1.PREFACE ___________________As the world moves toward a single standard for international pilot licensing, many nations have adopted the syllabi and regulations of the "Joint Aviation Requirements-Flight Crew Licensing" (JAR-FCl), the licensing agency of the Joint Aviation Authorities (JAA) . Though training and licensing requirements of individual national aviation authorities are similar in content and scope to the JAA curriculum , individuals who wish to train for JAA licences need access to study materials which have been specifically designed to meet the requirements of the JAA licensing system. The volumes in this series aim to cover the subject matter tested in the JAA ATPl ground examinations as set forth in the ATPl training syllabus , contained in the JAA publication , "JAR-FCl 1 (Aeroplanes)". The JAA regulations specify that all those who wish to obtain a JAA ATPl must study with a flying training organisation (FTO) which has been granted approval by a JAA-authorised national aviation authority to deliver JAA ATPl training . While the formal responsibility to prepare you for both the skill tests and the ground examinations lies with the FTO, these Jeppesen manuals will provide a comprehensive and necessary background for your formal training. Jeppesen is acknowledged as the world's leading supplier of flight information services, and provides a full range of print and electronic flight information services, including navigation data, computerised flight planning , aviation software products, aviation weather services, maintenance information , and pilot training systems and supplies. Jeppesen counts among its customer base all US airlines and the majority of international airlines worldwide. It also serves the large general and business aviation markets. These manuals enable you to draw on Jeppesen's vast experience as an acknowledged expert in the development and publication of pilot training materials. We at Jeppesen wish you success in your flying and training , and we are confident that your study of these manuals will be of great value in preparing for the JAA ATPl ground examinations . The next three pages contain a list and content description of all the volumes in the ATPl series.111

2. These materials are to be used only for the purpose of individua "' .. _ study and may not be reproduced in any form or medium, copied, stored in a ,etJ _ _ system lent, hired, rented, transmitted, or adapted in whole or in part without the prior _ . consent of Je esen.Copyright in all materials bound within these covers or attached hereto. ex~ Iha material which is used with the permission of third parties and acknowledged as SUCh, belongs exclusively to Jeppesen. Certain copyright material is reproduced with the permission of the Intemabona CMI AViation Organisation , the United Kingdom Civil Aviation Authority, and the Joint AviaOOil Authorities JAA .This book has been written and published to assist students enrolled in an approved JAA Air Transport Pilot Licence (ATPL) course in preparation for the JAA ATPL theoretical knowledge examinations. Nothing in the content of this book is to be interpreted as constituting instnuction or advice relating to practical fiying .Whilst every effort has been made to ensure the accuracy of the information contained within this book, neither Jeppesen nor Atlantic Flight Training gives any warranty as to its accuracy or otherwise. Students preparing for the JAA ATPL theoretical knowledge examinations should not regard this book as a substitute for the JAA A TPL theoretical knowledge training syllabus published in the current edition of "JAR-FCL 1 Flight Crew Licensing (Aeroplanes)" (the Syllabus). The Syllabus constitutes the sole authoritative definition of the subject matter to be studied in a JAA ATPL theoretical knowledge training programme. No student should prepare for, or is entitled to enter himself/herself for, the JAA ATPL theoretical knowledge examinations without first being enrolled in a training school which has been granted approval by a JAA-authorised national aviation authority to deliver JAA ATPL traininQ.Contact Details: Sales and Service Department Jeppesen GmbH Frankfurter Strasse 233 63263 Neu-Isenburg Germany Tel: ++49 (0)6102 5070 E-mail : fra-services@jeppesen.com For further information on products and services from Jeppesen, visit our web site at: www.jeppesen.com Jeppesen Sanderson Inc. , 2004 AU Rights ReservedJA310 102-000"ISBN 0-88487-352-8Printed in Germany 3. Table o/ContentsCHAPTER 1 The Form of the EarthShape of the Earth ........ .. .. .. ........ ...... . .. .......................... _ _ ... ........ _ ...... __________________ 1-1 The Poles ___________________________ __ __ .. ______ .......... __ .............. ____ .......... ___ .. ____ ............ ... _ __ __ ................ __ 1-2 __ .............. ______ ...................... ____ .............. ___ ............ .. .. __ .... _1-2 East and West... North Pole and South Pole . .. __ .... _ ...... ___ __ __ .. ____ .......... ______ ...... _1 -2 .... ........ _.... .......... _.. _____ .... ______________ .............. _ .... __ 1-3 Cardinal Directions_ ____ .... ____ .. __________ .. ________ .... _ .. ___________ 1-3 Great Circle .. .. .. .... .... ___ .. ___________ 1-4 Vertex of a Great Circle __________ .. __________ .. _____________ ...... __________ ...... __________ .... ________ .. .. ...... ___________ 1-5 Small Circle .... ____ ____ _______ ...... ___________ .. _____ __ _____ .... _________ ...... ______________ .... _________ .. _ _ .... ____ __________ ...... ___________ ........ _____________ ........ _________ .. _ 1-5 The Equator ___________ Meridians _ ...... _ _________ .. ... _ _________ .... ___ .. .. ___________ ...... ____________ .... _________ .. _1-6 Paraliels of Latitude ...... ______ __ _____ .... _________ .... ____________ .... _1-6 Rhumb Line .. _.. ________________ .. .. ________ .. _ .. .. .. ________________________________________ 1-7CHAPTER 2 Position on the Earth Angular Measurement ...... _____________ __________________ ________________________ ........ .2-1 Position Reference System.. __ .... _____________ ____________________ ______________________ .2-2 Latitude and Longitude _______________________________________________ .... __________ _ . .. .. .. ____________ __ ___ 2-2 Latitude __ __ __________________ __ ___________________________________________________________________________ .. ____________ __ _______________________ 2-3 Longitude _________________________________________________________ .. _______________________________ .... .. .. .... _.. .. ________ 2-3 Position Using Latitude and Longitude.. .. .. .. ________________ .. _________________________________________ .. .. ... ......... 2-4 ____ .. _________________ ........ 2-5 Change of Latitude (Ch Lat) .. .. Calculation of Change of Latitude _________ ...... _ _____________ .... .2-5 Mean Latitude: Mean Lat (Mlat) .. _____ .. .. .......... _ ...... .. .. ____ ...... .. ____________ __ 2-6 Change of Longitude (Ch Long) __ __ _________ __ __ .. __________ __________ __ __________ .. ________________ 2-7 _ __ .. _ .. 2-9 Mean Longitude ____ __ ______ .. ________________ .. _____________ .. __________ ____________________ ________________ Answers to Position Examples .. _ .. .. .. ........ .. ...... _ _ _________ .. _________________ .. __ __ ___________ .. .... ............. 2-1 0CHAPTER 3 DistanceIntroduction .. .. .... . Definitions.. .. ...... ____ .... _.___ .________________________ __________ .. _______ .. .. _ ..Conversion Factors ................ .................. ................. ............ .. ....... ............... Great Circle Distance .... ___ .. ____ _ ___ .. __ ______ _ _______ _____________________________________________ Departure (East - West Distance Calculalion) .... ___ ... .. __ _________________ _____________________ __ _ ____ ____ ______ __ ___________________ _______________ .. Distance Example Answers __ ______ ___ .. _____General Navigation~1.. .... .... _ ...... ________________________________ 3-1 ..... ............. 3-2 .............. .. .. .. _ 3-2 .... ..... 3-4 __ __________ .. ____ 3-6VII 4. Table oreontentsCHAPTER 4 Direction Introduction .................................................................................................................. ... ... ............. .......... 4-1 Definitions ........................................................................................................................ .......... .. ............. 4-1 True Direction ...................................................................................................................... ............ ..... ... .... 4- 1 Magnetic Direction ..... ... .... ... .. .... ........... ................................................................. ... ... ..... ....................... .. 4-1Variation ...................... Variation - Wes!... ... ............................................................................... .... ...... .. . 4-2 ................................................................................................... ... .................. 4-2Variation - East ..................................................... ........................................... ............ .. ..... 4-3Isogonal .. ...... ..... .... ......... .... .... ... . . ...... ... ..... .. ......... ....... .......................... 4-4 The Agonic Line .......................... ....................................................................................................... 4-4 Deviation ... ........... .............. ....... ... ........ ..... .......................... 4-4 Deviation - West ... . .... . .. ..... .......................................................................................................... 4-5 Deviation - East ............... ....... ............................................................... ..................... 4-6 ................................... ............................... 4-8 Relative Bearing ................ ......... ... .......... .. ...... Direction Example Answers...... ..... ..... .................................................................. 4-9CHAPTER 5 Speed Introduction ..................................... .................................................................................................... Airspeed .. ........................................................................................................................................ .. ... .. ... Airspeed Indicator Reading (ASIR ) ..................................................................................... .... ................... Indicated Airspeed (lAS) ....................... ........................................................ ............... Instrument Error ....... ......................... ..... ............................................... .... ...... ........... Rectified Airspeed (RAS) ............... ........................................... ....................................... .................. Position Error ... ............... ................................... ................................................5-1 5-1 5-1 5-1 5-1 5-2. ............................. 