Loading ...
Global Do...
News & Politics
18
0
Try Now
Log In
Pricing
Aircraft Engineering Principles Roll-Royce RB211-524 Engine fitted to a Boeing 747 Aircraft Aircraft Engineering Principles Lloyd Dingle Mike Tooley AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD • PARIS SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Butterworth Heinemann House, Jordan Hill, Oxford OX2 8DP porate Drive, Burlington, MA 01803 blished 2005 ght © 2005, Lloyd Dingle and Mike Tooley. All rights reserved ht of Lloyd Dingle and Mike Tooley to be identified as the of this work has been asserted in accordance with the ght, Design and Patents Act 1988 of this publication may be reproduced in any material form ng photocopying or storing in any medium by electronic means ether or not transiently or incidentally to some other use of this tion) without the written permission of the copyright holder n accordance with the provisions of the Copyright, Designs and Act 1988 or under the terms of a licence issued by the Copyright ng Agency Ltd, 90 Tottenham Court Road, London, d W1T 4LP. Applications for the copyright holder’s written ion to reproduce any part of this publication should be addressed ublishers Library Cataloguing in Publication Data Lloyd aft engineering principles ospace engineering e II. Tooley, Michael H. (Michael Howard), 1946– of Congress Cataloguing in Publication Data ogue record for this book is available from the Library of Congress 7506 5015 X formation on all Elsevier Butterworth-Heinemann publications ur website at www.books.elsevier.com by Charon Tec Pvt. Ltd, Chennai, India harontec.com and bound in Great Britain ontents e viii owledgements x T 1 INTRODUCTION 1 er 1 Introduction 3 1.1 The aircraft engineering industry 3 1.2 Differing job roles for aircraft maintenance certifying staff 3 1.3 Opportunities for training, education and career progression 7 1.4 CAA licence – structure, qualifications, examinations and levels 15 1.5 Overview of airworthiness regulation, aircraft maintenance and its safety culture 18 T 2 SCIENTIFIC FUNDAMENTALS 31 er 2 Mathematics 33 General introduction 33 Non-calculator mathematics 34 2.1 Introduction 34 2.2 Arithmetic 34 2.3 Algebra 53 2.4 Geometry and trigonometry 73 2.5 Multiple choice questions 100 er 3 Further mathematics 109 3.1 Further algebra 109 3.2 Further trigonometry 118 3.3 Statistical methods 131 3.4 Calculus 144 er 4 Physics 165 4.1 Summary 165 4.2 Units of measurement 165 4.3 Fundamentals 170 4.4 Matter 178 4.5 The states of matter 182 4.6 Mechanics 183 4.7 Statics 184 4.8 Dynamics 207 4.9 Fluids 240 4.10 Thermodynamics 257 4.11 Light, waves and sound 277 4.12 Multiple choice questions 297 3 ELECTRICAL AND ELECTRONIC FUNDAMENTALS 309 er 5 Electrical fundamentals 311 5.1 Introduction 311 5.2 Electron theory 313 5.3 Static electricity and conduction 315 5.4 Electrical terminology 319 5.5 Generation of electricity 322 5.6 DC sources of electricity 326 5.7 DC circuits 333 5.8 Resistance and resistors 341 5.9 Power 353 5.10 Capacitance and capacitors 355 5.11 Magnetism 369 5.12 Inductance and inductors 379 5.13 DC motor/generator theory 386 5.14 AC theory 397 5.15 Resistive, capacitive and inductive circuits 402 5.16 Transformers 414 5.17 Filters 418 5.18 AC generators 423 5.19 AC motors 429 5.20 Multiple choice questions 438 er 6 Electronic fundamentals 451 6.1 Introduction 451 6.2 Semiconductors 456 6.3 Printed circuit boards 511 6.4 Servomechanisms 515 6.5 Multiple choice questions 531 4 FUNDAMENTALS OF AERODYNAMICS 539 er 7 Basic aerodynamics 541 7.1 Introduction 541 7.2 A review of atmospheric physics 541 7.3 Elementary aerodynamics 545 7.4 Flight forces and aircraft loading 561 7.5 Flight stability and dynamics 570 7.6 Control and controllability 579 7.7 Multiple choice questions 587 NDICES 595 A Engineering licensing examinations 597 B Organizations offering aircraft maintenance engineering training and education 601 C The role of the European Aviation Safety Agency 603 D Mathematical tables 605 E System international and imperial units 615 F Answers to “Test your understanding” 623 637 This page intentionally left blank eface ooks in the series have been designed for ndependent and tutor assisted studies. For eason they should prove particularly use- the “self-starter” and to those wishing date or upgrade their aircraft maintenance e. Also, the series should prove a useful e of reference for those taking ab initio ng programmes in JAR 147 (now ECAR 47) and FAR 147 approved organizations hose on related aeronautical engineering ammes in further and higher education ishments. s book has primarily been written as one in es of texts, designed to cover the essential ledge base required by aircraft certifying anics, technicians and engineers engaged gineering maintenance activities on com- al aircraft. In addition, this book should l to the members of the armed forces, udents attending training and educational ishments engaged in aircraft engineering enance and other related aircraft engineer- arning programmes. his book we cover in detail the under- ng mathematics, physics, electrical and onic fundamentals, and aerodynamics nec- to understand the function and operation complex technology used in modern air- The book is arranged into four major ns: oduction ntific fundamentals trical and electronic fundamentals damentals of aerodynamics he Introductory section you will find infor- n on the nature of the aircraft mainte- industry, the types of job role that you xpect, the current methods used to train ducate you for such roles and informa- n the examinations system directly related il aviation maintenance engineering. In on, you will find information on typical career progression routes, professional recogni- tion, and the legislative framework and safety culture that is so much a part of our industry. In the section on Scientific fundamentals we start by studying Module 1 of the JAR 66 (now ECAR Part-66) syllabus (see qualifications and levels) covering the elementary mathematics necessary to practice at the category B technician level. It is felt by the authors, that this level of “non-calculator” mathematics is insufficient as a prerequisite to support the study of the physics and the related technology modules, that are to follow. For this reason, and to assist students who wish to pursue other related qualifications, a section has been included on “further math- ematics”. The coverage of JAR 66 Module 2 on physics is sufficiently comprehensive and at a depth, necessary for both category B1 and B2 technicians. The section on Electrical and electronic fun- damentals comprehensively covers ECAR 66 Module 3 and ECAR Part-66 Module 4 to a knowledge level suitable for category B2 avionic technicians. Module 5 on Digital Techniques and Electronic Instrument Systems will be cov- ered in the fifth book in the series, Avionic Systems. This book concludes with a section on the study of Aerodynamics, which has been written to cover ECAR Part-66 Module 8. In view of the international nature of the civil aviation industry, all aircraft engineering main- tenance staff need to be fully conversant with the SI system of units and be able to demon- strate proficiency in manipulating the “English units” of measurement adopted by international aircraft manufacturers, such as the Boeing Air- craft Company. Where considered important, the English units of measure will be emphasized alongside the universally recognized SI system. The chapter on physics (Chapter 4) provides a thorough introduction to SI units, where you will also find mention of the English system, conversion tables between each system provided at the beginning of Chapter 4. reinforce the subject matter for each major there are numerous worked examples and our knowledge written questions designed hance learning. In addition, at the end ch chapter you will find a selection of ple-choice questions, that are graded to ate the depth and breadth of knowledge ed by individuals wishing to practice at the nic (category A) or technician (category el. These multiple choice question papers d be attempted after you have completed study of the appropriate chapter. In this you will obtain a clearer idea of how well ave grasped the subject matter at the mod- vel. Note also that category B knowledge uired by those wishing to practice at the ry C or engineer level. Individuals hop- pursue this route should make sure that horoughly understand the relevant infor- n on routes, pathways and examination given later. ther information on matters, such as pace operators, aircraft and aircraft onent manufacturers, useful web sites, tory authorities, training and educational shments and comprehensive lists of terms, ions and references, appear as appendices at the end of the book. References are annotated using superscript numbers at the appropriate point in the text. Lloyd Dingle Mike Tooley Answers to questions Answers to the “Test your understanding” questions are given in Appendix F. Solutions to the multiple choice questions and general questions can be accessed by adopting tutors and lecturers. To access this material visit http://books.elsevier.com/manuals and follow the instructions on screen. Postscript At the time of going to press JAR 66 ad JAR 147 are in the process of being superseded by the European Civil Aviation Regulations (ECAR) 66 and 147. Wherever in this volume reference is made to JAR 66 and JAR 147, then by impli- cation, these are referring to ECAR Part-66 and ECAR Part-147 (see Appendix C for details). cknowledgements uthors would like to express their grati- o those who have helped in producing this my Cox and Mike Smith of Britannia Air- for access to their facilities and advice rning the administration of civil aircraft