This book represents the professional statement of my 30+ year career. Working with my aerospace engineering students, pilot students, and air traffic controller students over many generations has been challenging in the best possible way. Debates, ideas and questions in the classroom were very productive in setting the contents.

This is a book on paper meant to be read in an Internet-based world. Some issues are presented as curiosity starters, inciting the reader to look further online. That feature allows the book to be comprehensive, while remaining in a single volume.

Many facts are illustrated with pertinent stories, examples, and case studies. It can be considered a story book, and my experience with the students showed that this approach brings the audience closer to the subject and raises the involvement. People behind these stories are often fascinating, and many personalities are briefly mentioned, bringing in emotions, which normally do not belong to a typical science and technology book. However, young generations of students seem to be attracted to this approach.

Case studies accompany various chapters. Their role is to connect the text to reality, providing real life examples, as an aid for learning. Aviation is an intelligent domain, because every accident or incident is an opportunity to learn useful lessons. Actually, the development of aviation is sometimes shaped by the reaction of the aviation community to such unwanted events. Each aircraft system and procedure has a history of accidents and incidents behind its current shape, role, and functionality. Case studies in this book are essentialised on a single page format, in contrast to the hundred of pages of aircraft investigation reports. Obviously, there is a heavy loss of significance in this reduction process. Readers are encouraged to search the details on the Internet, where most official accident reports are found.

Numerical examples called Numerical Close-Ups are essential to this book. In my 30+ years of experience as a professor, I often had the illusion of clearly understanding technical issues by reading theory, and yet everything collapsed when I tried the first numerical example. In the end, after I managed to make the numerical example work, I realised that my initial understanding had been superficial. This book does not try to explain things for which the author is not capable of providing a numerical implementation. This feature appeals to a fraction of the readers who are attracted to the practical side of things and to calculations. The numerical methods in the book can be easily included in software written by the readers themselves, because they are the opposite of the Matlab style black boxes. Numerical examples reflect the problem solving nature of the book, above anything else.

Much of the complexity of air navigation is illustrated in this book with graphics made by the author. I did it since 1995, when my first book was published by a prestigious technical editor (Editura Militară of Bucharest). Since then, I have noticed that splitting the work between authors of text and professional illustrators is often counterproductive. Many drawings and diagrams that I see in the literature miss essential points from the text if not worse (misconceptions and errors), and this is a fracture which I hope I managed to avoid.

The book is original and this originality is intended. Decision what to include and what to exclude from this book starts with fresh and hopefully original ideas (to my surprise, many original ideas that I thought I had I have found somewhere else in the end, but I took that as a nice confirmation). Originality in aerospace engineering is a tough bet though.

This book is useful to the aerospace engineering students and engineers, but also for those curious pilots and air traffic controllers who want to order their knowledge in a more structured way and to understand why the systems are so complex in aviation and how do they work. Also the book helps computer scientists and scientists of adjacent disciplines, who want to study a subject of aviation.

At this stage the book is 85% finished. Chapters 10 and 11 are still in progress and Chapters 9 and 12 are advanced but not finished. The scaffolding for this book started way too early, back in 1992, but I have really committed myself since June 2020 to it. Microsoft Word tells me 54,692 minutes of editing, and that is just the text. Corel Draw does not have a minutes counter. I hope they are minutes well spent. Until I finish it in 2022, I hope to find a good way to publish it and to make it available to that niche audience that would enjoy it and find it useful.

Octavian Thor Pleter

Bucharest, 10 January 2022



Ch. Chapter Title Pages
0 Intro 6
1 Navigation Jargon 6
2 Geodesy 48
3 Atmosphere 84
4 Directions, Azimuths, Horizon 80
5 Time 48
6 Vertical and Horizontal Navigation 46
7 Aircraft 80
8 Radio Navigation 144
9 Trajectory 56
10 Air Traffic Management 48
11 Flight Planning and Management 32
12 Navigation Optimisations 48
13 References 8
14 Index 24
  Total 758


List of Case Studies

Ch. Case Key facts Page
2 A333, THY 726, Kathmandu, Nepal, 4/03/15 truncating errors in coordinates, landing below minima 60
3 An-148, Reception flight, Voronezh, 5/03/11 accelerating at 30 kts over VNE due to gross ASI errors 126
3 A332, AFR 447, Tasil Point, Atlantic Ocean, 1/06/09 dissimilarity principle disregarded, Pitot icing, flying pilot fails to control manually in direct law 130
3 B757, PLI 603, Lima, 2/10/96 static vents blocked 131
3 Boeing 737 MAX, LNI 610, Java Sea, 29/10/18 AOA sensor failure, single point of failure design error, pilots not made aware of the MCAS system 141
3 Boeing 737 MAX, ETH 302, Bishoftu, Ethiopia, 10/03/19 AOA sensor failure, single point of failure design error, wrong technical note on the MCAS de-activation 142
3 A320, test flight, Perpignan, France, 27/11/08 AOA sensors frozen due to washing the aircraft with water under pressure 143
3 A321, LHA 1829, Bilbao, Spain, 5/11/14 AOA sensors blocked, 2 out of 3 logic beaten by circuit breaker 144
4 B752, AAL 965, Cali, Columbia, 20/12/95 CFIT by NDB identifier confusion and inadvertent turn 224
5 IS-28M2 formation flight to Australia record breaking motor gliders flight 272
6 A320, Air Inter 148, Mt. St. Odile, 20/01/92 confusion between FPA and VS autopilot descend functions 288
7 A310, RO 381, Paris Orly, 24/09/94 speed envelope protection not understood by pilots, who attempted to accelerate aircraft beyond VFE 351
7 A310, RO 371, Balotești, Romania, 31/03/95 ATHR software bug not corrected, pilot incapacitated, pilot flying not aware of the attitude and engines, not aware of the technical note on the ATHR problem 356
7 B772, AAR 214, San Francisco, CA, 6/07/13 poor airmanship in manual approach, wrong autopilot mode selection for the final approach (FLCH), pilots failed to monitor airspeed, special cockpit conditions 359
7 A320, AWQ 8501, Java Sea, 28/12/14 pilot resets AFCSs and fail to control manually in direct law 371
7 A320, LH 2904, Warsaw, 14/09/93 bad wind report by the Tower, all braking systems disabled by software under half touchdown circumstances 372
7 B773, UAE 521, Dubai, 3/08/16 pilots not aware that automated go around cannot be engaged after touchdown resulted in overrun 373
7 A388, QFA 32, Singapore, 4/11/2010 uncontained engine failure, multiple failures, resilient response from the crew 380
7 MD-82, Spanair 5022, Madrid Barajas, 20/8/2008 wrong take-off configuration (zero flaps) not warned due to improper maintenance 383
8 B732, Varig 254, Amazonian Jungle, Brazil, 3/09/89 bad navigation, change of flight plan format, NDB confusion 443
8 B738, THY 1951, Schipol, the Netherlands, 25/2/09 single RA in APP mode fails, throttle retards, pilots fail to monitor airspeed, special cockpit condition 489
8 A343, AF 3093, Paris, CDG, 13/03/12 false glideslope interception, obsolence of the ILS-GP system as per new ways to navigate (CDA) 526
10 XPDR incidents latent condition of future midair collisions due to obsolence of FWS ranking XPDR as non-essential avionics
10 B752 and T154 midair collision, Uberlingen, 1/07/02 midair collision due to the  problems of principle with integrating TCAS in ATM
10 CL60 and A388, Arabian Sea, 7/01/17 enroute wake turbulence accident
11 DC10, TE 901, Mount Erebus, 28/11/79 pilots not aware of changed flight plan
11 RJ85, LaMia 2933, Mt. Cerro Gordo, Columbia, 28/11/16 wrong flight planning resulting in fuel starvation
11 A310, Hapag Lloyd 3378, Vienna, Schwechat, 12/07/00 wrong assumption by the pilots that FMS does accurate fuel management calculations resulting in fuel starvation
12 B742, KAL 007, Sakhalin Island, 1/09/83 gross navigation error resulting in flying in a prohibited area
12 B772, MH370, Indian Ocean, 8/03/14 hijacking
12 B772, BAW 38, London, Heathrow, 17/01/08 obsolence of engine design as per new ways to navigate (CDA)




