Aerodynamics

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CChhaapptteerr 55:: AAeerrooddyynnaammiiccss

12th March 2007

Group 4

Written by:

Marvin Anthony Rodrigo Saverymuthapulle


-- iiii --

Three-View

5 x LD3-45W Containers

General Details

Model

Description

Aft fuselage mounted engines,

high T tail, narrow body.

List Price SR/ER

($US)

2005: 49M / 55M

2015: 61M / 68.5M Launch 2010

Entry into Service 2015

Accomm.(STD PAX) 150 PAX

Single(max) HD/dual 150 / 132

Design Criteria

Max Operating Vmo/Mmo 360 kts CAS / 0.84

Dive VD/MD -

Certified Max Alt. 41000 ft

Landing Gear VLO/VLE 235 KCAS / 320 KCAS

Max. Flaps VFE 162 KCAS

External Geometry

Overall Length 38.25m / 125.49ft

Overall Height 8.87m / 29.10ft

Wingspan (excl Wlts) 32.27m / 105.87ft

Wing Area (gross) 126m2 / 1356.25 sq.ft

Wing Area (ESDU) 106m2 / 1141 sq.ft

Wing ARatio 9.16

1/4 Chd Swp (Airbus) 30º

t/c - Root / Kink 1

/ Kink 2 / Tip

0.14/ 0.12 / 0.10 /

0.10

Cabin Geometry

Cabin lngth / volume 25.6m / 83.99ft

159.0m3 / 5615.0cu.ft Max cbn wdth / hght 3.73m / 12.24ft

2.13m / 6.99ft Cabin floor width 3.67m / 12.04ft

Fuslge wdth / hght

(external)

3.94m / 12.93ft

Fwd/Aft + Aux cargo 17.5m3/0m3

618cu.ft/0cu.ft + 8m3

Unpress. cargo vlume 0 cu.ft

Systems Engine Rolls Royce V2500 (Scaled)

APU Sundstrand APS 3200

Avionics

Suite

Honeywell, Sundstrand,

Collins, Smith Ind.

Payload-Range Diagram Spec. OWE,

LRC

A315 Atlas


-- iiiiii --

A315 SR

Weights & Loadings Maximum Ramp Weight 65174kg / 143685lb

Maximum Takeoff Weight 65156kg / 143645lb

Maximum Landing Weight 55383kg / 122099lb

Max Zero-Fuel Weight 54950kg / 121145lb

Operationl Weight Empty 39951kg / 88076lb

Maximum Payload 16848kg / 37144lb

Maximum Usable Fuel: 13231kg / 29170lb

** 6.75 lb per USG 4321 USG

Payload at max. fuel 11974kg / 26399lb

Wing Loading (MTOW) 517.1 kg/m²

105.9 lb/sq.ft

Thrust (max) to Weight 0.317

Empty Weight/STD Accom. 587.2 lb/PAX

OWE/MTOW Fraction 0.613

(MZFW-OWE)/MTOW Fractn 0.230

Max Fuel Fraction 0.203

Performance Engine Rating

Takeoff Rating – Max 101.2kN / 22750lbf

Flat Rating ISA + 15 deg.C

Airfield Performance (MTOW/MLW)

TOFL, ISA, SL 1820m / 5971ft

TOFL, ISA+20ºC, 5000 ft 2450m / 8038ft

LFL, ISA, SL 1164m / 3820ft

Approach Speed (MLW) 135 KCAS

En route Perf: Climb (AEO, ISA, MTOW br.)

Time to Climb to FL 350 -

Time to Climb to ICA 20.9 min

Initial Cruise Altitude 35000 ft

En route Performance: Cruise

Long Range Cruise M0.80 / 435 KTAS

High Speed Cruise M0.84 / 460 KTAS

Payload-Range

Reserves Description

FAR121,200 nm alt.

Accommodtn / Weight ea. 150 PAX / 100 kg

Design range for given

accommodation [@ LRC]

1800 nm

Block Performance (given PAX, ISA, s.a.)

Assumptions: 100 kg per PAX, LRC speed

500 nm Block fuel 2395kg / 5279lb

Block time 91 mins

TOGW 59844kg / 131934lb

Max Range Block fuel 7697kg / 16968lb

Block time 262 mins

TOGW 65156kg / 143645lb

A315 ER

Weights & Loadings

Maximum Ramp Weight 70527kg / 155485lb

Maximum Takeoff Weight 70509kg / 155445lb

Maximum Landing Weight 59933kg / 132129lb

Max Zero-Fuel Weight 54950kg / 121145lb

Operationl Weight Empty 39951kg / 88076lb

Maximum Payload 16848kg / 37144lb

Maximum Usable Fuel: 16983kg / 37442lb

** 6.75 lb per USG 5547 USG

Payload at max. fuel 13575kg / 29927lb

Wing Loading (MTOW) 559.6 kg/m²

114.6 lb/sq.ft

Thrust (max) to Weight 0.346

Empty Weight/STD Accom. 587.2 lb/PAX

OWE/MTOW Fraction 0.567

(MZFW-OWE)/MTOW Fractn 0.213

Max Fuel Fraction 0.241

Performance Engine Rating

Takeoff Rating – Max 119.7kN / 26911lbf

Flat Rating ISA + 15 deg.C

Airfield Performance (MTOW/MLW)

TOFL, ISA, SL 1960m / 6430ft

TOFL, ISA+20ºC, 5000 ft 2480m / 8136ft

LFL, ISA, SL 1210m / 3970ft

Approach Speed (MLW) 135 KCAS

En route Perf: Climb (AEO, ISA, MTOW br.)

Time to Climb to FL 350 -

Time to Climb to ICA 24.7 min

Initial Cruise Altitude 35000 ft

En route Performance: Cruise

Long Range Cruise M0.80 / 435 KTAS

High Speed Cruise M0.84 / 460 KTAS

Payload-Range

Reserves Description

FAR121,200 nm alt.

Accommodtn / Weight ea. 150 PAX / 100 kg

Design range for given

accommodation [@ LRC]

3000 nm

Block Performance (given PAX, ISA, s.a.)

Assumptions: 100 kg per PAX, LRC speed

500 nm Block fuel 2395kg / 5279lb

Block time 91 mins

TOGW 59844kg / 131934lb

Max Range Block fuel 13007kg / 28676lb

Block time 419 mins

TOGW 70509kg / 155445lb


-- iivv --

Number of Batteries 4

Extrnl AC or DC Hook-Up AC

Main Distrbtn System 3 Phase + 270V DC

ATA 27 - Flight Controls

Flight Control

Philosophy • Fly by wire, using Hydraulic

actuators and

EHAs

Aileron Actuation Mthod Hydraulic (prim)

EHA EHA (sec)

Description of Rudder Conventional

Rudder Actuation Method 1 x Hydraulic 2

xEHA

Fixed / Var. Incd. Tail Variable

Elevator Actuation Mthd Hydraulic (prim)

EHA EHA (sec) Stall Protection

Devices • Software controlled stall

protection

Flap System Overview • 2 panels per side • 4 tracks per side

Flap (Slat) Deflection

- Takeoff (Highest)

20O (None)

Flap (Slat) Deflection

- Landing Configuration

20O (None)

HI Lift LE Device None

HI Lift LE Dev. Actuatn None

HI Lift TE Device Single slotted flap

HI Lift TE Dev. Actuatn Hydraulic

Total Number of Roll

Splers / Flight Splers

/ Ground Splers / Total

4 / 8 / 8 / 8

Spoiler Actuation Hydraulic

ATA 28 - Fuel System

Tot. Usable Fuel Capac. 5547 USG

Tank Capacity (Wing) 4321 USG

Tank Capacity (Center) 1226 USG

Tank Cap. (Aux. + Trim) None

Fuel System Overview • 2 integral (wet wing) tanks

• 1 center tank (ER only)

• 2 Collector tanks located next to

the engines

Loctn Aux. Fuel Tanks none

Systems Description ATA-21 Air Conditioning

ECS Overview • 2 ECS packs • 2 zones (3 OPT) • emergency press. • ram air scoop located in wing-

fuselage fairing

• fan precooler

ECS Location Belly Fairing

Cockpit / Cabin

Pressure Control

automatic and

manual

Cockpit / Cabin

Temperature Control

automatic and

manual

No. Cabin Control Zones 1

Press. System Overview digital controller

Fresh Air Ratio • 2 recirc fans • 100% fresh air

Overpress. Valve Diff. 9.1 psi

Cabin Alt. at Max Alt. 8000 ft

Cooling Cycle Overview • 2 ECS packs with: 3-wheel air cycle

machine, dual

heat exchanger,

water separator

ATA 22 - Auto Flight

Auto Flght Cntrl Descr. Dual digital FCC

comp

Flight Director Descr. 2 FDs (1 per FCC)

Yaw Damper Descr. Provided by stall

management

Auto Pitch Trim Descr. Trim via variable

incidence H-stab.