enance; Peter Collier, chairman of the non-corporate accreditation committee, s advice on career progression routes; Aerospace Engineering lecturing team at Kingston University, in particular, Andrew Self, Steve Barnes, Ian Clark and Steve Wright, for proof reading the script; Jonathan Simpson and all members of the team at Elsevier, for their patience and perseverance. Finally, we would like to say a big ‘thank you’ to Wendy and Yvonne. Again, but for your support and under- standing, this book would never have been produced! P A R T 1 ntroduction This page intentionally left blank a p t e r 1 Introduction The aircraft engineering industry obal aircraft industry encompasses a vast rk of companies working either as large ational conglomerates or as individual nal and regional organizations. The two t international aircraft manufacturers are merican owned Boeing Aircraft Com- and the European conglomerate, Euro- Aeronautic Defence and Space Company S), which incorporates airbus industries. , together with the American giant eed-Martin, BAE Systems and aerospace lsion companies, such as Rolls-Royce and and Whitney, employ many thousands ople and have annual turnovers totalling ns of pounds. For example, the recently Lockheed-Martin contract for the Amer- oint Strike Fighter (JSF) is estimated to rth 200 billion dollars, over the next 10 A substantial part of this contract will e BAE Systems, Rolls-Royce and other UK anies. airlines and armed forces of the world uy-in aircraft and services from aerospace facturers are themselves, very often, large izations. For example British Airways our national carrier, even after recent down- employs around 50,000 personnel. UK s, in the year 2000, employed in total, ver 12,000 aircraft maintenance and over- personnel. Even after the events that took on 11th September 2001, the requirement aintenance personnel is unlikely to fall. A survey by the Boeing Corporation expects the demand for aircraft and their associ- omponents and systems rise by 2005, to vel of orders that existed prior to the tragic of 11th September 2001. art from the airlines, individuals with ft maintenance skills may be employed eral aviation (GA), third-party overhaul companies, component manufacturers or air- frame and avionic repair organizations. GA companies and spin-off industries employ large numbers of skilled aircraft fitters. The UK armed forces collectively recruit around 1500 young people annually for training in aircraft and associated equipment maintenance activities. Aircraft maintenance certifying staff are recognized throughout Europe and indeed, throughout many parts of the world, thus opportunities for employment are truly global! In the USA approximately 10,000 airframe and propulsion (A&P) mechanics are trained annu- ally; these are the USA equivalent of our own aircraft maintenance certifying mechanics and technicians. Recent surveys carried out for the UK sug- gest that due to demographic trends, increasing demand for air travel and the lack of trained air- craft engineers leaving our armed forces, there exists an annual shortfall of around 800 suit- ably trained aircraft maintenance and overhaul staff. Added to this, the global and diverse nature of the aircraft maintenance industry, it can be seen that aircraft maintenance engineer- ing offers an interesting and rewarding career, full of opportunity. 1.2 Differing job roles for aircraft maintenance certifying staff Individuals may enter the aircraft maintenance industry in a number of ways and perform a variety of maintenance activities on aircraft or on their associated equipments and components. The nature of the job roles and responsibilities for licensed certifying mechanics, technicians and engineers are detailed below. The routes and pathways to achieve these job roles, the opportunities for career progression, the certification rights and the nature of the ary examinations and qualifications are ed in the sections that follow. The aircraft maintenance fying mechanic the aircraft maintenance industry is highly ted, the opportunities to perform com- maintenance activities are dependent on mount of time that individuals spend eir initial and aircraft-type training, the edge they accrue and their length of expe- in post. Since the knowledge and experi- equirements are limited for the certifying nic (see later), the types of maintenance y that they may perform, are also lim- Nevertheless, these maintenance activities e people with a sound basic education, re able to demonstrate maturity and the to think logically and quickly when act- der time constraints and other operational tions. activities of the certifying mechanic e the limited rectification of defects and apability to perform and certify minor uled line maintenance inspections, such as checks. These rectification activities might e tasks, such as a wheel change, replace- of a worn brake unit, navigation light ement or a seat belt change. Scheduled enance activities might include: replen- nt of essential oils and lubricants, lubri- of components and mechanisms, panel owling removal and fit, replacement of fasteners, etc., in addition to the inspec- f components, control runs, fluid systems ircraft structures for security of attach- corrosion, damage, leakage, chaffing, uction and general wear. these maintenance activities require a ng knowledge of the systems and struc- being rectified or inspected. For example, lenish the hydraulic oil reservoirs on a rn transport aircraft requires knowledge particular system, the type of oil required e 1.1), the replenishment equipment being all related safety considerations and edge of the correct positioning of the ulic services prior to the replenishment. Figure 1.1 Identification label showing the type of oil contained within the drum. Figure 1.2 Boeing 767 hydraulic reservoir charging point, showing contents gauge, changeover valve and hydraulic hand pump. In addition, for this task, the mechanic must be able to recognize the symptoms for internal or external hydraulic oil leakage when carrying out these replenishment activities on a particular hydraulic system reservoir. For example, Figure 1.2 shows the hydraulic reservoir replenishing point for the Boeing 767. The replenishment process requires the changeover valve to be selected and oil sucked into the reservoir, via the replenishment hose (Figure 1.3) which is placed in the oil container. The certifying mechanic then operates the hand pump (see Figure 1.2) to draw the hydraulic fluid up into the reservoir. When the reservoir is full, as indicated by the contents gauge, the hose is withdrawn from the container, blanked and stowed. The changeover valve is put back into the flight position, the panel is secured and the e 1.3 Hydraulic reservoir replenishment emoved from stowage point. priate documentation is completed by the ing mechanic, who will have a company val to perform this task. this job role, like all those that follow, is a statutory requirement for a particu- riod of training and experience before a enance mechanic is issued with limited ing privileges. hin the armed forces a similar job role for those who have undergone training as ft mechanics, for flight line operations or r maintenance activities. The aircraft maintenance gory B certifying technician ole of the category B certifying technician divided into two major sectors: category echanical) and category B2 (avionic). B1 enance technicians will have an in depth edge of airframe, engine and electrical systems and equipment in addition to a ugh knowledge of aircraft structures and ials. While category B2 maintenance tech- s will have an in-depth integrated knowl- f aircraft electrical, instrument, autopilot, radar, communication and navigation ms. knowledge and skills gained from their training, together with aircraft-type edge and a substantial period of practical ence, will enable category B technicians, granted approvals, to undertake one or Figure 1.4 Boeing 767 flap drive motor and asso- ciated drive mechanism. more of the following maintenance operations: • In-depth scheduled inspection activities. • Complex rectification activities. • Fault diagnosis on aircraft systems, propul- sion units, plant and equipments. • Embodiment of modifications and special technical instructions. • Airframe and other aircraft repairs. • Strip-down and aircraft re-build activities. • Major aircraft component removal, fit and replacement tasks. • Use and interrogate built-in test equipment (BITE) and other diagnostic equipments. • Functional tests and checks on aircraft sys- tems, propulsion units and sub-systems. • Trouble-shooting activities on base and away from base. • Aircraft engine ground running activities. • Rack and re-rack avionic equipments and carry out operational tests and checks on avionic systems. • Supervise and certify the work of less experi- enced technicians and mechanics. As can be seen from the above list of mainte- nance operations, the category B maintenance technician can be involved in a very wide and interesting range of possible activities. For example, Figure 1.4 shows a photograph of the Boeing 767 flap drive motor and associated linkage mechanism. The main source of power is via the hydraulic motor, scheduled servicing may involve the 1.5 Technicians working at height consi- the alignment of the APU prior to fit. tion and inspection of this complex sys- which in turn requires the certifying cian to not only have the appropriate m knowledge, but also the whole aircraft edge to ensure that other systems are not ted inadvertently. Figure 1.5 shows two cians working at height on highway stag- onsidering the alignment of the aircraft ary power unit (APU), prior to raising it osition in the aircraft. perform this kind of maintenance, to the ed standards, individuals need to demon- maturity, commitment, integrity and an to see the job through, often under lt circumstances. ilar technician roles exist in the armed , where the sub-categories are broken a little more into, mechanical, electrical/ ment and avionic technicians, as well as ft weapons specialists known as armament cians or weaponeers. act, it is planned from January 2004 that oyal Air Force (RAF) will begin initial ng that follows the civil aviation trade cat- s. That is mechanical technicians, who ndertake airframe/engine training and to a extent electrical training and avionic tech- s, who will eventually cover all avionic ms, in a similar manner to their civil coun- ts. Cross-training of existing maintenance nnel is also planned to take place over xt 10 years. The armament technician and oneer will still remain as a specialist trade . 