Analysis Study on Avionics System
Research Report
Zheng Du
Student ID: B0605428
ENG499 Capstone Project Course
A thesis submitted to SIM University
in partial fulfillment of the requirements for the Degree of
Bachelor of Engineering.
2009
ACKNOWLEDGEMENTS
As my thesis draws to a conclusion, I would like to take this opportunity to thank all
of those individuals who assisted me to accomplish this dissertation.
My deepest gratitude goes first and foremost to Mr. Chaganti and Mr. Toh Ser Khoon
my supervisor, for their valuable guidance and understanding. They have walked me
through all the stages of the writing of this thesis. From the very beginning of
literature researching to the final draft, they help me a lot as it always. Without their
consistent and illuminating instruction, this thesis could not have reached its present
form.
I am also most grateful to all my friends who have been very supportive, and generous
in offering their help and advice
i
Abstract
The project objectives were to give an analysis study about commercial avionics
system architecture. Seldom has similar reports suitable to readers who are out of
aviation industry, to help them build some systemic concepts, and some fundamental
factors relate to flight.
The project was split in two phases. The first phase studied 2 major used aircrafts
avionics system architecture. The main outputs of this phase were the system layout
and a model of the avionics functional architecture. The second phase focused on the
flight analysis and flight planning.
System Architecture:
 Cockpit design principles
 Cockpit architecture introduction
 AIRBUS A340 Flight Deck Introduction
 BOEING B747-400 Flight Deck
Flight Analysis and Flight Planning:
 Trajectory Analysis
 Dynamic Equations
 Trajectory Prediction
 Atmospheric Models
 Standard Atmosphere
 Exponential Atmosphere
 Forecast Temperature
 Maneuver Profile
 Dynamic Equations
 Weight Equation
 Aerodynamics: Functional Relations
 Accelerated Climb
 Lateral Profile
 Motion Equation
 Vertical Profile
 Motion Equation
 Performance Computations
ii
Table of Contents
ACKNOWLEDGEMENT …………………………………………………………...i
ABSTRACT…………………………………………………………………...……...ii
LIST OF FIGURES……………………………………………………...……...…..iii
CHAPTER 1
INTRODUCTION……………………………………………………………………1
1.1 Objective Background…………………………………………………………...1
1.2 Overall Objective…………………………………………………………………1
1.3 Proposed Approach and Method………………………………………………..1
1.4 Skill Review……………………………………………………………………….1
1.4.1 Criteria and Targets for Assessment of Project…………………………….1
1.4.2 Skill to achieve Targets……………………………………………………….2
1.5 Project Plan……………………………………………………………………….3
CHAPTER 2
INVESTIGATION OF PROJECT BACKGROUND……………………………...4
2.1 Introduction………………………………………………………………………4
2.2 Cockpit design principles………………………………………………………...4
2.3 Cockpit architecture introduction………………………………………………5
2.4 AIRBUS A340 Flight Deck Introduction………………………………………..6
2.4.1 General Provisions…………………………………………………………...6
2.4.2 Pilots’ field of vision………………………………………………………….8
2.4.3 Control and Indication panels……………………………………………….9
2.4.3.1 Main features…………………………………………………………….10
2.4.3.2 Sidestick arrangement…………………………………………………..10
2.4.3.3 Sidestick operation………………………………………………………10
2.4.3.4 Main instrument panels…………………………………………………11
2.4.3.5 Main center panel………………………………………………………..11
2.4.3.6 Glareshield……………………………………………………………….12
2.4.3.7 Central pedestal………………………………………………………….12
2.4.3.8 Overhead panel…………………………………………………………..13
2.4.3.9 Slats/flaps………………………………………………………………...13
2.4.3.10 Slats/flaps controls……………………………………………………...14
2.4.3.11 Landing Gear…………………………………………………………...14
2.4.3.12 Fuel System……………………………………………………………..15
2.4.3.13 Electronic Instrument System…………………………………………15
2.5 BOEING B747-400 Flight Deck………………………………………………..16
2.5.1 General Provisions………………………………………………………….16
2.5.2 Control and Indication Panel………………………………………………18
2.5.2.1 Integrated Display System, IDS………………………………………...19
iii
2.5.2.2 Engine Indicating and Crew Alerting System, EICAS……………….19
2.5.2.3 Instrument Landing System, ILS………………………………………19
2.5.2.4 Input/Output Instrument……………………………………………….19
2.5.2.5 Autopilot…………………………………………………………………19
2.5.2.6 Flight Management Computer, FMC………………………………….20
2.5.2.7 Central Maintenance Computer, CMC…..............................................21
2.5.2.8 Inertial Reference System, IRS………………………………………...21
2.5.2.9 Standby Instruments……………………………………………………21
2.5.2.10 Communication………………………………………………………..22
2.5.2.11 Air Traffic Control, ATC……………………………………………..22
2.5.2.12 Ground Proximity Warning System, GPW………………………….22
2.5.2.13 Flight Control………………………………………………………….23
2.5.2.14 Fuel System…………………………………………………………….23
CHAPTER 3
FLIGHT PLANNING………………………………………………………………25
3.1 INTRODUCTION………………………………………………………………25
3.2 BASIC CONCEPTS……………………………………………………………25
3.3 FLIGHT PLANNING…………………………………………………………..26
3.4 TRAJECTORY ANALYSIS……………………………………………………26
3.4.1 Introduction………………………………………………………………….26
3.4.2 Dynamic Equations………………………………………………………….27
3.4.3 Trajectory Prediction………………………………………………………..28
3.5 ATMOSPHERIC MODELS……………………………………………………30
3.5.1 Introduction………………………………………………………………….30
3.5.2 Standard Atmosphere……………………………………………………….30
3.5.3 Exponential Atmosphere……………………………………………………31
3.5.4 Forecast Temperature………………………………………………………32
3.6 MANEUVER PROFILE………………………………………………………33
3.6.1 Dynamic Equations…………………………………………………………33
3.6.2 Weight Equation……………………………………………………………33
3.6.3 Aerodynamics: Functional Relations………………………………………34
3.6.4 Accelerated Climb…………………………………………………………...35
3.6.5 Thrust and Specific Fuel Consumption (SFC)……………………………..36
3.7 LATERAL PROFILE………………………………………………………….41
3.7.1 Introduction…………………………………………………………………41
3.7.2 Motion Equation…………………………………………………………….42
3.8 VERTICAL PROFILE…………………………………………………………44
3.8.1 Introduction…………………………………………………………………44
3.8.2 Motion Equation…………………………………………………………….45
3.9 PERFORMSANCE COMPUTATIONS………………………………………47
CHAPTER 4
CONCLUSION……………………………………………………………………...48
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CHAPTER 5
FUTURE WORK…………………………………………………………………...49
REFERENCE……………………………………………………………………….50
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CHAPTER 1
INTRODUCTION
1.1 Objective Background
This project concerns the study and analysis of avionics system architecture. It
focuses on study the cockpit, or says flight deck layout with major instruments
function installed inside; and aircraft flight analysis. From introduction of some
commercial airplane cockpit, and study the fundamentals of flight mechanics, try to
realize modern avionics systems.
1.2 Overall Objective
This project will help readers to understand the purpose of avionics system
architecture design to illustrate recognizable advances, and the analysis of aircraft
flight performance by deriving formulas and algorithms of each profile model
trajectory analysis, atmospheric, climbing, thrust and specific fuel consumption,
maneuver types comprise the flight system. The latter part is more complicate because
a lot of mathematics and physics formulas derivation and calculation involved, but all
these are considered as foundation of flight analysis.
1.3 Proposed Approach and Method
In order to achieve the objective of the project, spend great much effort on
researching the relative information and knowledge is very necessary, following by
studying the principle and equations of flight mechanics, collecting data based on
simulated condition, calculated by related formulas with understanding.
