Case Studies

Midrange Aircraft (Airbus 320 class)

All computations carried out herein follow the book instructions. The results are not from the Airbus industry. Airbus is not responsible for the figures given here. They are used only to substantiate the book methodology with industry values to gain confidence. The industry drag data are not available but, at the end, it will be checked if the payload-range matches the published data.

Given: LRC Speed and Altitude: Mach 0.75 at 36,089 ft.

Dimensions (to scale the drawing for detailed dimensions)

Fuselage length = 123.16 ft (scaled measurement differs slightly from the drawings) Fuselage width = 13.1 ft, Fuselage depth = 13 ft.

Wing reference area (trapezoidal part only) = 1,202.5 ft2; add yehudi area =

118.8 ft2

Span = 11.85 ft; MACwmg = 11.64 ft; AR = 9.37; Д1/ = 25deg; Cr = 16.5 ft, X = 0.3

H-tail reference area = 330.5 ft2; MACH-tail = 8.63 ft V-tail reference area = 235.6 ft2; MACV-tail = 13.02 ft Nacelle length = 17.28 ft; Maximum diameter = 6.95 ft Pylon = measure from the drawing Reynolds number per ft is given by:

Reperfoot = (Vp)/n = (aMp)/n = [(0.75 x 968.08)(0.00071)]/

(0.7950 x 373.718 x 10-9)

= 1.734 x 106 per foot

Drag Computation Fuselage

Table D1 gives the basic average 2D flat plate for the fuselage, CFfbasic = 0.00186. Table D2 summarizes the 3D and other shape-effect corrections, ДCFf, needed to estimate the total fuselage CFf.

Figure D1. Airbus 320 three-view with major dimensions (Courtesy of Airbus)

Table D1. Reynolds number and 2D basic skin friction CFbasic

Parameter

Reference area (ft2)

Wetted area

(ft2)

Characteristic length (ft)

Reynolds

number

2D CFbasic

Fuselage

n/a

4,333

123.16

2.136 x

108

0.00186

Wing

1,202.5

2,130.94

11.64 (MACw)

2.02 x

107

0.00255

V-tail

235

477.05

13.02 (mACvt)

2.26 x

107

0.00251

H-tail

330.5

510.34

8.63 (MACht)

1.5 x

107

0.00269

2 x nacelle

n/a

2 x 300

17.28

3x

107

0.00238

2 x pylon

n/a

2 x 58.18

12 (MACp)

2.08 x

107

0.00254

Table D2. Fuselage ACFf correction (3D and other shape effects)

Item

ACFf

% Of CFfbasic

Wrapping

0.00000922

0.496

Supervelocity

0.0001

5.36

Pressure

0.0000168

0.9

Fuselage-upsweep of 6 deg

0.000127

6.8

Fuselage-closure angle of 9 deg

0

0

Nose-fineness ratio

0.000163

8.7

Fuselage nonoptimum shape

0.0000465

2.5

Cabin pressurization/leakage

0.000093

5

Passenger windows/doors

0.0001116

6

Belly fairing

0.000039

2.1

Environmental Control System Exhaust

-0.0000186

-1

Total ACFf

0.0006875

36.9

Therefore, the total fuselage CFf = CFfbasic + ACFf = 0.00186 + 0.0006875 = 0.002547.

Flat-plate equivalent ff (see Equation 9.8) = CFf x Awf=0.002547×4333 =

11.3 ft2.

Add the canopy drag fc = 0.3 ft2.

Therefore, the total fuselage parasite drag in terms of ff+c = 11.33 ft2.

Wing

Table D1 gives the basic the average 2D flat plate for the wing, CFwbasic = 0.00257, based on the MACw.

The important geometric parameters include the wing reference area (trape­zoidal planform) = 1,202.5 ft2 and the gross wing planform area (including Yehudi) =

1,320.8 ft2. Table D3 summarizes the 3D and other shape-effect corrections needed to estimate the total wing CFw.

Table D3. Wing ACFw correction (3D and other shape effects)

Item

A CFw

% of CFwbasic

Supervelocity

0.000493

19.2

Pressure

0.000032

1.25

Interference (wing-body)

0.000104

4.08

Excrescence (flaps and slats)

0.000257

10

Total ACFw

0.000887

34.53

Therefore, the total wing: CFw = CFwbasic + ACFw = 0.00257 + 0.000889 = 0.00345.

Flat-plate equivalent: fw(Equation 9.8) = CFw x Aww = 0.00345 x 2,130.94 = 7.35ft2.