1.2.3 The base maintenance category C certifying engineer Before detailing the job role of the category C licensed engineer, it is worth clarifying the major differences in the roles performed by line main- tenance certifying staff and base maintenance certifying staff. In the case of the former, the inspections, rectification and other associated maintenance activities take place on the aircraft, on the “live side” of an airfield. Thus the depth of maintenance performed by “line maintenance personnel” is restricted to that accomplishable with the limited tools, equipment and test appa- ratus available on site. It will include “first-line diagnostic maintenance”, as required. Base maintenance, as its name implies, takes place at a designated base away from the live air- craft movement areas. The nature of the work undertaken on base maintenance sites will be more in-depth than that usually associated with line maintenance and may include: in-depth strip-down and inspection, the embodiment of complex modifications, major rectification activities, off-aircraft component overhaul and repairs. These activities, by necessity, require the aircraft to be on the ground for longer peri- ods of time and will require the maintenance technicians to be conversant with a variety of specialist inspection techniques, appropriate to the aircraft structure, system or components being worked-on. The category C certifier acts primarily in a maintenance management role, controlling the progress of base maintenance inspections and overhauls. While the actual work detailed for the inspection is carried out by category B tech- nicians and to a limited extent, category A base maintenance mechanics, in accordance with the written procedures and work sheets. These indi- vidual activities are directly supervised by cate- gory B maintenance certifying technicians, who are responsible for ensuring the adequacy of the work being carried out and the issuing of the appropriate certifications for the individual activities. The category C certifier will upon completion of all base maintenance activities sign-off the air- craft as serviceable and fit for flight. This is done using a special form known as a certificate of e 1.6 Category C maintenance engineer ning the complexity of the technical log to the . e to service (CRS). Thus the category C ing engineer has a very responsible job, requires a sound all-round knowledge of ft and their associated systems and major onents (Figure 1.6). The CRS is ultimately le responsibility of the category C certify- gineer, who confirms by his/her signature ll required inspections, rectification, mod- ons, component changes, airworthiness ves, special instructions, repairs and air- re-build activities have been carried out ordance with the laid-down procedures at all documentation have been completed ctorily, prior to releasing the aircraft for Thus, the category C certifying engi- will often be the shift maintenance man- esponsible for the technicians and aircraft his/her control. requirements for the issuing of an indi- category C licence and the education, ng and experience necessary before the of such a licence are detailed in the sections ollow. military equivalent of the category C e holder will be an experienced main- ce technician who holds at least senior ommissioned officer (SNCO) rank and significant period of experience on air- ype. These individuals are able to sign-off ilitary equivalent of the CRS, for and half of all trade technicians, who have ipated in the particular aircraft servicing ies. 1.3 Opportunities for training, education and career progression Those employed in civil aviation as aircraft cer- tifying staff may work for commercial aircraft companies or work in the field of GA. The leg- islation surrounding the training and education of those employed in GA is somewhat differ- ent (but no less stringent) than those employed by passenger and freight carrying commercial airline companies. The opportunities and career progressions routes detailed below are primar- ily for those who are likely to be employed with commercial carriers. However, they may in the future, quite easily, be employed by GA organizations. Commercial air transport activities are well understood. In that companies are licensed to carry fare paying passengers and freight, across national and international regulated airspace. GA, on the other hand, is often misunderstood for what it is and what place it holds in the total aviation scene. Apart from including flying for personal pleasure, it covers medical flights, traffic surveys, pipeline inspections, business aviation, civil search and rescue and other essen- tial activities, including pilot training! With the advent of a significant increase in demand for business aviation, it is likely that those who have been trained to maintain large commercial trans- port aircraft will find increasing opportunity for employment in the GA field. In the UK, and indeed in many countries that have adopted our methods for educat- ing and training prospective aircraft mainte- nance personnel, there have been, historically, a large number of different ways in which these personnel can obtain initial qualifications and improver training. Since the advent of the recent Joint Aviation Requirements (JAR) legis- lation on personnel licensing, the methods for obtaining initial education and training have become somewhat more unified. Although there still exist opportunities for the “self-starter”, achievement of the basic license may take longer. The schematic diagrams that follow are based on those issued by the Civil Aviation Author- ity (CAA),1 Safety Regulation Group (SRG). They show the qualification and experience /pathways for the various categories of ft maintenance certifying staff, mentioned . Category A certifying hanics 147 approved training pathway AR 147 approved training organization e to offer ab initio (from the beginning) ng programmes that deliver JAR 66 basic edge and initial skills training that satisfy gulatory authority criteria. In the case of K our regulatory authority is the CAA. 1.7 Category A qualifications and experience pathways. Note that a list of CAA JAR 147 approved training organizations, together with other use- ful education and training institutions, will be found in Appendix B, at the end of this book. Ab initio programmes in approved training organizations often encompass the appropriate CAA examinations. If the examinations have been passed successfully, then an individual requires 1 year of approved maintenance experi- ence before being able to apply for a category A aircraft maintenance license (AML). Note also the minimum age criteria of 21 years, for all certifying staff, irrespective of the category of license being issued (Figure 1.7). d worker pathway equirement of practical experience for entering the profession as non-aviation cal tradesmen is 2 years. This will enable on-orientated skills and knowledge to be ed from individuals who will already have cessary basic fitting skills needed for many tasks likely to be encountered by the ory A certifying mechanic. pted military service pathway ienced line mechanics and base mainte- mechanics, with suitable military expe- on live aircraft and equipments, will have practical experience requirement reduced months. This may change in the future armed forces personnel leave after being trained. gory B2 AML pathway kills and knowledge required by category tifying mechanics is a sub-set of those ed by B1 mechanical certifying techni- Much of this knowledge and many of the required for category A maintenance tasks t relevant by the category B2 avionic cer- g technician. Therefore, in order that the ory B2 person gains the necessary skills and edge required for category A certification, r of practical maintenance experience is dered necessary. tarter pathway oute is for individuals who may be taken smaller approved maintenance organiza- or be employed in GA, where company vals can be issued on a task-by-task basis, perience and knowledge are gained. Such duals may already possess some general ft knowledge and basic fitting skills by suc- lly completing a state funded education amme. For example, the 2-year full-time ma that leads to an aeronautical engineer- alification (see Section 1.3.4). wever, if these individuals have not prac- as a skill fitter in a related engineering line, then it will be necessary to complete the 3 years of practical experience applicable to this mode of entry into the profession. 