D
md
= 2
C
D
0
= 0
.
0200
Substituting values, we find
R
= 122
.
5 km.
Assuming that
L
=
W
cos
γ
≈
W
and approximating the density the constant value
ρ
=
ρ
(1500 m) =
1
.
0581 kg
/
ft
3
, we have
E
≈
Δ
h
radicalbigg
ρS
2
W
C
(3
/
2)
L
C
D
Endurance in gliding flight is maximum for constant power flight conditions, i.e., for
C
L
=
C
L
mp
=
radicalbigg
3
C
D
0
K
= 1
.
4142
and
C
D
=
C
D
mp
= 4
C
D
0
= 0
.
0400
Substituting values, we find
E
= 1
.
16 hours.
To test our assumptions, first notice that

γ
= arctan(
C
D
mp
/C
L
mp
) = 1
.
62
◦
so it is quite reasonable to
assume cos
γ
≈
1. We may check the assumption of constant density by breaking the descent into to phases
of 1500 meters each, and using some average density over the respective segments. Doing so, and using
densities at 2200 and 800 meters, respectively, we still find that
E
= 1
.
16 hours, so the assumption of
constant density is reasonable for this problem.
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Problem 2.
A business jet has the following parameter values
b
= 50 ft
,
S
= 325 ft
2
,
C
D
0
= 0
.
015
,
e
= 0
.
85
.
The maximum weight is 20,000 lb, which includes the full fuel capacity of 1000 gallons (at a fuel density of
6.67 lb/gal). Each of the twin engines can produce a maximum 3500 lb of thrust at sea level. The weight
specific fuel consumption is
γ
t
= 0
.
55 (lb
fuel
/
hr)
/
lb
thrust
.
Find the maximum range and the maximum
endurance at sea level (constant altitude) for filght at a constant angle of attack.
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 Fall '09
 Fluid Dynamics, Aerodynamics, Specific impulse, Brake specific fuel consumption, Drag Rise

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