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Diploma Thesis

Performance assessment of a hybrid electric-powered long-range

commercial airliner

Thomas Zld

June 2012

Thomas Zold Diploma Thesis Kungliga Tekniska Hgskolan

ii

This diploma thesis is presented within the framework of the T.I.M.E. double-degree programme

between the Technical University Munich and the Royal Institute of Technology in Stockholm.

Technical University Munich

Department of Aircraft Design

Boltzmannstrasse 15

DE - 85748 Garching bei Mnchen

Germany

Examiner TUM: Professor Dr.-Ing. Mirko Hornung

Examiner KTH: Arne Karlsson, Senior Lecturer

Supervisor: Dipl.-Ing. Malte Schwarze


iii

ABSTRACT

Despite the recent increase in the amount of smaller electric general aviation aircrafts, a fully

electric airliner is not likely to fly in the near future. Partially inspired by the automotive industrys

success with the hybrid car, this thesis investigated the feasibility of an electric-hybrid propulsion

system for an Airbus A340-600 on a long-haul flight and its effect on the aircrafts performance.

First, an analysis was done of the reference aircraft, A340-600, using conventional propulsion.

Second, a 5700 nautical miles flight was modelled to determine performance data such as the

power and thrust requirements during the different flight phases. Third, the flight phases where

electric propulsion would be implemented were identified and an optimum ratio between

conventional and electric propulsion was calculated. Finally, a detailed performance analysis of

the new hybrid electric aircraft comparing it to a conventional aircraft was conducted.

The maximum available conventional thrust was reduced to a certain percentage of the maximum

thrust. Primarily conventional thrust is used, however when it is no longer sufficient, additional

thrust is gained through electric propulsion. Conventional thrust ratio of 69.5%, 63.5% and 59.5%

of total thrust was investigated yielding 8680 kg, 10500kg and 8585kg of payload decrease

respectively. Net energy of 6.70MWh, 11.71MWh and 31.06MWh is required and the electric

engines need to provide 21.3 MW, 25.5 MW and 28.3 MW of net power respectively.

Partial electric propulsion will result in increased weight; however, it will also give room for

further performance optimisation and technical innovations. On the one hand, the conventional

engines will run at a constant speed throughout the flight allowing for better optimisation at a

specific design point. On the other hand, electric engines are more reliable and require less

maintenance than conventional engines. Furthermore, lower fuel consumption means less

carbon-dioxide emissions. An exemption from CO2-taxes, similar to measures implemented for

hybrid cars in certain countries, could financially justify use of the aircraft by airlines and

compensate for the decrease in payload. Since a fully electric propelled airliner is not likely to fly

for several decades, a hybrid-airliner would be a suitable alternative for the transition period from

fossil fuels to electric energy.


iv

TABLE OF CONTENTS

Abstract .............................................................................................................................................. iii

Table of contents ............................................................................................................................... iv

List of Figures .................................................................................................................................... vii

List of Tables ....................................................................................................................................... ix

Nomenclature .................................................................................................................................... xi

1 Introduction ............................................................................................................................... 1

2 The Airbus A340-600 .................................................................................................................. 2

2.1 History and Background ..................................................................................................... 2

2.2 Development of the Airbus A340-600 ............................................................................... 3

2.3 Data .................................................................................................................................... 4

2.4 Rolls-Royce Trent 556 ........................................................................................................ 6

2.5 The Thrust Lever................................................................................................................. 7

2.6 High Lift Devices ................................................................................................................. 8

3 Performance ............................................................................................................................... 9

3.1 Zero lift drag ....................................................................................................................... 9

3.1.1 Wing Reference Area ................................................................................................. 9

3.1.2 Wetted area ............................................................................................................... 9

3.1.3 Component Buildup Method ................................................................................... 12

3.1.4 Howe's Method ........................................................................................................ 16

3.1.5 Equivalent Skin Friction Method .............................................................................. 16

3.1.6 Result, Comparison and Conclusion ......................................................................... 17

3.2 -factor ............................................................................................................................ 17

3.2.1 Raymer: Oswald Span Efficiency Method ................................................................ 17

3.2.2 Howe's Method ........................................................................................................ 18

3.2.3 Frost and Rutherford method .................................................................................. 18

3.2.4 Result Comparison Conclusion ................................................................................. 19

3.2.5 Polar break ............................................................................................................... 19

3.3 Airspeed ........................................................................................................................... 22

3.4 Initial Climb Speed............................................................................................................ 22


v

3.5 Thrust Lapse Rate ............................................................................................................. 23

3.5.1 Reference Values ...................................................................................................... 24

3.5.2 Models ...................................................................................................................... 25

3.5.3 Evaluation ................................................................................................................. 26

3.5.4 Conclusion ................................................................................................................ 27

3.6 Maximum Climb Thrust .................................................................................................... 28

3.7 Optimum Cruise Altitude ................................................................................................. 31

3.8 Fuel planning .................................................................................................................... 32

3.9 Payload Range Diagram ................................................................................................... 35

4 Model ....................................................................................................................................... 37

4.1 Taxi and Take-off (T/O) .................................................................................................... 39

4.2 Climb (CLB) ....................................................................................................................... 39

4.3 Cruise (CRZ) ...................................................................................................................... 43

4.4 Descent (DES) ................................................................................................................... 46

4.5 Go-Around (GA) ................................................................................................................ 47

4.6 Flight to alternate ............................................................................................................. 47

4.7 Hold (HLD) ........................................................................................................................ 47

4.8 Summary .......................................................................................................................... 48

5 Electric Propulsion.................................................................................................................... 51

5.1 Electric Flight .................................................................................................................... 51

5.2 The Electric Propulsion System ........................................................................................ 52

5.2.1 Fan ............................................................................................................................ 53

5.2.2 Electric Engine .......................................................................................................... 53

5.2.3 Control unit and wiring ............................................................................................ 54

5.2.4 Power Supply............................................................................................................ 55

5.2.5 Efficiency .................................................................................................................. 57

6 The Hybrid Electric Powered Long Range Airliner ................................................................... 58

6.1 Analysis ............................................................................................................................. 58

6.2 Electric Engine Ratio Optimization ................................................................................... 62

6.3 Performance Analysis ....................................................................................................... 71

6.3.1 Payload Range .......................................................................................................... 76


vi

7 Financial Justification ............................................................................................................... 79

8 General Conclusion and Outlook ............................................................................................. 82

9 Bibliography ............................................................................................................................. 84

10 Appendix A Thrust Model ................................................................................................. 86

11 Appendix B Matlab Code ................................................................................................... 87

12 Appendix C Colour Plots .................................................................................................... 89


vii

LIST OF FIGURES

Figure 2-1. The Airbus A340-300 ........................................................................................................ 3

Figure 2-2. Airbus A340-600 3-view drawing with dimensions. ........................................................ 4

Figure 2-3. The Rolls Royce Trent 556. ............................................................................................... 6

Figure 2-4. Thrust Lever ..................................................................................................................... 7

Figure 3-1. Engine dimension definitions. ........................................................................................ 11

Figure 3-2. Pie chart of the wetted areas of the different components. ......................................... 12

Figure 3-3. R factor for the Frost and Rutherford method. ............................................................. 18

Figure 3-4. Stalling speeds Airbus A340-642. ................................................................................... 20

Figure 3-5. Maximum lift coefficient for different settings of the high lift devices, weights and altitude. .. 21

Figure 3-6. CL as a function of Mach number. ................................................................................. 22

Figure 3-7. Example of manufacturers uninstalled engine performance data for a subsonic turbofan. ..... 23

Figure 3-8. Maximum Climb Thrust according to BADA. ................................................................. 24

Figure 3-9. Comparison of thrust Lapse rate models. ...................................................................... 27

Figure 3-10. Change of thrust with Mach number during take-off ................................................. 28

Figure 3-11. Thrust lapse rate after T/O. ......................................................................................... 28