ATA 23 - Communications

Comms System Overview • 2VHF 2HF systems • SATCOM • FlySmart • CVR • cockpit audio sys

ACARS STD

SELCAL STD

ATA 24 - Electrical Power

Main Power Type Separate AC, DC

Power Distr. Frequency 370 - 770 Hz

Number of Main Genrtors 4

Main Generator Power 150kVA / 70kVA

Aux. Generator & Power

(APU)

1 x 90 kVa

Emergency Power Source 70kVa AC RAT

Main System DC voltage 28 V

Battery Type & Power Ni-Cd @ 50Ah


-- vv --

ATA 32 - Landing Gear

Landing Gear Actuation hydrlc, man. bckup

Emerg. Extension

Procedure • manual release • gravity extension

Main Landing Gear Type cantilever

Location of MLG wing aux spar +

gear rib MLG Strut Type oleo-pneumatic

Tire Size - MLG H43 x W17.5 – R17

Tire Pressure - MLG 175 psi

MLG Braking System • Electrically powered

• autobrake (3 set) • carbon brakes • anti-skid

Nose Landing Gear Type cantilever

Spatial Direction for

Retraction of NLG

Forward

NLG Strut Type oleo-pneumatic

Tire Size - NLG H30 x W8.8 - R15

Tire Pressure - NLG 190 psi

NLG Steering Overview Electric

(integrated with

the Wheel Tug

system)

ATA 34 – Navigation

Number of ADS Computers 2

Number of AHRS 2

STD / OPT GPS STD

EFIS Displays Overview 8 of 8.0x8.0 LCDs

Number of IRS 2 STD

STD / OPT EGPWS STD

STD / OPT TCAS STD

No. of Radio Altimeters 2 STD

STD / OPT HUD STD

STD / OPT CatIIIa Appr. STD

STD / OPT CatIIIb Appr. STD

STD / OPT Autoland STD

GPWS / Wind Shear Detec STD

Digital Weather Radar STD

STD / OPT EVS STD

STD / OPT MLS STD

Number of VHF Radios 2 STD

No. of HF Transceivers 2 STD

Number of ADF Receivers 2 STD

No. of DME Transceivers 2 STD

STD / OPT Mode S Trnspn STD

STD / OPT Coupled VNAV STD

RNP Capability Yes

Overview of FMS System 2 FMS

ATA 35 - Oxygen

Fuel Pump Overview • 4 boost pumps in main tank

• 2 boost pumps in centre tank (ER

only)

• 4 boost pumps in collector tanks

• 1 boost pump for the APU feed

Cross-Feed Capability yes

Single Pt Refuel Capab. yes

Gravity Refuel Capablty yes

Location of Fuel Filler

Ports

LE of right wing

for pressure

ATA 29 - Hydraulic Power

Hydrlic System Overview Two Hydraulic lines

Hydraulic Bay Location belly fairing

Number of Main Systems 2

Hydraulic Fluid Type(s) phosphate ester

family

Nominal Working Pressre 3000 psi

Hydraulic Pumps • 1 engine-driven per engine

• 1 electrical per engine

• 1 RAT

Hydraulically Actuated

Items • Undercarriage • Elevators • Ailerons • THS • Rudder • Yaw Damper • Spoilers • Flaps

ATA 30 - Ice and Rain Protection

Anti-Ice System

Overview • Electro thermal heating mats on

the leading edge

of the wing and

pneumatic cowl

anti-icing Wing Electro-heated mats

H-tail no protection

V-tail no protection

Nacelle Intake 5th stage engine

bleed air

Probes & Sensors electriclly heated

Windshield • electrically heated for: anti-

icing, defogging,

defrost

• two wipers for rain protection

• Rain Repellent


-- vvii --

Struct. & Material -

Vertical tail • 2 spars • composite with CarbonF TE panels


Rudder

1 piece, carbon

fibre

Structure & Material -

Wing • 2 spars • machined ribs • extruded machined string. rivetd to

chem-milled skins

• aluminium wingbox Wing Tip Geometry Type Blended upper

surface winglet

Structure & Material -

Aileron

carbon fibre

Structure & Material HI

Lift LE Device

None

Structure & Material HI

Lift TE Device

trailing edge:

Carbon fibre al

honeycomb

Structure & Material

Speed Brakes

carbon fibre

ATA 71-80 – Engine

Engine Manufacturer Rolls Royce

Engine Designation V2500 (Scaled)

Turbofan No. of Stages

Fan/Boost/Compaxial +

Compcent//HPT/LPT

1 / 4 / 10 + 0 // 2

/ 5

Number of Engines 2

Mounting Point Aft Fuselage

Max. Takeoff Thrust

each

101.2kN / 22750lbf

119.7kN / 26911lbf Flat Rating Temperature ISA + 15

Thrust Reversr Overview Bucket Type

Bypass Ratio 5

Overall Pressure Ratio 35

TSFC at M0.80, FL 350 0.5776 lb/lb.hr

FADEC or DEEC FADEC

ETOPS Capability 90 min

External Noise, MTOW (ICAO Annex 16)

Takeoff / Stage 4 Limit 76.25/91.23 EPNdB

Sideline / Stage 4 Lim. 95.4/97.16 EPNdB

Approach / Stage 4 Lim. 96.8/100.36 EPNdB

Cumultv Margin to Stg 4 15.72 EPNdB

Emissions (ICAO LTO cycle)

NOx TBD

CO TBD

Unburnt Hydrocarbons TBD

Oxygen System Overview • crew: 114 cu. ft capacity

• chemical oxygen genertrs for PAX

ATA 36 - Pneumatics

Pneumatic System Overvw port switching

Location of Bleed Ports

and Capacity • fan: yes • int: 5th stage • high: 9th stage Pneumatic Source & Use • Engine cowl anti icing (supplied

byengine)

• Engine start up (supplied by APU)

Bleed Leak Detection yes

ATA 39 - Electrical / Electronic Panels

Loc. of Major Elec.

Components & System

cockpit

Main Display Panels LCD screens

Main Display Size (HxW) 8.0 X 8.0

No. Main Display Panels 8

Avionics Suite Designtn VIA

Avionics Suite

Manufacturer

Honeywell,Rockwell

Collins, Smiths

Avionics Rack Location underfloor of

forward cabin

ATA 49 - Auxiliary Power Unit

Std / Opt APU STD

APU Designation APS 3200

APU Manufacturer Sundstrand

APU Location Tailcone

APU Reqrd for Dispatch no

APU Operation & Control FADEC

APU Fire Extinguishing Yes

APU Max Start. Altitude 41000 ft

APU Max Oper. Payload Range Diagram For Advanced Conventional Aircraft

0

5 000

10 000

15 000

20 000

25 000

30 000

35 000

40 000

45 000

0 1 000 200 0 3 000 400 0 5 000 600 0 7 000

Ra nge (n m)

Payload(lb)