5-2Equivalent Airspeed (EAS) ........ ............................................................. ............. True Airspeed (TAS) ....... ........................................... ............. . ........................ Density Error .... ....... ............................................................................... ...................... .......... Groundspeed ......... ..... .. .. ... .. ...... .... ....... ........... ..... .... .............. ............. ......... .......................... Mach Number .... ..... ....... ..... ....... ......... ........................................................................................................ Summary of Speed .... .. ......................... ... .. ... ....... ....... .......................... ....................................... ..................... ... ....... ....... .. Introduction to Relative Speed ..........5-2 5-2 5-2 5-3 5-3 5-3 5-4CHAPTER 6 Triangle of Velocities Introduction .. .......... ..... .. .. ............................................................................ .......................... .......... .......... The Components of the Triangle of Velocities ................................................................................ ....... The Air Vector .... .......................... .............................................................................. ... ... ................ The Wind Vector ...................................................... ..................................... .... ............................. The Ground Vector............................. .................... ................ .............. ...... ... ............. Answers to the Triangle of Velocities Examples................ ...................... ..............V III6-1 6-1 6-1 6-2 6-3 6-4Genera l N avigation 5. Table of ContentsCHAPTER 7 Pooley's CRP 5 - Circular Slide Rule Introduction ............... .. ............................... .................................................................. 7-1 Multiplication , Division, and Ratios ...................... .. ..................................................................... ..7-2 Multiplication ... .... ....... ...... ..... . ........... ....................................................................7-2 Division. ... ............ ..... . ....... .............................................................................7-4 Ratios . ................................ ............. ........................................................7-5 Conversions ..... ........ .................. ............................. ...... ... ............................... 7-6Feet - Metres - Yards ......... .. ..................... .. .............................................................7-7 Conversion between Weight and Volume ................................... ......... . ................................. 7-8 Fahrenheit to Centigrade .........................................................................................................................7-9 Speed, Distance, and Time ....... .............. ............................. . .. ....... ....... .. ................... 7-10 Groundspeed .. ....... .. ....................... ............................ .. ....................................... 7-10 ... . .................................. ................ ..................... ............... .............. .. .............. 7-10 Time .. Distance Travelled ..................... .............................. ............. .............. ...................... .. .............. 7-10 Calculation of TAS Up to 300 Kn ots ........................ ..................................... .. ................ 7-11 Calculation of TAS Over 300 Knots ............... ........................ ....................... ............. .. ..... 7-12 Calculation of TAS from Mach Number .. . . .............. ........................ .. ......................... 7-13 Temperature Rise Scale .................... ..................... ........................ .. .................... .7-15 Calculation of True Altitude ....................................................................................................................7-16 Calculation of Density Altitude ........................... ............................... ............... .............. .7-17 Answers to CRP 5 Examples ................... ........................... ................ ........................ .. ..... 7-18CHAPTER 8 Pooley's - The Triangle of Velocities . ................ .................. ................................. .. .. 8-1 Introduction .. Computer Terminology ............................. .. ........................... 8-1 Tips for Usage ..................................... .. .. .......... .. ............. 8-2 Drift Scale ............................. ....... ....... .. ............. .... .. .............. .. ...................... 8-4 Obtaining Heading ...................... ......... .. .... .. . .. .. ...... .. ..... .... .. .. ..................................... 8-4 To Calculate Track and Groundspeed ..... .................... .. ......................................... 8-5 To Find the Wind Velocity .......................... ................... .................... .. ........... 8-7 To Find Heading and Groundspeed ... .. ........................ ...... .. .... .........................................................8-8 Take-Off and Landing Wind Componen!.. ........... .......... .. ... .... .. ................ ..................... .. ......... 8-10 Tailwind Component ..................... ................. ........................ .. .......................................... 8-1 2 Crosswind and Headwind Limits ................................................................................... ............................ 8-1 2CHAPTER 9 Maps and Charts - Introduction Introduction ......... .... .. .......... .............. ..................................................... .. ............. .. ...... ... ................... 9-1 Properties of the Ideal Chart .............. ...................... .......... .............. ......................... .. ............. 9-1 Shape of the Earth ...................... .................................. .................................... .. ...................... 9-2 Vertical Datum ............. ...................... ...... .. ....................... ............. .... .. ... .. .. .. ................. 9-2 .. ...... 9-2 Chart Construction .. .. .... .. .................................. ................ ...................... .. ............. .. ..... ....... .. ..... Earth Convergence ....................................... ......................................... . ..... 9-3 Calculation of Convergence ... .................. .............................. .................. .. ...... 9-4 Map Classification .. .................. ................................................. .. ........... 9-7 ~~............................ ~Distances ...... .. ................. .... .. .................. ....................... ................... ... .. ............. 9-8 Geodetic and Geocentric Latitude ............... .. .............. 9-10 Geodetic (Geographic) Latitude ... ...................... .. .......... 9-10 Geocentric Latitude ..... ............. ......................... .. ............................................................... 9-11 Maps and Charts Answers ............ ................ .. .............. .................................. ... .. .. .. ........... 9-12General NavigationIX 6. Table o/ContentsCHAPTER 10 Maps and Charts - Mercator Introduction . .... ......... ................. ........ ................ ...................... ....................................... 10-1 Properties of the Mercator Chart ......................................................................................... 10-2 Scale ............. ......... ... ..... ............. ....................... ........... ........................................ 10-2 Measurement of Distance ................... ...................................... .............................................. 10-3Use of Chart.. ... ..... .............. ........ ................................................................................................. 10-3 Plotting on a Mercator Chart. .. .... ....... ............ ............. ... ... .................... ............. .................... ....... .... 10-3 Plotting Using VORs ................ ..... ..................................... ............. ............. .. ....... 10-6 Summary of Plotting ... ... ....... .... .. .. ...... ....................... ........................................ 10-7 Mercator Problems ....... ...... ...... ........... ..... ............................... .................... ............... ... 10-8 Answers to Mercator Problems. ................................................................................................ 10-9CHAPTER 11 Maps and Charts - Lambert's Conformal Introduction ........................ .................... ................ .... ........... .......... ................................................ 11-1 Conical Projection .................................................................................................................................. 11-1 1/6 Rule ..................... .......................... ............................ .................................................. 11-3 Meridians and Parallels ........................................................................................................................ 11-3 Constant of the Cone................... .. ......................................... ........................... 11-4 Properties of the Lambert's Conformal. ... .......................... ............................................................... 11-4 Plotting on a Lambert's Conformal Chart ........ ...... ......... ...... . .. .................. ............................... .. ..... 11-5 Summary of Plotting of Bearings.. .................... .... .................................. .......................... .. .. 11-7 Lambert's Problems ............................................................................................................................... 11-7 Answers to Lambert's Problems.. ............................. ............................. .. ........ 11-8CHAPTER 12 Maps and Charts - Polar Stereographic Introduction ........................................................................................................................................... 12-1 Shapes and Areas .................................................................................................... 12-2 Great Circle ... .......... ............. .. .... ............................................ 12-2 Rhumb Line.............. ...... ....................... .... ........... .............. ............ ............ .................................. .. .. 12-2 Convergence ...... .. .... .... .. ...... .................. ........ ............... ...................................... ... 12-2 S~e.. .............................................................. .................1~ Uses of the Polar Stereographic Chart ................................................................................................. 12-2 Grid and Plotting on a Polar Chart ......... ................................ .. ........ ........ ............................... 12-3 Aircraft Heading ................ .............................. ............................ ....................................... . . . 1 2-6 Answers to Polar Stereographic Examples .......... ...................... ............ ..... .......... ............... 12-11CHAPTER 13 Maps and Charts - Transverse and Oblique MercatorIntroduction........................... .. .............Transverse Mercator .... ... .................... ... ............................................. .. . ................. .......................................... 13-1 . ... 13-1Oblique Mercator. .................................................................................................................................. 13-3xGeneral Navigation 7. Table o/ContentsCHAPTER 14 Maps and Charts - SummaryMercator .... .............................. .................................................................................................... 14-1 Lambert's Conformal.. .... ............. .. ......................... ....................................................... 14-1 Polar Stereographic.. ............. .. ................................................................. 14-2 Transverse Mercator . ........... ...... .... ............................................................. 14-2Oblique Mercator .... .................... .............. .................... ................. ................................... ................. ........................ 14-3CHAPTER 15 Pilot Navigation TechniqueIntroduction ...... ....................... ............. ...... ............ ...... ........ .. ........................................ 15-1 The Need for Accurate Flying. . ............ .. .............................................. 15-1 Pre-Flight Planning ... . .. .... ................. ................................................. 15-1 Flight Planning Sequence ...... ............... .. ................ ....................... .. ............. 15-2 Aircraft Performance ... ............... ............... ............... .. .................. ........................... 15-2 Mental Dead Reckoning .......... .............. ................ ................... ........ ........... .. ............. 15-2 Estimation of Track Error ................. .................. ................................. ....................... .. ... 15-3 Correction for Track Error.. ............ .... ............ ............ ............... ....... 15-3The 1 in 60 Rule ................ ........................ ..................................... ........................................ 15-3 Estimation of TAS. ... .......... ...... ...... ... .. ........ . .. ......................................... 15-4 Chart Analysis and Chart Reading ............ .................. .................. .. ............................ 15-4 Chart Scale ....... ................. ............... ................... ....................... ......................... 15-5 RelieL ........... ......................... ............... ............... ..................... . ............................................ 15-5 Relative Values of Features .... .. ............................................................................................................ 15-5 Principles of Chart Reading .... .... ............. .................. ............... .. .................... 15-6 Direction ....... ....... ...... .......... .. .... ............ ............... ...... .......... .. ........ 15-7 Distance ................... .................... .............. .................. .. ........................ 15-7 Anticipation of Landmarks ................ ............... .................. .................. ................ .................... .. 15-7 Identification of Features ............................... ................. ................... ...... .............. ... ................ .15-7 Fixing by Chart Reading .................. . .............. ................... .................... ................... . ..... 15-7 Chart Reading in Continuous Conditions.... ................... ...................... .. ... 15-8 Chart Reading at Unpredictable Intervals ............................................................................. .................... 15-8 Use of Radio Aids. .. ........... .... ............ . ...... ............ ................... .................... ........... 15-8 ICAO Chart Symbols.. .... .... ...... ............. .......... .. ..... ................... .. ..................................... 15-9CHAPTER 16 Relative Velocity Introduction ....... ....... ....... ...... ............ ....... ......... ................... ................. ........ ........ .............. .. .. 16-1 Aircraft on the Same or Opposite Tracks ........................ .................. ................ .. ........ 16-1 Calculations ... ..................... .................. ................... .................. .... ...................... . ............ 16-3 Meeting.. .......... ..... .. .... .. ............ ................. ................ ......... . 16-3 Overtaking.. . ...... .................................................................... 16-4 Speed Adjustment...... ......... .... .... .... .. .. ......................... 16-5 Distance Between Beacons...... .... .... ...... ......................Graphical Solution for Calculating Relative Velocity... .................General Navigation.. .... .... .......... 16-6.. .... ............ 16-7Xl 8. Table o/ConlenlsCHAPTER 17 Principles of Plotting Introduction ............... ................................ 17-1 Plotting Instruments .................... ............... ............ ................................ 17-1 Plotting Symbols ............... ... .... ..... ... ..................... ............. .. ................. 17-1 The Track Plot .... ........ ................. ............. ...................................................................................... 17-2 The Air Plot ........ ................ .......... .... ....... ....................... ........................ 17-3 Restarting the Air Plot ........ .................................. ........................ 17-4 Establishment of Position .... ..................... ................................................................................. 17-4 DR Position ..... ....... ..... ........ ...... ......................, 17-4 Track Plot Method ......... ......... ........... ...................... ........................................................... 17-4 Air Plot Method.. .............. .. ........................... ................. .................... ................. 17-5 Fixing.... ... .......... ........ ... ....... .............. ... .................... ............................... 17-5 Position Lines. ........................ . .............. ......................... .............................. ................ .......... 17-5 Sources of Position Lines .... ............ ..................................... .......... .......... 17-5 Plotting an NOB Position Line.. ............................. ........................ ......... 17-7 VORNDF Position Lines ...... ............................................................................................................. 17-8 DME Position Lines.. ......................................... ................................................................... 17-9 Uses of Position Lines ............... ............................................. .......................................................... 17-9 Checking Track ....... ....................... ........................................... ............................ ...................... 17-9 Checking Groundspeed/ETA .... ....................... ........................................ ..................... 17-10 Fixing by Position Lines .................................................................................................................... 17-10 Transferring Position Lines .. ................. ........................ ................ ................... 17-10 Radar Fixing .................... ......... ..... .............. ......................... .............................. ....... 17-15 Climb and Descent. ................... ..................... .................................................................... 17-15 Climb. ..... ....... ... .. ..................... ............................... ............... ................... ......... 17-15 Descent ..................... .............. ................. .............................................................. 17-16 Answers to Plotting Questions. ...................................... ............ ...... ..................... 17-19CHAPTER 18 TimeIntroduclion ............ .... .. ............. .............. ... ............ .................... ................................ 18-1 The Universe... ..... ....... ... ... .......... ........... ..... ... ........ ....................... ............... ...... 18-1 Definition of Time .................. .............................. ..................................................................... 18-2 Perihelion ... ... .. ............. ................................... ...................................... ....... ............ ........ 18-2 Aphelion................. .................... ........ ........ ................ .... ..................... ............. ............... ....... 18-2 Seasons of the Year ................... ........................................... ..................... ............... .................... 18-3 The Day ................... .. .. .... ............ ......... ....... . .. ..... ...... ........... ... .. ...... .... ....... ................. 18-3 The Apparent Solar Day. . ..... ... ........ .......................... ..... ..... ........ ..... .......... 18-4 The Mean Sun ....................... ............................................................. ... ...... 18-4 The Mean Solar Day ..... ................. ...... ........ ........ .......................................................................... 18-4 The Civil Day ............... ..................... ................ .................... ........ .............. 18-4 The Year.. ....................... ............. ..................................... ........... .............. 18-4 Local Mean Time (LMT) .. ..................................................................... 18-5 Universal Co-Ordinated Time (UTC) .. .. ... ...... ............... ...... ................... ... ... ........ .... .... ................. 18-6 Conversion of LMT to UTC . ................ .... .... .... ................... ....................... ........... 