List of Case Examples

Ch. Case Key facts Page
2 Douglas Aircraft World Cruiser 1924 from Santa Monica, California Frederick L. Martin and others first circumnavigation flight 18
2 Concorde AF1995 Air France 1995 around the globe from JFK airport in New York, USA and fastest circumnavigation with passengers in 31.5 hrs 19
3 A320, Atlasglobal Ukraine KK-1010 near Istanbul on 27/07/2017 hail 103
3 BAC 111 One Eleven test flight deep stall due to the T-tail 139
7 BA3271 landed at Edinburgh instead of Dusseldorf flight plan mistake 342
7 AirAsia from Sidney to Kuala Lumpur, Malaysia, landed in Melbourne flight plan mistake 342
7 Helios Airways 522 at Grammatiko, Greece on 14/08/05 pilots incapacitated by hypoxia 344
7 A320, LHA 044, Hamburg, 1/03/08 insufficient amplitude of lateral movement of the sidestick after half touchdown, pilots not made aware of the gain adaptation feature 364
7 B738, ETH 409, Beirut, 25/01/10 A/P failed to engage due to interlock, CRM failure, loss of situational awareness 365
7 Trident BEA and DC9 Inex Adria midair collision, Zagreb, 10/09/76 Wrong climb clearance in Serbo-Croatian, chronic overload of ATCOs, many precursor incidents 389
7 E170 LOT 7293 and Dassault Falcon 900 airprox, Varna, 30/06/15 Near collision due to transponder failure not processed by ATC 395
8 US Air Force CT-43A near Dubrovnik 1996 flying NDB instrument approach with single ADF 447
8 GPS jamming New Jersey
12 Formation flying




List of Personalities

Ch. Personality (order of appearance in the book) Page
2 Friedrich Robert Helmert – founder of modern geodesy 13
2 Pythagoras 13
2 Erathostenes of Cyrene 13
2 Cristofor Columbus 15
2 Ferdinand Magellan 16
2 Piri Reis 17
2 Francis Joyon – fastest circumnavigation by boat 18
2 Frederick L. Martin – first circumnavigation in flight 18
2 Alva L. Harvey – first circumnavigation in flight 18
2 Lowell H. Smith – first circumnavigation in flight 18
2 Leslie P. Arnold – first circumnavigation in flight 18
2 Leigh P. Wade – first circumnavigation in flight 18
2 Henry H. Ogden – first circumnavigation in flight 18
2 Erik H. Nelson – first circumnavigation in flight 18
2 John Harding Jr – first circumnavigation in flight 18
2 Humphrey, Duke of Gloucester – founder of Royal Observatory of Greenwich (England) 33
2 Pierre Louis Maupertuis – introduced rotation ellipsoids as Earth approximators 38
3 Alexandr Fedotov – flight at the record height 78
3 Phillip Dalton – inventor of flight computer 90
3 Sadi Carnot 104
3 Henri Pitot 109
4 John Bird – co-inventor of sextant 152
4 Capt. John Campbell – co-inventor of sextant 152
4 John Hadley – inventor of octant 153
4 Cornelius Douwes – first mathematician to formulate the astronomical positioning problem 156
4 Capt. Thomas Hubbard Sumner – inventor of astronomical positioning method 157
4 Marcq de Saint Hilaire– inventor of astronomical positioning method 158
4 Archibald Smith – inventor of compass deviation compensation method 181
4 Leonhard Euler 192
4 Peter Guthrie Tait – co-author of a formalisation of the Euler angles adapted to aviation 192
4 George H. Bryan – co-author of a formalisation of the Euler angles adapted to aviation 192
4 William Hamilton – inventor of quaternions 194
4 Jurgis Kairys – aeronautical engineer and aerobatic pilot 213
5 Jerrold Zacharias 1953 – first atomic clock 227
5 Julius Caesar 230
5 Pope Gregorius the XIII-th 230
5 Johannes Kepler 233
5 Iosif Silimon – aeronautical engineer 251
5 Gemma Frisius – discovered longitude-time dependency 258
5 Philipp Eckerbrecht – cartographer 258
5 Galileo Galilei 258
5 Christiaan Huygens – inventor of pendulum clock 258
5 John Harrison – inventor of navigation chronograph 258
6 Viktor Georgiyevich Pugachyov – pilot, inventor of Cobra manoeuvre 280
6 Sir Isaac Newton 306
6 Charles Stark Draper – inventor of Inertial Navigation System 309
7 Orville Wright – co-inventor of the controlled airplane 320
7 Wilbur Wright – co-inventor of the controlled airplane 320
7 Robert Esnault-Pelterie – inventor of flying stick 320
7 Montgolfier brothers – inventors of hot air balloon 321
7 Jean-François Pilâtre de Rozier – first balloon flight 321
7 François Laurent d’Arlandes – first balloon flight 321
7 Count Ferdinand von Zeppelin – inventor of dirigible 321
8 James Clerk Maxwell 399
8 Heinrich Herz 403
8 Nikola Tesla – co-inventor of radio technology 405
8 Guglielmo Marconi – co-inventor of radio technology 405
8 Edwin Howard Armstrong – inventor of superheterodyne 434
8 Robert Hanbury Brown – co-inventor of Radar, inventor of the Rebeka-Eureka precursor of DME 464
9 Gerardus Mercator
9 Johann Bernoulli
9 Elrey B. Jeppesen
10 Ernst Mach
12 Rudolf Kalman