1.3.2 Category B certifying technicians The qualification and experience pathways for the issue of category B1 and B2 AMLs are shown in Figures 1.8 and 1.9. Having discussed in some detail pathways 1–5 for the category A licence, it will not be necessary to provide the same detail for the category B pathways. Instead you should note the essential differences between the category B1 and B2 pathways as well as the increased experience periods required for both, when compared with the category A license. Holders of the category A AML require a number of years experience based on their back- ground. This is likely to be less for those wishing to transfer to a category B1 AML, rather than to a B2 AML, because of the similarity in main- tenance experience and knowledge that exists between category A and B1 license holders. Conversion from category B2 to B1 or from B1 to B2 requires 1 year of practical experi- ence practicing in the new license area. Plus successful completion of the partial JAR 66 examinations, as specified by the CAA and/or JAR 147 approved training organization. 1.3.3 Category C certifying engineers The three primary category C qualification path- ways are relatively simple to understand and are set out in Figure 1.10. Qualification is either achieved through prac- tising as a category B1 or B2 certifying tech- nician, for a minimum period of 3 years or entering the profession as an engineering gradu- ate from a recognized degree. Those individuals wishing to gain a category C AML, using the category B route, will already have met the examination criteria in full. However, those entering the profession as engineering graduates will have to take category B1 or B2 knowledge examinations in full or in part, depending on the nature of the degree studied. Examples of 1.8 Category B1 qualifications and experience pathways. 1.9 Category B2 qualifications and experience pathways. Figure 1.10 Category C qualifications and experience pathways. Figure 1.11 Non-standard qualification and expe- rience pathways. 1.12 Routes to an honours degree and category A, B and C licenses. andard entry methods and graduate entry ds, together with the routes and pathways fessional recognition are given next. Non-standard qualification experience pathways 1.11 illustrates in more detail two possi- f-starter routes. The first shows a possible ession route for those wishing to gain the priate qualifications and experience by ini- serving in the armed forces. The second s a possible model for the 18+ school employed in a semi-skilled role, within a ely small aircraft maintenance company. In the case of the semi-skilled self-starter, the experience qualifying times would be depen- dent on individual progress, competence and motivation. Also note that 18+ is considered to be an appropriate age to consider entering the aircraft maintenance profession, irrespective of the type of license envisaged. 1.3.5 The Kingston qualification and experience pathway In this model, provision has been made for qual- ification and experience progression routes for category A, B and C AML approval and appro- priate professional recognition (Figure 1.12). e 1.13 Fast-track routes to category B and C AML. ure 1.13 also shows the various stopping- oints, for those individuals wishing to ce as either category A, B or C certifiers. ure 1.13 shows two possible fast-track for the qualification and award of either gory B or C license. Fast track in this case that because of the partnership between ton University2 and KLM the total pro- me is recognized by the CAA for ab initio val, which reduces the qualifying times to mum, as shown in Figures 1.8–1.10. The priate practical experience being delivered M’s JAR 147 approved training school at ich Airport. gston University also has a partnership he City of Bristol College, which is a JAR pproved organization. With the expan- f Kingston’s highly successful programme will be more opportunities for 18+ l leavers, to undertake ab initio train- ading to the CAA examinations and the award of a foundation or full B.Eng.(Hons) degree. The Royal Aeronautical Society (RAeS) recog- nizes that full category B JAR 66 AML holders, with appropriate experience and responsibili- ties, meet the criteria for professional recogni- tion as incorporated engineers and may, subject to a professional review, use the initials I.Eng. after their name. Honours degree holders, who also hold a full category C AML may, with appropriate fur- ther learning to masters degree level, apply for recognition as chartered engineers through the RAeS. This is the highest professional accolade for engineers and recognized internationally as the hallmark of engineering ability, competence and professionalism. Figure 1.14 shows where the full category A, B and C aircraft maintenance certifiers sit, within the professional engineering qualification framework. Thus the category A mechanic, can 1.14 Routes to aerospace engineering professional recognition. ble 1.1 pe of engineering degree Module exemption echanical engineering bias Module 1 Mathematics and Module 2 Physics ronautical engineering or Air Module 1 Mathematics, Module 2 Physics and nsport engineering bias Module 8 Basic aerodynamics ctrical or Electronic engineering bias Module 1 Mathematics, Module 2 Physics, Module 3 Electrical fundamentals and Module 4 Electronic fundamentals ionic engineering bias Module 1 Mathematics, Module 2 Physics, Module 3 Electrical fundamentals, Module 4 Electronic fundamentals and Module 8 Basic aerodynamics ngston University B.Eng.(Hons) aircraft Complete exemption from Modules 1 to 10. gineering degree (mechanical engineering bias) Approved as fast-track route to “C” licence suitable structured training and experi- gain engineering technician status. The ategory B technician, again with appro- structured training and experience, can for Incorporated Engineer recognition. ategory C engineer, can with an appro- masters degree or bachelor (Hons) degree urther learning to masters degree level, ually gain professional recognition as a red engineer. tial exemptions from JAR 66 examina- may be awarded to recognized engineering degrees, dependent on the type of degree being studied. These limited exemptions, by degree type are detailed in Table 1.1. No other exemp- tions are allowed and all other modules applica- ble to the licence category need to be passed by CAA approved JAR 66 examination. Note: The one exception, where a large amount of exemption is given for graduates of the Kingston B.Eng.(Hons) aircraft engineering degree, which is directly aimed at preparing aircraft maintenance engineers, for their licence examinations. CAA licence – structure, ifications, examinations and levels Qualifications structure censing of aircraft maintenance engineers ered by international standards that are hed by the International Civil Aviation nization (ICAO). In the UK, the Air Nav- n Order (ANO) provides the legal frame- to support these standards. The purpose licence is not to permit the holder to per- maintenance but to enable the issue of cation for maintenance required under the legislation. This is why we refer to licensed enance personnel as “certifiers”. present the CAA issue licences under two ent requirements depending on the maxi- take-off mass of the aircraft. aircraft that exceeds 5700 kg, licenses are under JAR 66. The JAR 66 license is on to all European countries who are full ers of the Joint Aviation Authority (JAA). eal being that the issue of a JAR 66 licence y full member country is then recognized ing equal status in all other member coun- hroughout Europe. There are currently 20 countries throughout Europe that go ake-up the JAA. In US, the US Federal on Administration (USFAA) is the equiv- of the JAA. These two organizations have harmonized to the point where for exam- cences issued under JAR 66 are equiva- o those licences issued under FAR 66, in ries that adhere to FAA requirements. ders of licences issued under JAR 66 ements are considered to have achieved an priate level of knowledge and competence, will enable them to undertake maintenance ies on commercial aircraft. ences for light aircraft (less than 5700 kg) r airships, continue to be issued under the ational Licensing Requirements laid down itish Civil Airworthiness Requirements R) Section L. The intention is that within a ears, light aircraft will be included within 66. At present, this has implications for e who wish to work and obtain licences , where many light aircraft are operated. Much of the knowledge required for the JAR 66 licence, laid down in this series, is also relevant to those wishing to obtain a Section L licence for light aircraft. Although the basic Section L licence is narrower (see Appendix B) and is con- sidered somewhat less demanding than the JAR 66 licence it is, nevertheless, highly regarded as a benchmark of achievement and competence within the light aircraft fraternity. As mentioned earlier, the JAR 66 license is divided into categories A, B and C, and for category B license, there are two major career options, either a mechanical or avionic techni- cian. For fear of bombarding you with too much information, what was not mentioned earlier was the further subdivisions for the mechanical license. These sub-categories are dependent on aircraft type (fixed or rotary wing) and on engine type (turbine or piston). For clarity, all levels and categories of license that may be issued by the CAA/FAA or member National Aviation Authorities (NAA) are listed below. Levels Category A: Line maintenance certifying mechanic Category B1: Line maintenance certifying technician (mechanical) Category B2: Line maintenance certifying technician (avionic) Category C: Base maintenance certifying engineer Note: When introduced, the light AML will be category B3. Sub-category A A1: Aeroplanes turbine A2: Aeroplanes piston A3: Helicopters turbine A4: Helicopters piston Sub-category B1 B1.1: Aeroplanes turbine B1.2: Aeroplanes piston B1.3: Helicopters turbine B1.4: Helicopters piston that the experience requirements for all e above licences are