BGW

HGW

41000 ft

ATA 53, 54, 55 & 57 - Structure

Strctrl Press. Diffrntl 8.3 psi

Struc. Life cycle 75000 cyc

Structure Overview 35% Composite, 55%

Ali, 10% Other

Structure & Material

Nacelle / Pylon

Pylon – Aluminium

Nacelle - CFRP


Horizontal tail • 2 spars • composite with CarbonF TE panels


Elevator

1 piece, carbon

fibre


-- vviiii --

15.00m

37.88

38.25m

5.44m

26.50m

27.35m

21.65m

4.00m

1.20m

12°m

0.51m

3.93m

1.44m

3.82m

35°m

4.10m

3.06m

4.82m

40°m

5 x LD3-45W Containers

43.88m

30°m

1.44m

8.50m

6.50m

33.98

3.43m

1.74m

Ø2.26m0.75

12.34m

7.38m

6.00m

27°m

FEDR Configuration

All Dimensions in metres

12th March 2007


-- vviiiiii --

List of Tables 05-03-01 Available Supercritical Aerofoils 2

05-04-01 Lifting Characteristics of the A315 Atlas 14

05-04-02 Skin Roughness Value k (Raymer3) 15

05-04-03 Drag Calibration for the wing 16

05-04-04 Total Drag Calibration and Calculation at Cruise 16

05-04-05 Subsonic Drag due to High Lift Devices 17

05-04-06 Transonic Parasite Drag 17

05-04-07 Lift to Drag Ratios 18

List of Figures 05-02-00 Aerodynamics Iteration Flow Chart 1

05-03-01 MDD Variation with Sweep [Raymer3] 3

05-03-02 LFDD: Lift Adjustment for MDD [Raymer3] 4

05-03-03 The Sensitivity of Block Fuel to Aspect Ratio 5

05-03-04 Maximum Aspect Ratio for Tip Stall Boundary 5

05-03-05 Variation of Twist over Span 6

05-04-01 Variation of Cl vs Incidence for NASA (SC) 0610 8

05-04-02 Variation of Cd vs Incidence for NASA (SC) 0610 8

05-04-03 Variation of Cl/Cd vs Incidence for NASA (SC) 0610 9

05-04-04 Variation of Chordwise Cp for NASA (SC) 0610 9

05-04-05 Chordwise Cp distribution for NASA (SC) 0610 9

05-04-06 Lift Curve Slope at Mach 0.8 (Excluding Buffet) 11

05-04-07 Maximum Lift Adjustment at Higher Mach Numbers 11

05-04-08 Buffet Onset Boundary 12

05-04-09 Spanwise Lift Distribution at Mach 0.8 12

05-04-10 Efficiency of a Slotted Flap at varying deflections 13

05-04-11 Cl vs Mach Numbers along Flight Profile 18

05-04-12 L/D vs Mach number along Flight Profile 19

05-04-13 L/D vs CL at different Mach numbers 19

05-04-14 CD vs CL (constant conditions) 20

05-04-15 MLD vs M (constant conditions) 20


-- iixx --

Nomenclature Utilised Notation Definition Units

A Aspect Ratio -

Amax Total Exposed (Wetted) Surface Area m2

α Alpha (angle of attack) °

a Wing lift curve slope (with -

b Span (including winglets) m

croot Root Chord Length m

ctip Tip Chord Length m

CD Coefficient of Drag (Total) -

CD0 Skin Friction Drag Coefficient (Profile) -

∆CDDR ∆ CD Transonic Drag (due to Compressibility) -

∆CDLD CD Increment due to Lift Dump deployment -

∆CDEI CD Increment due to inoperative engine -

CDi Coefficient of Induced Drag -

Cl Aerofoil 2D lift coefficient -

CL Wing Lift Coefficient -

CLmax(approach) Max Lift Coefficient at Approach -

CLmax(take-off) Max Lift Coefficient at Take off -

CLmax(cruise) Max Lift Coefficient at Cruise -

d Fuselage Diameter m

E Oswald Efficiency Factor -

F Fuselage Lift Factor -

F0 Form Factor -

K Lift Dependant Drag Constant -

M Mach number -

Mc Critical Mach number -

MDD Drag Divergent Mach number -

MAC Mean Aerodynamic Chord -

q Dynamic Pressure -

Sref Reference Wing Area m2

Sexposed Exposed (Wetted) Wing Area m2

t/c Thickness to Chord Ratio -

(t/c)70 t/c at 70% semi-span -

Vapp Approach Speed ms-1

Vstall Stall Speed ms-1

V Airspeed ms-1

β Prandtl-Glauert correction factor -

λ Taper ratio -

Λc/4 Sweep (Quarter Chord) °

Λc/2 Sweep (Half Chord) °

ΛLE Sweep (Leading Edge) °

ΛMax(t/c) Sweep of Maximum thickness line °

MTOW Maximum Take-off Weight N

MLW Maximum Landing Weight N

OWE Operating Weight Empty N

L/D Lift to Drag Ratio


-- xx --

Contents

General Arrangement Drawing i

Design Data Sheet ii

List of Tables v

List of Figures v

Nomenclature Utilised vi

05-01-00 Introduction 1

05-02-00 Iteration Procedure 1

05-03-00 Sizing and Design 2

05-03-01 Aerofoil Selection 2

05-03-02 Wing Sizing 2

05-03-03 Wing Sweep 3

05-03-04 Thickness to Chord Ratio and Taper 4

05-03-05 Aspect Ratio 5

05-03-06 Wing Twist 6

05-03-07 High Lift Devices 7

05-04-00 Lift and Drag 8

05-04-01 Aerofoil Analysis 8

05-04-02 Lift Curve Slopes 10

05-04-03 Lift Distribution 12

05-04-04 High Lift Devices 13

05-04-05 Subsonic Drag Estimation 14

05-04-06 Transonic and Induced Drag Estimation 17

05-04-07 Lift-Drag Polars 19

05-05-00 Other Aerodynamic Considerations 21

05-05-01 Engine Integration 21

05-05-02 Winglets 21

05-05-03 Fuselage 22

05-05-04 Active and Passive Flow Control? 22

05-05-05 Impact of Future Derivatives 22

05-06-00 References 23


-- 11 --

MTOW obtained from Weights and

Balance Team. Geometric limits

obtained from design Specification

Wing and High lift System sized for

Derivative at cruise, climb, takeoff

and approach

Sweep, Thickness to chord ratio,

Aspect Ratio and Taper Selected

Wave Drag,

Buffet Cl, Tip stall

Boundary

condition met?

Yes No

Lift ad Drag values Estimated and

Passed onto Performance Team.

Performance requirements met?

Yes

No

Aerodynamic Loads Calculated

and Passed on to Structures. Loads

and Fuel/Part Volume acceptable?

Pass on Wing Area to Weights Team

Has MTOW

changed?

Yes

No

No Yes

Fix design and

optimise other

Aerodynamic

Parameters

05-01-00 Introduction The morphology of the A315-Atlas was selected to minimise the turnaround time and

maintenance on the ground and maximise takeoff/approach capability without

impinging on cruise performance. This approach has been continuously adhered to

in terms of aerodynamics (as well as its influence in other aspects) in the evolution of

the Atlas. The aerodynamic considerations, tradeoffs made and the final best

compromise values used are outlined in this document. All calculations were verified

and validated whenever possible and only consistent methods were used, mainly

from the sources listed in Section 05-06-00.

05-02-00 Iteration Procedure Figure 5-02-01 below summarises the iteration procedure adopted in the basic design

development.


-- 22 --

Figure 5-02-01: Aerodynamics Iteration Flow Chart

05-03-00 Sizing and Design

05-03-01 Aerofoil Selection The initial calculation of lift and drag required the input of basic aerofoil properties.

Although the final design would utilise a tailored 3D wing section, a basic airfoil shape

was needed for the sizing. The obvious choice considering the transonic design cruise

speed was the NASA Supercritical series (designed from the Whitcomb Airfoil). These

are named NASA (SC) XXXX with the first 2 letters representing the design lift

coefficient and the last 2 denoting the thickness to chord ratio. Detailed data on the

suitable aerofoils was obtained1, 2 and analysed [See section 05-04-01]. The list of

aerofoils is shown in Table 05-03-01 below. The aerofoils chosen were the SC 0614 for

the root section and the SC 0610 for the rest of the wing.

Design CL = 0 CL = 4 CL = 6 CL = 7 CL = 10

t/c = 6% - 0406 0606 0706 1006

t/c = 10% 0010 0410 0610 0710 1010

t/c = 12% 0012 0412 0612 0712 -

t/c = 14% - 0414 0614 0714 -

Table 05-03-01: Available Supercritical Aerofoils (NASA (SC) XXXX)

05-03-02 Wing Sizing The Maximum Takeoff Weight for a 180 passenger derivative was obtained from the

Weights and Balance Team (approximately 15% higher than Extended Range variant

MTOW). This value was modified by the Performance team to allow for fuel burn at

different altitudes in the cruise-climb profile. These weights were then used in

conjunction with the maximum lift coefficient available [See section 05-04-02] to

determine the wing area required to sustain lift or climb. It was found that the cruise

and approach conditions were most critical due to buffet and approach speed

limitations. Climb was not an issue due to the amount of thrust and CL available.

The wing area was initially sized at maximum cruise altitude using the maximum lift

coefficient produced after transonic buffet reductions (CLmax (cruise) = 0.667 at Mach

0.8 at FL 410). This was done in accordance with JAR 25.251 ‘Vibration and Buffeting’.