Figure 3-12. Maximum climb thrust as a function of Mach number and altitude. ......................... 30

Figure 3-13. Error in Maximum Climb Thrust model ....................................................................... 30

Figure 3-14. Optimum Cruise Altitude @ M0.83. ............................................................................ 31

Figure 3-15. Optimum altitude is presented at any given velocity and weight. .............................. 32

Figure 3-16. Payload Range diagram. .............................................................................................. 36

Figure 4-1. Flight profile for model. ................................................................................................. 37

Figure 4-2. 5700NM great circle range from Munich (EDDM), Germany ........................................ 38

Figure 4-3. Climb profile for a climb to FL320 with speed profile 250/320/M0.82 and cruise at

M0.85. .............................................................................................................................................. 40

Figure 4-4. Velocity, fuel flow (all engines), altitude and mass during the climb phase. ................ 43

Figure 4-5. Step-climb profiles. ........................................................................................................ 44

Figure 4-6. Velocity, fuel flow, altitude and mass during cruise. ..................................................... 45

Figure 4-7. Altitude for entire flight. ................................................................................................ 48

Figure 4-8. Fuel flow entire flight for all engines. ............................................................................ 49

Figure 4-9. Climb angle during beginning and end of flight. ............................................................ 49

Figure 4-10. Lift coefficient during entire flight. .............................................................................. 50

Figure 5-1. The e-Genius. ................................................................................................................. 51

Figure 5-2. The EADS VoltAir and Boeings SUGAR Volt ................................................................... 52

Figure 5-3. Simplified schematic and segmentation of the electric propulsion system. ................. 52

Figure 5-4. Power out-put per engine for model flight. ................................................................... 53

Figure 5-5. Selected volumetric and weight energy densities. ........................................................ 55

Figure 5-6. Energy density vs. power density. ................................................................................. 56


viii

Figure 6-1. Maximum available Thrust and the Thrust Required. ................................................... 58

Figure 6-2. Electric energy required EElec for different electric propulsion ratios. ........................... 60

Figure 6-3. Fuel saved for different electric propulsion ratios. ....................................................... 60

Figure 6-4. Required electric power ................................................................................................. 61

Figure 6-5. Required electric power for T/O, Step Climb and Go-Around. ...................................... 61

Figure 6-6. Power Setting Conventional Engines ............................................................................. 62

Figure 6-7. Electric engine mass ....................................................................................................... 64

Figure 6-8. Example of Battery and Capacitor use depending on characteristics of power curve. . 65

Figure 6-9. Battery and capacitor mass. .......................................................................................... 67

Figure 6-10. Mass change from electric propulsion. ........................................................................ 68

Figure 6-11. Additional weight required to increase electric propulsion with 1 percentage point. 69

Figure 6-12. The two design points for electric to conventional thrust ratio. ................................. 70

Figure 6-13. Mass distribution with electric propulsion. ................................................................. 70

Figure 6-14. Comparison of Altitude profile for conventional and hybrid aircraft. ......................... 73

Figure 6-15. Climb performance comparison of conventional and hybrid aircraft. ........................ 73

Figure 6-16. Thrust produced by electric and conventional engines at 30.5% electric. .................. 74

Figure 6-17 Thrust produced by electric and conventional engines at 36.5% electric. ................... 74

Figure 6-18. Thrust produced by electric and conventional engines at 40.5% electric. .................. 74

Figure 6-19. Detailed view of thrust produced by electric and conventional engines during ......... 75

Figure 6-20. Power setting of electric and conventional engine. .................................................... 75

Figure 6-21. Hybrid Airliner Payload Range Diagram ....................................................................... 77

Figure 6-22. Detailed view of Hybrid Airliner Payload Range Diagram ........................................... 78

Figure 12-1. Comparison of thrust Lapse rate models. .................................................................... 89

Figure 12-2. Climb profile for a climb to FL320 with speed profile 250/320/M0.82 and cruise at M0.85. .. 89

Figure 12-3. Step-climb profiles. ...................................................................................................... 90

Figure 12-4. Required electric power ............................................................................................... 90

Figure 12-5. Required electric power for T/O, Step Climb and Go-Around. .................................... 91

Figure 12-6. Power Setting Conventional Engines ........................................................................... 91

Figure 12-7. Mass change from electric propulsion. ........................................................................ 92

Figure 12-8. Mass distribution with electric propulsion. ................................................................. 92

Figure 12-9. Comparison of Altitude profile for conventional and hybrid aircraft. ......................... 93

Figure 12-10. Power setting of electric and conventional engine. .................................................. 93

Figure 12-11. Hybrid Airliner Payload Range Diagram ..................................................................... 94

Figure 12-12. Detailed view of Hybrid Airliner Payload Range Diagram ......................................... 94


ix

LIST OF TABLES

Table 2-1. Basic Aircraft Data ............................................................................................................. 5

Table 2-2. RR Trent 556 Engine data. ................................................................................................. 6

Table 2-3. Flaps and slats configurations ........................................................................................... 8

Table 3-1. Reference values for zero-lift-drag calculations ............................................................... 9

Table 3-2. Wetted area of each aircraft component. ...................................................................... 11

Table 3-3. Input variables and results for calculating the skin friction coefficient. ......................... 14

Table 3-4. Raw data, equations and results of form factor calculations. ........................................ 15

Table 3-5. Component interference factor. ..................................................................................... 15

Table 3-6. In-data for zero-lift-drag coefficient calculations according to Howe. ........................... 16

Table 3-7. Results for Zero-lift-drag calculated using different methods. ....................................... 17

Table 3-8. Results for K-factor .......................................................................................................... 19

Table 3-9. Altitude and Mach number for BADA Model .................................................................. 24

Table 3-10. Constants for calculating the thrust lapse rate according to the method by Howe. .... 26

Table 3-11. Thrust lapse rate model error. ...................................................................................... 27

Table 3-12. Division of thrust spectrum. .......................................................................................... 29

Table 3-13. Equation coefficients for the maximum climb thrust model. ....................................... 29

Table 3-14. Fuel Reserves. ............................................................................................................... 34

Table 3-15. Summary of fuel on-board. ........................................................................................... 35

Table 3-16. Numerical values for initial and final masses for payload vs. range calculations. ........ 35

Table 4-1. Climb 1 parameters. ........................................................................................................ 40

Table 4-2. Acceleration 1 parameters. ............................................................................................. 41






Table 4-8. Time, distance flown, fuel burnt and mass after climb phase. ....................................... 43

Table 4-9. Cruise parameters ........................................................................................................... 45

Table 4-10. Step climb parameters .................................................................................................. 45

Table 4-11. Time, distance flown, fuel burnt and mass after cruise phase. .................................... 45

Table 4-12. Descent parameters. ..................................................................................................... 46

Table 4-13. Time, distance flown, fuel burnt and mass after descent phase. ................................. 46

Table 4-14. Go-around parameters ................................................................................................. 47

Table 4-15. Hold climb parameters .................................................................................................. 47

Table 4-16. Time, distance flown, fuel burnt during Holding. ......................................................... 48

Table 6-1. Engine and Energy/Power source weights. ..................................................................... 71

Table 6-2. Fuel Reserves................................................................................................................... 71


x

Table 6-3. Summary of fuel on-board and the Top of Descent weight. ........................................... 72

Table 6-4. Basic Performance Data comparing the Hybrid and Conventional Airliner. ................... 72

Table 6-5. Energy and Power required from electric engines. ........................................................ 76

Table 6-6. Hybrid Airliner TOW and TOD mass for Payload Range calculations .............................. 76

Table 6-7. Hybrid Airliner Payload Range numerical values ............................................................ 77