Vertical Tail

Table D1 gives the basic average 2D flat plate for the V-tail:

CFVTbasic = 0.00251 based on the MACVT; V-tail reference area = 235 ft2

Table D4 summarizes the 3D and other shape-effect corrections (ACFVT) needed to estimate the V-tail CFVT.

Table D4. V-tail ACFVT correction (3D and other shape effects)

Item

ACfvt

% Of CFVTbasic

Supervelocity

0.000377

15

Pressure

0.000015

0.6

Interference (V-tail – body)

0.0002

8

Excrescence (rudder gap)

0.0001255

5

Total ACfvt

0.000718

28.6

Therefore, the V-tail: Cfvt = CFVTbasic +ACfvt = 0.00251 + 0.000718 = 0.003228 Flat-plate equivalent fVT (see Equation 9.8) = CFVT x AwVT = 0.003228 x 477.05 = 1.54ft2.

Horizotal Tail

Table D1 gives the basic average 2D flat plate for the H-tail:

Cmnask = 0.00269, based on the MACHT; the H-tail reference area SHT =

330.5 ft2

Table D5 summarizes the 3D and other shape-effect corrections (ACFHT) needed to estimate the H-tail CFHT.

Table D5. H-tail ACFHT correction (3D and other shape effects)

Item

ACfht

% of CFHTbasic

Supervelocity

0.0004035

15

Pressure

0.0000101

0.3

Interference (H-tail – body)

0.0000567

2.1

Excrescence (elevator gap)

0.0001345

5

Total ACfht

0.000605

22.4

Therefore, the H-tail: Cfht = CFHTbasic + ACfht = 0.00269 + 0.000605 = 0.003295

Flat-plate equivalent fHT (see Equation 9.8) = CFHTxAwHT = 0.003295×510.34 = 1.68 ft2.

Nacelle, CFn

Because the nacelle is a fuselage-like axisymmetric body, the procedure follows the method used for fuselage evaluation but needs special attention due to the throttle – dependent considerations.

Important geometric parameters include:

Nacelle length = 17.28 ft Maximum nacelle diameter = 6.95 ft

Average diameter = 5.5 ft Nozzle exit-plane diameter = 3.6 ft Maximum frontal area = 37.92 ft2 Wetted area per nacelle Awn = 300 ft2

Table D1 gives the basic average 2D flat plate for the nacelle:

CFnbasic = 0.00238, based on the nacelle length

Table D6 summarizes the 3D and other shape-effect corrections, ACFn, needed to estimate the total nacelle CFn for one nacelle.

For nacelles, a separate supervelocity effect is not considered because it is accounted for in the throttle-dependent intake drag; pressure drag also is accounted for in the throttle-dependent base drag.

Table D6. Nacelle ACFn correction (3D and other shape effects)

Item

ACFn

% Of CFnbasic

Wrapping (3D effect)

0.0000073

0.31

Excrescence (nonmanufacture)

0.0005

20.7

Boat tail (aft end)

0.00027

11.7

Base drag (aft end)

0

0

Intake drag

0.001

41.9

Total ACPn

0.001777

74.11

Thrust Reverser Drag

The excrescence drag of the thrust reverser is included in Table D6 because it does not result from manufacturing tolerances. The nacelle is placed well ahead of the wing; hence, the nacelle-wing interference drag is minimized and assumed to be zero.

Therefore the nacelle: CFn = CFnbasic + ACFn = 0.00238 + 0.001777 = 0.00416 Flat plate equivalent fn (Equation 9.8) = CFnt x Awn = 0.00416 x 300 = 1.25 ft2 per nacelle.

Pylon

The pylon is a wing-like lifting surface and the procedure is identical to the wing para­site-drag estimation. Table D1 gives the basic average 2D flat plate for the pylon; CFpbasic = 0.0025 based on the MACp.

The pylon reference area = 28.8 ft2 per pylon. Table D7 summarizes the 3D and other shape-effect corrections (ACFp) needed to estimate CFp (one pylon).

Table D7. Pylon ACFp correction (3D and other shape effects)

Item

ACpp

% of CFpbasic

Supervelocity

0.000274

10.78

Pressure

0.00001

0.395

Interference (pylon-wing)

0.0003

12

Excrescence

0

0

Total ACFp

0.000584

23

Therefore, the pylon CFp = CFpbasic + ACFp = 0.0025 + 0.00058 = 0.00312 Flat-plate equivalent: fp (see Equation 9.8) = CFp x Awp = 0.182 ft2 per pylon.