A wing area of 126m2 was chosen as this would be just enough to allow the 180 pax

derivative to cruise at Mach 0.8. Sizing for takeoff and landing was done in parallel

and it was found that with the addition of flaps, the wing was of adequate area.

More details of wing sizing with high lift system deployed are in section 05-04-03.

A furthur study was conducted into the effects of wing area on MDD. This was done

because the drag divergence Mach number is dependent on the lift coefficient at

cruise. A larger wing area would have increased the speed at which drag

divergence occurs. The study showed that a relatively large change in wing area was

needed to cause small increments in MDD. This method was therefore not an

effective means of delaying MDD. The wing area thus chosen produced the maximum

benefit in terms of L/D for the given weight.

The wing area therefore meets all performance requirements. As weight was critical,

margin was not left for wing area beyond the 15% increase in MTOW from the ER

variant. This should not pose a problem later on in the design as the weights estimate

was conservative and tailplane lift contributions were not accounted for.


-- 33 --

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

0.92

20 22 24 26 28 30 32 34 36

Sweep (c/4)

MDD (boeing) t/c

0.04

0.06

0.08

0.010

0.012

05-03-03 Wing Sweep The range requirements of 1800 and 3000 nautical miles are hard requirements in the

design specification. This directly results in a significant portion of the flight spent at

cruise [350 minutes out of a block time of 420 minutes for a 3000nm journey and 200

out of 260minutes for the 1800nm flight]. As a consequence, the cruise performance

must almost completely be uncompromised. The most efficient way of ensuring this is

by reducing the wave drag at transonic speeds. Wing thickness and sweep play a

major role in this.

The Raymer3 method was used to calculate the MDD for the wing. The equation for this

is given below.

MDD = MDDL=0 LFDD – 0.05CLdesign (Eqn 05-03-01)

MDDL=0 (the drag divergence Mach number for an uncambered wing at zero lift) can be found from Figure 05-03-01 and LFDD (which adjusts MDD to the actual lift

coefficient) can be found from Figure 05-03-02. Both these curves were reproduced

from Raymer3. They show how a reduction in thickness to chord ratio and lift

coefficient (increase in wing area) or an increase in sweep can reduce MDD.

Figure 05-03-01: MDD Variation with Sweep

The thickness to chord ratio (discussed in section 05-03-04) was set in later iterations as

10% along most of the wing. As a supercritical aerofoil is being used, the thickness

ratio is multiplied by 0.6 in order to use the figures. Thus the line showing a t/c of 0.06 is

the line that is applicable in this design case. The design lift coefficient was also fixed

with the use of the 0610 aerofoil and the cruise CL of approximately 0.6.

The only remaining parameter was the quarter chord sweep. Values ranging from 20-

35° were entered into the equation to find the resulting drag divergence Mach

numbers. A sweep of 30° or more was needed to produce a value above Mach 0.8.

The 30° sweep generated a MDD of 0.815 for the ER variant. Greater increments in

sweep reduced the drag furthur. However, this caused a significant increment in

weight and resulted in lower lift production in the wing. As the overall cost of


-- 44 --

0.85

0.87

0.89

0.91

0.93

0.95

0.97

0.99

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cl

LFdd

t/c

0.04

0.06

0.08

0.10

0.12

0.14

increasing the drag divergent Mach number furthur outweighed any aerodynamic

benefits, the sweep was set at the minimum of 30°. Although the method utilised was

from an updated publication of Raymer3, the calculation seems conservative when

compared to recent aircraft (e.g. A330, 777) utilising improved supercritical

technology. It is expected that with further detailed calculations, the sweep angle

could be reduced in later stages of the design.

Figure 05-03-02: LFDD: Lift Adjustment for MDD

05-03-04 Thickness to Chord Ratio and Taper The thickness to chord ratio has just as much of an impact on MDD for the wing as the

sweep. The thinner the wing, the higher its performance at high cruise speeds. This

however affects the maximum lift generated (reducing the t/c below 12% reduces

the available lift4 (page 86)). More significantly however, reductions in t/c dramatically

increase the structural complexity and weight. Space for sufficient fuel is another

contributing factor. The ideal t/c required for the fuel tanks was 0.8. Therefore the only

available aerofoil that will just exceed this t/c is one with a thickness of 10% [See Table

05-03-01]. This therefore just meets the structural/fuel requirements whilst still providing

excellent aerodynamic capabilities. An aerofoil with a t/c of 14% was used at the root

to accommodate landing gear/fuel. In the early calculations, this aerofoil was

assumed to continue till 40% of the semi span with a sudden shift to 10%. The t/c

should be gradually changed during later design stages to produce the appropriate

aerodynamic characteristics. The t/c at 70% span however, should remain at 10%.

The taper ratio was set to 0.24. Taper ratios between 0.2 and 0.4 produce the least

amounts of induced drag4 (page 172). This is done by producing a near elliptic lift

distribution. The taper ratio must not be too close to 0.4 as it would produce a high lift

coefficient on the outer wing and cause early flow separation. Too low a ratio would

cause structural difficulties as well as problems with manufacturing and fuel

accommodation. Although no trade studies or calculations were done regarding this

parameter, the value of 0.24 was chosen as many aircraft of its type employ a similar

value. A more detailed study will be required in later stages of the design.


-- 55 --

05-03-05 Aspect Ratio As the wing area was already fixed by hard requirements, the aspect ratio depended

solely on the span. Higher aspect ratios produce greater aerodynamic performance.

However, the ICAO Code C airport compatibility limits that apply to the A315-Atlas

restrict the wingspan to 35m. Furthur restrictions arise from the structural complexity

that increases with increasing span, thereby increasing the weight of the aircraft and

the tip stall boundary condition.

In order to quantitatively determine the “optimum” span, a trade study was

conducted. Figure 05-03-03 shows the decrease in block fuel with increasing aspect

ratio. The blue line shows how the increased L/D alone contributes to the block fuel

reduction. The red line also takes into account the increment in weight that the

lengthened span generates. The curve does not flatten out till aspect ratios greater

than 11 are utilised. Therefore the higher the A, the better the fuel consumption is.

Please note that the values for block fuel quoted on the figure are based on

calculations carried out much earlier in the design phase. The values have now

changed due to changed in the MTOW etc. However, the trend in fuel reduction can

still be applied as it has not changed.

Figure 05-03-03: Sensitivity of Block Fuel to Aspect Ratio

Figure 05-03-04: Maximum Aspect Ratio for Tip Stall Boundary

The only remaining consideration was the tip stall boundary condition. This was

calculated using Eqn 05-03-02 and the results of these calculations are shown on

Figure 05-03-04 above. The value for the left hand side of the equation was 5.714 for

Sensitivity of Block fuel to aspect ratio

23000

23500

24000

24500

25000

25500

26000

26500

27000

7 7.5 8 8.5 9 9.5 10 10.5 11

Aspect Ratio

Block Fuel (lbs) Decrease in Block fuel with higher Aspect Ratio

(increment in weight and aerodynamic

performance cosidered)

Aspect Ratio vs Sweep Required to Avoid Tip Stall

20

22

24

26

28

30

32

34

36

38

7 7.5 8 8.5 9 9.5 10 10.5 11Aspect Ratio

Sweep (degrees)

AR Range to optimise for

high speed cruise

Ideal Aspect

Ratio at a 30

degree sweep =

9.16


-- 66 --

-3

-2

-1

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1 1.2

Eta (Spanwise Location- 2y/b)

Jig Twist angle (Degrees)

Approximate Twist Distribution

Calculated using ESDU 95010

Estimated Twist Distribution For

proposed tailored 3D wing

the Atlas. The final values for sweep, aspect ratio and t/c were then entered into the

Korn equation to ensure that they were consistent with each other. As equation 03-

03-03 from the Design Manual5 shows, the values calculated are in fact correct. The

left hand side is exactly equal to 0.90.

A.(tan Λc/4)0.86 < 5.715 Eqn 05-03-02

90.0cos

)/(

cos10

23.1cos)05.0(

2/

70

2/

22/ =Λ

+Λ×

×+Λ×−

cc

Lccruise

ctCM Eqn 05-03-03

Assumptions and inputs

Mcruise is 0.05 greater than the critical mach number (Mcruise = 0.83)

Critical area of the wing profile is at approximately 50% of the chord

Maximum CL is about 1.23 x mean CL (mean CL=0.6)

Maximum section CL occurs at 70% semispan.

Half chord Sweep Is 27.05 degrees.