Table 7-1. Cost of replacing 1kg kerosene with batteries ................................................................ 80


xi

NOMENCLATURE

Symbol Unit

A Area m

A Aspect Ratio -

b0 Specific Fuel Consumption kg/Ns

c Cord m

c Speed of sound m/s

c0 Speed of sound at mean sea level m/s

cD Drag coefficient -

cD0 Zero-lift-drag coefficient -

cL Lift coefficient -

CL Lift coefficient curve gradient -

d Diameter m

D Drag N

E Energy Ws

F Fuel kg

FF Fuel Flow kg/s

FL Flight level -

g Gravitational constant m/s

h Altitude m

l Length m

L Lift N

M Mach number -

m Mass kg

p Air Pressure at current altitude Pa

P Payload kg

P

p0

Power

Reference air pressure at mean sea level

W

Pa

Re Reynolds number -

S Area m

Sref Wing reference area m

Swet Wetted Area m2

(t/c) Airfoil Relative Thickness -

T Thrust N

T0 Thrust at mean sea level (ISA) N

VIAS Indicated Airspeed m/s

VTAS True Airspeed m/s

W Weight N


xii

Wf Final weight N

Wi Initial weight N

Greek Unit

Climb angle

T Power setting -

Efficiency -

Temperature K

0 Reference temperature at mean sea level K

Taper ratio -

Wing Sweep

Dynamic viscosity Ns/m2

Air density kg/m

0 Reference air density at mean sea level kg/m

Indices

( )50% chord line

( )CLB Climb

( )cont Continuous

( )conv Conventional

( )CRZ Cruise

( )DES Descent

( )e Engine

( )elec Electric

( )em Engine mount

( )f Fuselage

( )ftf Flap track fairing

( )HLD Hold

( )hs Horizontal stabiliser

( )lam Laminar

( )max Maximum

( )MCL Maximum Climb Thrust

( )min Minimum

( )r Root

( )t Tip

( )T/O Take-off

( )turb Turbulent

( )vs Vertical stabiliser

( )w Wing

( )wl Winglet


xiii

()wet Wetted

Abbreviations

A/C Aircraft

C-Eng Conventional Engine

CLB Climb

CRZ Cruise

DES Descent

E-Eng Electric engine

GA Go-Around

HLD Holding

ISA International Standard Atmosphere

KCAS Knots calibrated airspeed

KIAS Knots indicated airspeed

KTAS Knots true airspeed

lam Laminar

MAC Mean Aerodynamic cord

MTOW Maximum Take-off Weight

MZFW Maximum Zero Fuel Weight

OWE Operating Weight empty

SEP Specific excess power

T/O Take-Off

TOC Top of Climb

TOD Top of Descent

turb Turbulent


1

1 INTRODUCTION Fully electric propulsion can already be seen in operation in a handful of smaller aircrafts flying in

the skies today. The concept of electric propulsion would also be an appealing technology in

commercial aviation considering its various advantages with regard to sustainability,

environmental impact, reliability and maintenance. However, the current state of technological

advancement in the field of batteries and energy storage makes the concept of fully electrical

airliners feasible only in the far future. Conversely, the automotive industry has successfully

launched several hybrid propulsion systems on to the market. These electric-hybrid systems could

serve as a great concept and inspiration for the future in aviation. The scope of this thesis is to

investigate the feasibility of an electric-hybrid propulsion system for an Airbus A340-600 on a

long-haul flight and its effect on the aircraft performance.

At first, an analysis will be done of the reference aircraft, A340-600, using conventional propulsion

to determine required data to model and analyse a long-haul mission of the aircraft. Next, a

5700 nm flight will be modelled to determine performance data such as the power and thrust

requirements during the different flight phases. Thereafter, the flight phases will be identified

where electric propulsion would be plausible. Also, the amount of additional weight from the

hybrid system has to be determined and the ratio between conventional and electric propulsion.

Further, possibilities for the incorporation of the hybrid electric system with the conventional

system will be investigated. Once an optimal ratio of electric to conventional thrust has been

determined, a detailed performance analysis of the new hybrid electric aircraft will be conducted.


2

2 THE AIRBUS A340-600 2.1 HISTORY AND BACKGROUND

The idea for the Airbus Industry consortium came to be from a decision to challenge the American

domination of the airliner market. The idea arose in the mid-1960s after major European airlines

had shown interest for a short to medium range airliner that could carry over 100 passengers at

low costs. In 1967, ministers from Germany, France and the United Kingdom had agreed at a

meeting that for the purpose of strengthening European co-operation in the field of aviation

technology and thereby promoting economic and technological progress in Europe, to take

appropriate measures for the joint development and production of an airbus1. The official birth of

the Airbus programme took place on the 29th of May 1969 at Paris Le Bourget Airshow, when the

German economics minister, Karl Schiller, and the French transportation minister, Jean Chamant,

signed an agreement for the go-ahead of the A300 programme. This aircraft would be the first

twin-engine wide-body passenger jet aircraft and was sought to satisfy the recent interest shown

by European airlines. The construction of the aircraft was to be done by the German-French

consortium and also involve the United Kingdom and the Netherlands.

Airbus industry was officially founded as Groupement dInteret conomique (Economic Interest

Group) on the 18th of December 1970 by a government initiative between France, Germany and

the United Kingdom. The name Airbus was coined by the industry for passenger aircrafts or an

airliner of a certain range and size. Initially, about three quarters of the share of the production

work were divided between Deutsche Airbus and Arospatiale. Hawker Siddeley, in turn, acquired

one fifth and the rest went to Fokker-VFW. These four companies would deliver their sections as

fully equipped ready-to-fly parts. In 1971, the Spanish company CASA and in 1977, British

Aerospace joined as shareholders.

The A300 completed its maiden flight in 1972 and the first production model, the A300B2,

entered commercial service in 1974. Initially, the consortium had little success, but by 1979

eighty-one of their aircrafts were being flown world-wide. Soon thereafter, Airbus launched the

A310, a shortened version of the A300. Following the success of the A300 and the A310, Airbus

decided to get into direct competition with its American rivals. The launching of the short- and

midrange single-aisle airliner, the A320, was a major success with over 400 units sold even before

the aircraft took to the air. It was also the first commercial aircraft fitted with a fly-by-wire

system. With this new technology in place, Airbus subsequently introduced several developments

of the A320, the shortened A319 as well as the A318, the elongated A321 and various corporate

1 Airbus Mission Statement, "Airbus history". Flight International (Reed Business Publishing). 29 October

1997.


3

jet models. Airbus became particularly known for their fly-by-wire technology and their concept

of cockpit communality, making crew training easier.

2.2 DEVELOPMENT OF THE AIRBUS A340-600

The first surveys were conducted in 1981 and in 1987 the A340 project was launched. Its goal was

to develop a long-range airliner complementing the mid-range A300 and the short-range A320. A

series of factors motivate the development of this new aircraft. On one hand, the 60 minute

ETOPS regulation of that time meant a large disadvantage for Airbus twin-engine aircrafts

compared to its three- and four-engine competitors. On the other hand, the popular Douglas

Corporation DC-10 and Lockheed Tristar L1011 were being phased out and airlines were looking

for replacements.

The A340 and the A330 were designed concurrently. They received the same fuselage and wing,

but also much of the avionics originally designed for the A320. The first prototypes of both

aircrafts, which were also the first ones built with composite materials, were manufactured on the

same production line.

The first A340 completed its maiden flight on the 25th of October 1991 and the A340-200 and -

300 entered into service in 1993 in the colours of Lufthansa and Air France. Due to the high

similarities between the cockpits of A320, A330 and A340, pilots, who had previously flown the

A320, could be retrained to fly on the new models at a minimal cost and time.

Figure 2-1. The Airbus A340-300

The A340-600 was initially designed as a competitor to the Boeing 747. It possessed similar

passenger capacity as its Boeing rival, but could carry more payload and had lower operating

costs. It was an enhancement of the A340-300 with an extra twelve metres in length and an

additional four-wheel under-carriage on the centreline of the fuselage, in order to cope with the

additional weight.