18-6 Standard Time ............. ...................... ...................................................................... 18-7 International Date Line ........................................................................................................................... 18-7 Risings, Settings and Twilight ....... .................................... .. ............................................................... 18-9 Times of Visible Sunrise and Sunset.. ................................ ............................. ..................... ........ 18-9Twilight... ............................. .................. ............................... ........ 18-9 Duration of Civil Twilight .................................................................................................................... 18-10XIIGeneral Navigation 9. Table ojCotllel1lsCHAPTER 19 Point of Equal Time and Point of Safe Return and Radius of Action Introduction. .. .... ....... ... ................. .. ........................... 19-1 Point of Equal Time.. ...................... ....... ............ .... .. ........ .. ............................... 19-1 PET Formu la ....... ....................... .............. .................. ................. ................ .. ................... 19-1 Engine Failure PET ....... .. ........... .............. ................ ..................... .. ............. 19-3 Multi-Leg PET .. .... .. .............. .. ...... ............ .................. ................ .. ............... 19-4 Two Leg PET .......... .. ....... .. ............. .. .................................................................................... 19-4 Three Leg PET.. .................. ....... ...... ......... ....... .. .... 19-6 Point of Safe Return ............ ................ ................ ................. ................ .......................... ..19-7 Single Leg PSR.............. ................... ............. .................. ...................... ............... .. ...... 19-8 Multi-Leg PSR .. .......... .. .. ............... ................. ...................... .. .. 19-9 PSR wilh Variable Fuel Flow........... .................. ....................... .. ...................... 19-10 Multi-Leg PSR with Variable Fuel Flow...... .. .... .................................................................. 19-11 Radius of Action ................. .......... .. .................... ................ .................. .................. .. ... 19-13 PET & PSR Answers. .......... ....... .. .... ........... ................... ................... .. ... .... 19-14CHAPTER 20 Aircraft MagnetismPrinciples of Magnetism ..... ...... ....... ......... ....... .................. .. .... .20-1 Magnetic Properties ............. ............... ................. .. .............................................. .. .............. 20-1 Magnelic Moment ............ .. ................... .. ... 20-2 Magnet in a Deflecting Field .. .. ................ .. ............................. 20-3 Period of a Suspended Magne!.. ..... ............. ................... .............. .. ................... 20-4 Hard Iron and Soft Iron ....... .................. .................. ........ .......... .... ... ........ ...... .. ....... 20-4 Terrestrial Magnetism .... .................. ................ .................. ............. ...20-4 Magnetic Variation ........ .. ............ .................... ..20-5 Magnetic Storms.. .. .. ... ................................ .............. .. ...... .. 20-6 Magnetic Dip... ...... ..... .. ............... .......................... .. ......... 20-6 Earth 's Total Magnetic Force .. ...... .. ....... . ...... .. .. . .................... ...20-7 Aircraft Magnetism .. .... .... .... ............ .. ........ ... .. .. ............ ..20-8 Types of Aircraft Magnetism .... ................ .................... .. .................. 20-8 Hard Iron Magnetism .......... ............... .......... .. .... ................. ................. ............ .. .. ... 20-8 .. ............ ...20-8 Soft Iron Magnetism .. .. .......... .. ..... .. ............ ................ ................... ..................... Components of Hard Iron Magnetism . ...... .......... ................... ..................... .. ... 20-8 Components of Soft Iron Magnetism.. ................. ................... .................. ....................... .. .... 20-11 Determination of Deviation Coefficients ...... ............... .. ............... 20-12 Joint Airworthiness Requirements (JAR) Limits .... ................ .. .. 20-14 Compass Swing .... .. ................... ................ ................. .. .. .. .......... .. ......... 20-15 Deviation Compensation Devices ........... .................. .................... .................... ..Mechanical Compensation... Electrical Compensation.. ........ .20-17................... ..................... ................ .. .20- 17 .. .. .. ............. .. ................................ 20-18xiiiGeneral N avigation---- 10. Table of ContentsCHAPTER 21 Aircraft Magnetism. CompassesDirect Reading Magnetic Compass ............................................ .................................. 21-1 Principle of Operation .................................. .............................. ................................................ 21-1 Horizontality ............ ... ...... .. ...................... ......... ..................... ................................... 21-1 Sensitivity ............ .... .... ..... ... ........... ..... ............ .......... ....... ................................ 21-1 Aperiodicity ........... ...................................................... ........................ .......... 21-2 "E" Type Compass Description ..... ....................................................... ..................... 21 -3 Serviceability Tests - Direct Reading Compass . ............................................... 21-4 Acceleration and Turning Errors ............................. .............................................. ...... 21-4 Acceleration Error ................................................................................................................................... 21-5 Turning Errors ..... . . .................. ..... ..... ........................................................................ 21-8 Gyro Magnetic Compasses ........ ................ ..................................................... 21-11 Basic Principle of Operation ...... ......... .............................. .............................................. 21-11 Components. . ...... ........ ............ 21 -12 Flux Detector Element... ......... .................... . ... ... ................................................... 21 -12 ........................................................... 21 -16 Detector Unit .. ....... ....... .... Components of the Flux Detector Element. ............... . .................................................. 21-16 Transmission System.. ................... ...................... ...... 21 -17 ............................. ............................... 21-1 8 Gyroscope and Indicator Monitoring ... .................. .... Gyroscope Element... ............... . ....................... ............. . 21-1 9 Heading Indicator. ............ ............... ................... ..................... ...... ...................... 21 -1 9 Modes of Operation ....... ..... ....... ..... .. ........ .................... 21-20 Synchronising Indicators . .... ................ ........ .. ....... ...... .......... .... ... ....................... 21 -20 Manual Synchronisation .... ... ........................ ................. .. 21-20 Operation in a Turn ............................. .. .. ............................ ... ............ ......... ............. ................ 21-20 Advantages of the Remote Indicating Gyro MagnetiC Compass. . ..................................... 21 -2 1 . .2 1-2 1 Disadvantages of the Remote Indicating Gyro Magnetic Compass ...................XIVGeneral Navigation 11. Table o/ContentsCHAPTER 22 Inertial Navigation Accelerometers ....................................................................................................................... ...... . ... ... .. ... 22-1 Principles and Construction .................... ........... . ..................... .. .... ...... .... ...... .22-1Performance .................................................... ......................................................................... ...... .22-3 Gyro Stabilised Platform ...................... ....................................................................... ... .... .... ........ 22-3 Rate GyroslPlatform Stabilisation ........ .................................................................... , ............................... 22-3 Setting-Up Procedures ............................................. ......................... ....................................... .. ... 22-4 Levelling ........................................... ................................................... .... ....... ........ ..... ........ 22-5 Alignment ...................... .... .................. ...... .................. ................................. ............... 22-5 Inertial Navigation System (Conventional Gyro) ......... ............................................................................ 22-5 Corrections .......... ............ ........... ............................................ ................................. ....... .22-7 .. ...................... ..................................................... ..... 22-8 Errors ..... ............................. The Schuler Period .............. .................................................. ........... ........ ................ ...... 22-8 Bounded Errors.. . ......................................................... .......... 22-8 Unbounded Errors .............. .................................................................. ................ ... 22-9 Inherent Errors ............. ................... .. .................................................. ............ 22-9 Radial Error .......................... .............. ....................................................................................... 22-9 ................................ . .. .... ......... ..... 22-10 Advantages.. ................... Disadvantages.. . .............................................................................. 22-10 ........................... ............... .22-10 Operation of INS .................................. CDU ......... ............................................... ...... 22-11 Display Selection - TKlGS.. .... ............... .................................................................. 22-12 Display Selection - HDG/GA. . .................................................................................... 22-13 Display Selector - XTKlTKE.. ............................................................................................. 