B)
The type of the airfoil that we used is NACA 4418.
During Cruising at altitude of 27000 ft.
ℜ= ρvLμ
Constant variables: ρ=0.000993 slug / ft3, v=654.735 ft /s, and μ=0.000000317 lb / ft . s
L=9.443 ft
Manipulating variables: M=6.0 , .61 ,6.2,6.3 ,6.4 ,6.5
By substituting all the variables into ℜ= ρvLμ
, we get
Mach number Re0.60 178807080.61 181787200.62 184767320.63 187747440.64 190727560.65 19370767
By inserting all the above Reynold number values into the XFoil software, we can get the graph of Cl vs α. The value of α is restricted from 0 to 3 degree only because our aircraft fixed angle of attack is 3 degree.
After that, the data from Xfoil is exported to Microsoft Excel and the of the gradient of Cl vs Alpha graph is calculated using 2-known-points.
Mach number clα
0.6 6.05221
0.61 6.096001
0.62 6.141492
0.63 6.188787
0.64 6.237947
0.65 6.289064
`
Lift Coefficient
CLα=2 πA
2+√4+ A2β2Ƞ2 (1+ tan2⋀max t
β2 )(SexposedSref
)(F)
CLα=203.44298
2+√4+ 65.68849Ƞ2
All the unknowns in the formula are fixed variables except for the Ƞ=
clα
( 2πβ
). By substituting
clα=4.775939 into Ƞ, we get CLα= 6.063/rad.
Using equation y=mx+c. y-intercept data is obtained xfoil. Finding CL at 2 degree.
CL=6.04492×20( 3.142180 )+0.4054
¿0.550267
The same steps are repeated for the other Reynold numbers.
Re CL17880708 0.68206718178720 0.682418476732 0.682718774744 0.68303319072756 0.683319370767 0.68356717880708 0.682067
The graph of CL vs Reynold number is plotted as shown below.
`
For drag coefficient.
`
17800000 18000000 18200000 18400000 18600000 18800000 19000000 19200000 19400000 196000000.681
0.6815
0.682
0.6825
0.683
0.6835
0.684
CL Vs Reynold
Reynold Number
CL
CD 0=0.005(1−2c lRw)τ [1−0.2M N+0.12(MN (cos⋀1/4 )0.5
A f−t /c )20
]RwT f S−0.1
¿0.005(1−2 (1 )5.5 )(1.04963) [1−0.2(0.60)+0.12( (0.60 ) (cos−1.858 )0.5
0.75−0.18 )20
](5.5)(1.4)(0.52)
¿0.01287303
CDi=[(1−0.12MN
6 )π (AR)
(1+(0.42+ f ( λ ) AR (10 t /c )0.33)
(cos⋀1 /4)2 +
0.1(3N e+1)(4+AR)0.8
)]C L2
¿ [(1−0.12(0.60)6)
π (10.66)(1+
(0.42+ (5.5671875×10−3 ) (10.66 ) (1.2141 ))0.99895
+0.1(3(2)+1)(4+10.66)0.8
)]C L2
¿0.0296CL2
CD=CDO+CDi
CD=0.01287303+0.0296C L2
Re CL CD17880708 0.682067 0.0266418178720 0.6824 0.02800418476732 0.6827 0.02987218774744 0.683033 0.03241719072756 0.6833 0.03586219370767 0.683567 0.04050417880708 0.682067 0.02664
`
From the previous table, the graph of CD vs Reynold number can be plotted as shown below:
For both comparsion.
`
17800000
18000000
18200000
18400000
18600000
18800000
19000000
19200000
19400000
196000000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
CD & CL Vs Reynold
CLCD
Reynold Number
Coeffi
cient
17800000 18000000 18200000 18400000 18600000 18800000 19000000 19200000 19400000 196000000
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
CD Vs Reynold
Reynold Number
CD
C)
Relationship of aircraft lift and drag coefficient during cruise with respect to the change of wing sweep and aspect ratio.During cruising, the aircraft travel with Mach number of 6.5 and at altitude of 27000 ft.Cruising with the range 0.6 to 0.65 Mach number at 27000 ft. The Reynold number produced are around 1800000 to 20000000 Reynold number. For the data of airfoil 4418 at these Reynold number have
almost same CLalpha (gradient of graph Cl vs Alpha). The graph generated shown below.
Below is the table of available parameter of the aircraft.
`
CLbasic 0.675cl 1RW 5.5MN 0.65∧1/4 -1.84t /c 0.18T f 1.4
S−0.1 73.94A f 0.75N 2
AR 10.8Sex/Sref 0.74
Β2 0.5775F 1.315634
CLalpha(1/rad) 6.4125n 0.775474
i) Effect of variation of swept angle to the C L and CD (At Mach number 0.65)
At flight cruise condition. The swept angle is fixed into -1.894 for swept of quarter chord. The aspect ratio is varying from 3 to 21.