Roughness Effect

The current production standard tolerance allocation provides some excrescence drag. The industry standard uses 3% of the total component parasite drag, which includes the effect of surface degradation in use. The value is froughness = 0.744 ft2, given in Table D8.

Trim Drag

Conventional aircraft produce trim drag during cruise and it varies slightly with fuel consumption. For a well-designed aircraft of this class, the trim drag of ftrim = 0.1 ft2 may be used.

Aerial and Other Protrusions

For this class of aircraft, faerial = 0.005 ft2.

Air-Conditioning

This is accounted for in the fuselage drag as ECS exhaust. It could provide a small amount of thrust.

Aircraft Parasite Drag Buildup Summary and CDpmin

Table D8 provides the aircraft parasite drag buildup summary in tabular form.

Table D8. Aircraft parasite drag buildup summary and CDpmin estimation

Wetted area Aw ft2

Basic CF

ACf

Total CF

f (ft2)

CDpmin

Fuselage + undercarriage

4,333

0.00186

0.00069

0.00255

11.03

0.00918

fairing

Canopy

0.3

0.00025

Wing

2,130.94

0.00255

0.00089

0.00346

7.35

0.00615

V-tail

477.05

0.00251

0.00072

0.00323

1.54

0.00128

H-tail

510.34

0.00269

0.00061

0.0033

1.68

0.0014

2 x Nacelle

2 x 300

0.00238

0.00178

0.00415

2.5

0.00208

2 x Pylon

2 x 58.18

0.00254

0.000584

0.00312

0.362

0.0003

Rough (3%)

0.744

0.00062

Aerial

0.005

0.000004

Trim drag

0.1

0.00008

TOTAL

25.611

0.0213

Notes:

CDpmin = °.°213.

Wing reference area Sw =1,202 ft2; CDpmin = f/Sw ISA day;36,089-ft altitude;and Mach 0.75.

ACDp Estimation

The ACDp is constructed, corresponding to the CL values, as given in Table D9.

Table D9. ACDp estimation

Cl

0.2

0.3

0.4

0.5

0.6

ACDp

0.00044

0

0.0004

0.0011

0.0019

Induced Drag, CDi The wing aspect ratio:

AR

induced drag, CD=0-034CL

Table D10 gives the CDi corresponding to each CL.

Cl

0.2

0.3

0.4

0.5

0.6

0.7

0.8

CDi

0.00136

0.00306

0.00544

0.0085

0.01224

0.0167

0.0218

Table D10. Induced drag

Total Aircraft Drag Aircraft drag is given as:

CD = CDpmin + &-CDp + CDi + [CDw = 0]

The total aircraft drag is obtained by adding all the drag components in Table D11. Note that the low and high values of CL are beyond the flight envelope.

Table D11. Total aircraft drag coefficient, CD

Cl

0.2

0.3 0.4

0.5

0.6

CDpmin

0.0213 from Table 7.9

&Cdp

0.00038

0 0.0004

0.0011

0.0019

CDi

0.00136

0.00306 0.00544

0.0085

0.01224

Total aircraft CD

0.0231

0.02436 0.02714

0.0309

0.03544

Table D11 is drawn in Figure D2 to show that the PIANO software aircraft drag checks out well with what is manually estimated in this book; hence, the PIANO value is unchanged.

Figure D2. Aircraft drag polar at LRC

Engine Rating

Uninstalled sea-level static thrust = 25,000 lb per engine. Installed sea-level static thrust = 23,500 lb per engine.

Weight Breakdown (with variations)

Design cruise speed, VC = 350 KEAS Design dive speed, VD = 403 KEAS Design dive Mach number, MD = 0.88

Limit load factor = 2.6

Ultimate load factor = 3.9

Cabin differential pressure limit = 7.88 psi

Component Weight (lb) Wing 14,120 Flaps + slats 2,435 Spoilers 380 Aileron 170 Winglet 265

Percentage of MTOW

Wing group total

17,370

(above subcomponent weights from [10])

Fuselage group

17,600

(Torenbeek’s method)

H-tail group

1,845

V-tail

1,010

Undercarriage group

6,425

Total structure weight

44,250

Power plant group (two)

15,220

Control systems group

2,280

Fuel systems group

630

Hydraulics group

1,215

Electrical systems group

1,945

Avionics systems group

1,250

APU

945

ECS group

1,450

Furnishing

10,650

Miscellaneous

4,055

MEW

83,890

Crew

1,520

Operational items

5,660

OEW

91,070

Payload (150 x 200)

30,000

Fuel (see range calculation)

41,240

MTOW This gives:

162,310

Wing-loading = 162,310/1,202.5 = 135 lb/ft2

Thrust-loading = 50, 000/162310 = 0.308

The aircraft is sized to this with better high-lift devices.