05-03-06 Wing Twist The spanwise lift distributions for several aircraft of the same type were obtained in

the initial design stages. These lift distributions were then utilised to determine the

possible spanwise twist for the A315-Atlas. The spanwise lift distribution is shown in

section 05-04-02.

The spanwise lift distribution for different twist changes was calculated using the ESDU

software numbered 950106. This utilises steady lifting surface theory based on the

Multhopp-Richardson solution. The program calculated the loading distributions of

local lift due to incidence, due to camber at zero incidence and twist at zero

incidence. These separate values were summed assuming that their contributions are

linear. The results were verified at 3 spanwise stations (10%, 50% and 90%) using ESDU

data sheet 830407. It was assumed that the NASA 0614 aerofoil was used up to 40% of

the semi span with the NASA 0610 aerofoil covering the remainder of the wing. This

approximation greatly reduced the complexity of the calculation as only the camber

at 2 locations needed to be entered. The Multhopp spanwise and chordwise

collocation stations entered were 33 and 3 as the camber distribution was simple and

βA is 5.4. A single crank was assumed in the planform description. The twist was

modified till the integrated lift coefficient equalled the design CL of approximately 0.6.

Figure 05-03-05: Variation of Twist over Span.


-- 77 --

Figure 05-03-05 shows the variation in twist with span for the A315. Note that the points

on the graph indicate a steep change in twist at the 40% span location. This is a direct

result of the 2 aerofoil section approximation made. A more accurate method could

not be found as information on possible intermediate aerofoils was not available to

improve the twist distribution. Also note that the effect of the fuselage was not taken

into account into the analysis and was ignored. The red line drawn shows the possible

twist distribution that would be present with the use of a tailored 3D aerofoil with a

smoothly varying t/c ratio. The resulting spanwise lift distribution is in Fig 05-04-09. The

resulting fuselage inclination angle at cruise is 0 degrees.

05-03-07 High Lift Devices The high lift devices on the A315-Atlas comprise of continuous single slotted trailing

edge fowler flaps. When fully deployed, these produce a total flapped wing area of

163m2. They are designed to produce this area with a 20° deflection on takeoff. At

the landing setting, the flaps will be deployed to 30° without an appreciable increase

in area- i.e the flap will simply droop down.

This mechanism can be achieved with the use of a hooked flap track. The other

proposed mechanism is an upside down forward link in conjunction with a straight

track on a fixed structure as aft support. It will be designed so that the pivot point on

the carriage is close to the centre of pressure of the flap. This would greatly reduce

the overturning loads on the drive, thereby easing the actuation loads required17. A

continuous flap will be used (as there is no need for engine exhaust clearance). This

would allow better flap performance. It would also enable the use of a single

redundant flap track mechanism as opposed to 2- thereby cutting both

manufacturing and maintenance costs. The efficiency of the flaps would enable a

lower thrust setting to be used- thereby cutting down on both noise and emissions on

approach and takeoff17.

The wing area was found to be adequate for takeoff and landing of the more critical

ER variant. The angle of attack required is below the maximum permissible angle of

attack with respect to pilot’s visibility and with regards to stall. As a result of this slats

were not required. This would greatly cut down on the maintenance costs involved.

Detailed calculations are outlined in section 05-04-03.

The chord length of the flap is only marginally smaller than the space remaining

behind the rear spar. Therefore flap deflection alone will not be sufficient for takeoff

and landing if the MTOW increases significantly. Although small margins were allowed

in the design either the wing area or takeoff/approach speeds would need to be

increased slightly if the 180 pax derivative is to take off in the same field length. The

increment in effective wing area can be achieved by adding a triangular slice to the

trailing edge of the outboard wing and a constant chord increment to the inboard

wing as done on the Airbus A32117. The ailerons could also be drooped when required

with the spoilers used to produce roll control in such an event.


-- 88 --

-1

-0.5

0

0.5

1

-10 -5 0 5 10 15

Alpha (deg)

Cl- NASA SC 0610

NASA 0610

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

-8 -6 -4 -2 0 2 4 6 8 10 12

Alpha

Cd- NASA (SC) 0610

05-04-00 Lift and Drag

05-04-01 Aerofoil Analysis The aerofoil coordinates were obtained1, 2, converted into DAT files and analysed in X-

Foil8. Values taken from X-Foil were tabulated and plotted on Excel. This produced lift

curve slopes, pressure distributions and drag polars for the 2 chosen aerofoil sections.

Such diagrams were then verified whenever possible using References 1 and 2 and

then input into all the lift and drag calculations performed. Figures 05-04-01 to 05-04-

05 are copies of the lift curves produced for the NASA 0610 aerofoil. The figures

indicate that the ideal lift coefficient of 0.6 occurs at zero aerofoil incidence and that

the Cl is zero at -3° of incidence. Also note that the minimum drag occurs at -3° and

0° incidence where the value for Cl is 0 and 0.6 respectively.

Figure 05-04-01: Variation of Cl versus Incidence (alpha)

Figure 05-04-02: Variation of Cd versus Incidence (alpha)


-- 99 --

-30

-20

-10

0

10

20

30

40

50

60

70

-8 -3 2 7 12

Alpha

Cl/Cd- NASA (SC) 0610

Figure 05-04-03: Variation of Cl/Cd versus Incidence (alpha)

Figure 05-04-04: Variation of Chordwise Cp (alpha = 1.5degrees)

Figure 05-04-05: Chordwise Cp distribution (alpha = 2.5degrees)

The pressure coefficient distribution diagrams were a direct output from Profili which is

an aerofoil management software that utilises X-Foil. Note that due to the

compressibility limitations on X-Foil, all calculations were run at Mach 0.7.

05-04-02 Lift Curve Slopes Equation 05-04-01 shows the semi-empirical formula obtained from Raymer3 to

calculate the wing lift curve slope (per radian). This is accurate up to MDD and

reasonably accurate up to Mach 1 for a swept wing.

( )FS

S

A

AC

ref

osed

ct

L

Λ+++

exp

2

)/max(

2

2

22 tan142

2

βηβ

πα Eqn 05-04-01


-- 1100 --

Where, 22 1 M−=β Eqn 05-04-02

95.02

≈=βπ

η αlC

Eqn 05-04-03

( )2107.1 bdF += Eqn 05-04-04

The inputs (such as Sexposed = 102.5m2 and of ΛMax (t/c) =27.5) to the above equations yielded a lift curve slope 6.29 per radian or 0.11/° for cruise. As the speed of the

aircraft did not exceed Mach 0.85, no transonic or supersonic lift curves were

calculated.

The maximum lift attainable was then calculated, once again using the Raymer3

method for consistency. This required the calculation of the leading edge parameter,

which is defined as the vertical separation between the points on the upper surface

which are 0.15% and 6% of the aerofoil chord back from the leading edge. This

parameter was easily calculated using the aerofoil coordinates obtained1, 2. The

method of calculation, which Raymer3 obtained from the USAF Digital Datcom2 is

outlined in equation 05-04-05. The value for this was 2.502.

max

max

max

maxmax L

l

L

lL CC

CCC ∆+

= Eqn 05-04-05

Where maxlC is the aerofoil maximum lift coefficient at M = 0.2

max

max

l

L

C

Cwas found from Fig12.8 in Raymer3 to be 0.78 when the leading

edge sweep is 32° for a wing with a leading edge parameter of 2.502.

maxLC∆ was found in Fig12.9 in Raymer3. This is dependant on Mach number.

The value for this was -0.177 at Cruise Mach number. The fuselage lift factor

was also taken into account by multiplying the whole equation by it and

wing area ratio.

The angle at which maximum stall occurred was divided by the gradient of the lift

curve slope added to the negative angle at which zero lift occurs [see section 05-04-

01] and the correction for nonlinear effects of vortex flow [found to be 3.6 from

Raymer3] The lift curve slope (at cruise) is drawn in figure 05-04-06. Note that this does

not take into account buffeting effects or the effects of varying camber or twist that

a 3D aerofoil would possess.


-- 1111 --

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-5 0 5 10 15

alpha (degrees)

CL

-3

0.974

9.477

3.6 degrees

Figure 05-04-06: Lift Curve slope at Mach 0.8 (buffet not included)

The maximum lift attainable is reduced near transonic speeds by shocks forming on

the wing (buffet). The maximum lift the wing can achieve is furthur limited by

structural considerations, controllability and flexibility. Figure 05-04-07 taken from

Raymer3 takes into account the decrease in lift from Mach 0.5 onward due to these

constraints. The maximum CL was multiplied by the reduction factor in the curve to

obtain the available CL after buffet. According to the Design Manual5, a furthur

margin of 1.3 was to be applied to this value. The design manual was not used in the

calculation of the buffet boundary as its values were based upon the wing geometry

of the A330. The final variation of available lift with Mach number before and after

the application of this margin is shown in Fig 05-04-08. The red line shows the final CL

available. This was the value used in the sizing of the wing for the 180 pax derivative.