shown in Figures 10. aft-type endorsements 3 rs of JAR 66 aircraft maintenance licences gory B1, B2 and C may apply for inclusion aircraft-type rating subject to meeting the wing requirements. e completion of a JAR 147 approved or A/NAA approved type training course on type of aircraft for which approval is ng sought and one which covers the sub- matter appropriate to the licence category ng endorsed. mpletion of a minimum period of practical erience on type, prior to application for e rating endorsement. e training for category C differs from that ed for category B1 or B2, therefore cat- C type training will not qualify for type sement in category B1 or B2. However, ourses at category B1 or B2 level may the licence holder to qualify for category l at the same time, providing they hold a ory C basic licence. ence holders seeking type rating endorse- from the CAA must hold a basic JAR 66 e granted by the UK CAA. JAR 66 syllabus modules and cability AR 66 syllabus may be taught and exam- n a module-by-module basis. The subject r of individual modules may vary accord- the category of licence being studied. epth of the subject matter may also vary ding to the category. Where this is the n this series of books, the greatest depth owledge required by category will always vered. In all, there are currently 17 mod- n the JAR 66 syllabus. These modules are ted in Table 1.2, together with Table dicating their applicability to a particular ory and mechanical sub-category. Table 1.2 Syllabus modules by subject Module Content 1 Mathematics 2 Physics 3 Electrical fundamentals 4 Electronic fundamentals 5 Digital techniques and electronic instrument systems 6 Materials and hardware 7 Maintenance practices 8 Basic aerodynamics 9 Human factors 10 Aviation legislation 11 Aeroplane aerodynamics, structures and systems 12 Helicopter aerodynamics, structures and systems 13 Aircraft aerodynamic structures and systems 14 Propulsion 15 Gas turbine engine 16 Piston engine 17 Propeller 18 Airship (to be developed) 1.4.3 Examinations and levels The JAR 66 examinations are modular and designed to reflect the nature of the JAR 66 syllabus content. These modular examinations may be taken on CAA premises, or on the premises of approved JAR 147 organizations. The number and type of examination conducted by JAR 147 approved organizations will be dependent on the exact nature of their approval. A list of approved organizations and examina- tion venues will be found at the end of this book in Appendix A. For candidates taking the full modular JAR 66 examinations, information on the conduct and procedures for these examina- tions will be found in Chapter 23 of the JAA Administrative and Guidance Material.4 The JAR 66 module content may vary in terms of the subjects covered within the module and the level of knowledge required according to whether or not a category A, B1 or B2 license is being sought. Thus, in this book, we will cover in full JAR 66 Modules 1, 2, 3, 4 and 8. Module 1 (Mathematics, Chapter 2 in this book), will Table 1.3 Module applicability to category and mechanical sub-category Module A or B1 aeroplanes with: A or B1 helicopter with: B2 avionic Turbine engine Piston engine Turbine engine Piston engine 1 2 3 4 a a a a 5 6 7 8 9 10 11b – – – 12 – – – 13c – – – – 14d – – – – 15 – – – 16 – – – 17 – – – a This module is not applicable to category A. b Module 11 is applicable only to mechanical certifying staff. c Module 13 is only applicable to B2 avionic certifying technicians. d Module 14 offers a less in depth treatment of propulsion, designed for study by B2 avionic certifying technicians. vered to the depth required by the B1 2 technician examination. Further math- cs (chapter 3) is also included, which is ed to assist understanding of Module 2, s. The further mathematics is not subject R 66 examination but is still considered e authors to be very useful foundation edge. Those studying for the category A e should concentrate on fully understand- he non-calculator mathematics given in er 2 of this book. They should also be able wer all the test questions at the end of this er. dule 2 (Physics, Chapter 4 in this book) ered to a depth suitable for category B cians, no distinction is made between B1 2 levels of understanding,5 the greatest being covered for both categories, as priate. The Module 2 content not required egory A mechanics, is mentioned in the uction to the chapter and reflected in the s test questions given at the end. Module 3 (Electrical fundamentals, Chapter 5 in this book) is covered at the category B technician level, with clear indications given between the levels of knowledge required for the category A and B license requirements. Module 4 (Electronic fundamentals, Chapter 6 in this book) is not required by category A mechan- ics but, as before, the treatment of the differing levels of knowledge for category B1 and B2 will be taken to the greater depth required by B2 technicians. The differences in level again being reflected in the test questions given at the end of the chapter. Module 8 (Basic aerodynamics, Chapter 7 in this book) will be covered in full to cate- gory B level, with no demarcation being made between category A and B levels. For the sake of completeness, this chapter will also include brief coverage of aircraft flight control taken from Module 11.1. The typical examination questions directly related to Module 8 will be clearly identified at the end of the chapter. overage of the specialist aeroplane aerody- s, high-speed flight and rotor wing aero- mics, applicable to Modules 11 and 13 e covered in the third book in the series, ft Aerodynamics, Structural Maintenance epair. mination papers are mainly multiple- type but a written paper must also be d so that the licence may be issued. Can- s may take one or more papers, at a examination sitting. The pass mark for multiple-choice paper is 75%! There is nger any penalty marking for incorrectly ring individual multiple-choice questions. ultiple-choice questions set by the CAA y approved organizations have exactly the orm. That is, each question will contain a the question being asked), two distracters rect answers) and one correct answer. The ple-choice questions given at the end of chapter in this book are laid out in this multiple-choice examination papers are approximately 1 min and 15 s, being ed for the reading and answering of each on (see Table 1.4). The number of ques- asked depends on the module examination taken and on the category of licence being t. The structure of the multiple-choice s for each module together with the struc- f the written examination for issue of the e are given in Table 1.4. re detailed and current information on ature of the license examinations can be in the appropriate CAA documentation,6 which the examination structure detailed ble 1.4 is extracted. n paper ritten paper required for licence issue con- our essay questions. These questions are n from the JAR 66 syllabus modules as ws: ule Paper Question Maintenance practices 2 Human factors 1 Aviation legislation 1 1.5 Overview of airworthiness regulation, aircraft maintenance and its safety culture 1.5.1 Introduction All forms of public transport require legislation and regulation for their operation, in order to ensure that safe and efficient transport oper- ations are maintained. Even with strict regu- lation, it is an unfortunate fact that incidents and tragic accidents still occur. Indeed, this is only to self-evident with the recent spate of rail accidents where the Potters Bar accident in 2002, may very likely be attributable to poor maintenance! When accidents occur on any public transport system, whether travelling by sea, rail or air, it is an unfortunate fact, that loss of life or serious injury may involve a substantial number of peo- ple. It is also a fact that the accident rate for air travel is extremely low and it is currently one of the safest forms of travel. The regulation of the aircraft industry can only lay down the framework for the safe and efficient management of aircraft operations, in which aircraft maintenance plays a significant part. It is ultimately the responsibility of the individuals that work within the industry to ensure that standards are maintained. With respect to aircraft maintenance, the introduc- tion of the new harmonized requirements under JAA and more recently ECAR should ensure that high standards of aircraft maintenance and maintenance engineering training are found not only within the UK, but across Europe and indeed throughout many parts of the world. In order to maintain these high standards, individuals must not only be made aware of the nature of the legislation and regulation sur- rounding their industry, but also they need to be encouraged to adopt a mature, honest and responsible attitude to all aspects of their job role. Where safety and personal integrity must be placed above all other considerations, when undertaking aircraft maintenance activities. It is for the above reasons, that a knowl- edge of the legislative and regulatory framework of the industry and the adoption of aircraft 1.4 Structure of JAR 66 multiple-choice examination papers le Number of Time allowed Module Number of Time allowed questions (min) questions (min) hematics 10 Aviation Legislation ory A 16 20 Category A 40 50 ory B1 30 40 Category B1 40 50 ory B2 30 40 Category B2 40 50 ics 11 Aeroplane aerodynamics, structures and systems ory A 30 40 Category A 100 125 ory B1 50 65 Category B1 130 165 ory B2 50 65 Category B2 – – trical fundamentals 12 Helicopter aerodynamics, structures and systems ory A 20 25 Category A 90 115 ory B1 50 65 Category B1 115 145 ory B2 50 65 Category B2 – – tronic fundamentals 13 Aircraft aerodynamics, structures and systems ory A – – Category A – – ory B1 20 25 Category B1 – – ory B2 40 50 Category B2 130 165 tal techniques/electronic instrument systems 14 Propulsion ory A 16 20 Category A – – ory B1 40 50 Category B1 – – ory B2 70 90 Category B2 25 30 erials and hardware 15 Gas turbine engine ory A 50 65 Category A 60 75 ory B1 70 90 Category B1 90 115 ory B2 60 75 Category B2 – – ntenance practices 16 Piston engine ory A 70 90 Category A 50 65 ory B1 80 100 Category B1 70 90 ory B2 60 75 Category B2 – – c aerodynamics 17 Propeller ory A 20 25 Category A 20 25 ory B1 20 25 Category B1 30 40 ory B2 20 25 Category B2 – – man factors ory A 20 25 ory B1 20 25 ory B2 20 25 The time given for examinations may, from time to time, be subject to change. There is currently a review pending of ations time based on levels. Latest information may be obtained from the CAA website. enance safety culture, becomes a vital part education for all individuals wishing to ce as aircraft maintenance engineers. Set this section is a brief introduction to the atory and legislative framework, together maintenance safety culture and the vagaries man performance. A much fuller coverage craft maintenance legislation and safety procedures will be found in, Aircraft Engineer- ing Maintenance Practices, the second book in this series. 