Calculation of Cruise lift coefficient
CLC=0.65 (CLbasic /1.5 )cos∧1 /4
CLC=0.65 (0.675/1.5 ) cos−1.84
CLC=¿0.2923
Calculation of Cruise drag coefficient
τ=[ (RW−2)RW
+1.9RW
(1+0.526( tc0.25 )
3
)]τ=[ (5.5−2)5.5
+ 1.95.5
(1+0.526( 0.180.25 )3
)]τ=1.0496
CD 0=0.005(1−2C 1RW)(1.0496) [1−0.2M N+0.12(MN (cos∧1 /4)
0.5
A f−t /c )20 ]RW T f S
−0.1
CD 0=0.005(1−2 (1 )5.5 )(1.0496) [1−0.2(0.65)+0.12( 0.65(cos−1.84)0.50.75−0.18 )
20 ]5.5∗1.4∗0.55CD 0=¿0.032448
f ( λ )=0.005∗(1+1.5 (1.3 /4−0.6 )2)
f ( λ )=0.005851
CDi=¿
CDi=¿0.065361
CD=CD0+CDi
`
CD=¿0.097809
Graph
`
0 5 10 15 20 25 30 350.23
0.24
0.25
0.26
0.27
0.28
0.29
0.3
Cl vs Sweep Angle
Swept angle CL CDO CDI CD
0 0.2925 0.032448 0.065361 0.0978095 0.291387 0.031651 0.065359 0.09701
10 0.288056 0.029426 0.065352 0.09477815 0.282533 0.026211 0.06534 0.09155120 0.27486 0.022589 0.065322 0.08791125 0.265095 0.01912 0.065297 0.08441730 0.253312 0.016212 0.065263 0.081475
`
0 5 10 15 20 25 30 350
0.02
0.04
0.06
0.08
0.1
0.12
Cd vs Sweep Angle
0 5 10 15 20 25 30 350
0.05
0.1
0.15
0.2
0.25
0.3
0.35
CL & Cd vs Sweep Angle
cdCl
Swept Angle
Coeffi
cient
ii) Variation of Aspect ratio to the C L and CD (At Mach number 0.65)
At flight cruise condition. The swept angle is fixed into -1.894 for swept of quarter chord. The aspect ratio is varying from 3 to 21.
Calculation of Cruise lift coefficient
β2=1−M 2
β2=1−0.652
β2=0.5775
n=C lα
2 π / β
n= 6.41252 π /0.76
n=0.7755
F=1.07(1+ db )2
F=1.07(1+ 3.04828 )2
F=1.315
CLα=2πAR
2+√4+ AR2 β2n2 (1+ tan2∧maxt
β2 )(SexposedSref
)(F)
CLα=2π (3 )
2+√4+ 32 (0.5775 )0.7755 (1+ tan
21.20.5775 )
(0.74 )(1.315)
CLα=3.303
CL=CLα (α−αCL=0 )
CL=3.30304∗¿ (From the xfoil data)
CL=¿0.3522
`
Calculation of Cruise drag coefficient
τ=[ (RW−2)RW
+1.9RW
(1+0.526( tc0.25 )
3
)]τ=[ (5.5−2)5.5
+ 1.95.5
(1+0.526( 0.180.25 )3
)]τ=1.0496
CD 0=0.005(1−2C 1RW)(1.0496) [1−0.2M N+0.12(MN (cos∧1 /4)
0.5
A f−t /c )20 ]RW T f S
−0.1
CD 0=0.005(1−2 (1 )5.5 )(1.0496) [1−0.2(0.65)+0.12( 0.65(cos−1.84)0.50.75−0.18 )
20 ]5.5∗1.4∗0.55CD 0=¿0.0283
f ( λ )=0.005∗(1+1.5 (1.3 /4−0.6 )2)
f ( λ )=0.005851
CDi=¿
CDi=¿ 0.013
CD=CD0+CDi
CD=¿0.0413
`
Aspect Ratio CLalpha CL CDO CDi CD
3 3.303042 0.352235 0.028296 0.012973 0.0412696 4.469583 0.476635 0.028296 0.011879 0.0401759 4.984336 0.531528 0.028296 0.009849 0.038145
12 5.269213 0.561907 0.028296 0.008255 0.0365515 5.449318 0.581113 0.028296 0.007062 0.03535818 5.573281 0.594333 0.028296 0.006155 0.03445121 5.66375 0.60398 0.028296 0.005448 0.033744
Graph
`2 4 6 8 10 12 14 16 18 20 22
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Cd vs Aspect Ratio
2 4 6 8 10 12 14 16 18 20 220
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Cl vs Aspect Ratio
`
2 4 6 8 10 12 14 16 18 20 220
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Cl & Cd vs Aspect Ratio
CdCl
Aspect Ratio
Coeffi
cient