List of Photos

Ch. Photo Keywords Page
1 Mircea barque, the traditional training ship for the Romanian Navy sea, maritime navigation 8
1 Open sea sea 9
1 Nasa: Earth picture from the Moon orbit, Apollo 11 Earth, Apollo 12
2 Friedrich Robert Helmert Helmert 13
2 Erathostenes of Cyrene Erathostenes 13
2 Cristofor Columbus Columbus 15
2 Viajes_de_colon Columbus voyages 15
2 Ferdinand Magellan Magellan 16
2 Magellan_Elcano_Circumnavigation-fr Magellan voyage 16
2 Piri Reis map of South America Piri Reis 17
2 Francis Joyon – IDEC SPORT trimaran Joyon 18
2 Frederick L. Martin Martin 18
2 Douglas Aircraft World Cruiser Douglas 19
2 Concorde Air France Concorde, Air France 20
2 water drop 21
2 paperclip and insect superficial tension 21
2 sphere 21
2 tetraedron 22
2 raindrop 22
2 Earth from space: Celestis memorial spaceflights Earth 25
2 Earth’s Geoid as seen by GOCE Earth, geoid 28
2 ECEF frame ECEF 30
2 Humphrey, Duke of Gloucester Humphrey 33
2 Royal Observatory of Greenwich Greenwich 33
2 Prime Meridian set in stone Greenwich, Prime Meridian 33
2 plumb bob plumb bob 55
2 NGA, Earth’s EGM2008 Geoid Earth, geoid 55
3 barometer barometer 61
3 cruise head to head encounter cruise 81
3 Aristo Aviat flight calculator flight calculator 89
3 de-icing a Boeing 777 in snowfall de-icing 104
3 B-52 B-52 105
3 Henri Pitot Pitot 109
3 B737 EFIS EFIS 118
3 machmeter machmeter 123
3 slideslip angle on PFD sideslip 140
4 cardinal and ordinal points cardinal points 145
4 wind rose wind rose 145
4 azimuth dial azimuth dial 146
4 long exposure night sky quiz night sky 148
4 sextant on board Boeing KC-135A sextant KC-135 156
4 Ilyushin Il-14 with astonomic observation cupole Il-14 159
4 Chinese South Pointer (200 AD) spoon-like magnetic compass 168
4 Typical maritime magnetic compass (horizontal) magnetic compass 169
4 aviation magnetic compass magnetic compass 169
4 wander of Magnetic North pole Magnetic North 171
4 TN, MN, and ARC MN VAR chart symbols 173
4 ARC example MN VAR ARC 174
4 Runway marks RWY 33L runway 176
4 Jeppesen low level radio navigation chart aeronautical chart 176
4 compass deviation diagram compass deviation 183
4 gyroscope and its spin axis gyroscope 189
4 Jurgis Kairys sideslip flying sideslip flying 213
4 turn from B737 cockpit photo by Patrick Lutz, a Top 100 cockpit 218
4 Turn Coordinator TCI 219
4 HDG select and bank limit knob on MCP B737 bank limit 220
4 60° bank turn from Dassault Falcon-2000 cockpit by Fabrice Sanchez, 60° bank turn 222
5 Giza pyramids, Cairo, Egypt pyramid complex 225
5 astronomical clock, Prague, Czechia astronomical clock 225
5 Stonhenge, Gr. Britain stone calendar 225
5 apparent movement of the Sun in the sky from sunrise to sunset Sun movement 226
5 egg egg 227
5 liquid outer core of the Earth in cross section Earth cross section 227
5 first atomic clock based on Caesium (Jerrold Zacharias 1953) atomic clock 227
5 modern atomic clock based on Rubidium installed at BNM-LPTF, Paris atomic clock 227
5 IERS measurements of the Earth spin with atomic clocks between 1960 and 2020 Earth spin diagram 229
5 Julius Caesar Julius Caesar 230
5 Pope Gregorius the XIII-th Pope Gregorius the XIII-th 230
5 twilight Dumitru Oprisiu twilight 237
5 EOT display, the clock of Piazza Dante, Naples EOT 243
5 navigation lights of an airplane navigation lights 249
5 Blériot-Spad 46 airplane of the French-Romanian Navigation Company over Constantinople FRNA 250
5 Iosif Silimon at ICA Ghimbav Silimon 251
5 IS-28M2 and Airbus A300 at Paris Air Show 1975 IS-28M2, A300 251
5 IS-28M2 prototype flying over Sibiu IS-28M2 252
5 John Harrison Harrison 259
5 24 Time Zones and the Civil Times worldwide time zones 260
5 Solar Time compared to the Standard (Local) Time solar time, local time 261
5 Daylight Saving Time (DST) DST 262
5 Date Change Line opposed to the Prime Meridian 264
5 Salvador Dali 270
6 Viktor Georgiyevich Pugachyov Pugachyov 280
6 Air Inter 148 approach trajectory 289
6 Air Inter 148 vertical and horizontal wind triangles 290
6 Wind triangle 292
6 Flight computer CX-2 295
6 Flight computer Aristo Aviat 296
6 holding pattern displacement by wind hold 304
6 Sir Isaac Newton Newton 306
6 Charles Stark Draper Draper 309
6 Excel formula for integration inertial navigation 316
6 Diagram of acceleration and integrated speed inertial navigation 316
6 Diagram of acceleration, integrated speed, and double integrated distance inertial navigation 317
7 Orville and Wilbur Wright 320
7 The Wright Flyer 320
7 USS Macon flies above New York in 1933 323
7 ROMBAC One-Eleven 325
7 Airbus sidestick 363
7 Boeing column and steering wheel 363
7 LHA 044 A320 incident at Hamburg RWY 23 364
7 A/P instinctive Cut-Out button 365
7 Boeing 737-700 FMS CDU snapshot from PMDG Flight Sim FMS CDU 376
8 James Clerk Maxwell 399
8 Wave/Electromagnetic theory vs. Corpuscular/Quantum theory 403
8 electromagnetic propagation phenomena 404
8 Nikola Tesla 405
8 Guglielmo Marconi 405
8 radio communications 405
8 radio communications broadcast 406
8 radio location 407
8 passive radio location 408
8 primary radio location 408
8 secondary radio location 410
8 directivity diagram of a stick antenna 423
8 directivity diagram of a rectangle antenna 424
8 rectangle antenna with more loops to multiply sensitivity 424
8 cardioid 425
8 horizontal and vertical directivity diagrams of a highly directive antenna 425
8 primary radar antenna with a parabolic reflector 426
8 parabolic reflector cross section 426
8 demodulator 431
8 Edwin Howard Armstrong 434
8 superheterodyne block diagram 435
8 landscape for visual navigation in daylight 442
8 night time landscape with fires to mark the flight route 442
8 radio beacons replacing fires 442
8 ADF-NDB system 442
8 ADF on ND Map Mode 445
8 ADF on ND VOR Mode 445
8 VDF antenna 448
8 VDF unit 448
8 VDF control panel 449
8 VOR radial 458
8 DME transponder Moog 473
8 DME transponder ground antenna 475
8 DME locator Collins 476
8 Radar altimeter measurement principle 477
8 Radar altimeter errors 481
8 Boeing 737-700 flight plan KDTW-KORD first part 504
8 Boeing 737-700 flight plan KDTW-KORD second part 504
8 Boeing 737-700 – cockpit front panel, ND on Map Mode 505
8 Boeing 737-700 – cockpit front panel ND on VOR Mode 505
8 Boeing 737-700 on the final – cockpit front panel 506
8 Boeing 747-400 on short final 515
9 LROP-LRTR direct route on map
9 LROP-LRTR direct route diagram
9 Gerardus Mercator
9 LROP-LRTR loxodrome diagram
9 YSSY-KORD orthodrome on map
9 YSSY-KORD  orthodrome diagram
9 LROP-PAFA loxodrome diagram
9 Typical wind rotor
9 2D Brachistochrone results
9 2D Brachistochrone genetic algorithm convergence diagram
9 3D Brachistochrone results
9 3D Brachistochrone genetic algorithm convergence diagram
12 Rudolf Kalman
12 Diagram of Kalman filter positioning results
12 Diagram of Kalman filter velocity results




List of Figures

Figure Legend Page
2.1 Erathostenes of Cyrene calculated the circumference of the globe around 200 BC with an outstanding accuracy (4%) 14
2.2 The Earth represented as a sphere, in its Eastward rotation with the angular speed W 23
2.3 The Earth represented as an oblate  rotation ellipsoid, as flattened by the unevenly distributed application of the centrifugal force generated by its spin around the polar axis 24
2.4 The meridian circle of the Earth is an ellipse, almost all celestial bodies and their trajectories

in the universe are ellipses

2.5 The major semiaxis a and the minor semiaxis b of an ellipse; c is the distance of the focal points F1 and F2 from the centre O; the ellipse is the locus of the points Q for which F1Q+F2Q=constant 27
2.6 A meridian cross-section of the geoid (blue) and the rotation ellipsoid (magenta); the geoid is exaggerated in this drawing to improve visibility; in reality the differences are less than 0.0015% in elevation (undulation), and less than 30″ of arc in deflection of the vertical 29
2.7 Earth Centered Earth Fixed (ECEF) frame in green versus Geodetical Spherical Coordinates (GSC) in red, the most frequently used frames in air navigation 34
2.8 The four approximations of the shape of the Earth with their model equation, timeline, and accuracy 38
2.9 The apparent weight as the sum of the two vectors: mass attraction and centrifugal force, the three verticals, the three latitudes and the acceleration of gravity along the astronomic vertical 44
2.10 For an aircraft A located at a position P on the surface of the Earth, flying at an altitude H, the latter forms a red triangle with R the local radius of the Earth, and r, the distance to the centre of the Earth O 45
2.11 Variation of the acceleration of gravity with altitude (above) and with latitude (below)


