Exercise 9: Consider our aircraft is flying, W = 160000N, Wing area is 42
m
2
,
power available of engine is 2 MW and the parabolic drag polar is
C
D
= 0,014 +
0,05
C
L
2
a) Find angle of climb and rate of climb. If aircraft’s velocity at mean sea level
is 120 m/s (Assume L =W)
b) Find the max angle of climb and the climb rate under that condition
c) Find the max rate of cimb and the angle of climb under that condition
Answer
L=W = 160000 N
S = 42
m
2
P
Avai
= 2 MW = 2.
10
6
W
C
D
= 0,014 + 0,05
a) V = 120 m/s
γ
and RC =?
L =
1
2
ρ V
2
S C
L
160000 =
1
2
.1,225 .120
2
.42 .C
L
C
L
= 0,432
C
D
= 0,014 + 0,05
C
L
2
C
D
= 0,014 + 0,05.
0,432
2
= 0,023
sin
γ=
P
Avai
W . V
C
D
C
L
=
2.10
6
160000.120
0,023
0,432
γ=¿
0,05 rad = 2.86 degree
RC = V.
sinγ
= 120.0,05 = 6 m/s
b)
γ
max
and RC =?
A =
P
Avai
W
3 /2
.
1
2
. ρ. S
=
2. 10
6
160000
3/ 2
.
1
2
.1,225 .42
= 0,158
k.
-
A
2
.
C
L
3/ 2
-
C
d
= 0
0,05.
C
L
2
-
0,158
2
.
C
L
3/ 2
- 0,014 = 0
C
L
= 2,712
C
D
=0 , 3817
sin
γ=
P
Avai
W
.
1
2
. ρ. S . C
L
W
C
D
C
L
γ
max
=0,12 rad degree=6,9
RC =
P
Avai
W
P
Req
W
=
P
Avai
W
C
D
C
L
. cosγ .
2 mg cosγ
ρ . C
L
. S
= 5,8 m/s
c)
RC
max
and
γ=¿
?
C
D
mp
=4 C
d
=4.0,014=0,056
C
L
mp
=
3 C
d
k
=
3.0,014
0,05
=0,91
V
EAS
mp
=
2 mg
ρ
0
, S
.
(
k
3 C
d
)
1 / 4
=
2.160000
1,225.42
.
(
0,05
3.0,014
)
1/ 4
=82,37
sin
γ=
P
Avai
W . V
C
D
C
L
=¿
2. 10
6
160000.82,37
0,056
0,91
γ=0,09rad =5,16 degree
RC = V.
sinγ
= 82,37.0,09 = 7,413 m/s = 1456 ft/min

Preview text:

Exercise 9: Consider our aircraft is flying, W = 160000N, Wing area is 42 m2,
power available of engine is 2 MW and the parabolic drag polar is CD= 0,014 + 0,05C 2 L
a) Find angle of climb and rate of climb. If aircraft’s velocity at mean sea level is 120 m/s (Assume L =W)
b) Find the max angle of climb and the climb rate under that condition
c) Find the max rate of cimb and the angle of climb under that condition Answer L=W = 160000 N S = 42 m2 PAvai = 2 MW = 2.106 W C 2
D = 0,014 + 0,05C L a) V = 120 m/s γ and RC =? 1 L = ρ V 2 S C 2 L  1
160000 = .1,225 .1202 .42 .C 2 LCL= 0,432 C 2
D = 0,014 + 0,05C L
CD= 0,014 + 0,05.0,4322 = 0,023 P C sin γ= Avai D = 2.106
− 0,023 γ=¿ 0,05 rad = 2.86 degree W . V C 160000.120 0,432 L
RC = V. sinγ = 120.0,05 = 6 m/s b) γmax and RC =? P 2. 106
A = Avai .√ 1.ρ.S =
. √ 1.1,225.42 = 0,158 W 3/2 2 1600003/ 2 2 A k. 3/ 2 C 2 - . C - C L 2 L d = 0 0,158 0,05.  C 2 - . C 3/2  C =0,3817 L - 0,014 = 0  C 2 L L = 2,712 D . ρ . S . C P
√12 L C γ =0,12rad=6,9degree max sin γ = Avai .D W W CL P P P C
RC = AvaiReq = Avai D . cosγ . √2mgcosγ = 5,8 m/s W W W C ρ . C . S L L
c) RCmax and γ=¿ ?
C =4 C =4.0,014=0,056 D d mp
C =√3Cd=√3.0,014=0,91 Lmp k 0,05 V =
.( k )1/4=√2.160000 .( 0,05 )1/4=82,37 EAS √2mg mp ρ , S 3 C 1,225.42 0 d 3.0,014 P C sin γ= Avai D =¿ 2. 106
−0,056 γ=0,09rad =5,16 degree W . V CL 160000.82,37 0,91
RC = V. sinγ = 82,37.0,09 = 7,413 m/s = 1456 ft/min