1.4 Skills Review
1.4.1 Criteria and Targets for Assessment of Project
With the completion of this project, the outline and foundation knowledge of the
commercial avionics system architecture will be attained, and knowing some critical
units with their important function. And the knowledge of analysis the performance
about airplane flight will be achieved, understand basic concept and calculation about
trajectory analysis, atmospheric models, maneuver profile, lateral profile, vertical
profile and performance computation. As we know, fighting is an expansive cost, and
recent few years many airlines starting to pay close attention to the protection of the
ecological environment, so the related flight cost became an essential factor should be
considered, this is called performance computation. With calculation of real data, can
help readers to have some understanding about decisions the airlines and pilots made.
When go through the study journey of this project, the skill of researching and
compiling is highly acquired, and some mathematics and physics knowledge also
required.
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1.4.2 Skill to achieve Targets
Due to domain of avionic system, is no so familiar to most people, cause normally
not much chances to visiting pilot’s work station and most instruments used inside
quit different with commercial electronics equipment, to achieve the project target is a
challenging job, researches and literature reviewing on study of avionics system
architecture are essential.
Considering the purpose of this project mostly is a research report, so the skill to
present the contents from my understanding to make readers and audience understand
clearly, especially important. And how to introduce some complicated mathematics
equations with clear logic also no easy. Start from this report, expect the readers, will
increase their interest in avionics system with assistance of figures. Thus literature
describing skill also becomes critical in this report.
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1.5
Project Plan
2009
No.
Activities/
Start
End
Tasks
Date
Date
1
Planning
2
Literature
JAN
FEB
MARCH
Search
3
Study Guides/
Project
Material
4
Meeting
with
Tutor
5
Write
Initial
Report-TMA01
6
Implementing
system with
development
methods
7
Selection
of
project
methods:
Flight Analysis
8
Writing
skeleton
of
Final Report
9
Writing,
formatting and
finalizing
contents
of
Final Report
10
Make-Up Oral
Presentation
11
Oral
Presentation
3
APRIL
MAY
JUNE
JULY
AUG
SEP
OCT
NOV
CHAPTER 2
INVESTIGATION OF PROJECT BACKGROUND
2.1 Introduction
Simply, the avionic system architecture refers to the avionics instruments layout in the
cockpit. The English word “cockpit” originally meant a gaming enclosure where a
pair of domesticated male fowl fought. Although other for the work place of the pilot,
like work-station, crew station or flight-deck. The word “Cockpit” is usually
associated with small to medium sized airplanes. The word”flight-deck” is usually
associated with large airplanes. The aim of the designer is actually to provide the
antithesis, a place of calm, professional assurance and safely.
2.2 Cockpit design principles
The flight-deck is a workplace (Figure 2.1) that must supply the three basic needs
of the crew: (a) a view out into the world, (b) protection against the natural
environment and (c) means for interacting with the aircraft and its systems.
The major consideration should be taken in the layout of a cockpit or a flight deck:
1. The pilot(s) and other crew members must be positioned so that they can reach all
controls comfortably, from some reference position.
2. The pilot(s) and other crew members must be able to see all ‘flight essential’
instruments without undue effort.
3. Communication by voice or by touch must be possible without undue effort.
4. Visibility from the cockpit must adhere to certain minimum standards.
All cockpit layouts must account for dimensional limitation of the human body.
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Figure 2.1
2.3 Cockpit architecture introduction
Inside the cockpit bewildering array of instruments, control panels, sounds, light
modules and circuit breakers confronts.
It is traditional that the captain, or first pilot, sits in the left cock-pit seat and the
number two, or co-pilot, sits in the right seat, so all controls and instruments and
system circuit breakers on the left half of the cockpit are number one system devices
and are used by the captain of aircraft. There is no reason why the co-pilot should not
use avionic system located
on the captain’s side, but normally they use the avionic systems, headphones,
microphones and navigation instruments located in their own area of operation.
5
Figure 2.2 Area of responsibility
Here select 2 classic flight decks as samples to study and compare, which belongs
to AIRBUS A340 and Boeing 747-400.
2.4 AIRBUS A340 Flight Deck Introduction
2.4.1General Provisions
A340 is a long-distance aircraft the cockpit fully provides for a 3rd occupant seat,
and a folding 4th occupant seat.
In addition, an optional crew rest compartment, adjacent to the cockpit, is available
in place of a galley.
This proposed rest compartment features:
① 2 crew bunks;
② 2 folding tables/dining places;
③ A wardrobe and baggage stowage area;
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④ Direct view into the cockpit yet completes separation for effective crew rest;
⑤ Direct access to the cockpit.
A340 Flight Deck Figure1 Top Views
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A340 Flight Deck Figure2 Cockpit Interior Views (Forward)
2.4.2 Pilots’ field of vision
①Visibility
Windows are designed to meet or exceed the Aerospace standard. Geometry: Windshield panels: flat glass.
Lateral windows: curved acrylic.
② Pilots’ vision envelope
③Pilots’ field of vision
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2.4.3 Control and Indication panels
A340 Flight Deck Figure3 (Forward)
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2.4.3.1 Main features
The main features, for the A320/A321/A330/A340 family are:
① Sidestick controllers which leave the main instrument panel unobstructed.
② Six interchangeable and switchable display units (DU) which are integrated into
the same system architecture (EFIS/ECAM).
2.4.3.2. Sidestick arrangement
① Sidesicks are installed on the Captain’s and First Officer’s forward lateral
consoles.
② To facilitate control, a dual pivot adjustable armrest with position indicators is
fitted on each seat behind the sidestick.
2.4.3.3. Sidestick operation
① Moving the sidestick results in “setting the aircraft trajectory” with a certain level
of “g” for the requested maneuver, depending on the amount of sidestick
movement.
② Accuracy of movements is very precise since backlash and friction are negligible.
③ Control of the flight path is performed by the Electronic Flight Control System
(EFCS) which links the trajectory order with aerodynamic data to stabilize the
aircraft and protect it from prohibited attitudes.
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2.4.3.4 Main instrument panels
A340 Flight Deck Figure4
Captain and First Officer panels
① The CAPT and F/O panels are mirror images of each other:
② Both incorporate two side-by-side Display Units (DUs) (7.25 in x 7.25 in):
③ A Primary Flight Display (PFD)
④ A Navigation Display (ND).
⑤ This arrangement provides:
i. Better visibility on all DUs in normal configuration and in case of
reconfiguration (PFD ND or ECAM ND)
ii.
A sliding table and a footrest in front of each pilot.
⑥ The PFD includes the complete Basic T with:
i. Attitude
ii. Airspeed/Mach (with all upper and lower limits)
iii. Altitude/vertical speed
iv. Heading
v. AFS status
vi. ILS deviation/marker
vii. Radio altitude.
⑦The ND offers up to three modes:
i. ROSE mode (ILS, VOR or NAV): Aircraft symbol in screen center,
with radar availability
ii. ARC mode: Heading up, horizon limited to a 90° forward sector, with radar
availability
iii. PLAN mode: North up, display centered on selected waypoint.
⑧Engine display: in case of an all DMC/ECAM failure, each pilot may display the
ENG STBY page on his ND.
Note: In ROSE-NAV, ARC, and PLAN modes, F-plan data from.
2.4.3.5. Main center panel
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The center panel includes:
Two DUs, one above the other, which are interchangeable with the CAPT and F/O
DUs :
i. Engine Display (DU 1), showing the:
a) Main engine parameters (N1, EGT, N2)
b) N1 limit, N1 command
c) Total fuel
d) Flaps and slats position
e) Memo and warning.
ii. System Display (DU 2) showing:
a) An aircraft system synoptic diagrams page, or
b) The aircraft status (list of all operationally significant items)
c) Standby instruments
d) Landing gear control and indications (including brakes)
e) Clock.
2.4.3.6. Glareshield
①The Flight Control Unit (FCU) provides short-term interface between the Flight
Management and Guidance Computer (FMGC) and crew for the:
i.Engagement of A/P, A/THR
ii.Selection of required guidance modes
iii.Manual selection of flight parameters SPD, MACH, ALT, V/SPD, HDG or track.