2.12 Defining the three verticals in geodesy, and the three surfaces these verticals are normal to 56
2.13 Undulation of three geoid models in a 140x140 NM area centred at Bucharest Aurel Vlaicu International Airport (LRBS) at 10x10 NM interpolated grid resolution 59
3.1 Elementary airplane flight dynamics: for the equilibrium flight, the lift must equal the weight, and the thrust must equal the drag; the unbalance between the lift and weight makes the aircraft to climb or descend, and the unbalance between the thrust and drag makes the aircraft to accelerate or decelerate 63
3.2 The differential hydrostatic equation is the expression of the balance of vertical forces acting on an infinitely small segment of a cylinder in the atmosphere 66
3.3 Earth’s atmosphere segmentation into thermal layers, each with own temperature gradient tk (the temperature values are multiannual averages, if the sea level (H=0) temperature is different from +15°C, the gradients apply from that starting point upwards, and the red polygonal line shifts horizontally) [*88] 73
3.4 International Standard Atmosphere (ISA) is an essential standard, the result of many years of measurements; it specifies how temperature, pressure, and density change with altitude or height above the mean sea level (MSL) 75
3.5 Classic altimeter with two needles and a cursor, or three needles (left); the long needle indicates hundreds of feet, the short needle thousands of feet, and the cursor, tens of thousands; the servoaltimeter (right) is more accurate, and combines the digital display with the analogical indication of hundreds of feet 82
3.6 Depending on the reference setting of the “BARO” knob, the altimeter displays: a) flight level (FL), with respect to the standard ISA pressure p0 = 1013.25 mbar, 101,325 Pa, 29.921 inHg, or 760 mmHg; b) height  above runway threshold, with respect to the pressure measured by the meteorological station at  the airport  pQFE; c) altitude, with respect to the calculated pressure pQNH, at the runway threshold, at the sea level 84
3.7 Barometric and geometric vertical distances in vertical air navigation 86
3.8 Barometric and geometric vertical distances (levels, altitudes, and heights) in Numerical example 3.4 90
3.9 Pressure and temperature fluctuations in the real atmosphere cause isobaric surfaces climb or descend 91
3.10 Defining the fourth vertical in vertical navigation; an aircraft flies along an isobaric surface pS 93
3.11 Effect on hail on an Airbus A320: Atlasglobal Ukraine incident on 27 July 2017 in Istanbul 103
3.12 The basic six instruments in a Romanian made aircraft of the 1930s: airspeed indicator, gyro-horizon as direction indicator, altimeter (top row), turn and slip indicator, and vertical speed indicator (bottom row); historic pictures belong to the Flight instrument Manual of Mr. Lintes [Lin] 106
3.13 Basic six classic flying indicators and their functioning principle (Cessna 172) 107
3.14 Four Pitot tubes are visible on the sides of the nose of this Boeing 747-400 airplane; they need access to a laminar airflow, without interference from other parts of the airplane; the nose is taken by the weather radar, so the next best position is on the sides of the nose, at a significant distance from the fuselage 109
3.15 Longitudinal section through the Pitot-static tube; the frontal hole is hit by the air coming with the airspeed V aka IAS; the lateral holes capture the static pressure (zero airspeed); the difference in pressure between the two channels is the dynamic pressure, from which we can calculate the indicated airspeed IAS 110
3.16 Typical Baro instruments layout for a classic general aviation airplane, with Pitot-static probe, which captures pt and ps 111
3.17 Airspeed Indicator ASI is a differential barometric instrument, the difference between pt and ps dilating the capsules and consequently moving the needle 112
3.18 Airspeed Indicator ASI scale; the normal airspeed envelope is marked green; the yellow arc is acceptable when the atmosphere is not turbulent; the gray arc is for flying with flaps 113
3.19 Evolution of IAS, CAS, EAS, and TAS with the pressure altitude H


3.20 Typical Baro instruments layout for fast classic airliners, with static vents; Mach number is important, so a Machmeter is included; Servo Altimeter and IVSI deliver better accuracy 121
3.21 Climbs and descents in three types of vertical thermal layers, with negative, zero and positive vertical temperature gradient 127
3.22 PUDSOD mnemonic helps the pilots to remember the anomalies caused by the blockages of the Pitot tubes and the static vents to ASI, most frequently due to ice; structural damages can also cause the opposite: leaks 128
3.23 Adiabatic heating and friction increase the temperature of the air sample in the TAT probe and the total air temperature is measured; the Outside Air Temperature is in fact the static air temperature SAT and it is calculated 133
3.24 Typical Baro instruments layout for a modern airliner with Air Data Computer (ADC) or Air Data Reference System (ADRS) and Electronic Flight Instrument System (EFIS) 134
3.25 Air Data Computer (ADC) or Air Data Reference (ADR) logic diagram; inputs are total pressure from Pitot tubes, static pressure from static vents, and total air temperature (TAT), which is used to calculate the outside air temperature (OAT) or T; outputs are pressure altitude on altimeter, vertical speed on VSI, Mach on machmeter, IAS on the ASI, and TAS on the Navigation Display 135
3.26 Typical functional redundancy in a modern airliner (Airbus A330) with three Air Data Reference Systems (ADRS) and Electronic Flight Instrument System (EFIS) to display the baro flight parameters; an additional standby baro instruments set is also fitted 136
3.27 The sensors of the aerodynamic instruments of Airbus A350 137
3.28 The orientation of the airspeed vector V is given by the two aerodynamic angles: AOA and sideslip 138
3.29 Stall Warning System uses Angle of Attack sensors and flaps position setting to trigger a warning

when a approaches aCRIT

4.1 The heading of an aircraft is measured clockwise from North; there are three references for it: true, magnetic, and compass (in case the compass is a classic one with explicit correction card) 147
4.2 The North Star’s proximity to the rotation axis of the Earth 151
4.3 The night sky in the Northern hemisphere 152
4.4 Sextant from 1766 made by Jesse Ramsden [Joh] 153
4.5 Finding the astronomic latitude with a sextant (the dumb way) 154
4.6 The elements of astronomical positioning 155
4.7 Influence of the height on the horizon; the horizon is the locus of the points where tangents from the point of view touch the Earth; its shape is a circle in case of the spherical Earth approximation 160
4.8 Coverage problem of targets flying at height HT by a locator flying at a height HL 164
4.9 Magnetic field of the Earth with its deflected axis and equator and inverted names of the poles 166
4.10 Magnetic field of the Earth generation and its horizontal and vertical components H and Z 167
4.11 Magnetic isogonal chart of the world (NOAA/NCEI and CIRES) 170
4.12 Direct Indicating Compass (DIC) 178
4.13 Hard and soft iron magnetic field components on the three axes to determine the magnetic

compass deviation d

4.14 The flux valve is a transformer with a primary, the excitation coil, and three secondary coils distributed in a regular pattern; it is kept horizontal; the Earth magnetic

field has a differential effect in each of the three pick-up coils; a given set of voltages Ux corresponds to a unique orientation of the flux valve with respect to the magnetic field

4.15 A classic Remote Indicating Magnetic Compass (RIMC) using selsyns to transmit the angular movement of the Mangnetic North reference as measured by the flux valve to the compass vertical card 186
4.16 The key azimuths used in air navigation: headings, courses, gisments, and relevments 188
4.17 Precession of a horizontal gyroscope: apply a vertical force to get a horizontal movement; apply a horizontal force to get a vertical movement 190
4.18 Aircraft attitude angles are Euler angles in the Tait-Bryan formalization: y is the yaw angle and also the heading of the aircraft measured in a horizontal plane; q is the pitch angle measured in a vertical plane, and j is the bank angle around the longitudinal axis; the angles are measured counter clockwise 191
4.19 RLG Laser Gyro use a source of light which emits two beam rays going in opposite directions but arriving at the same photocell sensors, being guided in a triangular path by mirrors; one beam goes clockwise and the other goes the same distance counter-clockwise; on arrival, interference between the two beams forms a fringe pattern; if the body of the gyro rotates one way, the same way beam must cover a longer distance and arrives a bit later, whereas the beam going opposite finds its target sooner; the difference can be measured by the width of the interference strips 198
4.20 Gyroscope with two degrees of freedom; the inner rotor spins around the spin axis with W; the

two articulated gimbals allow the inner rotor to maintain its spin axis, regardless of the angular movements of