Figure 05-04-07: Maximum Lift Adjustment at Higher Mach Numbers.

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

Mach Number

CLmax/CLmax(M0.5)

0.89


-- 1122 --

Figure 05-04-08: Buffet onset Boundary

05-04-03 Lift Distribution

Figure 05-04-09: Spanwise Lift Distribution at Mach 0.8

Figure 05-04-09 above shows the Spanwise Lift Distribution that was used to find the

ideal twist. Although the lift distribution is not perfectly elliptic, the maximum sectional

lift coefficient was required to be at 75% of the span according to the Korn Equation

in the Design Manual5 [see Eqn 05-03-03]. Note that this value is within the buffet

boundary. The other constraint was the integrated lift coefficient- which was to be

near 0.6 in order to maintain level flight at cruise. This lift distribution was different from

the preliminary calculation which was used by the Structures team. Despite this, the

wing structure was found to adequately accommodate the change in loads without

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85Mach No

CL

Available CL after application of Margin (1.3)

Buffet onset boundary

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Span

Sectional lift coefficient x local wing chord /

reference

Max Sectional Lift Coefficient at

75% Span (see Eqn 05-03-03)

Integrated Lift Coefficient = 0.596


-- 1133 --

major alterations. The centre of pressure was also calculated7 and was found to be at

44% along the span (from the root).

05-04-04 High Lift Devices The lift curve slope was then calculated with the flaps deflected. As the reference

area and exposed area were now different (Sreference = 163m2), the lift curve slope

(Eqn 05-04-01) was 6.44 at takeoff and approach speeds. Note that the same

flapped wing area is used at takeoff and approach. This was done to maximise the

lifting efficiency of the single slotted fowler flaps at both cases.

The efficiency of a single slotted flap is at its peak between 20-25 degrees9. The figure

below, taken from ESDU datasheet 930199 clearly shows this. The flaps are to be

designed so that they produce the maximum possible wing area at this deflection

angle. Furthur deflection (with no increase in area) will be used on landing to create

the necessary drag.

Figure 05-04-10: Efficiency of a

Single Slotted Flap at varying

degrees of deflection.

The ratio of flap chord to the

extended aerofoil chord as

defined in Reference 9 was set at

0.3. This was the maximum chord

length that was structurally

allowed (rear spar location).

Other inputs were the flap type

correlation factor (1.05), the

spanwise centre of pressure (0.44)

and the inboard and outboard

part span factors (0.1 and 0.7

respectively). The resulting

increment in aerofoil lift

coefficient was found (1.2) and

then used to calculate the

increment in wing lift coefficient

at zero angle of attack. The value

for this was 0.58. As a result, the

lift curve slope and hence the

incidence at which no lift was

generated was pushed to the left

by 3.45 degrees. Stall now occurs

approximately between 10.9 and

11.2° for all takeoff and landing

speeds.

The incidence required by the wing for takeoff and landing is approximately 8-10°

(See Performance document). Due to this and the sufficient wing area present, the

use of slats to delay the incidence at stall was not required, thereby eliminating a

significant contributor to maintenance costs. As the wing is attached to the

horizontal fuselage at a 5° inclination, the fuselage is not at more than a 5° incidence

at takeoff and landing. Therefore it is well within the 9° limit imposed in the

specification due to pilot visibility issues.


-- 1144 --

Additional lift forces are generated near the ground due to ground effect. This was

calculated from the equations in Fig 7.40 of the Design Manual5. At a height of 3

metres the incremental CL due to ground effect was 0.22. Table 05-04-01 summarises

the tail off lifting characteristics of the A315-Atlas.

A315- Atlas SR A315- Atlas ER 180 Pax Derivative

CL Top of Cruise [FL410], M0.8 0.58 0.59 0.67

CL Top of Cruise [FL410], M0.8 0.55 0.57 0.63

Max Available CL 0.67 0.67 0.67

Design CL 0.6 0.6 0.6

Wing Loading (Kgm-2) 517 560 644

Lift Curve Slope M0.8 (/ rad) 6.29 6.29 6.29

Lift Curve Slope Takeoff (/rad) 6.44 6.44 6.44

CL Max (takeoff)(with ground effect) 2.45 2.45 2.45+(droped ailerons)

CL Max (landing) 2.17 2.17 2.17+(droped ailerons)

Table 05-04-01: Lifting Characteristics of the A315 Atlas

05-04-05 Subsonic Drag Estimation The drag estimation was made using the Component Build-up method detailed in

Raymer3. This was done by calculating the flat plate skin friction drag coefficient (Cf)

and a component ‘form factor’ (FF). The interference effects on the component drag

are estimated as a factor Q and the total component drag is found as the product of

wetted area, Cf, FF and Q. Equation 05-04-06 outlines this method.

( )PDLDmisc

reference

wetccccsubsonicD CC

S

SQFFCfC &0 )( ++

Σ= Eqn 05-04-06

Where DmiscC is the miscellaneous drag for special features including

unretracted landing gear, aft fuselage upsweep, and base area and

PDLC & is the drag due to leakage and protuberances.

Cf is dependant on skin roughness, Mach number and Reynolds number (Reynolds

number, R is the product of the local air density, flow velocity and characteristic

length divided by the viscosity of the fluid). This coefficient has different values of

laminar and turbulent flow regimes. The method of calculation is shown in Equations

05-04-07 and 05-04-08.

RCf arla

328.1min = Eqn 05-04-07

( ) ( ) 65.0258.2

10 144.01log

455.0

MRCfturbulent

+= Eqn 05-04-08

In areas of the aircraft where the surface finish is rough, Cf will be higher than that

indicated in the above equations. This can be dealt with by the use of a ‘cut-off

Reynolds Number’ (see Equations 05-04-09 and 05-04-10). The lower value between

the Reynolds number and the cut-off Reynolds number is used.

053.1

_ )/(21.38 klR subsoniccutoff = Eqn 05-04-09

16.1053.1

_ )/(62.44 MklR transoniccutoff = Eqn 05-04-10


-- 1155 --

Where l = characteristic length

k = skin roughness value (see Table 05-04-02)

Surface k, m

Camouflage paint on aluminium 1.015 x 10-5

Smooth Paint 0.634 x 10-5

Production Sheet Metal 0.405 x 10-5

Polished Sheet Metal 0.152 x 10-5

Smooth Moulded Composite 0.052 x 10-5

Table 05-04-02: Skin Roughness Value k (Raymer)

The skin roughness values were used according to the surface finish and the materials

currently used in jet transports. It was assumed that the fuselage, tail and nacelle

were covered in a layer of smooth paint with the wing surface being polished sheet

metal.

Equations 05-04-11 to 05-04-14 outline the calculation of component form factors.

[ ]28.0

)/max(

18.0

4

, )(cos34.1100)/(

6.01 ct

m

tailwing Mc

t

c

t

cxFF Λ

+

+= Eqn 05-04-11

++=400

601

3

f

fFFfuselage Eqn 05-04-12

+=f

FFnacelle35.0

1 Eqn 05-04-13

( ) max4 A

l

d

lFFfuselage π

== Eqn 05-04-14

Where (x/c)m is the chordwise location of the aerofoil max thickness point (38%)

l is the characteristic length

d is the diameter.

Component interference factors were 1 for the wing and 1.3 for the nacelle as it was

less than one diameter away from the fuselage. Although this is slightly conservative in

light of recent advances in technology, it was nevertheless used for consistency in

calculation.

Miscellaneous drag contributions arose from the upsweep of the fuselage, landing

gear, flap deflection and base area drag. The formulae used in their calculation are

shown below as drag force over dynamic pressure (which can be divided by wing

reference area to yield the drag coefficient.

tioncrossfuselageupsweep AuqD sec__

5.283.3/ = Eqn 05-04-15

)10)(/)(/(0074.0_0 −=∆ flapreferenceflappedflapD SSCCfC δ Eqn 05-04-16

Where flapδ is the flap deflection in degrees

Cf is the chord length of the flap


-- 1166 --

The D/q for the wing mounted speed brakes was found by multiplying the brake

frontal area by 1.6. The D/q for the windshield was set at 0.07 times its frontal area. The

leakage and protuberance drag was assumed to be 2% of the total parasite drag.

