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 payloadrange 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
Htail reference area = 330.5 ft2; MACHtail = 8.63 ft Vtail reference area = 235.6 ft2; MACVtail = 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 109)
= 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 shapeeffect corrections, ДCFf, needed to estimate the total fuselage CFf.
Figure D1. Airbus 320 threeview with major dimensions (Courtesy of Airbus)
Table D1. Reynolds number and 2D basic skin friction CFbasic

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

Therefore, the total fuselage CFf = CFfbasic + ACFf = 0.00186 + 0.0006875 = 0.002547.
Flatplate 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 shapeeffect corrections needed to estimate the total wing CFw.
Table D3. Wing ACFw correction (3D and other shape effects)

Therefore, the total wing: CFw = CFwbasic + ACFw = 0.00257 + 0.000889 = 0.00345.
Flatplate 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 Vtail:
CFVTbasic = 0.00251 based on the MACVT; Vtail reference area = 235 ft2
Table D4 summarizes the 3D and other shapeeffect corrections (ACFVT) needed to estimate the Vtail CFVT.
Table D4. Vtail ACFVT correction (3D and other shape effects)

Therefore, the Vtail: Cfvt = CFVTbasic +ACfvt = 0.00251 + 0.000718 = 0.003228 Flatplate 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 Htail:
Cmnask = 0.00269, based on the MACHT; the Htail reference area SHT =
330.5 ft2
Table D5 summarizes the 3D and other shapeeffect corrections (ACFHT) needed to estimate the Htail CFHT.
Table D5. Htail ACFHT correction (3D and other shape effects)

Therefore, the Htail: Cfht = CFHTbasic + ACfht = 0.00269 + 0.000605 = 0.003295
Flatplate equivalent fHT (see Equation 9.8) = CFHTxAwHT = 0.003295×510.34 = 1.68 ft2.
Nacelle, CFn
Because the nacelle is a fuselagelike 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 exitplane 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 shapeeffect 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 throttledependent intake drag; pressure drag also is accounted for in the throttledependent base drag.
Table D6. Nacelle ACFn correction (3D and other shape effects)

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 nacellewing 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 winglike lifting surface and the procedure is identical to the wing parasitedrag 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 shapeeffect 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 (pylonwing) 
0.0003 
12 
Excrescence 
0 
0 
Total ACFp 
0.000584 
23 
Therefore, the pylon CFp = CFpbasic + ACFp = 0.0025 + 0.00058 = 0.00312 Flatplate 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 welldesigned 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.
AirConditioning
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
Notes: CDpmin = °.°213. Wing reference area Sw =1,202 ft2; CDpmin = f/Sw ISA day;36,089ft 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

Induced Drag, CDi The wing aspect ratio:
AR
induced drag, CD=0034CL
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 sealevel static thrust = 25,000 lb per engine. Installed sealevel 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) 
Htail group 
1,845 

Vtail 
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 
Wingloading = 162,310/1,202.5 = 135 lb/ft2 Thrustloading = 50, 000/162310 = 0.308 The aircraft is sized to this with better highlift 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

Diversionfuel calculation:
diversion distance = 2,000 nm, cruising at Mach 0.675 and at 30,000ft altitude Diversion fuel = 2,800 lb; contingency fuel (5% of mission fuel) = 1,700 lb
Holdingfuel calculation:
Holding time = 30 min at Mach 0.35 and at a 5,000ft 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 jettransport 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

[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. Lowpressure 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 mainwheel 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 twinwheel 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 bubbletype 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 manufacturingtolerance allocation.
[17] Front fuselage length, Lf = 3.5 m with a uniformly varying crosssection
[18] Midfuselage length LFm = 5.95 m with an average constant crosssection diameter = 1.75 m
[19] Aftfuselage length LFa = 5.79 m, with a uniformly varying crosssection
• Wetted area
• front fuselage, AwFf (no cutout) = 110 ft2
• Midfuselage, 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 wingbody 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] Vtail
• wetted area, AwVT = 81 ft2
• basic CFHtail = 0.003
It is a Ttail configuration with interference from the Ttail (add 1.2%).
• fVT = 1.262 x 0.003 x 81 = 0.307 ft2
• Htail
• wetted area, AwHT = 132.2 ft2
• basic CF_Vtail = 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%
• twopylon 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 gload
• maneuver gload
• roll rate gload
[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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