The aircraft is powered by four Rolls-Royce Trent 556 turbofan engines, described in section 2.4

below. After its maiden flight in 2001, the A340-600 entered into service in 2002 for Virgin


4

Atlantic Airways. In terms of length of fuselage, it is the second longest commercial airliner only

recently surpassed by the Boeing 747-8i. A total of 97 units of the A340-600s have been delivered

until now. In November 2011 Airbus announced that it would cease production of the Airbus A340

family but assured that it would continue to fully support the current global fleet.

2.3 DATA

The focus of this thesis will be on Airbus A340-642. Since different variations exist even within this

model specification, significant data used throughout the project is presented in this section. The

figure below shows a three-view drawing2 of the aircraft with the most important measurements.

Figure 2-2. Airbus A340-600 3-view drawing with dimensions.

2 Airbus A340-600 Flight Crew Operating Manual, 1.20.20 P1


5

In the table below significant numerical data is summarised of the aircraft.

Fuse

lage

Length 75.24 m

Width 5.64 m

Cockpit Crew 2

Maximum Seats (w/ over-wing exit) 475

Win

g

Area 437.3 m2

Span (w/o winglets) 61.20 m

MAC 8.35 m

Aspect Ratio 8.56

Taper Ratio 0.22

(t/c)tip 8.2 %

(t/c)average 10 %

(t/c)root 13.2%

Leading Edge Sweep 31.1

Chord Sweep 28

Ho

rizo

nta

l sta

bili

ser Area 93 m2

Span 21.5 m

Aspect Ratio 4.97

Taper Ratio 0.36

Leading Edge Sweep 30

Chord Sweep 27

Ver

tica

l sta

bili

ser

Area 47.65 m2

Height 9.44 m

Aspect Ratio 1.87

Taper Ratio 0.350

Leading Edge Sweep 45

Chord Sweep 40

Mas

s

Maximum Take-off Mass 368 000 kg

Maximum Zero Fuel Mass 245 000 kg

Operating Mass Empty 177 000 kg

Maximum Fuel Capacity 193 925 l

Maximum Payload 68 000 kg

Maximum Landing Mass 256 000 kg

Ran

ge

Maximum Payload Range 5700 NM

Design Range 7500 NM

Maximum Fuel Range 7800 NM

Ferry Range 8800 NM

Table 2-1. Basic Aircraft Data


6

2.4 ROLLS-ROYCE TRENT 556

In 1995, as Airbus was developing the two new long-range derivatives of the A340 aircraft, the

A340-500 and A340-600, it started a search for a new engine. The existing CFM International

CFM56 engine, which had powered the A340-200/-300, was at the limit of its developmental

capability and would not be sufficient for the power requirements of the new -500 and -600

models. Despite first signing an agreement with General Electric in 1996 to develop a suitable

engine, Airbus subsequently decided to withdraw, after that GE demanded an exclusivity deal for

the new aircraft. At the 1997 Paris Airshow, Airbus announced that it had selected the Trent 500

to power the A340-500 and -600 over a Pratt & Whitney model that was also under consideration.

The first test run of the Trent 500 was conducted in May 1999 and certification was achieved in

December 2000. It entered service with the inaugural commercial flight of the A340-600 with

Virgin Atlantic Airways in July 2002.

Figure 2-3. The Rolls Royce Trent 556.

The Airbus A340-500 and A340-600 are powered by the Trent 500 engines, which were certified

for 270 kN thrust, but derated to 249 kN as the Trent 556 for the A340-600.

In the table below the most important engine data is summarised.

Size

Length 4.689 m

Width 3.374 m

Fan Diameter 2.474 m

Dry Weight (excl. Nacelle) 4990 kg

Thru

st Maximum Take-off Thrust 260 000 N

Maximum Continuous Thrust 197 300 N

Specific fuel consumption in cruise b0 1.6210-5 kg/Ns

Overall Pressure Ratio 36.3:1

Bypass Ratio 7.6:1

Turbine Gas Temp. Max. T/O 900 C

Turbine Gas Temp. Max. Cont. 850 C

Table 2-2. RR Trent 556 Engine data.


7

2.5 THE THRUST LEVER

The thrust produced by each power-plant is controlled by a Full Authority Digital Engine Control

(FADEC) system. This is a digital control system that is in charge of the complete engine

management. Generally, when the aircraft is flown, the pilot does not set a specific power setting

using the thrust lever, but instead uses the thrust lever to set a specific range for the thrust and

the FADEC system then freely regulates the thrust within this upper and lower limit. There are

four main setting:

- TO GA - Take Off, Go Around

- FLX/MCT - Flex, Maximum Continuous

- CL - Climb

- IDLE - Idle

In the figure below, the settings and the ranges within which the FADEC can vary the thrust, are

visualised.

Figure 2-4. Thrust Lever


8

2.6 HIGH LIFT DEVICES

On each of its wings, the A340-600 is fitted with two flap surfaces and seven slat surfaces and also

has the ability to droop its ailerons. There are five settings that can be chosen from the flaps lever

in the cockpit: 0, 1, 2, 3 and FULL. Depending on the speed of the aircraft, when flaps setting 1 is

selected, the high lift devices will either go into configuration 1 or in configuration 1 + F. The table

below shows the different slats, flaps and aileron settings of the aircraft.

Lever Position

Slats Flaps Ailerons Indication Flight Phase

0 0 0 0 0

CRZ

1 21 0 0 1 HLD

17 10 1 + F T/O

2 24 17 10 2

APPR 24 22 10 2 T/O

3 24 29 10 3 LDG

FULL 24 34 10 FULL Table 2-3. Flaps and slats configurations

Further reference to a specific flap setting will be done naming the indication, i.e. 0, 1, 1+ F, etc....


9

3 PERFORMANCE 3.1 ZERO LIFT DRAG

For accurate performance calculations it is important to calculate a value for the

zero-lift-drag (CD0). This is done using several different methods for redundancy. In order to allow

for a comparison of the different methods used, a reference state is defined where the aircraft is

cruising at FL 390 with Mach 0.83 under standard atmospheric (ISA) conditions; reference values

for this specific state are given in the table below.

VTAS M h p T

244.9 m/s 0.83 39000 ft 0.3162 kg/m3 19664 pa -56.5 C 1.432310-5 Ns/m2

Table 3-1. Reference values for zero-lift-drag calculations

3.1.1 Wing Reference Area

The wing reference area is calculated from a three-view drawing using the Airbus Method, which

approximates the contribution from the fuselage to the wing reference area as a rectangle. The

wing reference area is:

Sref = 440 m2.

3.1.2 Wetted area

The total wetted area of the aircraft is calculated to be:

Swet = 2460.5 m2

The method for calculating the contributions from the different aircraft components is described

below.

Fuselage

The fuselage's wetted area is given by3:

(

)

(

) (3-1)

where .

3 (Torenbeek, 1982) eq. B-6


10

Wing

The wetted area of the wing is given by4:

( (

)

) (3-2)

where and ( ) ( ) . The exposed wing area Sw is measured from a

three-view drawing of the aircraft.

Horizontal stabiliser

As for the wing, equation (3-2) is used to calculate the wetted area of the horizontal stabiliser.

However, it is assumed that = = 1 since no accurate values where obtained for the relative

thickness of the airfoil's tip and root. This gives the following equation:

( (

) ) (3-3)

The exposed horizontal stabiliser area Shs is measured from a three-view drawing of the aircraft.

Vertical stabiliser

The wetted area of the vertical stabiliser is calculated in the same way as for the horizontal

stabiliser using equation (3-3). The exposed vertical stabiliser area Svs is measured from a three-

view drawing of the aircraft.

Winglet

The wetted area of the winglets is calculated in the same way as for the horizontal stabiliser

using equation (3-3). The exposed winglet area Swl is measured from a three-view drawing of the

aircraft.

Engine

The wetted area of the engine (excluding the engine pylon) is found using the following formula5:

[

( )

]

[

(

) ( (

)

)]

(3-4)

4 (Torenbeek, 1982) eq. B-11

5 (Torenbeek, 1982) eq. B-13, B-14, B-15,


11

The symbols and engine dimensions are defined in the figure below.