1.5.2 The birth of the ICAO The international nature of current aircraft maintenance engineering has already been mentioned. Thus the need for conformity of ards to ensure the continued airworthiness raft that fly through international airspace rime importance. ong ago as December 1944, a group of for- hinking delegates from 52 countries came er in Chicago, to agree and ratify the con- n on international civil aviation. Thus the ional International Civil Aviation Orga- on (PICAO) was established. It ran in this until March 1947, when final ratification 26 member countries was received and it e the ICAO. primary function of the ICAO, which was d in principle at the Chicago Convention in was to develop international air transport afe and orderly manner. More formerly, member countries agreed to undersign: ain principles and arrangements in er that international civil aviation may developed in a safe and orderly manner that international air transport services y be established on the basis of equality opportunity and operated soundly and nomically. us in a spirit of cooperation, designed to good international relationships, between er countries, the 52 member states signed the agreement. This was a far-sighted on, which has remained substantially nged up to the present. The ICAO Assem- the sovereign body of the ICAO respon- or reviewing in detail the work of ICAO, ing setting the budget and policy for the wing 3 years. council, elected by the assembly for a term, is composed of 33 member states. ouncil is responsible for ensuring that stan- and recommended practices are adopted ncorporated as annexes into the conven- n international civil aviation. The council sted by the Air Navigation Commission al with technical matters, the Air Trans- Committee to deal with economic matters he Committee on Joint Support of Air ation Services and the Finance Committee. ICAO also works closely with other ers of the United Nations (UN) and other overnmental organizations such as the International Air Transport Association (IATA) and the International Federation of Air Line Pilots to name but two. 1.5.3 The UK CAA The CAA was established by an act of par- liament in 1972, as an independent specialist aviation regulator and provider of air traffic services.7 Under the act it is responsible to the government for ensuring that all aspects of avi- ation regulation are implemented and regulated in accordance with the ANO formulated as a result of the act. Following the separation of National Air Traffic Services (NATS) in 2001, the CAA is now responsible for all civil aviation functions, these are: economic regulation, airspace policy, safety regulation and consumer protection. The Economic Regulation Group (ERG) reg- ulates airports, air traffic services and airlines and provides advice on aviation policy from an economic standpoint. Its aim is to secure the best sustainable outcome for users of air transport services. The Directorate of Airspace Policy (DAP) is responsible for the planning and regulation of all UK airspace including the navigation and com- munication infrastructure to support safe and efficient operations. Both civilian and military experts staff this group. The Consumer Protection Group (CPG) regulates travel organizations, manages the consumer protection organization, air travel organizers’ licensing (ATOL) and licenses UK airlines, in addition to other functions. The Safety Regulation Group (SRG) ensures that UK civil aviation standards are set and achieved in a cooperative and cost-effective manner. SRG must satisfy itself that aircraft are properly designed, manufactured, operated and maintained. It is also the responsibility of this group to ensure the competence of flight crews, air traffic controllers and aircraft maintenance engineers in the form of personal licensing. All the major functions of this group are shown in Figure 1.15. Note: with the recent introduction of European Aviation Safety Agency (EASA), e 1.15 CAA-SRG functions and responsibilities. of these functions (particularly with the cation of individuals and the approval of izations, concerned with aircraft mainte- ) will gradually be transferred from the SRG to EASA. Civil aviation requirements road international standards on airwor- s set up by the ICAO were backed up ailed national standards, overseen in the y the National Authority for Airworthi- he CAA. These national standards were n in the UK as BCAR and in the USA deral Airworthiness Regulations (FAR). other countries adopted one or the other se requirements, with their own national ions. nternational collaborative ventures became wide spread, there was increasing pressure oduce a unified set of standards, particu- n Europe. Thus came into being (under the auspices of the JAA) the European Joint Aviation Requirements or JAR, for short. Then, with increasing collaborative ventures between Europe, the USA and other major economies around the world, there became a need to harmonize these European requirements (JAR), with those of the USA, FAR. This harmoniza- tion process is still ongoing and is not without difficulties! It is unnecessary in this brief introduction to go into detail on the exact nature of JAA in over- seeing the European JAR airworthiness require- ments and design protocols. Suffice to say8 that the Civil Aviation Authorities of certain countries have agreed common compre- hensive and detailed aviation requirements (JAR) with a view to minimizing type cer- tification problems on joint aviation ven- tures, to facilitate the export and import of aviation products, and make it easier for maintenance and operations carried out in country to be accepted by the CAA in ther country. e or two of the more important require- applicable to aircraft maintenance orga- ons and personnel are detailed below: 5 – Requirements for large aircraft (over 5700 kg) – Requirements for aircraft engines 1 – Requirements for products and parts for aircraft 6 – Requirements for aircraft engi- neering certifying staff, including the basic knowledge requirements, upon which all the books in this series are based 45 – Requirements for organizations oper- ating large aircraft 47 – Requirements to be met by organi- zations seeking approval to conduct approved training/examinations of certifying staff, as specified in JAR 66. Aircraft maintenance neering safety culture and an factors u have managed to plough your way gh this introduction, you cannot have to notice that aircraft maintenance engi- g is a very highly regulated industry, safety is considered paramount! ry individual working on or around air- and/or their associated equipments, has onal responsibility for their own safety he safety of others. Thus, you will need to me familiar with your immediate work area cognize and avoid, the hazards associated t. You will also need to be familiar with ocal emergency: first aid procedures, fire utions and communication procedures. orough coverage of workshop, aircraft r and ramp safety procedures and pre- ns will be found in Aircraft Engineering enance Practices, the second book in the upled with this knowledge on safety, ospective maintenance engineers must oster a responsible, honest, mature and Figure 1.16 Control column, with base cover plate fitted and throttle box assembly clearly visible. professional attitude to all aspects of their work. You perhaps, cannot think of any circumstances where you would not adopt such attitudes? However, due to the nature of aircraft main- tenance, you may find yourself working under very stressful circumstances where your profes- sional judgement is tested to the limit! For example, consider the following scenario. As an experienced maintenance technician, you have been tasked with fitting the cover to the base of the flying control column (Figure 1.16), on an aircraft that is going to leave the mainte- nance hanger on engine ground runs, before the overnight embargo on airfield noise comes into force, in 3 hours time. It is thus important that the aircraft is towed to the ground running area, in time to complete the engine runs before the embargo. This will enable all outstanding main- tenance on the aircraft to be carried out over night and so ensure that the aircraft is made ready in good time, for a scheduled flight first thing in the morning. You start the task and when three quarters of the way through fitment of the cover, you drop a securing bolt, as you stand up. You think that you hear it