22-14 ............................................................. ..22-15 Display Selection - POS .............. Display Selection - WPT . ..............................................................................................22-15 .......... .. ..... .................... ................. ........... 22-16 Display Selection - DISITIME.. ...................................................................................................22-17 Display Selection - WIND.. Display Selection - DSR TKlSTS.. ................................................... .................................... ..... 22-18 Display Function - TEST ............................. ................................................ ..22-19 Display Format.. .......................................................................................................22-19 Solid State Gyros .................................. ..................................................................... ....... 22-20 Types of Solid State Gyros . ........................................................................................... 22-20 Ring Laser Gyro ......................................................................................................................................22-20 ................. 22-21 Fibre Optic Gyros.... .......... ................ ......... ..................................................... Advantages and Disadvantage of RLGs. . ........................................................... ............... .... 22-21 "Strap-down" INS ................... ............ . ..................................................... .................. 22-22 System Description.. ... .................. ....................................................... .............. 22-22 Alignment.. ............................................................................. 22-22 Performance . .................................................. ............... 22-22General Navigationxv 12. SHAPE OF THE EARTH For navigational purposes, the Earth is assumed to be a perfect sphere. In reality, it is slightly fiattened at the poles and can be described as an ellipsoid or oblate spheroid. The Earth's polar diameter is approximately 23 )1, nm shorter than the equatorial diameter. When considering the fu ll diameter of the Earth , this is negligible and can be disregarded for the purposes of practical navigation ......................Polar Radius Equatorial Radius6 356 752 metres 6 378 137 metres3432 nm 3443 nmNote: In the diagram above, the compression is greatly exaggerated. The compression ratio is the ratio between the polar diameter and the equatorial diameter and indicates the amount of flattening . The ratio is approximately '/297 but geodetic information obtained by satellite shows that the Earth is in fact pear-shaped with the larger mass being in the Southern Hemisphere. For navigation and mapping purposes, World Geodetic System 1984 (WGS-84) is the current ICAO standard.General Navigation~--- ---------------------I -I 13. Chapter 1The Form of the EarthTHE POLES The Earth rotates about an invisible axis which passes through the Earth and cuts the Earth's surface at two points. These two points are called the poles, as shown on the diagram below. NPSP NP SPNorth Pole South PoleEAST AND WEST East is the direction in which the Earth rotates. This direction is anti-clockwise to a person looking down on the North Pole. The direction opposite to East is West.NORTH POLE AND SOUTH POLE The North Pole is the pole which lies to the left of an observer facing East. If an observer stands:>>-l-2At the North Pole, all directions are South At the South Pole, all directions are NorthGeneral Navigation 14. ChapterThe Form oJthe EarthjCARDINAL DIRECTIONS The directions North, East, South , and West are known as the Cardinal Directions. NorthEastWestSouthGREAT CIRCLE A great circle is a circle drawn on the surface of a sphere wh ich has the centre of the sphere as its origin. These circles are the largest that can be drawn on the sphere's surface. A great circle can connect any two points on the Earth's surface. Normally, only one great circle ca n be drawn through any two points, as shown on the diagram below. The exception to this rule is that if the two points are diametrically opposed - the North Pole and the South Pole , for example - an infinite number of great circles may be drawn. The great circle joining two points has a long and a short path. The short path is always the shortest possible distance on the Earth's surface between the two points.North PoleABSouth PoleGenera l Navigation1-3 15. Chapter 1The Form oj the EarlhVERTEX OF A GREAT CIRCLE The vertices of a great circle are the most northerly and southerly points on that great circle. Vertex properties: ~ ~ ~The points are called antipodal ; the vertices are diametrically opposed The distance between the points is 10 800 nm At the vertex the direction of the great circle is 090 270 00-, .,'i} ".-.. ".~ ,""""'" "J" ""... ......"",},.,;,.~1)~."" < ,,"">>>-North is 0000 East is 090 0 South is 180 West is 270 0General Navigation '02-1 20. Chapter 2Position on the EarthWhere a direction is given, use three figures, e.g. 90 is reported as 090. Angles are always measured in a clockwise direction from north.POSITION REFERENCE SYSTEM In navigation , it is necessary to pinpoint an aircraft:1. Accurately 2. Unambiguously The Cartesian System is the simplest and most effective position reference system.yx, r:'----------x Point A can be defined as the position X, Y , . The Cartesian System is good for work on a fiat plane. For position on the Earth , a similar system can be employed .LATITUDE AND LONGITUDE On the Earth , position is described using latitude and longitude: ~ ~2-2The X-axis is the Equator and is defined as 0 Latitude. The Y-axis is aligned to the Greenwich Meridian (the Prime Meridian) and is 0 longitude.Genera l Nav igation 21. Position017Chapter 2the EarthLATITUDE The latitude is expressed as the arc along the meridian between the Equator and that point.NPLatitude has values up to 90' and is annotated wi th the hemisphere where the point is situated. Example 40' 25'N or 40' 25'8LONGITUDE The longitude of a point is the shorter angular distance between the Prime Meridian and the meridian passing through the point. Like latitude, long itude is expressed in degrees and minutes .NPIt is annotated east and west depending whether the point lies east or west of the Prime Meridian. Longitude cannot be greater than 180' W or 180' E. These two longitudes are coincident, and the meridian is referred to as the Greenwich Anti-Meridian . ExampleGeneral Navigati o n165'35'W or 165'35'E2-3 22. Chapter 2Position on Ihe EarthPOSITION USING LATITUDE AND LONGITUDE Position on the Earth is always expressed as latitude first, then longitude. The lines that form the parallels of latitude and the meridians are called the graticule. By using the graticule , any position on the Earth can be determined.II55'N54'NI ,C53'NA52'N.B 1'No 3'Wo 2'WOC1'W0o 1'Eo 2'EIn the above diagram: ~ ~~2-4Position A Position B Position C53' N O' EIW 51 ' 30'N 001 ' 30'W 53' 30'N 001 '30' EGeneral Navigat ion 23. Position on the EarthChapter 2CHANGE OF LATITUDE (CH LAT) Ch Lat is the shortest arc along a meridian between two parallels of latitude. It is expressed in degrees and minutes.CALCULATION OF CHANGE OF LATITUDE Where two points are in the same hemisphere , the Ch Lat is the difference between the two points. Example 1STEP 10Point A is 20 30'N and point B is 41 30'N. If an aircraft is travelling from A to B, what is the Ch Lat? First calculate the difference between the two points in degrees and minutes. Simply subtract the smallest from the largest:41 30' - 2030' = 21 STEP 2Note the direction of the change. In this case, the aircraft is travelli ng north so the Ch Lat is: 21NThe term 0 Lat can also be used. Where Ch Lat is given in degrees and minutes , 0 Lat is given in minutes alone. For Example 1, the answer would change to: STEP 3The 0 Lat is the Ch Lat expressed in minutes alone. Remember that there are 60' in 1. o Lat is: 21 x 60General Nav igat ion=1260'N2-5 24. Chapter 2Position on the EarthWhere the two points are in different hemispheres, the solution is the sum of the two latitudes. Example 20Point A is 20 30'N and poi nt B is 41 30'S. If an aircraft is travelling from A to B, what is the Ch Lat?STEP 1Calculate the difference between the two points. Simply add the two together:STEP 2Note the direction of the change . In this case, the aircraft is travelling south so the Ch Lat is : 62SPosition Example 1Calculate the Ch Lat and D Lat for the following (assume the aircraft is travelling from the first position to the second): Answers can be found at the end of the chapter.Position APosition B5435'N6734'N2333'S4J056'S3347'N2355'S2J025'NOJ044'N030 45'SCh LatD Lat7833' NMEAN LATITUDE: MEAN LAT (MLAT) You may be required to calculate the mean latitude. Mean latitude is the mid-point between two latitudes . If the two latitudes are in the same hemisphere, find the Mlat by adding the two values, then dividing by 2. Example 3 STEP 1Calculate the Mlat for the positions 65N and 25N. Add the two values of latitude:65 + 25 =90 STEP 2Divide the figure found in STEP 1 by 2:90 .;. 2 = 45 = 45N2-6General Navigation 25. Position 0 11 the EarthChapter 2If the positions are in different hemispheres, find the Mlat by first adding the two latitudes together, then dividing by two. This figure is then subtracted from the higher value . The higher latitude determines which hemisphere the Mlat is in . Example 4Calculate the Mlat for 65N and 25S.STEP 1Add the two values together: 65 + 25 = 90STEP 2Divide the figure found in STEP 1 by 2: 90+2=45STEP 3Subtract the figure found in STEP 2 from the higher latitude: 65.45 = 200N Remember the higher value determines the hemisphere that Mlat is in.CHANGE OF LONGITUDE (CH LONG) To express the difference between two meridians, Ch Long , the smaller arc, is used. Values are expressed in exactly the same manner as Ch La!. Remember that the value of Ch Long can never exceed 180. The suffixes E and Ware used in regard to the direction of travel.General Navigation27 26. ------- ----Position on the EarthChapter 2Example 1Calculate the Ch Long between position A 165W and position B 103W. Assume that the aircraft is flying from A to B. Find the numerical difference between A and B. The two points are in the same hemisphere , so subtract the smaller from the larg er:165 W:x103W /WestEast~"Remember that anti-clockwise measurement is east. When the two positions are in different hemispheres , the situation is slightly more complicated . Example 2Calculate the Ch Long between position A 165W and position B 1700E. Assume that the aircraft is flying from A to B. It is obvious the shortest distance between the two points is by crossing the 180 meridian . The difference between 165 and 180 is 15. The difference between 170 and 180 is 10. The Ch Long is therefore 25W because the movement is clockwise. 