②The EFIS control panels designed for the:
i.Selection of desired ND modes (ROSE-ILS, -VOR,
ii.NAV, ARC, PLAN, ENG) and ranges
iii.Selection of baro settings.
③The master warning, master caution, autoland and sidestick priority lights.
2.4.3.7. Central pedestal
In addition to the thrust levers and the engine control functions, the main features
on the pedestal are the:
①Multipurpose Control and Display Units (MCDU) for flight management functions
and various other functions such as data link, maintenance, etc.
②Radio Management Panels (RMP) for tuning all radio communications and the
radio navigation as a back-up to the normal operation through the Flight
Management and Guidance Computers (FMGC),
③Electrical rudder trim,
④Parking brake control,
⑤Speedbrake and flap/slat control levers.
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2.4.3.8. Overhead panel
①The overhead panel has a “single slope”.
②All controls on the overhead panel can be reached by either pilot.
③The following two main zones are separated by protective padding :
Forward zone for:
i.Most frequently used functions,
ii.System controls, arranged in three main rows:
iii.Center row for engine-related systems, arranged in a logical way.
iv.Lateral rows for other systems.
Aft zone, not used in flight, is mainly for a small maintenance panel
corresponding to some maintenance controls.
④The pushbutton philosophy is identical to that already applied on previously
existing Airbus aircraft.
2.4.3.9. Slats/flaps
①High lift control is achieved on each wing by:
i) Seven leading edge slats,
ii) Two trailing edge flaps,
iii)Two ailerons (ailerons droop function).
②Slat and flaps are driven through similar hydromechanical systems consisting of:
i) Power Control Units (PCU),
ii) Differential gearboxes and transverse torque shafts,
iii) Rotary actuators.
③Slats and flaps are electrically-signalled through the SFCCs :
i) Control lever position is obtained from the Command Sensor Unit (CSU) by the
two SFCCs.
ii) Each SFCC controls one hydraulic motor in both of the flap and slat PCUs.
④Aileron droop is achieved through the primary computers, depending on flap
position data received from the SFCC.
⑤The SFCC monitors the slats and flaps drive system through Feedback Position
Pick-off Units (FPPU) located at the PCUs and at the outer end of the transmission
torque shafts
⑥Wing Tip Brakes, (WTB) installed within the torque shaft system and controlled by
the SFCC, prevent asymmetric operation, blow back, or runaway.
⑦A pressure-off brake, provided between each hydraulic motor of the PCU and the
differential gearboxes, locks the slat or flap position when there is no drive
command from the SFCC.
⑧Flight Warning Computers (FWC) receive slat and flap position data through
dedicated Instrumentation Position Pick-off Units (IPPU) for warnings and
position indication on ECAM display units.
13
2.4.3.10 Slats/flaps controls
①High lift control is achieved on each wing by:
i) Seven leading edge slats,
ii) Two trailing edge flaps,
iii) Two ailerons (ailerons droop function).
②Slat and flaps are driven through similar hydromechanical systems consisting of :
i) Power Control Units (PCU),
ii) Differential gearboxes and transverse torque shafts,
iii) Rotary actuators.
③Slats and flaps are electrically-signalled through the SFCCs :
i) Control lever position is obtained from the Command Sensor Unit (CSU) by the
two SFCCs.
ii) Each SFCC controls one hydraulic motor in both of the flap and slat PCUs.
④Aileron droop is achieved through the primary computers, depending on flap
position data received from the SFCC.
⑤The SFCC monitors the slats and flaps drive system through Feedback Position
Pick-off Units (FPPU) located at the PCUs and at the outer end of the
transmission torque shafts.
⑥Wing Tip Brakes, (WTB) installed within the torque shaft system and controlled by
the SFCC, prevent asymmetric operation, blow back, or runaway.
⑦A pressure-off brake, provided between each hydraulic motor of the PCU and the
differential gearboxes, locks the slat or flap position when there is no drive
command from the SFCC.
⑧Flight Warning Computers (FWC) receive slat and flap position data through
dedicated Instrumentation
Position Pick-off Units (IPPU) for warnings and position indication on ECAM
display units.
2.4.3.11 Landing Gear
①Conventional landing gear with single bogie nose gear, an outer gear and a double
bogie main landing gear, with direct-action shock absorbers.
②The main landing gear is also provided with a shock absorber extension/retraction
system.
③The main gear retracts laterally; nose and center gears retract forward into the
fuselage.
④Electrically controlled by two Landing Gear Control/Interface Units (LGCIU).
⑤Hydraulically actuated (Green system) with alternative free-fall/spring downlock
mode.
⑥Alternating use of both LGCIUs for each retraction/extension cycle. Resetting the
landing gear control lever results in transition to the other LGCIU.
⑦Elimination of gear lever neutral position through automatic depressurization of
landing gear hydraulic supply at speeds above 280 kt.
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⑧Elimitation of microswitches by use of trouble-free proximity detectors for position
sensing.
2.4.3.12. Fuel System
The Fuel System is automatically controlled by the Fuel Control and Monitoring
System (FCMS).
The FCMS operates in a fully automatic mode.
Two identical Fuel Control and Monitoring Computers (FCMC) provide:
①Fuel quantity measurement and indication;
②Fuel transfer control;
③Center of gravity control;
④Level sensing;
⑤Fuel temperature indication;
⑥Refuel control;
⑦Aircraft gross weight and center of gravity calculation based on zero fuel weight
and zero fuel center of gravity entered by the crew;
⑧Indications:
Fuel data (quantity, temperature) are available from a Fuel Quantity Indication
(FQI) system.
⑨Fuel On Board (FOB) is permanently displayed on upper ECAM DU.
⑩Fuel system synoptic on lower ECAM DU is displayed according to ECAM logic.
⑾ Low level warning is totally independent from FQI.
2.4.3.13. Electronic Instrument System
The Electronic Instrument System (EIS) performs a display function for:
①Flight operation: EFIS (Electronic Flight Instrument System) located on each
crewmember's instrument panel:
i) 1 PFD (Primary Flight Display)
ii) 1 ND (Navigation Display)
②System operation: ECAM (Electronic Centralized Aircraft Monitor)
On the center instrument panel for both crewmembers:
i) 1 E/WD (Engine/Warning Display)
ii) 1 SD (System Display)
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2.5 BOEING B747-400 Flight Deck
2.5.1 General Provisions
Compared with AIRBUS A340, BOEING B747-400 also known as a famous
aircraft, its flight deck design a bit different with previous introduced, so from
following introduction may be able to find out.
There are 4 seats in the cockpit interior, besides Captain and First Officer, there
also arranged seats for First Observer and Second Observer, which behind the
Captain’s seat and First Officer’ seat.
B747-400 Flight Deck Figure1
1: Captain 2: First Officer, Co-Pilot
3: First Observer 4: Second Observer
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B747-400 Flight Deck Figure2
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2.5.2 Control and Indication Panel
B747-400 Flight Deck Figure 3
Flight Deck Instrument Panel and Control Stand
P461: Pilots Maintenance
P7: Overhead Circuit Breaker P5: Pilots overhead
P10: Automatic Flight Control
P72: Pilots Glareshield
P1: Captains Main Instrument
P2: Pilots Center Instrument
P3: First Officers Main Instrument
P9: Forward Pilots Electronics
P8: After Pilots Electronics
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2.5.2.1. Integrated Display System, IDS
Inside the cabin, there are 6 8inch x 8inch multiple function display screens, use to
indicate aircraft axes, speed, altitude, vertical speed, flight direction.
B747-400 Flight Deck Figure 4
Captain's Primary Flight Display (PFD)
2.5.2.2. Engine Indicating and Crew Alerting System, EICAS
①
②
③
④
Display aircraft 4 engines working status.
Report unusual state to pilots.
Reduce pilot’s work load.