travelling across the flight deck floor. After a substantial search by torch- light, where you look not only across the floor, but also around the base of the control column and into other possible crevices, in the immedi- ate area, you are unable to find the small bolt. Would you: (a) Continue the search for as long as possible and then, if the bolt was not found, complete e fit of the cover plate and look for the lt, when the aircraft returned from ground ns? ontinue the search for as long as possi- e and then, if the bolt was not found, orm the engineer tasked with carrying out e ground runs, to be aware that a bolt is mewhere in the vicinity of the base of the ntrol column on the flight deck floor. Then ntinue with the fit of the cover? ise an entry in the aircraftmaintenance log r a “loose article” on the flight deck. Then move the cover plate, obtain a source of ong light and/or a light probe kit and carry t a thorough search at base of control col- mn and around all other key controls, such the throttle box. If bolt is not found, allow craft to go on ground run and continue arch on return? ise an entry in the aircraft log for a “loose icle” on the flight deck. Then immedi- ely seek advice from shift supervisor, as to urse of action to be taken? you not been an experienced technician, would immediately inform your supervi- ction (d)) and seek advice as to the most priate course of action. As an experienced cian, what should you do? The course ion to be taken, in this particular case, not then be quite so obvious, it requires ments to be made. te clearly actions (a) and (b) would be g, no matter how much experience the cian had. No matter how long the search ued, it would be essential to remove the plate and search the base of the con- olumn to ensure that it was not in the y. Any loose article could dislodge during and cause possible catastrophic jamming uling of the controls. If the engine run is ceed, actions (a) and (b) are still not ade- A search of the throttle box area for the would also need to take place, as suggested ion (c). Action (c) seems plausible, with ddition of a good light source and thor- search of all critical areas, before the fit cover plate, seems a reasonable course of to take, especially after the maintenance log entry has been made, the subsequent search for the bolt, cannot be forgotten, so all is well? However, if you followed action (c) you would be making important decisions, on mat- ters of safety, without consultation. No matter how experienced you may be, you are not nec- essarily aware of the total picture, whereas your shift supervisor, may well be! The correct course of action, even for the most experienced engineer would be action (d). Suppose action (c) had been taken and on the subsequent engine run the bolt, that had been lodged in the throttle box, caused the throt- tle to jam in the open position. Then shutting down the engine, without first closing the throt- tle, could cause serious damage! It might have been the case that if action (d) had been fol- lowed, the shift supervisor may have been in a position to prepare another aircraft for the scheduled morning flight, thus avoiding the risk of running the engine, before the loose article search had revealed the missing bolt. In any event, the aircraft would not nor- mally be released for service until the missing bolt had been found, even if this required the use of sophisticated radiographic equipment to find it! The above scenario illustrates some of the pit- falls, that even experienced aircraft maintenance engineers may encounter, if safety is forgotten or assumptions made. For example, because you thought you heard the bolt travel across the flight deck, you may have assumed that it could not possibly have landed at the base of the con- trol column, or in the throttle box. This, of course, is an assumption and one of the golden rules of safety is never assume, check! When the cover was being fitted, did you have adequate lighting for the job? Perhaps with ade- quate lighting, it might have been possible to track the path of the bolt, as it travelled across the flight deck, thus preventing its loss in the first place. Familiarity with emergency equipment and procedures, as mentioned previously is an essen- tial part of the education of all aircraft main- tenance personnel. Reminders concerning the use of emergency equipment will be found in hangars, workshops, repair bays and in many 1.17 Typical aircraft hangar first aid station. areas where aircraft engineering mainte- is practiced. Some typical examples of ency equipment and warning notices are n below. Figure 1.17 shows a typical air- maintenance hangar first aid station, com- with explanatory notices, first aid box and itation bottles. ure 1.18 shows an aircraft maintenance r fire point, with clearly identifiable emer- procedures in the event of fire and the priate fire appliance to use for electrical er type of fire. ure 1.19 shows a grinding assembly, with ated local lighting and warning signs, for nd ear protection. Also shown are the down shields above the grinding wheels to nt spark burns and other possible injuries hands, arms and eyes. ure 1.20 shows a warning notice concern- ork being carried out on open fuel tanks arning against the use of electrical power. dition to this warning notice there is also Figure 1.18 Typical aircraft hangar fire point. a no power warning at the aircraft power point (Figure 1.21). You may feel that the module content con- tained in this book on principles is a long way removed from the working environment illus- trated in these photographs. However, consider for a moment the relatively simple task of inflat- ing a ground support trolley wheel (Figure 1.22). Still it is a common practice to measure tyre pressures in pounds per square inch (psi), as well as in bar (Figure 1.23). Imagine the consequen- ces of attempting to inflate such a tyre to 24 bar, instead of 24 psi, because you mis-read the gauge on the tyre inflation equipment! The need to understand units, in this partic- ular case is most important. It cannot happen I hear you say; well unfortunately it can, the above is an account of an actual incident. Fortu- nately the technician inflating the tyre, followed standard safety procedures, in that he stood behind the tyre, rather than along side it, during the inflation process. The tyre separated from e 1.19 Grinding wheel assembly, with asso- lighting and warning signs. e 1.20 Open fuel tanks warning notice. heel assembly and shot sideways at high ty. If the technician had been to the side of re and wheel assembly he would have sus- serious injury! At that time this technician naware of the difference in units between ar and for him, the more familiar impe- nits of psi. Thus the need to adopt a Figure 1.21 Ground power warning. Figure 1.22 Oxygen bottle trolley, showing trolley wheel. Figure 1.23 Pressure gauges graduated in bar and in psi. mature attitude to your foundation studies is just as important as adopting the necessary professional attitude to your on-job practical maintenance activities. pleting the maintenance mentation carrying out any form of maintenance y on aircraft or aircraft equipment, it lly important that the appropriate doc- ation and procedures are consulted and wed. This is particularly important, if the enance technician is unfamiliar with the or is new to the equipment being worked ven those experienced in carrying out a ular activity should regularly consult the enance manual, in order to familiarize elves with the procedure and to estab- he modification state of the aircraft or ment being worked on. modification state of the documentation hould not only be checked by the schedul- ff, but also by the engineer assigned to the o ensure currency. en certifying staff sign-up for a particu- intenance activity, there signature implies he job has been completed to the best of ability, in accordance with the appropri- hedule and procedures. Any maintenance eer, who is subsequently found to have ced work that is deemed to be unsatisfac- as a result of their negligence, during the tion of such work, may be prosecuted. It d always be remembered by all involved in ft maintenance engineering that mistakes ost lives. This is why it is so important ertifying staff always carry out their work highest professional standards, strictly ng to the laid-down safety standards and tional procedures. an factors bove examples concerning the dropped nd the mistakes made when attempting ate the ground support trolley tyre illus- he problems that may occur due to human . man factors9 impinges on everything an eer does in the course of their job in one r another, from communicating effectively olleagues to ensuring they have adequate ng to carry out their tasks. Knowledge of bject has a significant impact on the safety standards expected of the aircraft maintenance engineer. The above quote is taken from the CAA pub- lication (CAP 715) which provides an introduc- tion to engineering human factors for aircraft maintenance staff, expanding on the human factors syllabus contain in JAR 66 Module 9. A study of human factors, as mentioned ear- lier, is now considered to be an essential part of the aircraft maintenance engineers educa- tion. It is hoped that by educating engineers and ensuring currency of knowledge and techniques, that this will ultimately lead to a reduction in aircraft incidents and accidents which can be attributed to human error during maintenance. The study of human factors has become so important that for many years the CAA has co- sponsored annual international seminars ded- icated to the interchange of information and ideas on the management and practice of elim- inating aviation accidents, resulting from nec- essary