Figure 3-1. Engine dimension definitions.

Engine mount

The wetted area of the engine mount is measured from a three-view drawing of the aircraft.

Flap track fairing

The wetted area of the flap track fairing is measured from a three-view drawing of the aircraft.

Summary

Component Raw data Swet

Fuselage lf df

= 73.46 m = 5.64 m

1033.7 m2

Wing Sw (t/c)t (t/c)r

= 370.96 m2 = 0.0822 = 0.1323

764.78 m2

Horizontal stabiliser Shs (t/c)

= 98.1 m2 = 0.088

200.52 m2

Vertical stabiliser Svs (t/c)

= 51.4 m2 = 0.088

105.06 m2

Engine (each)

Dn

Dh ln lg lp

Dp Deg Dg Def

= 2.90 m = 3.40 m = 5.30 m = 1.50 m = 1.25 m = 0.302 = 1.00 m = 1.50 m = 2.10 m = 2.90 m

57.33 m2

Winglets Swl (t/c)r

= 2.15 m2 = 0.087

8.79 m2

Engine mount (each)

17.01 m2

Flap track fairing (each)

4.4 m2

TOTAL 2460.5 m2 Table 3-2. Wetted area of each aircraft component.


12

The figure below shows the ratios of the wetted areas of the different components.

Figure 3-2. Pie chart of the wetted areas of the different components.

3.1.3 Component Buildup Method

The first method used is the component buildup method6. A flatplate skin friction coefficient is

calculated for each component of the aircraft along with a form factor FF that incorporates the

pressure drag caused by viscous separation. The product of these two terms, the wetted area and

a component interference factor , estimating interference effects, gives the components

contribution to the total drag. An additional term, takes into account additional drags

caused by unretracted landing gear, flaps, etc. Further, CDL&P incorporates additional drag due to

leakage and protuberances. The zero lift drag is given by:

( ) ( )

(3-5)

where the subscript c means the value is component specific.

The aircraft is divided into the following components for the calculations:

- Fuselage

- Wing

- Horizontal stabiliser

- Vertical stabiliser

- Engine

- Winglets

- Engine mount

- Flap track fairing

6 (Raymer, 2006) chapter 12.5

42%

31%

< 1%1%

3%

4%

8%

10%

Fuselage

Wing

Winglets

Flap Track Fairing

Eingne Pylon

Vert. Stabiliser

Horiz. Stabiliser

Engine

Fuselage

Wing

Engine Horizontal Stabiliser

Vertical Stabiliser

Engine Pylon Flap Track Fairing Winglets


13

3.1.3.1 Flat-Plate Skin Friction Coefficient (Cf)

The flat-plate skin friction coefficient for laminar flow is expressed by:

(3-6)

and for turbulent flow:

( ) ( )

(3-7)

where is the non-dimensional Reynolds number defined as:

(3-8)

where is the characteristic length defined for each component in the 2nd column of Table 3-3.

The dynamic viscosity is given by Sutherland's formula as follows:

( )

(

)

(3-9)

where

T is the input temperature

0 is the reference viscosity at reference temperature T0, 0 = 18.2710-6 Ns/m2

T0 is the reference temperature, T0 = 291.15 K

C is the Sutherland's constant, C = 120

Since the flat-plate skin friction coefficient is also affected by surface roughness, the value for Cf

might be inaccurate for very rough surfaces if is defined by equation (3-8). Consequently, a cut

off Reynolds number, which takes into account the skin roughness, is calculated and the smaller of

the two Reynolds numbers is used. The cutoff Reynolds number for subsonic flight is defined as:

( )

(3-10)

where is the skin roughness value. For a smooth paint surface it is given as7 .

Since the flow over the different aircraft components can be both laminar and turbulent the final

skin friction coefficient is defined taking into account the ratio between the laminar and the

turbulent flow.

( ) (3-11)

7 (Raymer, 2006) Table 12.4


14

where is defined as the fraction of the length of the component that has laminar flow over

it.

The numerical calculated values for the flat plate skin-friction coefficient for the different

components are presented in the table below.

Component Characteristic

length R

[106] Rcutoff

[106] klam Cflam

[10-3]

Cfturb [10-3]

Cf [10-3]

Fuselage Length 73.46 m 397.16 986.31 0.1 0.0666 1.661 1.661 Wing MAC 8.37 m 45.23 100.11 0.3 0.1975 2.242 2.038 Horizontal stabiliser

MAC 4.63 m 25.01 53.63 0.2 0.2656 2.449 2.231

Vertical stabiliser

MAC 6.27 m 33.89 73.87 0.2 0.2281 2.340 2.129

Engine Length 6.69 m 36.14 79.05 0.0 0.2209 2.318 2.318 Winglets MAC 1.50 m 8.11 16.39 0.2 0.4663 2.922 2.676 Engine mount Length 6.54 m 35.36 77.24 0.0 0.2233 2.325 2.325 Flap track fairing Length 5.75 m 31.087 67.45 0.0 0.2382 2.370 2.370 Table 3-3. Input variables and results for calculating the skin friction coefficient.

It can be noted that the Reynolds number was smaller than the cutoff Reynolds number for every

component and was hence used in the calculation.

3.1.3.2 Component Form Factor (FF)

The form factor is given by the following equations for the corresponding components:

- wing, horizontal & vertical stabiliser, strut, pylon

[

( ) (

) (

)

] [ ( ) ] (3-12)

- fuselage and smooth canopy

(

) (3-13)

- Nacelle and smooth external store

(

) (3-14)

where

( ) (3-15)

where Amax is the maximum cross-section area, ( ) is the relative point of maximum thickness

of the airfoil along its cord and m is the wing sweep at the line of maximum thickness.


15

The numerical calculated values for the form factor along with the relevant in-data and the

equations used are presented in the table below.

Component Raw data Equation FF

Fuselage lf

df

= 73.46 m

= 5.64 m

(3-13) 10.597

Wing (x/c)max

(t/c)

m

= 0.3

= 0.1

= 31

(3-12) 15.017

Horizontal

Stabiliser

(x/c)max

(t/c)

m

= 0.3

= 0.088

= 29.9

(3-12) 14.716

Vertical

Stabiliser

(x/c)max

(t/c)

m

= 0.3

= 0.088

= 39.5

(3-12) 14.244

Engine lf

df

= 6.685 m

= 3.1 m

(3-14) 11.623

Winglets (x/c)max

(t/c)

m

= 0.3

= 0.087

= 40

(3-12) 14.188

Engine mount lem

dem

= 6.54

= 0.6

(3-14) 1.021

Flap track

fairing

lftf

dftf

= 5.75

= 0.75

(3-14) 10.457

Table 3-4. Raw data, equations and results of form factor calculations.

Since, data concerning the point of maximum thickness could not be obtained; this value was

approximated to 0.3, which is a common value for subsonic airfoils.

3.1.3.3 Component interference factor (Q)

The component interference factor Q incorporates the additional drag resulted by the

interference effect components have on each other. Interference factors for the different

components are displayed in the table below.8

Component Fuselage Wing Horizontal stabiliser

Vertical stabiliser

Engine Winglets Engine mount

Flap track fairing

Interference factor

1.0 1.0 1.03 1.03 1.3 1.03 1.5 1.5

Table 3-5. Component interference factor.

3.1.3.4 Result

Substituting the results from the sections above into equation (3-5) yields a zero-lift-drag

coefficient for the reference state of CD0 = 0.0146.

8 (Raymer, 2006) p. 332


16

3.1.4 Howe's Method

The second method used approximates the zero-lift-drag as9:

(

)

[

[ ( )

(

)

]

]

(3-16)

where, Af is an airfoil factor dependent on the airfoil design cl is the fraction of chord of the wing over which the flow is laminar

1/4 is the wing sweep at the cord line Rw is a factor given by the ratio of Sref and Swet Tf is a factor incorporating deviation from the streamlined ideal shape is a correction factor for wing thickness given by the following equation:

[

( (

)

)] (3-17)

The type factor variable is given as10 Tf = 1.1. The fraction of chord of the wing over which the flow

is laminar has been approximated to be 10%. The airfoil factor is given as11:

(3-18)

where, AF is 0.95 for a modern airfoil12 and the lift-coefficient is calculated for the current cruise

flight conditions using equation (3-49) to be CL = 0.523.