There are 2 display screens to showing data and messages called Main EICAS
and Auxiliary EICAS, also Master warning/caution light used to alert pilot for the
new warning message.
2.5.2.3. Instrument Landing System, ILS
ILS can be divided into 2 systems: Localizer (LOC) offers cross direction guidance
help aircraft aim on the run way. Glide Slope (G/S) offers vertical direction guidance
help aircraft landing followed some certain sliding angle.
2.5.2.4 Input/Output Instrument
Include CDU (Control Display Unit) and Printer. CDU play as an output of CMC
and FM, also provide ACARS and ACMS as interface between human and aircraft.
2.5.2.5. Autopilot
The critical part of Autopilot is 3 sets Flight Control Computer FCC, actually just
need only 1 set then can perform Autopilot function. FCC receiving each signal to
determine how to flight, and then going to control flight control panel, to execute
pilot’s command.
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2.5.2.6. Flight Management Computer, FMC
Actually there are 2 systems, one is Autopilot, and the other one is FMC. The
application of FMC based on Autopilot function, FMC stored flight routes data, and
use the aircraft current location, send commands to Autopilot to fix flight on the
determined track.
FMC main functions: Navigation, Guidance, Performance, Thrust management.
There are 3 methods FMC use to navigation station to positioning:
①DME/DME
B747-400 Flight Deck Figure 5
②VOR/DME
B747-400 Flight Deck Figure 6
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③VOR/VOR
B747-400 Flight Deck Figure 7
2.5.2.7. Central Maintenance Computer, CMC
CMC can get all system controlled computer’s data by EIU, all components failures
directly shown on the cockpit screen, offers reference for troubleshooting.
2.5.2.8. Inertial Reference System, IRS
In old system, this be called Inertial Navigation System, INS, either flight deck
interior display, or give Autopilot commands, all provided by INS. IRS provides data
about: Position, Attitude, Heading, Ground Speed, Track, Drift Angle, Wind speed,
Vertical Speed, Acceleration.
There is an important operation called “Align” to reset IRS when aircraft stand still
on the ground to make sure IRS working properly.
2.5.2.9. Standby Instruments
There has a “T Rule” about the arrangement of Airspeed Indicator, Attitude
Instrument, Altimeter, and Magnetic Compass on the Control Panel. Their operation
is isolated from main system, included electric power and signal receiving. They have
more simple function but play quite important role.
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2.5.2.10 Communication
Communication system included internal communication system, like Flight
Interphone, Service Interphone, and Cabin Interphone etc. External communication
systems are like HF, VHF and SATCOM etc. But pilots can control both systems from
one panel, which is Audio Control Panel, ACP. And Radio Control Panel, RCP use to
select HF and VHF frequency.
2.5.2.11. Air Traffic Control, ATC
There have high power radar, called Primary Surveillance Radar, PSR on the
ground, to get all airplanes location within this area, and display on the screen. The
other radar called Secondary Surveillance Radar, SSR is communicated with aircraft
system, SSR will emit electric wave to aircraft, when aircraft received, then will
feedback its own data to SSR. The system on the aircraft to respond SSR called ATC
transponder (Transmitter + Responder).
B747-400 Flight Deck Figure 8
2.5.2.12. Ground Proximity Warning System, GPWS
Only when aircraft prepare to landing then will close to the ground, any other time
shouldn’t do that during the flying. So aircraft installed GPWS to warn the pilots the
abnormal situation. The critical part of GPWS is Ground Proximity Warning
Computer, it will collect related info to judge whether aircraft’s position is too close
to ground. There are 2 class signals, one is Warning, the other one is Alert. Warning
signal is more serious.
22
2.5.2.13. Flight Control
B747-400 Flight Deck Figure 9
The aircraft movement following 6 directions (3 straight directions and 3 roll axis),
flight control is refer to Roll Axis, Pitch Axis, Yaw Axis control. Roll Axis control
done by Aileron, Pitch Axis control done by 4 Elevators on the tail, Yaw Axis control
done by Rudder Ratio Change.
2.5.2.14. Fuel System
The fuel used on 747-400, is Jet-A1, normally one long distance flight, need to use
around 150,000 liter fuel. These fuel occupy 1/3 weight of whole aircraft.
The tanks location on the aircraft body:
23
B747-400 Flight Deck Figure11
24
CHAPTER 3
FLIGHT ANALYSIS AND FLIGHT PLANNING
3.1 INTRODUCTION
This chapter is primarily concerned with analytical solutions of airplane flight
mechanics problems. For commercial airplanes including business jets, the mission
legs are take-off, climb, cruise, descent and landing. These will give airplane’s
performance. And actual collected data is based on these performances; to load in
flight management system (FMS) which installed in the aircraft provides the flight
planning, optimized route determination for the aircraft during the flight. FMS
normally comprised with such functions: Flight Planning, Trajectory Analysis and
Prediction.
3.2 BASIC CONCEPTS
Flight mechanics is a discipline. As such, it has equations of motion, acceptable
approximations, and solution techniques for the approximate equations of motion. The
force equations (F=ma) are uncoupled from the moment equations (M=I  ) is the
basic for the most analysis and derivation.
The resulting equations are referred to 3DOF model, and subsequent construction
of the 4 dimensional aircrafts trajectory defined by the specified flight plan,
constraints and the aircraft performance, is the core functionality of FMS.
Flight plan and trajectory prediction work together to produce the 4-dimensional
trajectory and consolidate all the relevant trajectory information into a flight
plan/profile buffer.
① The flight planning function to allows the pilots to build a specific routing for the
aircraft.
② The trajectory analysis and prediction function to responsible for computing the
predicated aircraft profile along the entire specified routing.
③ The performance function to provides the pilots with aircraft unique performance
information such as takeoff speeds, altitude capability, and profile optimization
advisories.
There are typically two loadable databases that support the core flight management
functions. These are the navigation database which must be updated on a 28-day
cycle and the performance database that only gets updated if there’s been a change in
the aircraft performance characteristics.
The performance of database contains aircraft/engine models, data including drag,
thrust, fuel flow, and speed/altitude envelop, thrust limits, and a variety of optimized
and tactical speed schedules that are unique to the aircraft.
25
3.3 FLIGHT PLANNING
The basis of the FMC flight profile is the route that the airplane is to fly from the
departure airport to the destination airport. The FMS flight planning function provides
for the assembly, modification, and activation of this route data known as a flight plan.
Route data are typically extracted from the FMC navigation data base and typically
consists of a departure airport and runway, a standard instrument departure (SID)
procedure, en route waypoints and airways, a standard arrival (STAR) procedure, and
an approach procedure with a specific destination runway. Normally the destination
arrival (or approach transition) and approach procedure are not selected until the
destination terminal area control is contacted. Once the routing, along with any route
constrains and performance selections, are established by the pilots, the flight plan is
assembled into a buffer that is used predominantly by the trajectory predictions in
computing the lateral and vertical profile the aircraft is intended to fly from the
departure airport to the destination airport.
Flight plans are normally constructed by linking data stored in the navigation data
base.
3.4 TRAJECTORY ANALYSIS
3.4.1 Introduction
Trajectory analysis is used to derive formulas and/or algorithms for computing the
distance, time, and fuel along each mission leg.
An important part of trajectory analysis is trajectory optimization. Ordinarily,
trajectory optimization is a complicated affair involving optimal control theory
(calculus of variations) and/or the use of numerical optimization techniques.
To study trajectories, the force equations (F=ma) are uncoupled from the moment
equations (M=I  ) by assuming that the airplane is not rotating and that control
surface deflections do not change lift and drag.
The resulting equations are referred to as the 3DOF model, and their investigation
is called trajectory analysis.
Most trajectory analysis problems involve aircraft rotation rates and are studied
through the use of the three degree of freedom (3DOF) equations of motion, that is,
the translational equations. These equations are uncoupled from the rotational
equations by assuming negligible rotation rates and neglecting the effect of control
surface deflections on aerodynamic forces. For example, consider an airplane in
cruise. To maintain a given speed an elevator deflection is required to make the
pitching moment zero. This elevator defection contributes to the lift and the drag of
the airplane.