165W XII:. West~2-8East~General Navigation 27. Position on the EarthPosition Example 2Chapter 2Calculate the Ch Long and Dlong for the following (assume the aircraft is travelling from the first position to the second ):Position APosition B00933W'15645'W15333'E07844'E14423'W10233'E07J055'W17844'E14324'ECh Long17915'ED LongMEAN LONGITUDE Mean longitude is calculated in the same way as mean latitude. Rarely used in navigation , mean longitude is not discussed further.General Navigat ion2-9 28. Chapter 2Position 0 11 fhe EarlhANSWERS TO POSITION EXAMPLES Position Example 1 Position APosition BCh Lato Lat5435'N6734'N1259'N779'N2333'S47"56'S2423'51463' S334TN2355'S5742'53462'527"25'ND744'N1941'51181'S3D045'S7833'N10918'N6558 'NPosition APosition BCh Longo LongDD933'W15645'W14712'W8832'15333'ED7844'E7449'W4489'14423'W1D233'E11304'W6784'D7755'W17844'E10321 'W6201 '14324'E17915'E3551 'E2151 'Position Example 22-10General Navigation 29. INTRODUCTION This chapter describes the definitions and methods of calculating the distance between two points.DEFINITIONS KilometreThe length of '/,0000 of the average distance between the Equator and a pole. The distance from the Equator to either pole is 10 000 km . The circumference of the Earth is 40 000 km.MetreThe length equal to '/ lOOoth of a kilometre.FootAn Imperial measurement equal to 0.304 m.Statute MileA statute mile is defined as 5280 ft.Nautical Mile Assuming that the Earth is a perfect sphere, the nautical mile is the length of arc which subtends an angle of one minute at the centre of the Earth. However, the Earth is not a perfect sphere, and the length of the nautical mile varies:>>>-The Standard Nautical Mile is 6080 ft. At the pole, a Nautical Mile is 6108 ft. At the Equator, the Nautical Mile is 6046 ft.The average value of the nautical mile is approximately 6076 ft. This is the International Nautical Mile, which is approximately 1852 m. The ICAO Nautical Mile is 1852 m exactly.General N avigation3- 1 30. Chapler 3DistanceCONVERSION FACTORS The CRP-5 has the conversions required for the JAR-FCL examinations. Use of these scales is discussed in a later chapter. 54 nautical miles (nm) = 62 statute miles (sm) = 100 kilometres (km) Or: 1 nm 1.85 km 1 nm 1.15 sm Other useful conversion 1 metre 1 centimetre 1 metre 1 foot 1 foot 1 inch 1 ya rdfactors are: 100 centimetres 10 millimetres 3.28 feet 12 inches 30.5 centimetres 2.54 centimetres 3 feetGREAT CIRCLE DISTANCE The definition of a nautical mile, which is the length of arc which subtends an angle of one minute at the centre of the Earth, helps in the calculation of the great circle distance between two points. For most great circle calculations, use spherical geometry. Where the two points are on a meridian or the Equator, the calculation is much easier. Note: The use of spherical geometry is not required in the JAR examination. Example 1Both positions in the same hemisphere - What is the shortest distance between A (6435'N 010 00'W) and B (5315'N 010 00'W)? 00STEP 1If the points are on the same meridi an, calculate the o La!: 6435' - 5315' = 11 20' = 680'STEP 2Using the definition of the nautical mile, 1 min ute of arc is equivalent to 1 nm : 680' is equal to 680 nmExample 2Both positions in different hemispheres - What is the shortest distance between A (6435'N 010 00'W) and B (5315'8 010 00'W)? 0STEP 1If the points are on the same meridian, calculate theo La!: 6435' + 5315' STEP 23-20=11750' =7070'Using the definition of the nautical mile, l ' is equivalent to 1 nm : 7070' is equal to 7070 nmGeneral Nav igation 31. DistanceChapter 3Example 3Both positions on the meridian and antimeridian in the same hemisphere - What is the shortest distance between A (6435'N 010 00'W) and B (5315'N 170 00'E)? If both positions are in the same hemisphere , the shortest distance of travel is over the North Pole . 00Find the distance to travel from A to the North Pole and from B to the North Pole . A: 90 - 6435' = 2525'= 1525' = 1525 nm B : 90 - 5315' = 3645' = 2205' = 2205 nmSTEP 1Example 4Both positions on the meridian and antimeridian in different hemispheres - What is the shortest distance between A (6435'N 010 00'W) and B (5315'5 170 00'E)? It does not matter whether the calculation uses the South Pole or the North Pole . 00STEP 1If travel was by the North Pole, the approximate distance would be: 90 - 6435' = 2525' = 1525 nm 90 + 5315' = 14315' = 8595 nm Total 10 120 nmSTEP 2If the calculation had been done using the South Pole : 90 + 6435' = 15435' 90 5315' = 3645' Total = 191 20' The answer is more than 180, which is the longer distance of the two, and therefore not of commercial use.STEP 3Subtract the answer found in STEP 2 from 360. 360 191 20' = 16840' = 10 120' Total 10 120 nmExample 5STEP 1General NavigationTwo points on the Equator - What is the great circle distance between A (OOO N/S 01200'W) and B (OOO N/S 01200'E)? OO' OO' The calculation is the same as for two points on the same meridian. Calculate 0 Long between A and B. A to the Prime Meridian is 12 B to the Prime Meridian is 12 Total 24 = 1440' = 1440 nm3 3 32. Chapter 3DistanceDistance Example 1Calculate the shortest distances between the following points:Position APosition B3r14'N 030 000'W 5834'N 120034'E45 35'S 030 000'W 1945'N 120 034'E4256'N 01 0035'E5533'N 16925'WOooOO'N/S 12335'E 2533'S 070 014'WOooOO'N/S 00326'WDistance6647'N 10946'EDEPARTURE (EAST - WEST DISTANCE CALCULATION) When calculating D Lat, a change in 1 minute of latitude was found to be equivalent to 1 nm . A change in 1 minute of longitude is only equivalent to 1 nm where the East - West direction follows a great circle - the Equator. Because the merid ians converge , the distance between them decreases with increasing distance from the Equator: ;.. ;..At the Equator, the distance between two meridians is 60 nm At the poles, the distance between the meridians is 0 nmAn aviator requires a method of calculating the distance East-West between two points.In the above diagram: r=Rcos8 Where :R r83-4Radius of the Earth Radius of the parallel of latitude to be found Latitude in degreesGenera l Navigation 33. Chapter 3DistanceThe radius varies with the cosine of the lalitude. The distance between two merid ians va ries at a constant rate. Therefore , the distance between two meridians 1 degree apart is: 60 cos Lat Where 60 is the D Long between two meridians . The formula can also be expressed as a function of D Long: Departure = D Long cos Lat ExampleCalculate the distance between two meridians that are 10' apart at latitude 60' N= 10 x 60 =600'STEP 1D LongSTEP 2Formula: Departure = D Long cos Lat 600 cos 60 = 600 x 0.5 = 300 nmDistance Example 2What is the distance between 00500W and 01000E at a latitude of 35' S?Distance Example 3The distance between 01000W and 00500W is 200 nm . What is the latitude?Distance Example 4Starting at position 5000N OOOOOEIW, an aircraft fiie s due west for 1000 nm. What is the final position ?General Nav igation3-5 34. Chapter 3DistanceOIST ANCE EXAMPLE ANSWERS Distance Example 1 Position APosition B0Distance03r14'N 030 00'W4535'S 030 00'W004969 nm5834'N 120 34'E1945'N 120 34'E2329 nm4256'N 010 35'E5533'N 16925'W4891 nmOooOO'N/S 12335'EOooOO'N/S 00326'W7621 nm6647'N 10946'E8326 nm002533'S 070 14'W Distance Example 2Distance Example 3D Long=15 x 60 =900'900 cos 35 = 900 x .819 737 nm Departure = D Long x cos Lat cos Lat Departure I D Long cos Lat 200 1300 Inverse cos 0.66 = 48.2 Latitude 48.2 D Long Departure I cos Lat 10001 cos 50 - 10001.642 = 1557 . 6' -= =Distance Example 4=2557 .6' Ch Long Final Position 50 00'N 02557.6'W 03-6General Navigation 35. ..II .....I."IJI .INTRODUCTION Direction is used to: ~ ~Provide a datum for following a line across the surface of the Earth Relate positions to each otherDEFINITIONS Course Heading TrackThe intended track The direction in which the fore-and-aft axis of the aircraft is pointing The flight path that the aircraft has followed (Also known as Track Made Good)TRUE DIRECTION True direction is a reference to the direction of the Geographic North Pole, whether the aircraft is in the Northern or Southern Hemisphere.MAGNETIC DIRECTION It is not possible to directly determine true direction in an aircraft. Instead, use what is called magnetic direction. The Earth 's magnetic field acts as if there are two magnetic poles . These magnetic poles are not co-located with the North and South Geographic poles, and unlike the geographic poles, they move annually. The magnetic North Pole and the geographic North Pole are separated by approximately 900 nm. The magnetic North Pole rotates around the True North Pole approximately every 960 years. Unlike the geographic poles, the magnetic poles are not antipodal. The Earth 's magnetic field has a horizontal and a vertical component (this is described more fully in Chapter 20 - Aircraft Magnetism). A magnet freely suspended indicates the position of the magnetic poles. Magnetic direction can be measured by reference to a freely suspended magnet. Aircraft compasses have a magnet which detects the horizontal component of the Earth's magnetic field , giving the magnetic direction.General Navigation4- 1 36. Chapter 4DirectionI " ........, ',,, f ---------- ....~'Magnetic - _ __ North Pole./.- .-I//I;"/, .... - --- - -/~"",Pole,, ,,~~/,,I, I I II IMagneticEquator (Aclinic Line)Equator--Geographical South PoleI II I I//.- .) .- .-, "I----- ...Magnetic '" South PoleI,,I' ....Ir/VARIATION Variation is the angular difference between magnetic north and true north at any given point. Variation is measured in degrees with the suffix W (west) or E (east).VARIATION - WEST When magnetic north lies to the west of true north, the variation is west. For the following diagrams: ArrowDesignation Magnetic North 4-2True North Compass NorthGeneral Navigation 37. DirectionChaprer4The diagram below indicates that the magnetic heading is larger and : Variation + True Heading = Magnetic Heading+--..Variation (W)eading (T)A useful aide memoire for this goes as follows:VARIATION WEST Example 1MAGNETIC BEST 0If the aircraft is heading 130 T and the variation is 15W, what is the magnetic heading?STEP 1Variation (W) + True Heading = Magnetic Heading 15 + 130 = 145MVARIATION - EAST When magnetic north lies to the east of true north , the variation is said to be east. From the diagram below, notice that the magnetic heading is smaller and: True Heading - Variation (E) = Magnetic HeadingGeneral Navigation4-3 38. Chapler 4DirectionThe equivalent aide memoire for this is:VARIATION EASTExample 2STEP 1MAGNETIC LEASTIf the aircraft is heading 130"T and the variation is 15"E, what is the magnetic heading? True Heading - Variation (E)=Magnetic Heading130" _15" = 115"MISOGONAL On all aeronautical charts, places of equal magnetic variation, i50gonal5 , are marked. Variation is applied to the magnetic direction to give true direction and vice versa.A pecked or dashed blue line is used to indicate the isogonal on an aeronautical chart.THE AGONIC LINE The Agonic Line is an isogonal where the value of variation is zero. This is described more fully in Chapter 20 - Aircraft Magnetism.DEVIATION Because of the aircraft's inherent magnetic fields, a compass settles on what it interprets as magnetic north. The causes of aircraft magnetism are discussed the Chapter 20 . The angle between what the compass indicates as magnetic north (compass north) and the real magnetic north is known as deviation. Like