the airframe (in blue), providing pitch and bank references

4.21 Topple is a vertical change of rigidity axis, and drift is a horizontal change; vertical gyroscopes can only topple, but the horizontal ones can have both type of wander 202
4.22 Apparent wander (drift and topple) due to Earth rotation 203
4.23 Artificial Horizon Indicator (AHI) or Attitude Indicator (AI) driven by a pneumatic gyro; indications are (from left to right) q=j=0; q=–30°; q=+30°; j=30° Left 205
4.24 Artificial horizon indicator (AHI), with its blue and brown representation of the outside world, was combined with the flight director indicator (FDI, the cross needles which show the autopilot current intentions for the stick movement);  the hybridization result was called attitude director indicator (ADI); later, it was completed with the airspeed indicator, the altimeter and the vertical speed indicator, to give the current primary flight display (PFD) 206
4.25 Primary Flight Display (PFD) and the meaning of the elements in the display; the significance of colours is as follows: white = useful information, magenta = desired or target setting, green = selected setting, red = danger, yellow = alert (except the arrows), blue = sky, brown = ground (Boeing 737-700) 207
4.26 This snapshot from a Cessna C172 illustrates the two main sources of heading information in flight: the magnetic compass (DIC) and the heading indicator (HI) or gyro direction indicator (GDI); HI has a cursor to set the desired heading and also a calibration knob to align with compass when drifting 207
4.27 Gyro Direction Indicator (gyrocompass) with slaving loop using reference of Magnetic North from the flux valve 208
4.28 The heading indicator (HI) and the gisment indicator (GI) evolved into the radio-magnetic indicator (RMI), the most popular classic navigation indicator; both HI and RMI use a rotating dial, and the heading is read at the top, on a fixed cursor; the aircraft symbol is used when the reference of the indicator is the longitudinal axis of the aircraft, otherwise the reference is North 209
4.29 Side by side comparisson between the horizontal navigation situation of an aircraft and the radio-magnetic indicator (RMI) indications; VOR and NDB are radio beacons and the magenta line is the desired route inbound the VOR 210
4.30 The course deviation indicator (CDI) is a qualitative navigation instrument displaying the course

deviation (CD) angle; if the horizontal navigation is right, CD=0 and the needle is centred; if there is a

deviation off course, the needle shows the correct trajectory and the central dot is a symbol of the

aircraft trajectory; in Case 2, pilots need to take corrective action, starting with a left turn, fly straight

for a while, and when the needle approaches the centre, turn back right

4.31 The Horizontal Situation Indicator (HSI) represents a fusion between the classic RMI and the CDI; in the electro-mechanical integration stage of aviation instruments integration (up to the 1980s), it was the state of the art of navigation flight instruments; even now it can be reproduced electronically on the Electronic Flight Instrument Systems (EFIS) navigation panel; HSI integrates all features of predecessors 211
4.32 The Navigation Display (ND) is the navigation panel of the Electronic Flight Instrument Systems (EFIS), its format mode is selectable from map mode (left), plan mode (right) [*B8], VOR mode (a HSI display); in the map mode the aircraft position is symbolised by the tip of a white triangle, and the vertical of the display is the longitudinal axis; in the plan mode, the aircraft has a silouhette, and the vertical in True North 212
4.33 Turn Indicator gyroscope in a Turn and Slip Indicator (T/S); the output is a vertical needle to the right side, part of the basic six instrument panel; the needle inclines more if the rate of turn is higher, in the direction of the turn, as an effect of the amplitude of the rudder control 214
4.34 The coordinated turn is balanced, the slip indicator ball is centred; in the skidding turn, the ball and the turn indicator go in opposite directions, the aircraft has a sideslip angle outside the turn;  in the slipping turn, the ball and the needle go to the same direction, there is a sideslip angle inside the turn 215
4.35 In a coordinated turn, the resultant of the weight W and the centrifugal force C is perpendicular on the plane, along the vertical axis of the aircraft (z), so the slip indicator ball stays right in the middle 216
4.36 Standard Rate-1 Turn as shown on Primary Flight and Navigation Displays (Boeing 737-700) 221
5.1 A complete rotation of the Earth around its polar axis takes one Sidereal Day (23h 56m 4s); the rest up to 24h is needed for the Earth to rotate a bit extra, to compensate for the movement of the Earth on the orbit around the Sun by 1/365.242199 of the orbit 229
5.2 Movements types of an orbital celestial body like the Earth, around a central celestial body like the Sun 231
5.3 Kepler’s Three Laws of planetary movements 233
5.4 Earth’s orbit around the Sun 234
5.5 Daylight hours with latitude and season represented as isochrones; night time hours are

24 – daylight hours; equator is not at 12 as expected, there are 13 hours of daylight due to twilight

5.6 The three phases of twilight: civil, nautical, and astronomic make the transition between daylight and night; each phase occupies a range of 6° angular depth below the optical horizon 238
5.7 Sun’s apparent trajectory in the sky depends on the calendar day, reaching the heighest altitude at the Summer Solstice at noon (in the Northern hemisphere); at equinox, the maximum altitude is equal to the colatitude 240
5.8 Northern higher latitudes experience the white nights phenomenon in summer: the night never comes because the twilight after sunset merges with the twilight before sunrise; in winter, the same phenomenon affects the Southern latitudes 246
5.9 The twilight at equator at equinox lasts the least because the angular velocity of the Sun of 15°/hr is perpendicular to the horizon 247
5.10 The twilight at the poles is the longest, because there is no vertical component of the angular velocity of the Sun apart from that resulted from the revolution movement of the Earth 248
5.11 Each meridian has its own solar time, as the spin movement exposes each meridian in turn to the Sun rays (arriving from right in this top view) 257
5.12 The International Date Line (IDL) in red, and its deviations from the 180°E meridian (the dashed green line) 267
6.1 The phases of a flight in detail, with typical speeds: IAS (blue), Mach (green), and TAS (violet); in a broader view, the airborne flight consists of climb (up to T/C point), cruise (up to T/D point) and descent 273
6.2 The flight route and profile as defined by the flight plan; the route consists of legs connecting the waypoints, and the flight profile is the projection of the trajectory on a vertical plane 274
6.3 The four forces and the angles in climb; the aerodynamic path angle g is positive in climb 275
6.4 The four forces and the angles in level flight; the aerodynamic path angle g is zero during cruise 275
6.5 The four forces and the angles in descent; the aerodynamic path angle g is negative in descent 276
6.6 Navigation display wind is given in the format: direction from/velocity; to avoid to/from ambiguities, a small vector is visualised; in this picture, the wind blows from 149° M at 10 knots (Boeing 787, photo credit Capt. Dumitru Oprisiu) 278
6.7 Vertical navigation wind triangle, vectors and angles 279
6.8 Horizontal and Vertical Navigation Wind Triangle 285
6.9 Horizontal Wind Triangle with headwind and crosswind; tailwind is a negative headwind 286
6.10 Antonov An-2 is a biplane, and the wing surface is almost double than the wing surface of a monoplane; that creates double lift and reduces the stall speed to a value which cannot be determined in flight, due to the insufficient elevator authority (pulling the stick cannot keep the nose up) 299
6.11 The wind triangle problem in a graphic representation: drift angle DA and the GT=GS/TAS ratio are represented as surfaces depending on two variables: the wind impact angle z and the wind to TAS ratio x = WV/TAS 301
6.12 Wind triangle problem on opposite tracks with the same wind; the airplane on the left reaches its destination and then returns on the back course (BC); also this applies to the upwind and downwind of an aerodrome circuit 302
6.13 Classic Inertial Navigation System (INS) with a gyrostabilised platform 309
6.14 Horizontal navigation deviations: crosstrack XTK, track angle error TKE , course deviation 310
6.15 Control panel of a classic Inertial Navigation System (INS) with a gyrostabilised platform 311
6.16 Modern strap down Inertial Reference System (IRS) 312
7.1 A figther jet (McDonnell Douglas F-15 Eagle) firing a missile (AIM 7 Sparrow); the plane uses the atmosphere to create the lift force; the missile does not need the atmosphere to fly 319
7.2 Sensors, transducers, data transmission, processing, and storing of the flight parameters, and the machine to man interface: visual (displays), audio, and tactile 330
7.3 The the first half of the history of avionics records an increasing number of individual displays in the cockpit, in spite of a process of integration of some of the displays into combined displays in the electromechanical integration stage; BAE-Aerospatiale Concorde tops this list with over 200 individual displays; electronics, and then microprocessors allowed massive integration of

information in the second half of this history, ending the story with a stabilization at 6 major displays