Trajectory analysis takes one of two forms. First, given an aircraft, find its
performance characteristics, which is, maximum speed, ceiling, range, etc. Second,
given certain performance characteristics what is the airplane produces them. The
mission or flight profile is composed of take-off, climb, cruise, descent, and landing
segments, where the descent segment is replaced by an extended cruise because the
26
fuel consumed is approximately the same.
In each segment, the distance traveled, the time elapsed, and the fuel consumed
must be computed to determine the corresponding quantities for the whole mission.
The development of formulas or algorithms for computing these performance
quantities is the charge of trajectory analysis. And note that, with the exception of the
turns, each segment takes place in a plane perpendicular to the surface of the earth
(vertical plane). The turns take place in a horizontal plane.
3.4.2 Dynamic Equations
In order to derive the scalar equations, it is necessary to select a coordinate system.
While the local horizon system is used for obtaining the kinematic equations, a more
direct derivation of the dynamic equations is possible by using the wind axes system.
In this coordinate system, the forces acting on the airplane can be written as
T  T cos  i  T sin  k
D   Di
(3.1)
L   Lk
W  W sin  i  W cos  k
where T is the thrust, D is the Drag, L is the lift, W is the weight,  is referred to as
the thrust angle of attack, the angle between thrust direction and velocity. The wind
axes are orientated relative to the local horizon axes by the flight path angle  . The
unit vectors associated with the coordinate directions are denoted by i, j, and k with
appropriate subscripts. Since the local horizon axes are always parallel to the ground
axes, their unit vectors are equal, that is,
ih  i
(3.2)
kh  k
The wind axes unit vectors are related to local horizon unit vectors are:
i  cos  ih  sin  kh
(3.3)
k  sin  ih  cos  kh
So that the resultant external force becomes
F= ( T cos   D  W sin  ) i -( T sin   L  W cos  ) k
By definition of acceleration relative to the ground
dV
a=
dt
(3.4)
(3.5)
holding the ground axes unit vectors constant. Since the velocity is along the x axis, it
can be expressed as
V = Vi
(3.6)
27
where both the velocity magnitude V and the direction of the unit vector i are
functions of time. Differentiation leads to
di
a = V i  V 
dt
the acceleration of the airplane with respect to the ground is given by
(3.7)
a = V i  V  k
(3.8)
By combining Eqs (3.5.4) and (3.5.8), the following scalar equations are obtained:
V  ( g / W )(T cos   D  W sin  )
(3.9)
  ( g / WV )(T sin   L  W cos  )
where g is the constant acceleration of gravity and where the relation W = mg has
been used.
3.4.3 Trajectory Prediction
Given the flight plan, the trajectory prediction function computes the predicated
four-dimensional flight profile (both lateral and vertical) of the aircraft within the
specified flight plan constraints and aircraft performance limitations based on entered
atmospheric data and the crew-selected modes of operation. The lateral path and
predicated fuel, time, distance, altitude, and speed are obtained for each point in the
flight plan (waypoints as well as inserted vertical breakpoints such as speed change,
crossover, level off, top of climb (T/C), top of descent (T/D) points).The flight profile
is continuously updated to account for no forecasted conditions and tactical diversions
from the specified flight plan.
The flight path trajectory is broken into 2 parts, the lateral profile and the vertical
profile. The lateral path and vertical path are interdependent in that they are coupled
to each other through the ground speed parameter. Since the speed schedules that are
flown are typically constant CAS/mach speeds for climb and descent phases, the TAS
(or ground speed) increases with altitude for the constant CAS portion and mildly
decreases with altitude for the constant mach portion, as shown in the following
equations.
Mach = sqrt [(1/  {[1  0.2(CAS / 661.5)2 ]3.5  1}  1)0.286  1]
(3.10)
TAS = 661.5  mach  sqrt[ ]
(3.11)
CAS = calibrated airspeed in knots
TAS = true airspeed in knots
  atmospheric pressure ratio(actual temperature / S.L.std.temperature)
 = atmospheric temperature ratio(actual temperature / S.L.std.temperature)
28
29
3.5 ATMOSPHERIC MODELS
3.5.1 Introduction
Part of the flight planning process is to specify forecast conditions for temperatures
and winds that will be encountered during the flight. These forecast conditions help
the FMS to refine the trajectory predictions to provide more accurate determination of
estimated times of arrival(ETAs), fuel burn, rates of climb/descent, and leg transition
construction.
Forecast temperature used for extrapolating the temperature profile is based on the
International Standard Atmosphere (ISA) with an offset (ISA deviation) obtained from
pilot entries and/or the actual sensed temperature.
3.5.2 Standard Atmosphere
The real atmosphere is in motion with respect to the earth, and its properties are a
function of position (longitude, latitude, and altitude) and time. From an operational
point of view, it is necessary to have this information, at least in the region of
operation. However, from a design point of view, that is, when comparing the
performance of two aircraft, it is only necessary that the atmospheric conditions be
characteristic of the real atmosphere and be the same for the two airplanes. Hence, it
is not important to consider the motion of the atmosphere or to vary its characteristics
with respect to longitude and latitude. A simple model in which atmospheric
properties vary with altitude is sufficient.
There are two basic equations which must be satisfied by air at rest: the aerostatic
equation
dp= -  gdh
(3.12)
and the equation of state for a perfect gas
p=  R 
(3.13)
where p is the pressure,  the density, R the gas constant for air, and  the absolute
temperature. For the region of the atmosphere where airplanes normally operate, the
acceleration of gravity and the composition of air can be assumed constant
( g  32.174 ft / s 2 and R=1716.5 ft 2 / s 2 R).To complete the system of equations
defining the standard atmosphere, it is assumed that the temperature is a known
function of the altitude.
Actual measurements of atmospheric properties using balloons and sounding
rockets have shown that the atmosphere can be approximated by a number of layers in
which the temperature varies linearly with the altitude, that is, the temperature
gradient   d / dh is constant.
The layer of the atmosphere closest to the earth ( 0  h  36089 ft ) is called the
30
troposphere; the next two layers ( 36089  h  104,990 ft ) are part of the stratosphere;
and the dividing line between the troposphere and the stratosphere is called the
tropopause.
Because of the assumed temperature profile, the equations defining temperature,
pressure, and density can be written as
d   dh
dp / p  ( g / R )dh / 
d  /   ( g / R   )dh / 
(3.14)
where  is a constant for each layer of the atmosphere. For the troposphere
(   3.5662E  3 R / ft ), these equations can be integrated to obtain:
  518.69  3.5662 E  3h
p  1.1376 E  11 5.2560
  6.6277 E  15
(3.15)
4.2560
where the standard sea level conditions
 s  518.69 R
ps  2116.2lb / ft 2
(3.16)
 s  2.3769 E  3slugs / ft 3
have been used to evaluate the constants of integration. The initial conditions for the
first layer of the stratosphere are obtained by applying Eqs.(3.15) at the tropopause
(h = 36,089 ft) and are given by
 t  389.99 R
pt  472.68lb / ft 2
t  7.0613E  4slugs / ft
(3.17)
3
The integration of Eqs.(3.14) with  = 0 R/ft leads to
  389.99
p  2678.4exp(4.8063E  5h)
  1.4939 E  6 p
(3.18)
The end result of this analysis is that the atmospheric properties satisfy functional
relations of the form    (h), p  p(h),    (h), a  a (h),    (h) .
3.5.3 Exponential Atmosphere
An approximate atmosphere which may lead to analytical solutions is the
31
exponential atmosphere or isothermal atmosphere.
Here, the formula for the density is given by
  s exp(h /  )
(3.19)
where  s is the sea level density and λ is called the scale height. This form is
motivated by the stratosphere formulas where the temperature is constant and
exponential is exact. For the troposphere and the constant temperature part of the
stratosphere, a value of λ which gives an error on the order of 10% is λ= 26,600 ft.