variation , deviation is measured in degrees east (E) or west (W).4-4Generalavigati on 39. Chapter 4DirectionDEVIATION - WEST Where compass north lies to the west of magnetic north, the deviation is west. Magnetic Heading + Deviation (W) = Compass HeadingVariation (W)eading (T) Heading (C)A useful aide memoire for this is:DEVIATION WESTExample 3STEP 1Genera l NavigationCOMPASS BESTAn aircraft is flying a heading of 13D M; deviation is 1D W. What is the compass head ing? Magnetic Head ing + Deviation (W) = Compass Heading 130 + 10 = 140 C4-5 40. Chapler 4DirectionDEVIATION - EAST Where compass north is to the east of magnetic north , the deviation is east. Magnetic North - Deviation (E) =Compass HeadingHeading (C)~ tion (E)The equivalent aide memoire for this is: DEVIATION EASTExample 3STEP 1COMPASS LEASTAn aircraft is fiying a heading of 130' M; deviation is 10' E. What is the compass heading? Magnetic Heading - Deviation (E) = Compass Heading 130' -10' = 120'CIn the JAR examinations, deviation can sometimes be given as a positive or negative numeric val ue (+3 or -3). Add or subtract the value from compass heading to get the magnetic heading: +3 would be deviation 3E -3 would be deviation 3W Example 4 STEP 14-6Compass heading is 250'; deviation +3'. What is the magnetic heading ? Compass Heading + Deviation = Magnetic Heading 250' + 3 = MH MH =253'General Nav igation 41. DirectionChapter 4Example 5Magnetic heading is 017"; deviation +4" , What is the compass heading?STEP 1Compass Heading + Deviation = Mag netic Headi ng CH + 4" = 017"STEP 2Transpose the equation CH =017" -4" =013"Direction Example 1 True HeadingComplete the following table:150" 7" E 325"Magnetic HeadingDeviation170"Variation2"W125"4"W333"247"330" 260'12' W001 "5' E 15'W213'247"2"E 3'W9'W337"1E 330'17" EGeneral Nav igati on5' W 095'075'Compass Heading258'332' 3'W4-7 42. Chapter 4DirectionRELATIVE BEARING The relative bearing is always measured clockwise from the nose of the aircraft. To obtain a true bearing from an aircraft: True Bearing (TB)=Relative Bearing + Heading (T) Relative BearingTrue HeadingExample 6Assume in the diagram above that the aircraft is heading 110 T. An island is seen on a relative bearing of 270 (remember that the relative bearing is measured from the nose clockwise). What is the true bearing of the island from the aircraft?=STEP 1True Bearing Relative Bearing + Heading 110 + 270 = 380STEP 2Because the answer is greater than 360, 360 has to be subtracted from the answer.380 - 360=020The true bearing of the island from the aircraft is 020 T. As an alternative , the island could be said to be 90 left of the aircraft. Using left as minus and right as plus the calculation goes as follows: STEP 1Aircraft Heading Bearing Left or Right = True Bearing110 - 090 =020TUse whichever method is the easiest.4-8General Navigation 43. Chapler4DirectionDIRECTION EXAMPLE ANSWERS Direction Example 1 True HeadingVariationMagnetic HeadingDeviationCompass Heading150'20 0 W170 02W172 013207'E125 04W129 0325'8W333'247'12' W3E330'25901W260'05' W001 0001 '5' E356232 015W247'2' E245 0075'095'3' W098 021 3'20 0 W goW222 01' E221 0337'7E330 02W332 0275 017' E258'3' W261 0General Navigation4-9 44. INTRODUCTION Speed is the rate of change of position, or distance covered, per unit of time. It is expressed in li near units per hour. As there are three main linear units, there are three main expressions of speed: nautical miles per hour statute miles per hourKnotst (kt) Miles per hour (mph) Kilometres per hour (kph)These speeds represent how far an aircraft travels in one hour (i.e. a speed of 300 kt means that in one hour an aircraft travels 300 nm). Speed can be calculated from the formul a: SPEED= DISTANCE/TIMEThree groups of speed are used in air navigation: AirspeedThe speed of the aircraft through the ai rGroundspeedThe speed of the aircraft relati ve to the groundRelative SpeedThe speed of an ai rcraft relative to another ai rcraftAIRSPEED AIRSPEED INDICATOR READING (ASIR) The speed measured by the pitot-static system connected to the airspeed indicator without any co rrections.INDICATED AIRSPEED (lAS) Indica ted airspeed is the ASIR, corrected fo r instrument error due to imperfections in manufacture. The aircraft is fl own on lAS.INSTRUMENT ERROR Ca used by inaccuracies during the man ufacturing process. Normally, these errors are so small they are ignored.General Navigation-5- 45. Chapter 5SpeedRECTIFIED AIRSPEED (RAS) Rectified Airspeed , sometimes known as Calibrated Airspeed (CAS), is lAS corrected fo r Position Error. RAS equals TAS (True Airspeed ) in calibration cond itions, sea level tempera ture +15' C, with pressure 1013.25 mb .POSITION ERROR When the air fiow around the pi tot-static system is disrupted , inaccuracies can occu r. Position errors for different configurations are listed in the operating manual by using graph s or tables.EQUIVALENT AIRSPEED (EAS) Most ASls are calibrated for an ideal incompressible air fiow (Y,pv' ). As compression affects all speeds, EAS is RAS corrected for compressibility. In real terms, EAS is the speed equivalent to a given dynamic pressure in ISA conditions at mean sea level. By using a compressibility factor, RAS/CAS can be corrected to give EAS. The CRP-5 can be used for the calculation . Normally, compressibility is only corrected for a TAS of greater than 300 kt.TRUE AIRSPEED (TAS) TAS is the speed of the aircraft relative to the air mass through which the aircraft is fiying.True airspeed is EAS corrected for density error - pressure altitude and temperature . TAS can be mentally calculated by adding 2 percent of the RAS/CAS for each 1000 ft of pressure altitude. ExampleSTEP 1An aircraft is fi ying at 10 000 ft at an RAS/CAS of 150 kt. What is the TAS? Apply the fo rmul a TAS CAS + ((2 x CAS/,oo) x Altitude in 1000s of tt)=TAS=150 + ((2 x 1.5) x 10)TAS=150 + 30 =180 ktNote: The above is a rule of thumb only. A more accurate method for th is conversion exists using the Pooley's fiight computer and is described in a later chapter.DENSITY ERROR Air density decreases with : >- Higher temperatures >- Higher pressu re altitude Flying at the same groundspeed in still air, the ASI will indicate a lower speed if: >- The temperature increases >- The pressure altitude increases The correction for air density can be calculated mathematical ly or by use of the CRP-5 . 5-2General Nav igati on 46. SpeedChapter 5GROUNDSPEED Groundspeed is the speed of the aircraft relative to the ground. It takes into account the aircraft's movement relative to the air mass (TAS and heading) and movement of the airmass (wind velocity).MACH NUMBER An alternative method of measuring speed is to express it as a fraction of the local speed of sound (LSS). This fraction is known as the Mach Number (MN). The relati onsh ip of TAS to Mach Number is much simpler than that of RAS to TAS, as the only va riable factor is temperature. Therefore , at higher speeds it is usually easier to calculate TAS from Mach Number. The LSS depends upon the air rnass temperature and is calculated using the following formula : LSS = 39-VT'KWhere T is the temperature in degrees Kelvin. An approximate calculation is: LSS = (644 + 1.2t)Where t is in degrees centigrade. The formula for calculating the MN is based on TAS and the local speed of sou nd (LSS). MN = TAS/LSSSUMMARY OF SPEED The following flow chart shows the relationship between the various speeds. ASIRIInstrument ErrorlASIPosition ErrorRAS/CASICompressibilityEASIDensityTASIWindGroundspeedGenera l Navigation5-3 47. Chapter 5SpeedINTRODUCTION TO RELATIVE SPEED Relative speed is the speed of one object in relation to another. In the diagram below, the two aircraft are at different speeds, and the relative speed is the difference between the two: 360 - 300 = 60 ktAircraft A - 300 knotsAircraft B - 360 knotsWhere the aircraft are on reciprocal tracks, the relative speed is the sum of the two speeds .+ Aircraft A - 300 knotsAircraft B - 360 knotsIn this case, the relative speed (closing speed) is 360 + 300 = 660 kt. The relative speed can be used to calculate times of: >- Aircraft crossing >- When two aircraft wi ll meet Relative speeds and relative velocity are discussed more fully in Chapter 16 - Relative Velocity.5-4General Nav igation 48. INTRODUCTION A velocity is a combination of speed and direction. Speed is a scalar quantity, whereas velocity is a vector quantity. Velocity can be represented graphically by a straight line where: ~ ~The length of the line represents the speed. The direction of the line is measured from a datum.Any convenient scale can be used.THE COMPONENTS OF THE TRIANGLE OF VELOCITIES The components of the triangle of velocities are the air vector, the wind vector, and the ground vector. The ground vector is the vector sum , or resultant, of the other two components.THE AIR VECTOR This describes the path of the aircraft through the air. The heading is the direction the aircraft fiies in relation to the air mass. The aircraft's speed through the air is the tru e airspeed. The two subcomponents of the air vector are heading (H OG) and true airspeed (TAS). The air vector is shown below:Genera l Navigation6-1 49. Chapter6Triangle of VelocitiesTHE WIND VECTOR The wind vector describes the movement of the air mass through which the aircraft is travelling , over the surface of the Earth . Wind velocity, when written, includes the direction from which the wind is blowing and the speed (usually in knots). It is written as a 5 or 6 fig ure group, as shown below:330/25 330/125 The diagram shows the air vector and the wind vector:The vector summation of the air vector (heading and TAS) and wind velocity give the third component, the ground vector.THE GROUND VECTOR This describes the direction and speed of the aircraft over the ground . It comprises track (TRK) and groundspeed (GS). The diagram below shows the completed triangle of velocities:BAThe angle between the heading and the track is the drift angle. ~ ~6-2If blown to the right, as in the case above , it is Right Drift If blown to the left, it is Left Drift General I avigation 50. Triangle of VelocitiesChapter 6As the diagrams show, each vector is represented by its unique arrow convention: One Arrow Two Arrows Three ArrowsHeading and TAS Track (Course) and Groundspeed Wind VelocityEach of the three components is made up of two sub-components , a total of six sUb-components. Given any four of these, it is possible to determine the other two. Chapter 8 describes how the CRP-5 can be used to solve the triangle of velocities. To reinforce understanding of the chapter, solve the following problems graphically, using a sheet of plain paper: Triangle of Velocities Example 1Triangle of Velocities Example 2Triangle of Velocities Example 3General NavigationGiven: Heading TAS Wind Velocity Find the track and groundspeed.100 0 T 210 kt 020/25Given: Heading TAS Track Groundspeed Find the wind velocity.270 0 T 230 kt 280 0 T 215 ktGiven: 220 kt TAS 230 0 T Track 270/50 Wind Velocity Find the heading and groundspeed.6-3 51. Chapter6Triangle of VelocitiesANSWERS TO THE TRIANGLE OF VELOCITIES EXAMPLES Triangle of Velocities Example 1 STEP 1From any origin , draw a vector of 100' T. Represent the TAS by drawing the line to a sensible scale (1 cm equal to 20 nm ). The vector is then 10)1, cm long .STEP 2From the end of the head ing vector, draw the wind direction of 020'. Remember that the wind direction is always the dire ction from which the wind is blowing. Draw the line to 25 nm scale , using the same scale fo r the heading and TAS - 1.25 cm.STEP 3Measure the track and the length of the vector. Track 107' Groundspeed 208 ktTriangle of Velocities Example 2 STEP 1From any origin, draw a vector of 270' T. Represent the TAS (230 kt) by drawing the line to a sensible scale.STEP 2From the start of the heading vector, draw the track (280'), and mark off the groundspeed using the same scale as the heading/T AS vector.STEP 3Measure the wi nd velocity. Wind Velocity 207/42Triangle of Velocities Example 3 STEP 1 STEP 2From the ori gin , draw the track (230' ). Make the line of any length, as the groundspeed is unkn own.STEP 3From the head of the wind velocity, draw an arc using dividers, which represents the TAS .STEP46-4From any orig in , draw the wind velocity.Where the arc intercepts the track, measu re the heading groundspeed. Heading 239' Groundspeed 179 ktandGeneral Navigation 52. INTRODUCTION The circular slide rule found on the CRP-5 is depicted below. If used effectively, it can give reasonably accurate answers to calculations needed for both fiight planning and general navigation. The JAR-FCL General Navigation exa'mination requires numerous calculations which involve the CRP-5. It is important to learn to perform these calculations both quickly and accurately.General Navigation7-1 53. Chapter 7Pooley's CRP-5 Circular Slide RuleThe slide rule consists of two circular scales, an outer fixed scale and an inner moveable scale. Numbers are printed on both scales from 10 to 99.9. When doing any calculation , the user mentally places the decimal point before reading the answer off the slide rule . So 25 can represent .0025, .025, .25, 2.5, 25, etc. Note that the scale around the slide rule is not constant but logarithmic.MULTIPLICATION, DIVISION, AND RATIOS MULTIPLICATION Here are some simple examples to illustrate how the CRP-5 is used. ExampleConsider the simple multiplication 8 X 1.5. Mental arithmetic says the answer is 12.STEP 1STEP 2On the inner scale, go to the number 15 (1.5).STEP 3Read off the answer above this number.Answer7-2Rotate the inner scale so that the number 10 is under the number 80 (80 represents 8, and 10 represents 1).12General N avigation 54. Pooley's CRP-5 Circular Slide RuleExampleChapter 7Mu ltiply 1.72 by 2.Answer CRP Example 13.44 Answer the following questions:a . 70 x 213 b. .02 x.3 c. 31 x .75 d. 1.5x1 .7 e. 46 x 57Gene ral N avigation7-3 55. Chapter 7Pooley 's CRP-5 Circular Slide RuleDIVISION Division is the exact opposite of multiplication. ExampleUsing the same numbers for the multiplication, divide 12 by 1.5.STEP 1Place 15 on the inner scale under 12 on the outer scale.STEP 2On the inner scale, follow the numbers to 10.STEP 3On the outer scale , read off the answer. Answer: 8ExampleAnswer7-4Divide 34.4 by 20.1.72General Navigation 56. Chapter iPooley's CRP-5 Circular Slide RuleComplete the following questions:CRP Example 2a.70 + 213b . .02 + .3 c.31 + .75d.1.5 +1.7e.46 + 57RATIOS Any ratio can be read off the slide rule direct. ExampleFor AlB =cID , assume that A What is C?=30, 8 =15, and 0 =25.STEP 1Place 15(8) on the inner scale under 30(A) on the outer scale.STEP 2Follow the inner scale to 25(0).STEP 3Read off the answer on the outer scale.Answer50ExampleIf AGenera l Navigation=35 , 8 =20.4, and 0 =14, what is C?7-5 57. Chapter 7Pooley 's CRP-5 Circular Slide RuleAnswer24Conversions use the same principle as the multiplication , division, and ratio calculations.CONVERSIONS The conversions required for the JAR-FCL examination include: ~ Feet - metres - yards ~ Nautical miles - statute miles - kilometres ~ Knots - miles per hour (mph) - kilometres per hour (kph) ~ Imperial Gallons - US Gallons -litres ~ Kilograms - pounds ~ Volumes - weights ~ Fahrenheit to centigrade In order to correctly place the decimal point in an answer, use the following rough con version to get a ballpark estimate before doing the conversion on the CRP-5. ~ 1 yard = 3 feet ~ 1 metre = 3.3 feet ~ 1 nm = 1.2 statute miles = 2 km ~ 1 imp gal = 1.2 US gal = 4.5 litres ~ 1 kilogram 2.2 pounds=The above units are indicated in red on the outer scale of the slide rule with black arrows showing the datum point.7-6General N av igation 58. Pooley's CRP-j Circular Slide RilleChapter 7FEET - METRES - YARDS ExampleConvert 3 feet into yards and metres.STEP 1Under the feet arrow on the outer scale, place 3 on the inner scale.STEP 2On the inner scale, opposite the yards and metres datum arrows, read off the answers . 1 yard; 0,915 metresCRP Example 3 FeetYardsMetres65001.2. 3.2304.515.1700 9500The fo llowing conversions use exactly the same system as feet - yards - metres. Look for the red datum written on the outer scale, and read off the answer on the inner scale . ~ Nautical miles - statute miles - kilometres ~ Knots - miles per hour (mph) - kilometres per hour (kph) ~ Imperial Gallons - US Gallons - litres ~ Kilograms - poundsGeneral Navigation7-7 59. Chapter 7Pooley 's CRP-5 Circlliar Slide RilleCRP Example 4 Answer the following questions:1. 2. 3. 4. 5. 6. 7. 8.Convert 60 nautical miles into statute miles and kilometres. Convert 200 kilometres into nautical miles and statute miles. Convert 350 knots into mph and kph. Convert 450 kph into knots and mph. Convert 21 000 litres into US Gallons and Imperial Gallons. Convert 300 US Gallons into litres and Imperial Gallons. Convert 650 pounds into kilograms. Convert 345 kilograms into pounds.CONVERSION BETWEEN WEIGHT AND VOLUME To convert between weight and volume, start with the specific gravity (8G) of the fuel. The SG expresses the density of the fuel as a decimal fraction of the density of water. 1 litre of water weighs 1 kilogram. Fuel is less dense than water. For example, Avgas usually has an 8G of 0.72. One litre of Avgas with an SG of 0.72 weighs 0.72 kilograms. Both the volume datum point and the specific gravity datum points are used in these conversions. There are two SG datum points on the slide rule: ~ One centred around the pounds datum ~ One centred around the kilograms datum7-8General Navigation 60. Pooley's CRP-5 Circular Slide RuleExampleChapfer 7To convert 800 Imperial Gallons (5G 0.75) into kilograms and pounds .STEP 1Do a rough calculation first; 800 Imperial Gallons equates to about 3600 litres. Multiply by the 5G, to obtain 2700 kilograms .STEP 2Against the Imperial Gallon datum, align 8 on the inner scale.STEP 3Against the 5G scale for kilograms, read off the number of kilograms 2720 abeam 0.75STEP 4From the 5G datum for pounds, read off the number of pounds from the 6000 inner scale abeam 0.75FAHRENHEIT TO CENTIGRADE The conversion scale found at the bottom of the slide rule makes this a simple operation.ExampleThe temperature is 14 degrees centigrade. What is the temperature in Fahrenheit?AnswerGenera l NavigationFind 14 on the inner arc. Read off the temperature on the outer arc. 57F 7-9 61. Chapter 7Pooley's CRP-5 Circular Slide RuleSPEED, DISTANCE, AND TIME To calculate any of the variables, remember that minutes are always on the inner sca le. To remind the user, the inner scale has "minutes" written in red between 30 and 35. The calculations work on the factor 60. All speeds are a distance travelled in 60 minutes (I.e. one hour), so all calculations revolve around this number. The number 60 is in white , surrounded by a black triangle, to make it more prominent and as a reminder of which scale to use.GROUNDSPEED ExampleAn aircraft flies 210 nm in 25 minutes. What is the groundspeed?STEP 1Align the 25 on the inner scale against 210 on the outer scale.STEP 2Read off the groundspeed against the 60 triangle.503 knotsTIME ExampleUsing the same settings; at the groundspeed of 503 knots , how long will it take the aircraft to travel 210 nautical miles?STEP 1Align the 60 triangle on the inner scale against 503 on the outer scale .STEP 2On the outer distance scale, go to 210. Read off the time on the inner scale. 25 minutesDISTANCE TRAVELLED ExampleFor a groundspeed of 503 knots, how far will the aircraft travel in 35 minutes?STEP 1Align the 60 triangle on the inner scale against 503 on the outer scale.STEP 2On the inner minutes scale, go to 35. Read off the distance tra velled on the outer scale. 294 nautical milesFuel consumption, fuel flow, and time calculations are performed in the same manner.7-10General Nav igation 62. Pooley 's CRP-5 Circular Slide RilleCRP Example 5Complete the following table:DistanceTime250 nm1.Chapter 7Groundspeed25 minutes 37 minutes2.Fuel ConsumptionFuel flow200lb 350 knots200 imp gallhr 500 kg3.120 nm17 minutes4.300 nm270 knots5.240 nm210 knots2000lbl hr 30 US GallonsCALCULATION OF TAS UP TO 300 KNOTS There are three windows on the slide rule: the CaMP CaRR , ALTITUDE , and AIRSPEED . When calculating TAS from RAS, use the AIRSPEED window. For all these calculations, remember that RAS is on the inner scale and TAS on the outer scale. They are written in red as a reminder. ExampleThe pressure altitude is 35 000 ft, and the corrected outside air temperature (COAT) is - 65C. The RAS is 160 knots. What is the TAS?STEP 1STEP 2General NavigationFind the RAS of 160 knots on the inner scale. Read off the TAS on the outer scale. 275 knots7- 11 63. Chapter 7Pooley's CRP-5 Circular Slide RuleCALCULATION OF TAS OVER 300 KNOTS At high TAS, the air becomes compressed and causes extra pressure, which is sensed by the ASI. This compressibility results in a higher-than-actual TAS being calculated . To correct for this, a compressibility correction must be made using the COMP CORR window. ExampleThe pressure altitude is 35 000 ft, and the corrected outside air temperature (COAT) is - 65"C. The RAS is 21 0 knots. What is the TAS?'" h " 'Or...t ~ }>Expa nded in the East - West direction at high latitudes Expanded in the North - South direction away from the equatorTo make the chart orthomorphic, mathematical modelling is required . Once mathematical modelling is achieved , the scale is still only correct along the Equator where the cylinder touches the reduced Earth . At any other point on the chart, the scale is subject to expansion. Another way of saying the scale is correct is by saying that the Scale Factor is 1: SCALE FACTOR= CHART LENGTH +REDUCED EARTH LEN GTH0The length of the 90 line of latitude (i.e. the pole) is zero on the Earth and on the reduced Earth . So at the pole: Scale Factor = Chart Length + 0 = 00 (infinity) On a Mercator chart, the scale factor varies between 1 and infinity. This expansion away from the Equator is constant and is proportional to the secant (1/cosine) of the latitude. 10-2General Navigation 98. Maps and Charts-MercatorChapterlOThis gives the following formula: SCALE AT LATITUDE= SCALE AT E QUATOR X SE CANT LATITUDEThis formula can be further resolved to: COS LATA X S CALEDENOMINATOR LAT B= COS LAT B X S CALEDENOMINATOR LAT ANote: The above derived formula is very impor