The numerical values of the variables used in the equation (3-18) above are given in the table

below.

Af M cl Sref 1/4 t/c Rw Tf

0.90 0.83 0.1 440 m2 28 0.1 5.20 1.1

Table 3-6. In-data for zero-lift-drag coefficient calculations according to Howe.

The above values substituted into formula (3-17), (3-18) and then (3-16) yield CD0 = 0.0145.

3.1.5 Equivalent Skin Friction Method

The equivalent skin friction method approximates the zero-lift-drag using the following formula:

(3-19)

For a commercial airliners Cfe= 0.003013. Using Sref and Swet calculated in section 3.1.1 and 3.1.2,

the equation above yields CD0=0.0167.

9 (Howe, 2000) eq. 6.13a

10 (Howe, 2000) Table 6.4

11 (Howe, 2000) p 118

12 (Howe, 2000) p 118


17

3.1.6 Result, Comparison and Conclusion

The results from the three different methods above are summarized in the table below.

Component Buildup Method Dennis Howe Equivalent skin friction method

0.0146 0.0145 0.0167

Table 3-7. Results for Zero-lift-drag calculated using different methods.

The component buildup method and the equation by Denis Howe give surprisingly similar result.

Both methods take into account Mach number and component buildup method also takes into

account change with altitude. Therefore for future calculations the component buildup method

will be used. The Equivalent skin friction method is an exceptionally simplified method, which

may explain why its result deviates from the other two methods.

3.2 -FACTOR

The -factor was determined using four different methods. Due to the high velocity of the aircraft

the polar break also has to be taken into consideration.

3.2.1 Raymer: Oswald Span Efficiency Method

This method utilizes the Oswald span efficiency factor, e, and defines as:

(3-20)

where the Oswald span efficiency factor is given by:

( ) (3-21)

and for swept wings ( > 30) by:

( )( )

(3-22)

Equation (3-21) yields e = 0.795, which in turn gives = 0.0468 and equation (3-22) yields

e = 0.516 and = 0.072.

13

(Raymer, 2006) Table 12.3


18

3.2.2 Howe's Method

The -factor is given by the following equation14:

( )

[

( ) ( )

( )

( )

( ) ] (3-23)

where,

Ne is the number of engines that are located over the top surface of the wing

f() is a Taper ratio function given by:

( ) [ ( ) ] (3-24)

As the A340-600 has no engines above the top surface of its wing, Ne = 0, the equations above

yields = 0.0494.

3.2.3 Frost and Rutherford method

This method uses the following formula to calculate the Oswald span efficiency factor15:

( )

(3-25)

Where CL can be calculated as described in section 3.2.5.2 and the suction factor R is given as a

function of (A/cos()) in the figure below, where is the wing sweep.

Figure 3-3. R factor for the Frost and Rutherford method.

Given that (A/cos()) = 2.13, R = 0.94. Equation (3-31) gives CL = 5.45, which in turn gives an

Oswald factor of e = 0.902 using equation (3-25). Using equation (3-20) we get that = 0.0412.

14

(Howe, 2000) eq. 6.14a 15

(Donus, Kirchner, Myrczik, Schubert, & Schwarze, 2006), p33 eq. 4.17


19

3.2.4 Result Comparison Conclusion

The results from the four different methods above are summarized in the table below.

Raymer I Raymer II Howe F & R

0.0468 0.0700 0.0488 0.0412

e 0.7951 0.5312 0.7624 0.9021

Table 3-8. Results for K-factor

If considering the two Raymer methods, the first one is for aircrafts with straight wings, while the

second one is for aircrafts with a larger wing sweep, as the A340. However, the result from the

first method seems more accurate while the value obtained with the second method is

inconsistent with the other values. The method by Howe gives a reasonable answer while offering

simple application into the model being developed in the next section. For further calculations the

method according to Howe will be used.

3.2.5 Polar break

In order to compensate for change in the k-factor at high CL-values the polar break has to be taken

into consideration. The k-factor will increase when the lift coefficient exceeds a specific value CL,PB.

This is approximated by16:

(3-26)

With an average relative thickness of (t/c) = 0.1 the boundary value becomes CL,PB = 0.65. For

cases where the lift coefficient is above this boundary value, the following formula is used in

order to calculate the accurate -factor, which is denoted as 17 :

[

] (3-27)

Where k is the k-factor calculated without taking the polar break effect into account. How CLmax

and CL are calculated is described in the following two sections below.

3.2.5.1 Maximum lift coefficient CLmax

The maximum lift coefficient CLmax is derived from the aircrafts stall speed.

16

(Hornung, Flugzeugentwurf Vorlesungsskript, 2010), slide 5.30 17

(Hornung, Flugzeugentwurf Vorlesungsskript, 2010), slide 5.31


20

Figure 3-4. Stalling speeds Airbus A340-642.

18

Due to the construction of the fly-by-wire system and the inability to stall the aircraft, instead of

the stall speed, the VS1G speed is given in the charts above. The ratio between the given value and

the true stalling speed is:19

(3-28)

Data points where taken from the figure above and a line of best fit was calculated for the

approximation of stall speed at different aircraft weights and configurations. This is presented in

the equations below:

[

] [

]

[

] [

]

[

] [

]

(3-29)

Where conf. refers to the different flap and slat configurations, see section 2.6. The maximum lift

coefficient can then be calculated by:

(3-30)

The maximum lift coefficient has been plotted in the figure below for different settings of the high

lift devices, weights and altitude.

18

Airbus A340-600 Flight Crew Operating Manual, 3.01.20 P7 19

Airbus A340-600 Flight Crew Operating Manual, 3.04.10 P1


21

Figure 3-5. Maximum lift coefficient for different settings of the high lift devices, weights and altitude.

For configurations when flaps or slats are extended, the maximum lift coefficient is not calculated

for all altitudes since the aircraft normally only flies at lower altitudes when they are extended.

3.2.5.2 Gradient of Lift coefficient curve CL

The gradient of the lift-coefficient vs. angle of attack curve CL is approximated using Polhamus

equation. This equation was chosen because it yields accurate answer at subsonic speeds and the

aircraft is most likely to exceed CL,PB during the climb phase where speeds are low. It defines CL as:

(

)

(3-31)

where,

airfoil efficiency, approximated20 to = 0.95

is a compressibility factor given by:

(3-32)

The figure below shows the calculated values of CL for Mach numbers for 0 to 0.85 using the

equation above.

20

(Raymer, 2006) page 312

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.80

50

100

150

200

250

300

350

400A

ltitude [

FL]

CLmax

CLmax

Conf. 0 @ 360t

Conf. 0 @ 240t

Conf. 1 @ 360t

Conf. 1 @ 240t

Conf. 1+ F @ 360t

Conf. 1+ F @ 240t

Conf. 0 Conf. 1 Conf. 1 +F


22

Figure 3-6. CL as a function of Mach number.