3.5.4 Forecast temperature
Forecast temperature as known a function of ISAdev and altitude, and when ISAdev
become constant, this function is depend on the altitude only. Actually as the altitude
above 36,089 feet (stratosphere), the forecast temperature then can be considered as a
constant value. So there are 2 models for calculate forecast temperature:
Forecast temperature = 15+ISAdev-0.00198  altitude, altitude  36,089
Forecast temperature =-56.5, altitude  36,089
(3.20)
(3.21)
The pressure ratio  respected to troposphere layer and stratosphere layer, follow
different function method to derived, because pressure ratio is also a function of
altitude.
32
 (Pressure Ratio) = (1  0.0000068756  altitude)5.2561 altitude  36,089 (3.22)
 (Pressure Ratio)= 0.22336*e(4.8063*(36089-altitude)/100,000)
altitude  36,089
(3.23)
3.6 MANEUVER PROFILE
3.6.1 Dynamic Equations
Dynamics is used to derive the differential equations for V and flight path angle 
which define the velocity vector of the airplane center of gravity relative to the ground.
Newton’s second law states that
F = ma
where F is the resultant external force acting on the airplane, m is the mass of the
airplane, and a is the inertial acceleration of the airplane.
For the normal operating conditions of airplanes (altitude and speed), a reference
frame fixed to the earth is an approximate inertial frame. Hence, a is approximated by
the acceleration of the airplane relative to the ground.
The resultant external force acting on the airplane is given by
F = T + A +W
(3.24)
where T is the thrust, A is the aerodynamic force, and W is the weight.
These concentrated forces are the result of having integrated the distributed forces
over the airplane and having moved them to the center of gravity with appropriate
moments. Note that the moments are not needed because the force and moment
equations have been uncoupled.
By definition, the components of the aerodynamic force parallel and perpendicular
to the velocity vector are called the drag and the lift so that
A=D+L
(3.25)
3.6.2 Weight Equation
By definition of the fuel weight flow rate W fuel , the rate of change of the weight of
the aircraft is given by
W = - W fuel
(3.26)
Next, the specific fuel consumption
C
W fuel
T
(3.27)
is introduced because it has some special properties. The weight equation becomes
W =-CT
(3.28)
33
and gives the rate at which the weight of the aircraft is changing in terms of the
operating conditions of the propulsion system.
3.6.3 Aerodynamics: Functional Relations
The resultant aerodynamic force is the integrated effect of the pressure and skin
friction caused by the flow of air over the surface of the airplane. The lift and the drag
are the components of the resultant aerodynamic force perpendicular and parallel to
the velocity vector. They satisfy the relations:
1
1
L = C L SV 2 , D = CD  SV 2
(3.29)
2
2
where C L is the lift coefficient, C D is the drag coefficient,  is the density of the
atmosphere at the altitude of the airplane, V is the velocity of the airplane relative to
the atmosphere, and S is the wing planform area.
If the equations governing the motion of air (the continuity equation, the linear
momentum equations, the energy equation, and the perfect gas equation) and the
boundary conditions are nondimensionalized, the integration of the pressure and skin
friction coefficients over the surface of the airplane leads to the following functional
relations for the lift coefficient and the drag coefficient for a constant geometry
aircraft:
C L = C L (  , M , Re ), C D = C D (  , M , Re )
(3.30)
In these relations,  is the airplane angle of attack, while the Mach number and the
Reynolds number are defined as
M 
V

,
Re 
Vl

(3.31)
Here,  and  are the speed of sound and the viscosity of the atmosphere at the
altitude of the airplane, and l is a characteristic length of the airplane. In practice,
Reynolds number effects are neglected in the expression for the lift coefficient so that
Eqs. (3.30) become:
C L = C L (  , M ), C D = C D (  , M , Re )
(3.32)
if the C L equation is solved for  and the result is substituted into the expression
for C D , the following relations are obtained:
 =  ( C L , M), C D = C D (  , M , Re )
(3.33)
34
The equation for C D is referred to as the drag polar.
Another important aerodynamic characteristic of an airplane is the lift-to-drag ratio
or aerodynamic efficiency
E=
L CL

D CD
(3.34)
In terms of nondimensional variables, the lift-to-drag ratio satisfies the functional
relation
E = E ( C L , M, Re )
(3.35)
whereas the dimensional functional relation is given by
E = E(h, V, L)
(3.36)
The lift-to-drag ratio has a maximum with respect to the lift coefficient and with
respect to the velocity. Since E = L/D and the lift is held constant, the velocity for
maximum lift-to-drag ratio is identical with the velocity for minimum drag.
3.6.4 Accelerated Climb
A high-performance airplane increases its speed during the climb. Hence, to
analyze the climb performance of such an airplane, it is necessary to include the V
term in the equations of motion. To discuss an accelerated climb, the following
problem is studied: For a given power setting, find the climb schedule that minimizes
the time to climb from a given initial altitude to a given final altitude.
In order to analyze this problem, the standard assumptions of small thrust angle of
attack, negligible thrust component normal to the flight path, and small normal
acceleration are made. In addition, the weight is assumed to be constant since the
weight only changes 5-10% during the climb. With these approximations, the
equations of motion for flight in a vertical plane reduce to
x  V cos 
h  V sin 
V  ( g / W )[T (h, V , P)  D(h, V , L)  W sin  ]
(3.37)
0  L  W cos 
W  C (h, V , P)T (h, V , P)
Because the lift is not equal to the weight, these equations cannot be solved
analytically. The accelerated climb problem can be solved analytically if the drag can
be written as D (h, V,W). This can be accomplished in two ways. The first is to
35
assume small flight path inclination ( cos   1,sin    ) so that L=W. However, high
performance airplanes can climb at high values of  .The second approach is to
assume that that part of the drag which comes from L  W is negligible with respect to
the remainder. To see this, consider the parabolic drag expression:
D  (1/ 2)CD0  SV 2  2KL2 /(  SV 2 )
(3.38)
From Eqs. (3.8.14)
L2  W 2 cos2   W 2  W 2 sin 2 
(3.39)
So the drag can be rewritten as
D  (1/ 2)CD0  SV 2  2KW 2 /(  SV 2 )  2KW 2 sin 2  /(  SV 2 )
(3.40)
In either case, however, it is possible to write D=D (h, V, W). For a parabolic drag
polar, this means that the drag is approximated by
D  (1/ 2)CD0  SV 2  2KW 2 /(  SV 2 )
(3.41)
which is the drag for L = W.
The altitude and velocity equations are now given by
h  V sin 
(3.42)
V  ( g / W )[T (h,V , P)  D(h,V ,W )  W sin  ]
3.6.5 Thrust and Specific Fuel Consumption (SFC)
One manner of presenting engine data is in terms of corrected thrust and corrected
specific fuel consumption, that is,
Tc 
Cc 
T

(3.43)
C

where the dimension of thrust is lb and that of specific fuel consumption is l/hr. The
pressure ratio δ and temperature ratio θ are defined as:
36

p
ps


S
(3.44)
where the sea level static pressure ps is 2116.2 lb/ ft 2 and the sea level static
temperature  s is 518.69 R. The total pressure p and total temperature  for isentropic
flow of air (ratio of specific heats = 1.4) can be expressed as:
p  p (1  0.M 2 )3.5
(3.45)
   (1  0.2 M 2 )
the corrected thrust and specific fuel consumption satisfy functional relations of the
form
Tc  Tc (M , ), Cc  Cc (M , )
(3.46)
The corrected engine speed η is related to the power setting P  N / N max , where N
is the engine rpm.