The drag due to a windmilling (inoperative) engine was calculated using ESDU

datasheet 84005.

The input of all the characteristic lengths, areas, Reynolds numbers and coefficients

yielded values for drag. These were initially inaccurate as the components used either

laminar or turbulent skin friction coefficients. This is rarely the case as there are usually

some portions of a surface exhibiting laminar flow whilst the rest display a turbulent

flow regime. As there were insufficient sources of information on the amount of

laminar flow in aircraft, the information on the A330 was utilised to calibrate the drag

calculations. The detailed geometry of the A330 was entered along with the

reference Reynolds numbers presented in the Design Manual5. The component drag

values calculated were then compared against those for the A330. The percentage

of skin friction coefficient was then modified by considering different portions to have

laminar flow until the drag values coincided. This not only ensured that the amount of

laminar/turbulent flow used was accurate but also compensated for any errors in the

method utilised or inputs chosen. The validated spreadsheet was then used to

calculate the drag for the A315 Atlas at the different Reynolds numbers. The

component values obtained at set speeds are shown and compared against similar

values for the A330 in Table 05-04-03 for the wing and 05-04-04 for the rest of the

aircraft.

Wings- A315-Atlas A330

Characteristic length (m) 4.17 6.44

Reynolds Number 19900000 7220000

Skin Roughness Value (assumed fully polished sheet metal) 0.00000152 0.00000152

Cutoff Reynolds Number (Subsonic) 230000000 364000000

Cutoff Reynolds Number (Transonic) 20700000 328000000

Reynolds Number Used 19900000 7220000

Laminar Flat Plate Skin Friction Coefficient (Cf) 0.000298 0.000494

Turbulent Flat Plate Skin Friction Coefficient (Cf) 0.00255 0.00299

Cf used (assuming 40% laminar flow, 60% turbulent wing) 0.00169 0.00204

Chordwise location of aerofoil max thickness point ((x/c)m) 0.400 0.400

Sweep of max thickness line (deg) 27.2 25

t/c 0.10 0.10

Form Factor (FF) (valid upto drag divergence mach no) 1.43 1.43

Interference Factor (Q) 1.000 1.000

Swet 208 640

(Cfc x FFc x Qc x Swetc) 0.502 1.86

(Cfc x FFc x Qc x Swetc)/Sref (CD0) 0.00398 0.00513

Table 05-04-03: Drag Calibration for the wing

Component ∆CD0 A315- Atlas A330

Wing 0.00398 0.00513

Fuselage 0.00376 0.00438

Tailplane 0.000828 0.00085

Fin 0.000679 0.00074

Interference and Miscellaneous 0.00789 0.00403

Total Subsonic CD0 0.01578 0.01513

Table 05-04-04: Total Drag Calibration and Calculation at Cruise.


-- 1177 --

∆CD0 A315- Atlas A330

Takeoff Flaps 20°undercarriage up 0.033 0.0470 (approx)

Takeoff Flaps 20°undercarriage down 0.055 0.0698 (approx)

Landing Flaps 30°undercarriage down 0.0879 0.0580

∆CD0 Undercarriage down 0.0219 -

∆CD0 Windmilling engine 0.00259 -

∆CDLD (drag at maximum spoiler deflection) 0.0673 -

Table 05-04-05: Drag Calculation due to High Lift devices

The value for total subsonic drag was verified yet again using the basic equivalent

skin friction method.

wet

referenceD

FeS

SCC

×= 0

Eqn 05-04-17

The value for the equivalent skin friction coefficient obtained (using CD0 [0.0158],

Sreference [126] and Swetted [711.9] was 0.0028. Civil transports fall between 0.0025

and 0.0035. Therefore the subsonic parasite drag calculation is reasonable.

05-04-06 Transonic and Induced Drag Estimation The transonic parasite drag was considered during the wing sweep selection. The 30°

sweep yielded and MDD of 0.815. This is the point where the drag count increases to

20 from the subsonic level. Therefore the critical Mach number (where the drag

increment is 0) must be approximately 0.76. This is rather unlikely considering the high

speeds that modern airliners with similar sweep travel at. Therefore a more modern

compressibility drag rise estimation than that in Raymer3 was required. This was found

using the values from the A330 in the Design Manual.

The MDD calculated and the resulting drag counts at cruise speed are tabulated in

Table 05-04-06. Note that the drag increment from Mach 0.8 to Mach 0.82 is minor.

This makes high speed cruise (at Mach 0.82) an economical viability- thereby

reducing the block time (and if used frequently, increasing flexibility and utilisation).

The fuselage forward section (i.e the distance from the nose to the constant diameter

section) and the tailplane was also designed so that their compressibility drag onset

occurs after the wing.

Standard Range Extended Range

Drag Divergent Mach Number MDD(Raymer) 0.815 0.815

Drag Divergent Mach Number MDD(Manual) 0.858 0.857

∆CDDR at Mach 0.8 0.0012 0.0012

∆CDDR at Mach 0.82 0.00135 0.00136

Table 05-04-06: Transonic Parasite Drag

The induced drag contribution is the product of the induced drag proportionality

factor, K and the square of the lift coefficient. K was calculated using the leading

edge suction method as it is more accurate than the Oswald span efficiency

method. See Equation 05-04-18.

K= SK100 + (1-S)K0 Eqn 05-04-18

Where S is the leading edge suction parameter (this value is 0.93 for the A315

aerofoil at cruise as it is the most efficient near the design Cl).

K0 is the inverse of the lift curve slope


-- 1188 --

K100 is the reciprocal of (pi x aspect ratio)

The value for K calculated at cruise was 0.0434. This was verified by calculating K

using the Oswald Span Efficiency method (with e= 0.779) which yielded a K value of

0.0446. The aerofoil analysis conducted show that the minimum drag CL is both 0 and

0.6. The aerofoil is therefore treated as symmetrical by using the value of 0 for CL in

the induced drag calculation.

CDi = K(CL – CL min drag)2 Eqn 05-04-18

This produces a value of 0.0146 at cruise for the ER variant. The change in induced

drag for flap deflections was also calculated for takeoff/landing. This had a ∆CDi

value of 0.079.

05-04-07 Lift-Drag Polars The total drag coefficients and the lift to drag ratios calculated at the top of cruise

(Flight level 410, i.e. 41000ft) for the 2 variants are shown in Table 05-04-07. The weight

to thrust ratio was also determined at cruise to ensure that the L/D readings are

relatively correct. These are also shown on the table. The L/Ds estimated are only

slightly higher than their actual predicted values.

SR ER

CL Mach 0.8 top of cruise (41000ft) 0.579 0.594

CD Mach 0.8 top of cruise (41000ft) 0.0315 0.323

L/D Mach 0.8 top of cruise (41000ft) 18.34 18.39

L/D Mach 0.8 top of cruise (39000ft) 17.18 17.24

Weight at top of cruise (N) (41000ft) 585000 601000

Cruise Thrust (41000ft) 32100 32700

Weight/Thrust Ratio (41000ft) 18.23 18.32

Table 05-04-07: Lift to Drag Ratios

The main FEDR document contains all the high and low speed polar charts at fixed

weight and altitudes. The variation of required lift coefficient at different mach

numbers in the cruise-climb profile (varying altitude and weight) for the ER variant is

shown in Figure 05-04-11

Figure 05-04-11: CL vs Mach number along flight profile

0.35

0.4

0.45

0.5

0.55

0.6

0.55 0.6 0.65 0.7 0.75 0.8 0.85

Mach number

CL (along cruise profile)

Increase in required Cl

with altitude


-- 1199 --

Figure 05-04-12: L/D across different Mach Numbers along flight profile

Figure 05-04-12 shows how the lift to drag ratio varies with Mach number as the

aircraft climbs and cruises (at 39000ft and then 41000ft). This takes into account the

changes in aircraft weight as fuel is burned as well as the local atmospheric

conditions. Figure 05-04-13 shows the theoretical change in L/D vs lift coefficient if the

maximum takeoff weight and atmospheric conditions remained constant.

Figure 05-04-13: L/D vs CL at Different Mach No (constant conditions)

Figures 05-04-14 and 05-04-15 show the variation of the drag coefficient with lift

coefficient and the variation of ML/D vs M for different Mach Numbers. Both these

curves wee constructed assuming constant atmospheric conditions.