7.4 WWI fighter Fokker Dr. 1 Triplane replica with individual gauges (1918) 332
7.5 Human vision is based on two types of sensors: cones (colour perceptors) and rods (monochrome, more sensitive perceptors in darkness), with an interesting distribution,  which is the result of the optimization performed by the genetic algorithms: maximum visual accuity and colour perception stays in a central oval area, where the Basic 6 flight instruments are placed;

peripheral vision is more sensitive in low light and more perceptive to movement,  although it does not provide colour information

7.6 In the history of aviation, the navigator was a specialized flight crew member; he had a panel of navigation instruments and a table where aeronautical charts could be unfolded and used to graphically solve navigation problems; the navigator had access to a window; some airplanes offered a great view down from the belly of the cockpit, to visually measure the drift angle when

the visibility allowed (Lockheed L-1049 Constellation – top left, Ilyushin Il-76TD, bottom and right)

7.7 Flight engineer on board of a Boeing 747-300 (TAAG Angola Airlines) 335
7.8 The evolution of flight crew number and positions in the flight deck of a transport airplane is a direct consequence of flight deck automation, which made redundant most of the positions; in 2020, as the flight is automated (with the exception of the take-off phase), there is debate on the necessity of the remaining two crew members; cargo flight operators would like a crew of one, whereas air taxi operators would like fully automated operations 335
7.9 Layout of flight instruments and controls in a modern Airbus cockpit (Airbus A330/A340) 336
7.10 Layout of flight instruments and controls in a modern Boeing cockpit (B787) 336
7.11 Primary Flight Display (PFD) with Flight Director in split cue variant; the phase of flight is the take-off run; V1, VR, and V2 appear on the Airspeed Tape together with the airspeed trend vector (left); pitch limitation in amber colour indicate the maximum pitch which avoids tailstrike (Boeing 787) [*B8] 340
7.12 Navigation Display (ND) Vertical Navigation section (Boeing 787); target and actual flight profile

appear together with the final approach path and a section through the terrain [*B8]

7.13 The Inner Loop of the Roll Channel Autopilot; by defaults it levels the wings automatically 343
7.14 The Inner Loop of the Pitch Channel Autopilot; by defaults it maintains the initial pitch angle 344
7.15 The Inner Loop of the Yaw Channel Autopilot; by defaults it maintains the initial heading 345
7.16 Autopilot channel algorithm based on Proportional-Integral-Derivative logic and saturation logic 346
7.17 Autopilot outer loop functions for non-Fly-By-Wire aircraft (Boeing 747-400, Boeing 737-700) 348
7.18 Autopilot outer loop functions for Fly-By-Wire aircraft (Boeing 777-200, Airbus A330/A340) 349
7.19 Turbofan engines key parameters: EPR (TPR for Rolls Royce), N1, and EGT; example of EICAS display of the key parameters is Boeing 787-8; examples of turbofan engines:  Rolls Royce AE3007 fitted on the Embraer-145, delivering 40 kN of thrust each (left); General Electric CF34-8C5 deliver 59 kN each for the Canadair Regional Jet CRJ-900 (right)
7.20 Autothrottle functional diagram – adapted from [*OI] 354
7.21 Flight level (pressure altitude) acquisition A/P outer loop function prevents level busts 360
7.22 Boeing CWS (Control Wheel Steering – left and above) and TCS (Touch Control Steering – right) 362
7.23 CAT 3 Fail Passive and Fail Operational Autoland configurations: Boeing 737-700 Fail Passive (above); Boeing 787-8 Fail Operational Triple-Single (inset); Airbus A340 Fail Operational Dual-Dual (below)


7.24 The Flight Management System (FMS) consists of two or three Flight Management Computer (FMC) units, two or three Control Display Units (CDU); it can calculate on optimised 4D trajectory, then it can provide guidance for the auto-pilot to accurately fly it, while monitoring the fuel quantity remaining 375
7.25 Ground Proximity Warning System block diagram 384
7.26 GPWS Mode 1 protects against excessive descent rate (the sudden rise of static pressure) 384
7.27 GPWS Mode 2 protects against excessive closure of the gap between the aircraft and the terrain 385
7.28 GPWS Mode 3 protects against loss of altitude after take-off or go around 385
7.29 GPWS Mode 4 protects against landing without landing gear or flaps or flying too low 385
7.30 GPWS Mode 5 cautions on flying below the ILS glide slope on final approach 386
7.31 GPWS Mode 6 issues call outs during final approach and landing 386
7.32 GPWS Mode 7 protects against the windshear threat 387
7.33 The principle of the Traffic Collision Avoidance System (TCAS) is based on the Tau variable, which is the time left until the own aircraft and the target will be at the closest distance of each other, potentially colliding; 40 seconds before, a Traffic Advisory is issued (caution level – amber), and 25 seconds before, a Resolution Advisory (warning level – red); the trigger threshold is a function of range and range rate 391
7.34 The block and logic diagram of the Traffic Collision Avoidance System (TCAS) adapted after [*RT] 394
7.35 The TCAS logic sense and strength: the normal case, level crossing exception, and sense reversal 397
7.36 TCAS display symbols and meaning 398
8.1 Line of sight propagation is similar to visible light propagation; the range of a radio system is limited by the curvature of the Earth and also can be masked by mountains, hills, buidings etc. 412
8.2 Sky wave propagation: multiple refections between ionosphere and ground (sea water) occurs due to the particular feature of HF to be reflected by the ionosphere 413
8.3 Ground wave propagation: the radio waves follow the curvature of the Earth and the undulations of the surface (mountains, hills) 414
8.4 Radio systems features depend on frequency: antenna size, efficiency, energy consumption, cost and complexity, and range 416
8.5 Atmospheric attenuation of UHF+ radio waves due to absorption by Oxygen and by Water as a function of frequency – adapted from [*IT] 421
8.6 Radio telephony transmitter (above) and receiver (below) using amplitude modulation; insets show the wave forms; carrier is represented in black and the voice signal is in blue 430
8.7 Amplitude modulation variants (A is the normal variant and J is used for long distance radio telephony in HF via sky wave) 432
8.8 Example of frequency modulation of a triangular signal as used in the radar altimeter 433
8.9 The simple modulation types for pulses 433
8.10 Non directional (NDB) and omni directional beacons (VOR) allow goniometry, but in two distinct variants: gisments G and relevments R, respectively; radio telemetry (DME) provides the straight line distance

between the ground station and the aircraft rDME

8.11 Radio telemetry determines a distance (range) r1 between the locator (aircraft) and a target with known position x1, y1, z1; radio differential telemetry determines a difference of ranges r1r2 between two targets with known position and the locator 439
8.12 Automatic Direction Finder rectangular antenna is kept with the direction of nil reception twards the NDB in a closed automation loop, with the gisment being displayed on the GI 444
8.13 Automatic Direction Finder block diagram, with a phase shifter which rotates the cardiod by 90° 60 times per second, to sense which way to turn in case the direction of nil reception of the cardiod becomes misaligned due to the movement of the aircraft, to achieve nil reception back on the shortest way