With regard to the power setting, the following are accepted definitions:
P = 1.00, take-off thrust
P = 0.98, maximum continuous thrust
(3.47)
From combining above Eqs, the thrust and specific fuel consumption satisfy
functional relations of the form
T  T (h,V , P), C  C (h,V , P)
(3.48)
The Ideal Subsonic Airplane (ISA) is defined as an airplane that has a parabolic
drag polar with constant coefficients, a thrust independent of the velocity, and specific
fuel consumption independent of the velocity and the power setting. Hence, the drag is
given by
D  (1/ 2)CD0  SV 2  2KL2 /(  SV 2 )
and the thrust and specific fuel consumption satisfy the relations
T  Tt ( P)(  / t ) a , C  Ct (  / t )b
(3.49)
37
where the subscript t denotes the tropopause. The main features of these formulas are
that they are exact in the constant temperature part of the stratosphere (a=1, b= 0) and
that they are extended down into the troposphere by putting an arbitrary exponent on
the density ratio. These formulas are more valid near the tropopause than they are
near sea level.
Apply above Eqs to 2 types maneuver, one is unrestricted ascending and
descending segments, one form to calculate average vertical speed for fixed altitude
steps (dh is set integration step). Using fixed altitude steps for this type of segment
allows for deterministic step termination at altitude constraints. For descending flight
the thrust is generally assumed to be at or a little above flight idle.
(Tave  Dave )Vave
GW
V /S 
Tact Vave dVtrue

Tstd
g dh
(3.50)
Tave = Avg. thrust (lb)
Gave = Avg. drag (lb)
GW = A/C gross wt (lb)
Tact = Ambient temp (K)
Tstd = Std. day Temp (K)
Vave = Average true airspeed (ft/sec)
g = 32.174 ft/ sec2
dVtrue = Delta Vtrue (ft/sec)
dh = Desired altitude step (ft)
38
The projected aircraft true airspeed is derived from the pilot-selected speed
schedules and any applicable airport or waypoint-related speed restrictions. Drag is
computed as a function of aircraft configuration, speed, and bank angle. Fuel flow and
therefore weight change is a function of the engine thrust. Once V/S is computed for
the step the other prediction parameters can be computed for the step.
dt 
dh
V /S
where dt = delta time for step
(3.51)
ds=dt( Vtrue +average along track wind for segment),
where ds=delta distance for step
dw  dt  fuel flow(T), where dw=delta weight for step
39
(3.52)
(3.53)
Restricted ascending and descending segments, the following form of the equation
is typically used to compute the average thrust for fixed altitudes step (dh and V/S are
predetermined). Using fixed altitude steps for this type of segment allows for
deterministic step termination at altitude constraints. The average V/S is either
specified or computed based on a fixed flight path angle (FPA).
V / Save  GSave tan FPA , where GSave  segment ground speed (ft/sec)
(3.54)
The fixed FPA can in turn be computed based on a point to point vertical flight path
determined by altitude constraints, which is known as a geometric path. With a
specified V/S or FPA segment the thrust required to fly this profile is computed.
T
dV
W  V / Save
V
 (1  ave true )  D
Vave
g
dh
40
(3.55)
3.7 LATERAL PROFILE
3.7.1 Introduction
If the complete set of six-degree-of-freedom equations of motion (3D flight) is
linearized, it splits apart into two subsets. One subset is composed of the equations for
longitudinal motion, and the other subset is composed of the equations for
lateral-directional motion. The lateral directional motion of an airplane is associated
with the side force, the rolling moment, and the yawing moment, and its state
variables are the sideslip angle perturbation, the roll rate perturbation, and the yaw
rate perturbation, while its controls are the rudder angle perturbation and the aileron
angle perturbation. When the linearized lateral-directional equations are investigated,
it is seen that three modes exist: a non-oscillatory mode called the spiral mode which
is usually unstable, a non-oscillatory mode called the roll mode which is stable, and
an oscillatory mode called the dutch roll mode which is stable.
For the the Subsonic Business Jet (SBJ), the following results have been obtained:
Spiral mode: divergent TS = 992 s
Roll mode: convergent TR = 1.97 s
Dutch roll mode: convergent n = 1.63 rad/s,  = 0.036
Even through the spiral mode is unstable, the time constant is sufficiently large that
corrective action is easily taken by the pilot. Note that while the dutch roll mode is
stable, its damping is quite small.
Design problems associated with lateral-directional motion include making the
spiral mode stable or at least less unstable and making the dumping of the dutch roll
mode larger.
Computing these segments can be difficult because the turn transition distance and
certain leg termination points are a function of predicted aircraft speed, wind, altitude
which is dependent on how much distance is available to climb and descend. For
example, the turn transition at a waypoint requires a different turn radius and therefore
a different distance when computed with different speeds. The altitude (and therefore
speed of the aircraft) that can be obtained at a waypoints is dependent upon how much
distance is available to climb or descend. The interdependency between speed and leg
41
distance presents a special problem in formulating a deterministic set of algorithms
for computing the trajectory. This effect becomes significant for course changes
greater than 45 , with the largest effect for legs such as procedure turns which require
a 180 turn maneuver.
One purpose of the turn is to change the heading of the airplane. Turns occur in
many parts of a typical flight path. On take-off, the pilot may perform a climbing turn
in order to line up with the heading at which the climb to altitude is to be made. In
flying along controlled airways, it is often necessary to change from one heading to
another in order to change airways. These turns are made at constant altitude or in the
horizontal plane. Another purpose of the turn is to estimate the fuel required for air
combat. This is done by computing the fuel needed to perform a given number of
subsonic and supersonic turns at constant altitude (horizontal turns)
Here coordinated turns are considered, that is, turns with zero sideslip angles where
the velocity vector is always in the plane of symmetry of the airplane. As a
consequence, thrust, drag, and lift are also in the aircraft plane of symmetry.
3.7.2 Motion Equation
The subscript h refers to the local horizon system, and the subscript w denotes the
wind axes system. Also, is the heading angle, and  is the bank angle. Motion of
the airplane is restricted to a horizontal plane.
The kinematic equations follow from the definition of velocity
V = dEO/dt
where EO is the position vector of the airplane relative to the ground.
From the definition of acceleration
a = dV/dt
(3.56)
(3.57)
When drag and lift are balanced, we can build this equation:
0 = T(h, V, P) – D(h, V, P)
(3.58)
0 = Lcos  - W
(3.59)

 =gLsin  /WV
(3.60)
If the altitude, weight, and power setting are given, above equation can be solved
for the load factor (n = L/W) in terms of the velocity as
n= n(V )
The bank angle can be solved as
1
cos  =
(3.61)
n
42
1 2
n2  1
So that sin  = 1  ( ) =
n
n
(3.62)
Hence,  =  (V)
The objective of this study is to determine the distance, time and fuel consumed
during a turn from one heading angle to another. Hence, is made the variable of

integration. Before continuing, it is noted that the turn rate  is given by Eq. (3.6.5)
can be rewritten as
g n2  1
=
V


(3.63)

So that  =  (V)
The instantaneous turn radius is defined as integrand
r=
V

 (V )

V2
(3.64)
g n2  1
Simple way calculate Turn Radius and Turn Arc length if some condition offered
and fixed, lateral turn construction based on the required course change and the
aircraft’s predicted ground speed during the turn. If the maximum ground speed that
the aircraft will acquire during the required course is known, a turn can be constructed
as follows:
Turn Radius (ft) = (GS 2 ) /( g  tan )
(3.65)
Turn Arclength(ft) =  Course  Turn Radius
GS = maximum aircraft ground speed during the turn
g = acceleration due to gravity
 = nominal aircraft bank angle used to compute a turn
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Select 2 groups GS values and nominal aircraft bank angles to calculate Turn
Radius and Turn Arclength:
For legs such as constant radius to a fix (RF) where the turn radius is specified, a
different form of the equation is used to compute the nominal bank angle that must be
used to perform the maneuver.
 = arctan[ GS 2 / (turn radius  g)]
(3.66)
To determine the maximum aircraft ground during the turn the FMC must first
compute the altitude at which the turn will take place, and then the aircraft’s planned
speed based on the selected speed schedule and any applicable wind at that altitude.