16.5

17

17.5

18

18.5

19

19.5

20

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85

Mach

L/D L/D at 39000ft

8

10

12

14

16

18

20

0.5 1 1.5 2 2.5 3

Cl at Different Mach No

L/D


-- 2200 --

Figure 05-04-14: CD vs CL (constant atmospheric conditions)

Figure 05-04-15: MLD/M for different Mach Numbers

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.5 1 1.5 2 2.5 3

CL

CD

CD0

0

2000000

4000000

6000000

8000000

10000000

12000000

14000000

675000 677000 679000 681000 683000 685000 687000 689000 691000 693000

M (Newtons)

M L/D

Changes to

Climb/Cruise speeds


-- 2211 --

05-05-00 Other Aerodynamic Considerations

05-05-01 Engine Integration The aerodynamically efficient integration of the engine to the fuselage was an

extremely important issue. The goal was to reduce the interference factor to one and

minimise the formation of shocks in the convergent-divergent passage in between

the nacelle and the fuselage at transonic speeds. The placement of the engine took

into account factors such as the engine thrust line, debris ingestion, control aspects,

pylon attachment, disk burst, one engine inoperative yaw, evacuation and the

scrubbing of exhaust gasses against the fuselage. The final positioning of the engine

was determined mainly by these factors. This was then verified against common

practise11 for engine placement. This method is outlined below-

Y= pod vertical separation from wing

D= maximum diameter of the nacelle

Z= pod horizontal separation

c=wing mean chord

X=highlight/Stub wing leading edge separation

S=Pod/Fuselage separation

L= length of nacelle

0.9 ≤ Y/D ≤ 1.4 0.2 ≤ S/D ≤ 0.4

0 ≤ Z/c ≤ 0.25 0.05 ≤ X/L ≤ 0.15

All inputs were obtained from the CAD team and found to be within the limits shown

above.

Furthur research was conducted during the design phase into improving the

integration issues. The scarfed inlet produces noise reduction while the long cowl

improves specific fuel consumption (the increased profile drag has been accounted

for). The use of a thick tailored pylon and a nacelle with an “inswoop” or small toe in

angle should cause reductions in drag12 as well as structural complexity. The inswoop

is defined as a minor widening of the inlet on the inboard section to divert the airflow

through the engine instead of the nacelle-fuselage channel. The benefit is a 4-3

count drag reduction12. The most critical zone here is the longitudinal cut on the

nacelle located just below the pylon. All tailoring required the use of CFD and wind

tunnel testing and was therefore not conducted till date. Such analysis will need to be

performed during the detailed design of the A315-Atlas.

05-05-02 Winglets The wing span of the A315 atlas is marginally within the ICAO Code C boundary. This

is slightly over the maximum span allowable for the sweep used without encountering

tip stall issues. Therefore the use of winglets is currently not needed. However, it is

expected that detailed (and more up to date) calculations on drag divergent Mach

number will reduce the sweep required from the wing. This would enable to aspect

ratio to be increased furthur to improve overall efficiency. It was calculated that the

span limit is exceeded if the sweep drops below 28 degrees. As this was a high

probability, the installation of winglets was accounted for. The current design

proposal therefore has winglets with a large cant angle (waked wing tips) to allow for

the structural impacts of winglet integration in later design stages.


-- 2222 --

In the event that the span increment occurs, the wing tip extensions must be

designed for first, with the canted, blended winglets added afterward. This is because

the effective reduction in fuel burn for a 15% semi span high winglet can be achieved

for a wing tip extension with a length approximately half its height (8/15)13. Detailed

CFD analysis will be required prior to all winglet design work. The current winglet is

derived from a winglet for a similarly sized aircraft in Reference 13. The estimated

overall fuel saving is 3-4% (this has not been taken into account in any calculations).

The winglet currently used has a t/c of 8%, a cant angle of 60 degrees, a root chord

that is 60% that of the wing tip chord and a 30 degree sweep. All interfaces are

blended and smooth.

05-05-03 Fuselage The fuselage nose and tail section were lengthened to reduce the drag penalty

caused by their blunt profile. Furthur improvements will need to be made in detailed

design stages by tailoring the shape to reduce the drag to a minimum. In the event

that this cannot be achieved, the use of riblets or vortex generators will be viable in

the critical zones if issues with their reliability and practical integration (e.g.- the ability

to paint over riblets etc) are overcome.

05-05-04 Active and Passive Flow Control One of the areas that needed detailed research after the Preliminary Design Review

was the use of laminar flow control in the Atlas. The research conducted thus far show

that a certain degree of natural laminar flow can be attained with proper profile

tailoring in certain sections of the aircraft. This is done on many aircraft today. The use

of Active laminar flow however is unlikely due to the prohibitive nature of design issues

surrounding it. Although the reduction in fuel burn is appreciable, the clogging of the

suction ducts with dirt and ice is a severe problem that needs to be overcome14.

Much research was done on the subject in the 1990s until fuel prices dropped.

Although the viability of such a system has been the topic of much debate, with the

increase in fuel price, there may not be many other options to improve efficiency14.

In the event that active flow control is to be used, the ideal location is near the

upsweep of the fuselage. Bleed air can be utilised from the neighbouring engines to

reduce the pressure in a duct within the structure. If a system is to be installed in the

wings, a separate pump may be needed. An initial check shows that this can be

accommodated in the power budget. All calculations done to date do not include

the assumption of active laminar flow.

05-05-05 Impact of Future Derivatives Derivatives of the A315-Atlas have been accounted for in all aerodynamic

calculations. The changes made are outlined in the individual sections above. The

takeoff/approach case for the larger derivative was the most critical but was also

accommodated. The modifications needed to be made for a 120 or 180 passenger

version are almost negligible and will only be needed to reduce the margin

remaining! All calculations made were verified wherever possible and validated. The

morphology selected should, aerodynamically if not overall produce an efficient

family of aircraft that meets and exceeds competitor performance both now and in

the near future.


-- 2233 --

05-06-00 References

1. NASA Supercritical Airfoils, Charles D Harris, NASA Technical Paper

2969, Date: 1990

2. USAF DATCOM (Digital), D Hoak, D Ellison et al. Air Force Flight

Dynamics Lab, Wright Patterson AFB, Ohio

3. Aircraft Design: A Conceptual Approach, 4th Edition, Daniel P

Raymer, ISBN-13: 978-1-56347-829-1, Date: 2006

4. Aerodynamics, Aeronautics and Flight Mechanics, 2nd Edition,

Barnes McCormick, ISBN: 978-0-471-57506-1, Date: 1995

5. Design Manual, Airbus, University of Bristol, Date, 2003

6. ESDU 95010: Computer program for the Estimation of Spanwise

Loading of Wings with Camber and Twist in Subsonic

Attached Flow, Date : 1993.

7. ESDU 83040: Method for the Rapid Estimation of Spanwise Loading

of Wings with Camber and Twist in Subsonic Attached

Flow, Date : 1995

8. XFoil Subsonic Airfoil Development System, Mark Drela, Harold

Youngren, Date: February 2007

9. ESDU 93019: Wing Lift Coefficient Increment at Zero Angle of Attack

Due to the Deployment of Single-Slotted flaps at Low

Speeds, Date: 1995

10. ESDU 84005: Estimation of Drag due to Inoperative Turbo-Jet and

Turbo-fan engines using Data item Nos 81009 and 81004,

Date: 1989

11. Propulsion 3 Lecture Notes, NA (Sandy) Mitchell, University of Bristol,

Date: 2006

12. High Speed Aerodynamic Integration of a Fuselage Mounted

Turbofan Engine, David Yates and Keith Blodgett (GE

Aircraft Engines, Cincinnati, OH) and Fassi Fafyeke

(Bombardier Aerospace, Montreal, Canada), Date 1998,

AIAA 98-3421

13. ESDU 98013: Aerodynamic Principles of Winglets, Date: 1998

14. An Overview of Recent Subsonic Laminar Flow Control Flight

Experiments, F.S Collier Jr, NASA Langley Research

Center, Date: 1993

15. Aerodynamic Features of the DC-9, Shevell and Schaufele, Date:

1965, AIAA 65-738

16. Aerodynamic Design Philosophy of the 737, D. A Norton (Boeing

Co., Commercial Airplane Div., Renton, Wash.), Olason,

M. L. Date: 1965, AIAA-1965-739

17. High Lift Systems on Commercial Subsonic Airliners, Rudolph,

Peterkc.

18. Synthesis of Subsonic Airplane Design, E Torenbeek, ISBN-13:

9789024727247, Date: 1982

Aerodynamics

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