8.14 Positioning using two ground direction finder stations is similar to Theta-Theta navigation, two QTEs are requested and the position is found at the intersection of the two lines of position; Class C services (+10°) however have a substantial methodical error (Geometric Dilution of Precision, in yellow) 450
8.15 Radio markers (MKR) cover the uncertainty cone of any radio navigation aid used for goniometry by a directional transmission upwards, at the vertical, on a unique standard frequency; the vertical directivity of the NDB antenna is shaped like a doughnut, not covering the vertical 451
8.16 The radiodrome is the locus of points of zero gisment in flying into a non-directional beacon; it takes a spiral shape from integration of the wind triangle and is a direct consequence of the drift angle 453
8.17 VOR principle is to rotate a cardioid directivity antenna; an observer would receive a cycloid signal v (magenta); every time the cycloid passes through zero, another signal, an amplitude modulated cycloid r (cyan) also passes through zero, as a phase reference; thus, the phase of v gives the relevment 454
8.18 VOR locator block diagram shares the radio section with the ILS 455
8.19 Electrical rotation of the Alford loop antenna system is simulated with four perpendicular antennas which are energised by a cosine – sine law (above); VOR Brasov, Romania (BRV) in the Postavaru Mt. (left); VOR ground antenna seen from above with 50+1 Alford loop antennas over a counterpoise (right) 456
8.20 VOR inbound flight is made on a TO radial, so the indications of the Course Deviation Indicator (CDI) are consistent with the needle representing the desired trajectory and the centre dot the actual trajectory of the aircraft; VOR outbound flight requires a FROM radial; the two radials are opposite 459
8.21 Volume of service of three categories of VOR navigation aids: TVOR, low altitude VOR, and high altitude (enroute) VOR; the cone of silence is represented to scale, with a base radius of 11.8 NM at 60,000 ft 461
8.22 TVOR installed in the runway axis at the Geneva International Airport LSGG 463
8.23 The principle of the Distance Measuring Equipment (DME) system; the ground DME transponder automatically replies to all interrogations after a fixed delay, and based on that, the direct (slant) distance may be determined by the on board locator; times in ms correspond to the X channels, Y channels are different 465
8.24 Automated selection of frequency is transparent to the pilot, who only tunes in the main navigation aid the DME is associated with on NAV radio control panel 467
8.25 Generating a pair of DME pulses is a typical application of digital sequential circuits design, involving a digital clock, a Modulo-48 counter, a 6:64 decoder and some gates 468
8.26 Perturbation (spikes) are detected as variations of both pulse width and delay (left); collisions or jitter respect one but not both (right); a very close collision (under 0.15 NM) respects only the pulse delay 469
8.27 If the own pairs are in a random succession, this is the key to identify the own replies in the crowded sequence of replies to everybody; the own interrogation sequence is memorized and than shifted in time (delayed) until a positive match of times is found; the delay coresponds to the Dt 470
8.28 Random time generator using an integrator to trigger a monostable circuit 471
8.29 The DME block diagram including the random pulse clock, the pulse pair generator, the pair validity filter, the automatic gain control amplifier, the superheterodyne on 63 MHz, the search of own replies logic and the calculation and display of the rDME 472
8.30 To be used in horizontal navigation, the distance measured by the DME must be corrected 474
8.31 Radar altimeter transmitted wave Tx and the received echo Rx using frequency modulation of a triangular signal 478
8.32 Radar altimeter block diagram – first variant with large bandwidth IF amplifier 480
8.33 Radar altimeter block diagram – low bandwidth IF variant 481
8.34 Radar altimeter typical components 483
8.35 Primary Flight Display and the radar altimeter height window in the brown area of the artificial horizon indicating –4 ft above ground (B777-200H/ER Emirates, Photo Craig Murray) 484
8.36 Radar altimeter measurement at touchdown vs. front wheel touchdown (taxi posture) 485
8.37 RNAV airways do not require physical radio navigation aids along the route, just navigation fixes, which are database entries 491
8.38 RNAV airborne technology uses microprocessors to emulate by software a virtual VOR/DME wherever is needed, given a dense enough coverage of existent (real) VOR/DMEs 492
8.39 Original on board standalone RNAV equipment with its own control panels; there was no separate display, the RNAV calculated navigation information was displayed on CDI, RMI, or HSI (as above) 493
8.40 Rho-Theta navigation with wind triangle 496
8.41 Rho-Theta Geometric Dilution of Precision (GDOP); the position is found inside the area at the intersection of a triangle with a circular crown, with a given probability 497
8.42 Theta-Theta navigation 498
8.43 Theta-Theta Geometric Dilution of Precision 499
8.44 Rho-Rho navigation 500
8.45 Rho-Rho Geometric Dilution of Precision: a poor case, when the circles are almost tangent 502
8.46 Hyperbola is the locus of points where the difference in the time of arrival (the delay) of two signals from the two focal points is constant 511
8.47 LORAN receiver measures the delays of the slave signals 1 and 2; the position is found at the intersection of the two hyperbolas 512
8.48 LORAN pulse characteristics allow the extraction of the time reference based on the amplitude of the envelope in time, whereas the bandwidth demand is less than the one for a rectangular pulse 513
8.49 Instrument Landing System (ILS) consisting of Localizer (LLZ), Glide Path (GP), and three markers: Outer Marker (OM), Middle Marker (MM), and an optional Inner Marker (IM) 516
8.50 Decision Height (DH) and Runway Visual Range (RVR) are simultaneous constraints to meet in order to continue to land in a precision instrument approach based on instruments 518
8.51 Optimal Glide Slope angle is a trade-off between various conflicting goals factors 520
8.52 A precision approach procedure consists of a turn to intercept the runway extension line and a constant glide slope starting at FAP and ending above the runway, in the touchdown zone 521
8.53 Runway lights (left) or markings (right) are the visual clues that the pilots have to see at the decision height (DH) in order to continue to land; in absence of the visual contact, the approach is going missed and the aircraft performs a go-around 521
8.54 Kinematic diagram of the flare manoeuvre, including the decrab; this manouvre is performed at the end of the final approach segment, prior to touchdown, with the objective of a positive touchdown with a rate of descent limited to –120 fpm 522
8.55 The ILS-LLZ uses an equsignal principle to determine the position of the aircraft with respect to the runway axis; when the left and the right lobe signals are equally received, the aircraft is right in the middle of the two signals, on the bisector; the photo shows the ILS-LLZ antenna arrays 523
8.56 The ILS-GP uses the same equsignal principle to determine the position of the aircraft with respect to a plane descending to the landing position at the published glide slope angle between 2.5° and 4°; when the upper and the lower lobe signals are equally received, the aircraft is right on the bisector of the two slightly divergent lobes; the photos show the ILS-GP antenna arrays 524
8.57 Maintaining a correct stabilized precision approach requires centred needles on the cross hair indicator 525
8.58 ILS-GP was intended to be used using a level intermediary approach trajectory, thus avoiding the false paths which a generated by the multiple ground reflections 525
8.59 Three block diagrams corresponding to the ILS subsystems: ILS-LLZ (loclalizer) block diagram, sharing the radio section and the CDI display with the VOR; in the middle ILS-GP (glide path), tuning automatically on the channel associated to the ILS-LLZ frequency; below the ILS-MKR (marker) 527
8.60 Placement, directivity and identification signals of ILS markers 528
8.61 ILS perturbation factors 529
8.63 A satellite on a circumterrestial orbit of radius R+H is launched vertically then pushed tagentially until it reaches the speed V, for which the centrifugal force C balances the centripetal force W; the satellite continues to orbit indefinitely with no further supply of energy, since the orbit is outside the Earth atmosphere and thus there is no friction to slow it down
8.64 Navstar orbit with four unequally spaced satellites, inclined at 55° from Equator
8.65 All 6 Navstar orbits shifted at 30° increments for a uniform worldwide distribution of the satellites; side view (left) and topdown view (right); apparent size of the satellites suggests viewer distance
9.1 The loxodrome (in green) is the simplest long range navigation route, a “straight” line intersecting all meridians under the same angle (TClox or TKlox); in the inset there is a local infinitely small sample of the trajectory, which is a direct to line, as to this scale, parallels and meridians can be considered straight lines
9.2 The orthodrome (in red) alongside the loxodrome (in green); from the pilot’s perspective, the orthodrome is a giant turn; in the picture, the pilot starts at departure (D) due North-East, and ends up at A, on a South-Eastrly course
9.3 The orthodrome spherical triangle DNA where usually we know a and d as complementary to LATD and LATA respectively; also we know n as the difference between the two longitudes; the orthodrome distance DISORT results from the side n of the triangle, and the terminal tracks from d and a
9.4 A double rotation brings the North Pole onto the Departure Point D; in the rotated frame, all meridians are orthodromes departing from D in all directions
9.5 Crosswind is neutralized by the friction between wheels and ground surface when the aircraft is on ground; when airborne, it is carried by the wind, and its ground speed is deflected from the longitudinal axis by the drift angle (DA); there is a sudden change of track (TRK) at lift-off
9.6 Drift Angle (DA) is visible in these pictures; the crosswind causes the slant attitudes of these aircraft on short final; their tracks (courses) are along the runway axes; prior to touchdown, all these airliners will need to decrab using the rudder, so as the wheels run along the runway axis
9.7 Examples of fast aloft winds (Courtesy of Capt. A310/A318 Emil Dobrovolschi of Tarom): 186 kts (left), 149 kts (above), 132 kts (right), when the Ground Speed ranges from 286 kts to 621 kts
9.8 Crossing a river on the shortest distance (above) and in shortest time (below)
9.9 Thought experiment which illustrates the superiority of the brachistochrone over the orthodrome as air navigation trajectory (ETE is Estimated Time Enroute, the travel time)
12.1 The Cost Index (CI) setting in the Flight Management Computer is the trade-off parameter between economy (fuel savings and subsequently range) and performance (speed)