The desired bank angle required for a turn is predetermined based on a trade-off
between passenger comfort and airspeed required to perform a lateral maneuver.
3.8 VERTICAL PROFILE
3.8.1 Introduction
The aircraft’s vertical state is computed for the end of the step and the next step is
initialized with those values. Termination of an integration step can occur when a new
maneuver type must be used due to encountering an altitude or speed constrain, flight
phase change, or special segments such as turn transitions where finer integration
steps may be prudent.
Mainly aircraft used to flight in a vertical plane. This is not very restrictive because,
with the exception of turns, the basic trajectory segments of both mission profiles and
the stability calculations are in the vertical plane.
Most of the material in this discussion is limited to flight in a vertical plane because
the mission profiles for which airplanes are designed are primarily in the vertical
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plane.
As mentioned, with the exception of the turns, each segment takes place in a plane
perpendicular to the surface of the earth (vertical plane). The turns take place in a
horizontal plane.
The six-degree-of-freedom (6DOF) model for flight in a vertical plane is presented
in the wind axes system.
Formulas are derived for calculating the forces and moments.
3.8.2 Motion Equation
The translational equations for flight in a vertical plane in the wind axes system are
given by Eqs. (3.37).
From dynamics, it is known that the pitching motion of an airplane is governed by the
equation
M = I yy 
(3.67)
where  is the pitch angle, M is the resultant external moment (pitching moment),
where I yy is the mass moment of inertia and  is the angular acceleration, both
about the vertical axis. If the pitch rate Q =  is introduced, this second-order
equation can be replaced by two first-order equations:
=Q
Q = M/ I yy
(3.68)
In general, the moments acting on an airplane are due to the thrust force and the
aerodynamic force being moved to the center of gravity and due to the gyroscopic
effects of the rotating masses in the engines. For the longitudinal motion of a
conventional airplane, the gyroscopic moment vector lies in the vertical plane. Hence,
it causes small rotations about the roll and yaw axes (lateral-directional motion). For
small perturbations, lateral-directional motion does not cause longitudinal motion.
Therefore, the gyroscopic moment does not affect longitudinal motion so that the
pitching moment is given by
M = MT + M A
(3.69)
45
The complete set of the 6DOF equations of motion for flight in a vertical plane in the
wind axes system is given by
x  V cos 
h  V sin 
V  ( g / W )[T cos(   0 )  D  W sin  ]
  ( g / WV )[T sin(   0 )  L  W cos  ]
W  CT
Q
Q  M / I yy
(3.70)
where  =  + 
(3.71)
These equations contain several quantities (D, L, T, and C) which are functions of
variables already present.
If the airplane is pitching nose up about the center of gravity, the downward motion
of the tail increases its angle of attack. This increases the lift of the horizontal tail and,
in turn, opposes the rotational motion. This effect is modeled by including the pitch
rate Q in the aerodynamics. There is a wing contribution from the wing, but it has
been modeled in the literature by increasing the tail contribution by 10%. It is
assumed that the flow field around the airplane instantaneously adjusts itself to angle
of attack and velocity changes. This is possible because these changes are not made
rapidly. The deflection of the free stream by the wing, called downwash, moves from
the wing to the horizontal tail in a finite time. This is modeled by assuming that the
aerodynamics is a function of 
The effects of Q and  on the thrust, specific fuel consumption, drag, and thrust
moment are neglected. If the effect of elevator deflection  E on the drag is also
neglected, the propulsion and aerodynamic terms in the equations of motion satisfy
the following functional relations:
T = T(h, V, P), C = C(h, V, P)
D = D (h, V,  ), L= L (h, V,  ,  E , Q,  )
M T = M T (h, V, P), M A = M A (h, V,  ,  E ,Q,  )
(3.72)
Given the aerodynamics and propulsion characteristics of an airplane, these
46
equations can be used to perform a numerical simulation of its pitching motion. One
use of such a simulation is to study the stability characteristics of an airplane and its
response to control and gust inputs throughout the flight envelope. Since the motion is
only of interest for a short period of time, the atmospheric properties and the mass
properties can be assumed constant. As a result, the kinematics equations and the
mass equation uncouple from the system, and only the dynamic equations are
relevant.
3.9 PERFORMANCE COMPUTATIONS
The performance function provides the crew information to help optimize the flight
or provide performance information that would otherwise have to be ascertained from
the aircraft performance manual. FMSs implement a variety of those workload
reduction features; only the most common functions are discussed.
Part of the vertical flight planning process is the crew selection of performance
modes for each flight phase based on specific mission requirements. These
performance modes provide flight profile optimization through computation of flight
phase-dependent, optimized speed schedules that are used as a basis for the trajectory
prediction, generation speed targets, and other performance advisories.
The selection of a specific performance mode for each flight phase results in the
computation of an optimized speed schedule, which is a constant CAS, constant mach
pair, which becomes the planned speed profile for each flight phase.
It also be noted that one performance mode that is common to all flight phases is
the economy speed mode which minimizes the total cost of operating the airplane on a
given flight. This performance mode uses a Cost Index, which is the ratio of
time-related costs (crew salaries, maintenance, etc.) to fuel cost as one of the
independent variable in the speed schedule computation.
Cost Index (CI) = Direct Use Cost / (100*Related Fuel Price)
Direct Use Cost = Flight Time*Use Cost per hr + Related Fuel Price*
Cumulative Fuel Consumption
(3.73)
(3.74)
The Cost Index allows airlines to weight time and fuel cost based on their daily
operations
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CHAPTER 4
CONCLUSION
This project, starting from introduce the avionics system architecture to airplane flight
trajectory analysis, also can say from the physically appearance architecture to
theoretically principle of performance analysis, now coming to a conclusion.
This project main target is roughly figure out the commercial aircraft flight deck
operation construction and the theory behind the flight, or can say performance
analysis. I think can say the target is achieved. Related to real flight, explained flight
planning, try to make readers realize the how the pilots work co-operates with FMS
during flight. As a research report, I hope it can provide some benefits for readers.
During the journey of project study, I learned much new and interesting avionics
knowledge. On the other hand, planning is the other important part, I also learned how
to handle task within certain time span.
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CHAPTER 5
FUTURE WORK
The range this project covered is very wide, and related to many study areas. This
project can be developed and extended in many ways, cause the technology of
avionics also developing in every generation, but design principle of avionics industry
is stable and last long, compared to IT industry high frequency changing, the
fundamental still no much change in past 30 years. So it’s still quite valuable to
continue study thoroughly.
I suggested if possible, perform a thorough study in one of the aspects in this
system, and give a more professional research, then that one will be more valuable,
and it not only has meaning to normal readers, also help people working in this
industry.
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REFERENCES
[1] http://www.aviationtoday.com/av/categories/commercial/8420.html
[2] http://www.centennialofflight.gov/essay/Evolution_of_Technology/
Navigation_tech/Tech33.htm
[3] http://www.boeing.com/commercial/737family/index.html
[4] http://www.docin.com/p-527030.html#documentinfo
[5] http://www.boeing.com/commercial/aeromagazine/aero_04/textonly/
ps02txt.html#fig1
[6] http://www.globalsecurity.org/military/world/europe/a310.htm
[7] http://www.aerospace-technology.com/projects/boeing737_NG/
[8] http://www.flug-revue.rotor.com/FRHeft/FRH0003/FR0003a.htm
[9] “The Avionics Handbook edited” by Cary R.Spizer, AvioniCon, Inc Williamsburg,
Virginia.
[10] “Fundamentals of Airplane Flight Mechanics” ISBN-10 3-540-46571-5
David G. Hull
[11] “Cockpit Engineering”
ISBN 0-7546-1751-3
JARRETT.D.N
[12] “Avionics for the Pilot”
ISBN 978-1-86126-896-9 JOE JOHNSTOW
[13] “Instrument Flying Handbook” ISBN 0-07-136198-7 TURNER, THOMAS P.
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