Coursework Example: Civil Bizjet Aircraft

The discussion on subsonic aircraft continues linearly from previous chapters.

9.18.1 Geometric and Performance Data

The geometric and performance parameters discussed herein were used in previous chapters. Figure 9.13 illustrates the dissected anatomy of the coursework baseline aircraft.

Aircraft cruise performance for the basic drag polar is computed as follows:

• cruise altitude = 40,000 ft

• LRC Mach = 0.65 (630 ft/s)

• ambient pressure = 391.68 lb/ft2

• ambient temperature = 390 K

• ambient density = 0.00058 sl/ft3

• ambient viscosity = 2.96909847 x 10-7lbs/ft2

• Re/ft = 1.2415272 x 106 (use the incompressible zero Mach line, as explained in Section 9.7.1)

• CL at LRC (Mach 0.65) = 0.5

• Cl at HSC (Mach 0.7) = 0.43

Fuselage (see Figure 9.13)

• fuselage length, Lf = 15.24 m (50 ft)

• average diameter at the constant cross-section barrel, Df = 1.75 m (5.74 ft)
. Lf IDf = 8.71

• fuselage upsweep angle = 10 deg

• fuselage closure angle = 10 deg

Wing (see Figure 9.13)

• planform reference area, SW = 30 m[17] [18] [19] (323 ft2)

• span = 15 m (49.2 ft)

• aspect ratio = 7.5

• wing MAC = 2.132 m (7 ft)

• root chord at centerline = 2.86 m (9.38 ft)

• tip chord = 1.143 m (3.75 ft)

• quarter-chord wing sweep = 14 deg

• aerofoil: NACA 65-410 with 10% tic ratio for design CL = 0.4

Empennage (see Figure 9.13)

• V-tail: SF = 4.4 m2 (47.34 ft2)

• span = m (ft)

• MAC = (7 ft)

• H-tail: Sh = 6.063 m2 (65.3 ft2)

• span = 5 m (ft)

• MAC = (4.2 ft)

Nacelle (see Figure 9.13)

• nacelle length = 2.62 m (8.6 ft)

• nacelle diameter = 1.074 m (3.52 ft)

• nacelle fineness ratio = 2.62I1.074 = 2.44

9.18.2 Computation of Wetted Areas, Re, and Basic CF

An aircraft is first dissected into isolated components, as shown in Figure 9.15. The Re, wetted area, and basic 2D flat-plate CF_baSiC of each component are worked out herein.

Fuselage

The fuselage is conveniently sectioned into three parts:

• total wetted area, Awf = 110 + 340 + 170 + 50 = 670 ft2

• fuselage Re = 50 x 1.2415272 x 106 = 6.2 x 107

• from Figure 9.19b (fully turbulent) at LRC, the incompressible basic CFf =

0. 0022

Wing

• wing exposed reference area = 323 – 50 (area buried in the fuselage) = 273 ft2

• MAC = 2.132 m (7 ft), AR = 7.5

• For t/c = 10% of the wing wetted area, Aww = 2.024 x 273 = 552.3 ft2

• root chord, CR = 2.86 m (9.38 ft)

• tip chord, CT =1.143 m (3.75 ft)

• wing Re = 7 x 1.2415272 x 106 = 8.7 x 106

• from Figure 9.19b at LRC, the incompressible basic CFw = 0.003

Empennage (same procedure as for the wing)

• V-tail

• reference area, SV = 4.4 m2 (47.34 ft2)

• exposed reference area = 47.34 – 7.34 (area buried in the fuselage) = 40 ft2

• for t/c = 10% the V-tail wetted area, AwVT = 2.024 x 40 = 81 ft2

• taper ratio = 0.6

• MAC = 2.132 m (7 ft)

• V-tail

• Re = 7 x 1.2415272 x 106 = 8.7 x 106

• from Figure 9.19b (fully turbulent) at LRC, the incompressible basic

CF_V-tail = 0.003

• H-tail

• reference area, SH = 6.063 m2 (65.3 ft2); it is a T-tail and it is fully exposed

• for t/c = 10%, the H-tail wetted area, AwHT = 2.024 x 65.3 = 132.2 ft2

• taper ratio = 0.5

• MAC = 1.28 m (4.22 ft)

• H-tail Re = 4.22 x 1.2415272 x 106 = 5.24 x 106

From Figure 9.19b (fully turbulent) at LRC, the incompressible basic CF_H-tail = 0.003185.

Nacelle

• length = 2.62 m (8.6 ft)

• maximum diameter = 1.074 m (3.52 ft)

• fineness ratio = 2.45

• nacelle Re = 8.6 x 1.2415272 x 106 = 1.07 x 107

• two-nacelle wetted area, Awn = 2 x 3.14 x 3.1(Dave) x 8.6 – 2 x 5 (two pylon cutouts) = 158 ft2

• from Figure 9.19b (fully turbulent) at LRC, the incompressible basic CFnac =

0. 0029

Pylon

• each pylon exposed reference area = 14 ft2

• length = 2.28 m (7.5 ft)

Table 9.9. Summary of Bizjet component Reynolds number and 2-D basic skin friction

(CFbasic)

Reference Characteristic

Parameter

area ft2

Wetted area ft2

length ft

Reynolds number

2-D CF-basic

Fuselage

n/a

670.0

50

6.2

< 107

0.00220

Wing

323

552.3

7 (MACw)

8.7 >

< 106

0.00300

V-tail

47.34

81.0

7 (MACvt)