Payload Range (150 Passengers)

MTOM -162,000 lb

Onboard fuel mass: 40,900 lb

Payload – 200 x 150 = 30,000 lb

LRC: Mach 0.75, 36,086 feet (constant condition)

Initial cruise thrust per engine: 4,500 lb

Final cruise thrust per engine: 3,800 lb

Average specific range: 0.09 nm/lb fuel

Climb at 250 KEAS reaching to Mach 0.7

Summary of the Mission Sector

Sector

Fuel consumed (lb)

Distance covered (nm)

Time elapsed (min)

Taxi out

200

0

8

Takeoff

300

0

1

Climb

4,355

177

30

Cruise

28,400

2,560

357

Descent

370

105

20

Approach/land

380

0

3

Taxi in

135

0

5

Total

34,140

2,842

424

Diversion-fuel calculation:

diversion distance = 2,000 nm, cruising at Mach 0.675 and at 30,000-ft altitude Diversion fuel = 2,800 lb; contingency fuel (5% of mission fuel) = 1,700 lb

Holding-fuel calculation:

Holding time = 30 min at Mach 0.35 and at a 5,000-ft altitude Holding fuel = 2,600 lb

Total reserve fuel carried = 2,800 + 1,700 + 2,600 = 7,100 lb.

Total onboard fuel carried = 7,100 + 34,140 = 41,240 lb.

Cost Calculations (U. S.$ – Year 2000)

Number of passengers 150

Yearly utilization 497 trips per year

Mission (trip) block time 7.05 hrs

Mission (trip) block distance 2,842 nm

Mission (trip) block fuel 34,140 lb (6.68 lbs/U. S. gallons)

Fuel cost = 0.6 U. S.$ per U. S. gallon

Airframe price = $38 million Two engines price = $9 million Aircraft price = $47 million

Operating costs per trip – AEA 89 ground rules for medium jet-transport aircraft:

Depreciation Interest Insurance Flight crew Cabin crew Navigation Landing fees Ground handling

$6,923

$5,370

$473

$3,482

$2,854

$3,194

$573

$1,365

Airframe maintenance $2,848

Engine maintenance Fuel cost Total DOC DOC/block hour DOC/seat DOC/seat/nm

$1,208

$3,066 (5,110.8 U. S. gallons)

$31,356

$4,449

$209

0.0735 U. S.$/seat/nm

[1] 3 15

Maximum camber Maximum thickness of The last two digits are

position in % chord maximum camber in 1/10 maximum t/c ratio in %

of chord of chord

[4] Civil aircraft design: For the foreseeable future, aircraft will remain subsonic and operating below 60,000 ft (large subsonic jets <45,000 ft). However, aircraft size could grow even larger if the ground infrastructure can handle the volume

[5] Type 1: Unprepared Surface. A grass field or a gravel field, for example, is des­

ignated as a Type 1 surface. These are soft runways that are prone to depres­

sions under a heavy load. Low-pressure tires with a maximum 45 to 60 lb per

square inch (psi) and a total ESWL load less than 10,000 lb are the limits of operation on a soft runway. The ground friction is the highest and these airfields are not necessarily long. This type of runway is the least expensive to prepare and they serve remote areas, as an additional airfield close to a

business center, or as a private airfield. Small utility aircraft can operate from Type 1 airfields.

[10] The main-wheel load is computed at the aftmost CG, which gives lREAR = 9.4­

1.7 = 7.7 m (25.26 ft).

• Equation 7.2 gives Rmain = (IrEAr x MTOW)/lBASE = (7.7 x 11,000)/8.7 = 9,736 kg (21,463 lb).

• The load per strut is 4,868 kg (10,732 lb). It is better to keep the wheel load below 10,000 lb in order to have a smaller wheel and tire.

• Then, make the twin-wheel arrangement. For this arrangement, Equation 7.5 gives the ESWL = 4,868/1.5 = 3,245 kg (7,155 lb).

[11] Small variant aircraft MTOM = 7,000 kg (15,400 lb) (refined in Chapter 8)

• Fuselage length = 13.56 m (44.5 ft)

(i) Raised or bubble-type canopy or its variants. These canopies are mostly associated with military aircraft and smaller aircraft. The canopy drag

[13] Other effects on the fuselage (increments are given in a percentage of 2D CFf) are listed herein. The industry has more accurate values of these incre­

mental ACFf. Readers in the industry should not use the values given here – they are intended only for coursework using estimates extracted from industrial data. (See Section 3.21 for an explanation of the terminology used in this sec­tion.)