3.3 AIRSPEED

Due to the construction and method used to measure the airspeed of the aircraft, there is

deviation between the airspeed indicated to the pilot in the cockpit (VIAS) and the true airspeed of

the aircraft (VTAS). This is due to deviation in air density with altitude and a buffer effect at high

velocity. There is also a slight instrumental error, however that has been neglected in this case,

hence VIAS = VCAS. The conversion between indicated and true airspeed is done using the following

formula:

[

(

[ (

)

]

)

]

(3-33)

where,

c is the speed of sound [m/s]

c0 is the speed of sound at MSL [m/s]

p is the air pressure [pa]

p0 is the air pressure at MSL [pa]

VIAS is the indicated airspeed [m/s]

3.4 INITIAL CLIMB SPEED

After take-off, according to the FCOM21, the aircraft should fly with a speed of V2 + 10kts. Further,

V2 is defined22 as V2 = 1.2VS. It is assumed that at this stage the high lift devices of the aircraft are

in the 1 + F configuration (see section 2.6). The stall speed has already been calculated in section

3.2.5.1, thus we can define V2 as a function of the aircrafts mass as:

21

Airbus A340-600 Flight Crew Operating Manual, 3.03.62 22

Airbus A340-600 Flight Crew Operating Manual, 3.04.10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91.43

1.44

1.45

1.46

1.47

1.48

1.49

1.5

Mach number

CL


23

( [

] [

])

[

] [

]

(3-34)

3.5 THRUST LAPSE RATE

The thrust that can be produced by a turbofan aircraft engine is a function of altitude and Mach

number. In the figure below the general tendency of this change can be seen for a subsonic

turbofan engine.

Figure 3-7. Example of manufacturers uninstalled engine performance data for a subsonic turbofan

23.

Since no exact performance data could be obtained for the Trent 556 engines, a model has to be

generated to predict the maximum available thrust at different altitudes and Mach numbers. In

the figure above it can be seen that at low altitudes there is a higher dependency on Mach

number, while at higher altitudes thrust is only slightly influenced by the Mach number. Literature

provided very few and also very different methods for modelling the thrust lapse rate. There was

also great difference in complexity. Several different methods are investigated to find the most

suitable one.

23

(Roskam, 1990)


24

3.5.1 Reference Values

Two set of values will be used as reference based upon which the models will be evaluated. It is

assumed that the maximum climb thrust has the same general relation to the Mach number and

altitude as the maximum available thrust and will therefore be used as reference. The first set of

values are the maximum climb thrust values defined in section 3.6. The second reference is the

maximum climb thrust model for ISA conditions24 according to the Base of Aircraft Data (BADA):

( ) (

) (3-35)

where the aircraft specific coefficients are as given below25,

CTc1 = 0.54497 106

CTc2 = 0.57703 105

CTc3 = 0.20155 10-10

These values are defined for a specific set of Mach numbers given in the table below.

FL 0 5 10 15 20 30 40 60 80

Mach 0.28 0.28 0.29 0.30 0.30 0.34 0.39 0.42 0.44

FL 100 120 140 160 180 200 220 240 260

Mach 0.56 0.58 0.60 0.62 0.65 0.67 0.70 0.73 0.75

FL 280 290 310 330 350 370 390 410 415

Mach 0.78 0.80 0.81 0.81 0.81 0.81 0.81 0.81 0.81

Table 3-9. Altitude and Mach number for BADA Model

In the figure below the thrust lapse rate defined by equation (3-35) above can be seen.

Figure 3-8. Maximum Climb Thrust according to BADA.

24

EUROCONTROL EXPERIMENTAL CENTRE, BASE OF AIRCRAFT DATA (BADA) AIRCRAFT PERFORMANCE MODELLING REPORT, EEC Technical/Scientific Report No. 2009-009, Issued: March 2009, table 3-2 25

BADA, Aircraft Performance Operational File, File name: A364__.OPF

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 10

50

100

150

200

250

300

350

400

450

T/T0

Altitude [

FL]


25

3.5.2 Models

Below five different methods are presented for calculating the change of thrust with altitude.

I.

One of the most common approximations is given by:

(

)

(3-36)

where,

n lapse rate factor

No literature gives an exact value for the lapse rate factor but generally states that the values lies

in the range of 0.75-1 depending on engine type. n = 0.85 was assumed.

II. - Nikolai

The following method is similar to the previous one but instead of a lapse rate factor a

temperature coefficient is used. Thrust lapse rate is given by26:

(

) (

) (3-37)

where

is the outside temperature [K]

0 is the air temperature at sea level [K]

III. - Raymer

According to Raymer the lapse rate is a linear function that assumes 100% thrust at sea level and

0% thrust at 55000 ft. It is defined as:

(3-38)

where

C is the thrust gradient, C = 1.8 10-5

h is altitude in feet

26

(Nicolai, 2010) eq. 14.11 p 370


26

IV. - Howe

According to Howe27, the lapse rate is defined as:

( ( ) ) (

)

(3-39)

where the constants K1, K2,K3, K4 and s are given in the table below for a turbofan with a

bypass ratio of 8.

M K1 K1 K1 K1 h s

M < 0.4 1 0 -0.595 -0.03 h < 36100ft 0.7

M > 0.4 0.89 -0.014 -0.3 0.005 h < 36100ft 1

Table 3-10. Constants for calculating the thrust lapse rate according to the method by Howe.

V. - Torenbeek

The following equation is an alteration of an equation by Torenbeek28. It yields results with an

error below 1% for Mach numbers below 0.429. It defines the thrust lapse rate as:

( )

( )

( )

(3-40)

where

(

)

(

)

(

)

and G is the gas generator function, which is given as30 G = 1.1 for high bypass ratios.

3.5.3 Evaluation

Methods I, II and III don't take the effect of Mach number in account. Since it is known that the

accuracy of equation (3-40) is high for the low speeds it will be used to calculate the maximum

thrust for the take-off and methods I-III will only be used to calculate the thrust after this stage,

where Mach number has a less significant effect.

27

(Howe, 2000) eq. 3-7 & table 3.2 28

Assessment of Numerical Models for Thrust and Specific Fuel Consumption for Turbofan Engines, Oliver Schulz, 13.Mrz 2007 29

Assessment of Numerical Models for Thrust and Specific Fuel Consumption for Turbofan Engines, Oliver Schulz, 13.Mrz 2007 30

(Torenbeek, 1982) appendix H


27

The average is taken of the two reference data's and plotted in the figure below along with the

calculated values using the models above.

Figure 3-9. Comparison of thrust Lapse rate models.

The mean absolute error for each method is shown in the table below

I. II. III. IV. V.

2.36 % 1.26 % 3.84 % 21.97 % 22.14 %

Table 3-11. Thrust lapse rate model error.

The most accurate values are given by equation (3-37) when combined with equation (3-40) for

the take-off.

It should be noted that reference values are defined for a specific altitude and Mach number. The

range of speeds in which an airliner operates at a specific altitude is small; this might be the

reason why a simpler model is sufficient and more accurate. While the more complex models

might not be very accurate in the altitude and speed ranges where the aircraft normally flies, it

gives somewhat accurate values in the whole spectrum of speeds and altitudes. The simpler

models are accurate in the ranges where the aircraft normally flies but presumably, due to their

simplicity, give very inaccurate results in other areas, such as low altitude high Mach number or

high altitude low Mach number flight. However, since these are not of interest the simpler

methods become a better choice.

3.5.4 Conclusion

For the model in chapter 4, the thrust during take-off will be calculated using equation (3-40). The

figure below shows the change in thrust with Mach number.

0 1 2 3 4 5 6 7

x 105

0

50

100

150

200

250

300

350

400

450

Thrust

Altitude [

FL]

Refernce

I

II - Nikolai

III - Raymer

IV - Howe

V - Torenbeek


28

Figure 3-10. Change of thrust with Mach number during take-off

After take-off the thrust lapse is modelled using equation (3-37) using the value obtain from

equation (3-40) at the end of take-off as reference. The thrust lapse rate and the temperature

effect as well as the air density effect are shown in the figure below.

Figure 3-11. Thrust lapse rate after T/O.