8.7 >

< 106

0.00300

H-tail

65.30

132.2

4.22 (MACHT)

5.24 >

106

0.00320

2 x nacelle

n/a

152.0

8.6

1.07

< 107

0.00290

2 x pylon

2 x 12

48.6

7.5

9.3 >

106

0.00295

Table 9.10. Bizjet fuselage ACpf correction (3D and other shape effects)

Item

A CFf

% Of CFfbasic

Wrapping

0.0000132

0.60

Supervelocity

0.0000856

3.90

Pressure

0.0000233

1.06

Body pressurization

5

Fuselage upsweep of 10 deg

8

Fuselage closure angle of 9 deg

0

0

Nose fineness ratio 1.7 Aft-end cross-section – circular

6

Cabin pressurization/leakage

5

Excrescence (e. g., windows and doors)

3

Belly fairing

5

ECS exhaust

3.60

Total ACFf

0.0009060

41.16

(d) aft-end cross-sectional shape – circular: 6

• cabin pressurization leakage (if unknown, use higher value): 5%

• excrescence (nonmanufacturing types; e. g., windows)

(a) windows and doors (higher values for larger aircraft): 2%

(b) miscellaneous: 1%

• wing-fuselage-belly fairing, if any (higher value if it houses undercarriage):

5%

• ECS (see Section 9.8) gives 0.06 ft2: 3.6%

• Total ACFf increment: 41.8%

Table 9.10 gives the Bizjet fuselage ACFf components.

Add the canopy drag for two-abreast seating f = 0.1 ft2 (see Section 9.8.1). Therefore, the equivalent flat-plate area, f, becomes = CFf x AwF + canopy drag.

ff = 1.416 x 0.0022 x 670 + 0.1 = 2.087 + 0.1 = 2.187 ft2

Surface roughness (to be added later): 3%

Wing

The basic CFW = 0.003.

• 3D effects (Equations 9.14,9.15, and 9.16)

• Supervelocity

ACFw = CFw x 1.4 x (aerofoil t/c ratio)

= 0.003 x 1.4 x 0.1 = 0.00042(14% ofbasic Cfw) [20]

Item

ACFw

% Of CFwbasic

Supervelocity

0.0004200

14

Pressure

0.0000175

0.58

Interference (wing-body)

0.0000430

1.43

Flaps gap

5

Excrescence (others)

5

Total ACfw

26

Table 9.11. Bizjet wing ACFw correction (3-D and other shape effects)

• Interference

= 9.382 x 0.6 x [{0.75 x (0.1)3 – 0.0003}/552.3]

= 87.985 x 0.6 x (0.00075 – 0.0003)/552.3 = 0.02375/552.3 = 0.000043 (1.43% of basic CFv,)

• Other effects. For excrescence (nonmanufacturing; e. g., control-surface gaps):

flap gaps: 5% others: 5%

total ACFw increment: 25%

Table 9.11 gives the Bizjet wing ACFw components.

Therefore, the equivalent flat-plate area, f, becomes = CFw x Aww.

ff = 1.26 x 0.003 x 552.3 = 2.09 ft2

• surface roughness (to be added later): 3%

Empennage

Because the procedure is the same as for the wing, it is not repeated. The same per­centage increment as the wing is used for the coursework exercise. In the industry, engineers must compute systematically as shown for the wing. [21]

Table 9.12. Bizjet nacelle ACFn correction (3D and other shape effects)

Item (One Nacelle)

ACFn

% of CFnbasic

Wrapping (3D effect)

0.0000072

0.25

Excrescence (nonmanufacture)

22

Boat tail (aft end)

11

Base drag (at cruise)

0

0

Intake drag (BPR 4)

50

Total ACFn

83.25

Nacelle

• fineness ratio = 2.45

• nacelle Re = 1.07 x 107

• wetted area of two nacelles, Awn = 158 ft2

• basic CFnac = 0.0029

• 3D effects (Equations 9.14,9.15, and 9.16)

• Wrapping (Equation 9.9):

ACFn = CFn x 0.025 x (length/diameter) x R-02 = 0.025 x 0.003 x 2.45 x (1.07 x 107)-02 = 0.000184 x 0.0393 = 0.0000072(0.25% ofbasic CFf)

• Other increments are shown in Table 9.4 for one nacelle. For two nacelles (shown in wetted area):

fn = 1.8325 x 0.0029 x 158 = 0.84 ft2 • surface roughness (to be added later): 3%

Pylon

Because the pylon has the same procedure as the wing, it is not repeated. The same percentage increment as for the wing is used in the coursework exercise. There is interference on both sides of the pylon. [22]

Table 9.13. Bizjetparasite drag buildup summary and CDpmin estimation

Wetted area, Aw ft2

Basic CF

ACf

Total CF

f – ft2

CDpmin

Fuselage + U/C fairing

670

0.00220

0.000906

0.003106

2.080

0.006440

Canopy

0.100

0.000310

Wing

552.3

0.00300

0.000780

0.003784

2.090

0.006470

V-tail

81

0.00300

0.000786

0.003786

0.302

0.000950

H-tail

132.2

0.00320

0.000800

0.004000

0.529

0.001640

2 x nacelle

2 x 79

0.00290

0.002414

0.005314

0.840

0.002600

2 x pylon

2 x 28.35

0.00295

0.000767

0.003720

0.210

0.000650

Rough (3%)

Eq. 9.27

0.182

0.000560

Air-conditioning

0.100

0.000310

Aerial, lights

0.050

0.000155

Trim drag

0.130

0.000400

Total

6.610

0.020500

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