(a) Canopy drag. There are two types of canopy (Figure 9.4), as follows:

[16] Manufacturing origin. This includes aerodynamic mismatches as discreet rough­ness resulting from tolerance allocation. Aerodynamicists must specify surface – smoothness requirements to minimize excrescence drag resulting from the dis­crete roughness, within the manufacturing-tolerance allocation.

[17] Front fuselage length, Lf = 3.5 m with a uniformly varying cross-section

[18] Mid-fuselage length LFm = 5.95 m with an average constant cross-section diam­eter = 1.75 m

[19] Aft-fuselage length LFa = 5.79 m, with a uniformly varying cross-section

• Wetted area

• front fuselage, AwFf (no cutout) = 110 ft2

• Mid-fuselage, AwFm (with two sides of wing cutouts) = 352 – 2 x 6 = 340 ft2

• Aft fuselage, Aw Fs (with empennage cutouts) = 180 – 10 = 170 ft2

• Include additional wetted area for the wing-body fairing housing the under­carriage « 50 ft2

[20] Pressure

/ 6 0.125

ACfw = CFw x 60 x (aerofoil t/c ratio)4 x ar j

= (0.003 x 60) x (0.1)4 x (6/7.5)0125 = 0.18 x 0.0001 x 0.973 = 0.0000175(0.58% ofbasic Cfw)

[21] V-tail

• wetted area, AwVT = 81 ft2

• basic CFH-tail = 0.003

It is a T-tail configuration with interference from the T-tail (add 1.2%).

• fVT = 1.262 x 0.003 x 81 = 0.307 ft2

• H-tail

• wetted area, AwHT = 132.2 ft2

• basic CF_V-tail = 0.0032

• fHT = 1.25 x 0.0032 x 132.2 = 0.529 ft2

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

[22] each pylon exposed reference area = 14 ft2

• length = 2.28 m (7.5 ft)

• t/c = 10%

• two-pylon wetted area Awp = 56.7 ft2

• pylon Re = 7.5 x 1.2415272 x 106 = 9.3 x 106

• basic CFpylon = 0.00295

• for two pylons (shown in wetted area):

fpy = 1.26 x 0.00295 x 56.7 = 0.21 ft2 • surface roughness (to be added later): 3%

[23] 3D effects (Equations 9.9, 9.10, and 9.11):

• Wrapping:

ACFf = CFf x 0.025 x (length/diameter) x Re 0 2 = 0.025 x 0.0021 x (9.66) x (9.53 x 107)-02 = 0.000507 x 0.0254 = 0.0000129 (0.6% of basic CFf)

• Supervelocity:

ACFf = CFf x (diameter/length)15 = 0.0021 x (1/9.66)15 = 0.0021 x 0.033 = 0.0000693 (3.3% of basic CFf)

• Pressure:

ACFf = CFf x 7 x (diameter/length)3 = 0.0021 x 7 x (0.1035)3 = 0.0147 x 0.00111 = 0.0000163 (0.8% of basic CFf)

• Other effects on the fuselage (intake included – see Section 9.18):

Reference [3] suggests applying a factor of 1.284 to include most other effects except intake. Therefore, unlike the civil aircraft example, it is simplified to only the following:

• Intake (little spillage – remainder taken in 3D effects): 2%

[24] turn performance g-load

• maneuver g-load

• roll rate g-load

[25] Wing Dihedral Г (see Figure 12.5). Sideslip angle в increases the angle of attack, a, on the windward wing, Aa = (Vsin r)/u generating ALift. For small dihe­drals and perturbations, в = v/u, which approximates Aa = в Г. The restoring moment is the result of ALift generated by Aa. It is quite powerful – for a

[26] At zero thrust, Equation 13.29 becomes:

[27] Experiments cannot represent the real flight envelope (e. g., Re and temper­ature) and are limited by flow nonuniformity, wall effects, and transient – dependent separation.

• There are very high energy costs associated with large wind tunnels.

• CFD is faster and less costly than experiments for obtaining valuable insight at an initial stage.

[28] brittleness: when a sudden rupture occurs under stress application (e. g., glass)

• ductility: the opposite of brittleness (e. g., aluminum)

[29] Fuel charges

[30] parts list and tool list

• BOM definition

• bill of resources

• routings

• process sheets/work instructions

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