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