3.6 MAXIMUM CLIMB THRUST

A model has to be made to determine the maximum climb thrust TMCL. Raw thrust data was

obtained from a software called Piano X. Piano X is a performance software that gives fuel

consumption, environmental emissions, drag and performance characteristics at any range and

payload combination of a specific aircraft. After identifying that the values change with altitude

and Mach number a matrix was created with values for the maximum climb thrust at different

altitudes and Mach numbers (see Appendix A Thrust Model). After analysis of the nature of

0 0.05 0.1 0.15 0.2 0.25

0.75

0.8

0.85

0.9

0.95

1

Mach number

T/T

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

50

100

150

200

250

300

350

400

450

T/T0

Altitude [

FL]

Thrust Lapse Rate

Temperature Effect

Air Density Effect


29

data, it was divided into 6 blocks restricted by the conditions shown in the table below. A

separate model would be generated for each of the six blocks in order to increase accuracy.

Mach Number

0 < M < 0.6 0.6 M

Alt

itu

de

FL 0 h < FL 110 I. IV.

FL 110 h < FL 245 II. V.

FL 245 h III. VI.

Table 3-12. Division of thrust spectrum.

The model is generated by doing multiple linear regressions using the least square method for

each block of data. The general equation of the plane that is fitted to the data is given by:

(3-41)

where the coefficients a, b, c and d have to be found and FL is the flight level. Using Matlab, the

values are found for the coefficients and presented in the table below.

h M

a

[N]

b

[N/100ft]

c

[N]

d

[N/100ft]

I. FL 0 h < FL 110 0 < M < 0.6 67515 -127 -36461 136

II. FL 110 h < FL 245 0 < M < 0.6 70742 -158 -34088 116

III. FL 245 h 0 < M < 0.6 57115 -105 -13252 34

IV. FL 0 h < FL 110 0.6 M 62863 -122 -28708 128

V. FL 110 h < FL 245 0.6 M 65628 -143 -25566 91

VI. FL 245 h 0.6 M 56516 -108 -12253 40

Table 3-13. Equation coefficients for the maximum climb thrust model.

In the figure below the raw data points are displayed along with the calculated plane of best fit.


30

Figure 3-12. Maximum climb thrust as a function of Mach number and altitude.

The figure below shows the per cent error of the mathematical model compared to the raw data.

Figure 3-13. Error in Maximum Climb Thrust model

It can be seen that the model is matched well with data with a maximal error of roughly 1.5%.

050

100150

200250 300

350400 0.4 0.45

0.5 0.550.6 0.65

0.7 0.750.8

150

200

250

300

350

400

450

500

550

Mach Number

Altitude [FL]

Thru

st

[kN

]

050

100150

200250

300350

400

0.40.45

0.50.55

0.60.65

0.70.75

0.80

0.5

1

1.5

2

Altitude [FL]Mach Number

Err

or

[%]


31

3.7 OPTIMUM CRUISE ALTITUDE

The required thrust for cruise is given by:

(3-42)

Since cruise is done at a constant Mach number, the only variables are weight and air density. The

required thrust was calculated for a range of altitude and weights, and for each weight the

altitude at which the required thrust was a minimum was found. The optimum cruising altitude

where the minimum thrust is required is plotted as a function of aircraft mass in the figure below.

Figure 3-14. Optimum Cruise Altitude @ M0.83.

The data points above can be described by a line of best fit with the following function that has

also been plotted in the figure above:

[

] [

] [ ] (3-43)

In the figure below the optimum altitude is presented at any given velocity and weight.

180200220240260280300320340360280

300

320

340

360

380

400

420

Altitude [

FL]

Mass [t]

Optimal Cruise Altitude @ M0.83

Actual Model


32

Figure 3-15. Optimum altitude is presented at any given velocity and weight.

3.8 FUEL PLANNING

The boundary condition for when the cruise phase of a flight has to end at the latest is

determined by when the aircraft reaches a specific Top of Descent weight

W = WTOD

At this weight, the aircraft will still have enough fuel to descend and land and still have the

required amount of reserve fuel on-board upon landing. The WTOD is calculated backwards from

the landing weight. During flight the only cause of weight change of the aircraft is due to the

consumption of fuel. The fuel aboard an aircraft is a sum of the following:

- Trip Fuel (TF)

- Contingency Fuel (CF)

- Alternate Fuel (AF)

- Final Reserve Fuel (FR)

- Additional Fuel (ADD)

- Extra Fuel (XF)

These fuel amounts are defined in the COMMISSION REGULATION (EC) No 859/2008 also known

as the EU-OPS 1.

Trip Fuel

The trip fuel is the necessary fuel from break release at the departure airport to touchdown at the

destination airport. Included in this is the fuel required for the following segments:

- Take-off

- Climb to TOC

180200

220240

260280

300320

340360

200

220

240

260

280

300100

150

200

250

300

350

400

450

Weight [t]Speed [m/s]

Altitude [

FL]


33

- Cruise from TOC to TOD including step-climbs

- Descent from TOD to approach

- Approach

- Landing at destination airport

Contingency Fuel

For the type of missions flown by the aircraft in question the most relevant definition of

contingency fuel is 5% of trip fuel. However, if an en-route alternate airport is available according

to the conditions defined below then the contingency fuel can be reduced to 3% of the trip fuel.

The aerodrome shall be located within a circle having a radius equal to 20 % of

the total flight plan distance, the centre of which lies on the planned route at a

distance from the destination aerodrome of 25 % of the total flight plan distance,

or at least 20 % of the total flight plan distance plus 50 nm, whichever is greater,

all distances are to be calculated in still air conditions31

Generally this requirement is fulfilled unless the flight takes place over very remote areas, such as

the south pacific.

Alternate Fuel

Alternate fuel incorporates fuel for:

- Fuel for a go-around at the destination airport to missed approach altitude

- Fuel for climb from missed approach altitude to TOC altitude

- Fuel for cruise from TOC to TOD at alternate airport

- Fuel for approach and landing at alternate airport

Final Reserve Fuel

Final reserve fuel is the fuel required for a 30 minute holding at 1500 ft above the alternate

airport, in the case that no alternate is required for the flight then at the destination airport.

Additional Fuel

The minimum additional fuel is the fuel required for:

- the aeroplane to descend as necessary and proceed to an adequate alternate aerodrome

in the event of engine failure or loss of pressurisation, whichever requires the greater

amount of fuel based on the assumption that such a failure occurs at the most critical

point along the route, and

hold there for 15 minutes at 1 500 ft (450 m) above aerodrome elevation in

standard conditions; and

31

Appendix 2 of EU-OPS 1.255


34

make an approach and landing, except that additional fuel is only required, if the

minimum amount of fuel calculated in accordance with subparagraphs 1.2. to 1.5.

above is not sufficient for such an event, and

- Holding for 15 minutes at 1 500 ft (450 m) above destination aerodrome elevation in

standard conditions, when a flight is operated without a destination alternate

aerodrome;32

Generally, for the aircraft in question, the additional fuel will be covered by reserve fuels added in

accordance to the clauses concerning contingency fuel, alternate fuel and final reserve fuel.

Extra Fuel

Extra fuel shall be added at the discretion of the Capitan.

Calculating the Top of Descent Weight

To calculate WTOD all fuel amounts have to be known along with the fuel required for the descent.

Descent and reserve fuel estimations are shown in the table below.

Segment Reserve fuel category Fuel amount

Descent from FL390 Trip Fuel 660 kg

Go-around + CLB to FL80 Alternate Fuel 2060 kg

Flight to alternate at FL80 Alternate Fuel 3700 kg

Holding 30 min at FL15 Final Reserve 3700 kg

Table 3-14. Fuel Reserves.

The above values where calculated using an iterative method by assuming a value for WTOD from

which the descent and reserve fuels could be calculated and a new WTOD could be determined.

Then using the new value for WTOD the process was repeated; this was done until the value

converged.

Assuming 3% contingency fuel, the amount of fuel required can be calculated as follows:

( )

( )

(3-44)

Using the equation above for TF and knowing the fuel required for the descent FDES, the fuel

required for flight until TOD will be:

32

Appendix 1 to EU-OPS 1.255, 1.6


35

( )

(3-45)

Having a total fuel of Ftotal = 123 t on-board and using the reserve fuel values from the table above

it can be calculated that FTOD = 109.6

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