List of Tables

Table Legend Page
2.1 Rotation ellipsoids in geodesy 39
2.2 Acceleration of gravity correction for each meter of elevation above the ellipsoid 48
2.3 Polynomial correction coefficients 49
3.1 ISA Temperature functions (see Figure 3.3) 77
3.2 ISA Pressure functions (see Figure 3.3) 80
3.3 ISA Density functions (see Figure 3.3) 81
3.4 Basic six flight instruments 108
3.5 Synthesis of Baro Instruments 123
3.6 Baro Instruments Behaviour in case of Blockage and Leaks 129
4.1 Hard and soft iron 179
4.2 Standard turns 217
5.1 Wavelengths and Frequencies of Visible Light 236
5.2 Refraction of Light in the Atmosphere 236
5.3 International Date Line Crossing 266
5.4 Extreme Time Zone Places 267
6.1 Wind triangle particular cases 297
7.1 Buoyancy factor by different gases 322
7.2 ICAO Type Identifier for BAC One-Eleven 324
7.3 Special aircraft designators 325
7.4 Flight Fundamental Actions (the highest priority first) 326
7.5 Potential Reasons to Reject a Take-Off 328
7.6 How many lines of code? 329
7.7 Primary Flight Display information 338
7.8 Navigation Display information (Map Mode) 341
7.9 Airplane Automated Flight Control Systems (Autopilots) 343
7.10 A structured hierarchy of automation layers in aviation 347
7.11 Autoland Status 367
7.12 FBW Control Laws – Airbus and Boeing 369
7.13 Typical FMS software functions [Bu1] 377
7.14 Flight Warning System announcements (priority from highest to lowest) 379
7.15 Genuine / Nuisance / False Alerts 381
7.16 TCAS II V7.1 Alerts and Aural Annunciations 397
8.1 Speed of Electromangnetic Waves 401
8.2 Electromagnetic Spectrum 402
8.3 Radio Communications Disciplines 406
8.4 Radiolocation Disciplines and Examples 407
8.5 Pluses and Minuses of Passive Radiolocation 408
8.6 Pluses and Minuses of Primary Radiolocation 409
8.7 Pluses and Minuses of Secondary Radiolocation 410
8.8 Radio Bands – Carrier Frequency Do 411
8.9 Letter Based Nomenclature of the UHF+ Radio Bands 411
8.10 Bandwidth of typical radio transmissions 419
8.11 Atmospheric Noise Affecting Different Radio Bands (night time) 420
8.12 Classification of Emissions 428
8.13 Modulations Used in Aviation 429
8.14 Radio positioning methods (surveillance included) 438
8.15 Radio Navigation Systems Performance Parameters 440
8.16 Complex VOR Signal Components (see also Figure 8.18) 457
8.17 The allocation of DME channels to associated frequencies 466
8.18 DME channels frequencies and associated frequencies 467
8.19 Positioning Radio Navigation Systems 509
8.20 ILS channels and frequencies 528
8.21 Orbital parameters of the GNSS systems satellites
9.1 Classification of brachistochrones
12.1 Kalman filter algorithm




List of Numerical Close-ups

NCU Problem Page
2.1 GSC to ECEF Conversion and Back 35
2.2 Loosing Weight in Flight 51
2.3 Weight on the ISS 52
2.4 Aircraft weight and lift 52
2.5 Geoid and WGS84 Ellipsoid calculations 57
3.1 Extreme variations of isobaric surfaces due to weather pressure 65
3.2 Extreme variations of isobaric surfaces due to temperature 70
3.3 Standard Temperature Variation with Height or Elevation 78
3.4 Converting barometric vertical distances into geometric 88
3.5 Humidity impact on air density 98
3.6 Density altitude 100
3.7 Air speed calculations 118
4.1 The Dark Side of the Moon 161
4.2 ADS/B reception range 163
4.3 Coverage of an Aireon satellite 165
4.4 Magnetic compass variance 173
4.5 Magnetic compass swinging 182
4.6 Euler angles and quaternions 196
4.7 In flight gyroscope apparent drift 204
4.8 Turn dynamics 217
4.9 Holding pattern 222
5.1 Daylight and Twilight in VFR flight 251
5.2 Flight Time 268
5.3 New Year Double Party with Concorde 271
6.1 Soaring glider 281
6.2 Top of climb 282
6.3 Mt St Odile 289
6.4 Wind Triangle 292
6.5 Holding Pattern with Wind 304
6.6 Inertial navigation 314
8.1 Negative Radar Height 487
8.2 Rho-Theta, Theta-Theta, and Rho-Rho Navigation 503
9.1 Fly direct to
9.2 Loxodrome
9.3 Orthodrome trajectory
9.4 Orthodrome distance using rotations
9.5 Orthodrome vs. Loxodrome
9.6 2D Brachistochrone
9.7 3D Brachistochrone
12.1 Aircraft positioning optimisation using Kalman algorithm




Dan Stefanescu

Another fallen star of the Romanian aviation! The aviation community is in tears. Dan Ștefănescu was a top class pilot engineer, who fascinated us with his evolutions. There is so much left to learn from him. At the Aerobatic Yakers Aerodrome, pilots came to achieve...

Air Navigation Convention – The 13th Edition

Aviation Reborn: New opportunities, new challenges Going forward together with the same wish that has been passed down from generation to generation, that of bringing together aviation students, graduates, professors, and experts, through this passion that unites us,...

Air Navigation Convention 2021 Debrief

In today's world, air travel is all about efficiency, speed, interconnectedness, and universal accessibility. Aviation has certainly been at the forefront of innovation, becoming one of the world's safest and most trustworthy means of transportation nowadays. However,...

Joburi în dezvoltare ATM la JLG

Courtesy of our Alumnus Andrei Florea, graduate of Air Navigation 2019, we inform you about very attractive job openings in a prestigious Romanian company, JLG Consulting. This company exports IT solutions and software to important aviation companies, being also an...

Air Navigation Convention 2021

Air Navigation Convention – 12th Edition Aviation Emerging Challenges: Innovation and Coping with Change As we progress through the ages, we start to realize just how much the world of Aerospace has gone forward since its inception, at the beginning of the 20th...

EASN Conference 2021

  EASN is the largest and important scientific network in the aerospace field.  The EASN Conference 2021 will take place on 1-4 September 2021 in Salerno, Italy. The prestigious conference creates the opportunity of networking with the most important Eurpean aerospace...

Ciprian Dumitrache – awarded researcher 2020

  Alumnus 2010 Dr. ing. Ciprian Dumitrache was awarded the prestigious prize Ad Astra 2020 for excellency in scientific research, at the engineering sciences section. Graduate 2010 of the Faculty of Aerospace Engineering University Politehnica of Bucharest, propulsion...

Interview România Cultural

After 9 years, tomorrow, 18.02.2020, a new interview will take place with Mr. Conf. Petrișor Valentin Pârvu regarding the activity related to UAVs in the Faculty of Aerospace Engineering. The interview 9 years ago took place at the show Science Cafe, transmitted from...

Invitation to Conference

We are pleased to invite faculty and interested students to attend the International Conference: INTERNATIONAL CONFERENCE ON ENERGY, ENVIRONMENT AND STORAGE OF ENERGY ICEESEN 2020, Kayseri, Turkey Why this conference? relatively small participation fee: 350EUR for...