human intervention. Numerous learned articles and books have been written on human factors, where the motivation for its study has come from the need to ensure high standards of safety in high risk industries, such as nuclear power and of course air transport! Aircraft maintenance engineers thus need to understand, how human performance limita- tions impact on their daily work. For example, if you are the licensed aircraft engineer (LAE) responsible for a team of technicians. It is impor- tant that you are aware of any limitations mem- bers of your team may have with respect to obvious physical constraints, like their hearing and vision. As well as more subtle limitations, such as their ability to process and interpret information or their fear of enclosed spaces or heights. It is not a good idea to task a technician with a job inside a fuel tank, if they suffer from claustrophobia! Social factors and other factors that may affect human performance also need to be understood. Issues such as responsibility, moti- vation, peer pressure, management and supervi- sion need to be addressed. In addition to general fitness, health, domestic and work-related stress, time pressures, nature of the task, rep- etition, workload and the effects of shift work. nature of the physical environment in maintenance activities are undertaken to be considered. Distracting noise, fumes, nation, climate, temperature, motion, ion and working at height and in confined , all need to be taken into account. importance of good two-way communi- needs to be understood and practiced. munication within and between teams, logging and recording, keeping up-to-date he correct and timely dissemination of mation must also be understood. impact of human factors on performance e emphasized, wherever and whenever it is ht appropriate, throughout all the books series. There will also be a section in the d book in this series, on Aircraft Engineer- aintenance Practices, devoted to the study st incidents and occurrences that can be uted to errors in the maintenance chain. ection is called learning by mistakes. wever, it is felt by the authors that human s as contained in JAR 66 Module 9, is t that one section in a textbook, will not e subject justice. For this reason a list of nces are given at the end of this chapter, ich the reader is referred. In particular an ent introduction to the subject is provided CAA publication: CAP 715 – An Intro- n to Aircraft Maintenance Engineering n Factors for JAR 66. have talked so far about the nature of n factors, but how do human factors t on the integrity of aircraft maintenance ies? By studying previous aircraft inci- and accidents, it is possible to identify quence of events which lead to the inci- and so implement procedures to try and such a sequence of events, occurring in ture. The BAC One-Eleven accident ay of an introduction to this process, onsider an accident that occurred to C One-Eleven, on 10th June 1990 at d 7.30 a.m. At this time the aircraft, had taken off from Birmingham Airport, limbed to a height of around 17,300 ft Figure 1.24 A Boeing 767 left front windscreen assembly. (5273 m) over the town of Didcot in Oxford- shire, when there was a sudden loud bang. The left windscreen, which had been replaced prior to the flight, was blown out under the effects of cabin pressure when it overcame the reten- tion of the securing bolts, 84 of which, out of a total of 90, were smaller than the specified diam- eter. The commander narrowly escaped death, when he was sucked halfway out of the wind- screen aperture and was restrained by cabin crew whilst the co-pilot flew the aircraft to a safe landing at Southampton Airport. For the purposes of illustration, Figure 1.24 shows a typical front left windscreen assembly of a Boeing 767. How could this happen? In short, a task deemed to be safety critical was carried out by one individual, who also carried total respon- sibility for the quality of the work achieved. The installation of the windscreen was not tested after fit. Only when the aircraft was at 17,300 ft, was there sufficient pressure differen- tial to check the integrity of the work! The shift maintenance manager, who had carried out the work, did not achieve the quality standard dur- ing the fitting process, due to inadequate care, poor trade practices, failure to adhere to com- pany standards, use of unsuitable equipment and long-term failure by the maintenance man- ager to observe the promulgated procedures. The airline’s local management product sam- ples and quality audits, had not detected the existence of inadequate standards employed by the shift maintenance manager because they did onitor directly the work practices of shift enance managers. neering factors is no room in this brief account of the acci- o detail in full all the engineering factors lead up to the windscreen failure; how- ome of the more important factors in the of events are detailed below: orrect bolts had been used with the previ- installation (A211-7D). fficient stock of the incorrect A211-7D s existed in the controlled spare parts ousel dispenser. Although these bolts were rrect, they had proved through 4 years of to be adequate. reference was made to the spare parts logue to check the required bolts’ part mber. stores system, available to identify the k level and location of the required bolts not used. sical matching of the bolts was attempted as a consequence, incorrect bolts (A211- were selected from an uncontrolled spare- s carousel, used by the maintenance nager. uncontrolled torque limiting screwdriver set up outside the calibration room. i-hexagonal bit holder was used to wind wn the bolts, resulting in the occasional of the bit and the covering up of the head. Hence the maintenance man- was unable to see that the countersunk d of the bolts, was further recessed than mal. safety platform was incorrectly posi- ed leading to inadequate access to job. warning from the storekeeper that A211- bolts were required did not influence the ce of bolts. amount of unfilled countersunk left by small bolt heads was not recognized as essive. windscreen was not designated a “vital ” therefore no duplicate (independent) ection was required. Figure 1.25 Simplified schematic cross-section of a typical windscreen requiring external fit. • The windscreen was not designed so that internal pressure would hold it in place, but was fitted from the outside (Figure 1.25). • The shift maintenance manager was the only person whose work on the night shift was not subject to the review of a maintenance manager. • Poor labelling and segregation of parts in the uncontrolled spare-parts carousel. • The shift maintenance manager did not wear prescribed glasses when carrying out the windscreen change. The impact of human factors The above series of events does not tell the whole story. For example, why was it that the shift maintenance manager was required to perform the windscreen change in the first place? A supervisory aircraft engineer and a further LAE, normally part of the shift, were not available that night. In order to achieve the windscreen change during the night shift and have the aircraft ready for a pre-booked wash Table 1.5 Part No. Shank length (in.) Diameter (in.) Thread size Comments A211-8D 0.8 0.1865–0.1895 10 UNF Correct bolts A211-8C 0.8 0.1605–0.1639 8 UNC 84 bolts used A211-7D 0.7 0.1865–0.1895 10 UNF Bolts removed n the morning, the shift maintenance man- ecided to carry out the windscreen change mself. His supervisory aircraft engineer her airframe engineer were busy rectifying t on another BAC One-Eleven aircraft, needed to be completed before departure aircraft the following morning. o in the early hours of the morning when indscreen change took place, the bodies’ ian rhythms are at a low ebb. This, cou- with a high workload, may have lead to ess and a reduced ability to concentrate. highway staging platform was incorrectly oned for easy access to the job, had this orrectly positioned the maintenance man- may have been better able to notice that lt heads were recessed in the countersink, cantly more than usual. assumption that the bolts removed from rcraft windscreen were correct was made e maintenance manager. Thus one of the important dictums was ignored; never e, check! non-availability of the bolts (A211-7D) hough incorrect, in the controlled spare carousel, lead the manager to search in -controlled carousel, where parts were y labelled or incorrectly segregated. This n lead the manager to select the bolts visual and touch methods. This resulted final error, in the chain, being made. olts selected were of the correct length but crucially 0.026 of an inch, too small in ter. The illustrated parts catalogue (IPC), should have been consulted before replac- e old bolts, specifies that the attachment should be part number (A211-8D). The cation for these bolts, together with those ed from the carousel (A211-8C) are shown ble 1.5. windscreen change on this aircraft was onsidered a vital point. The CAA state that the term “vital point” is not intended to refer to multiple fastened parts of the structure, but applies to a single point, usually in an air- craft control system. In September 1985 BCARs introduced a requirement for duplicate inspec- tions of vital points, which are defined as: any point on an aircraft at which a single mal- assembly could lead to a catastrophe, resulting in loss of the aircraft or fatalities. Had the windscreen been considered a vital maintenance operation, then a duplicate inspection would have been performed and the excessive recess of the bolt heads may very well have been noticed. Also, there are no CAA requirements for a cabin pressure check to be called up after the work has been carried out on the pressure hull. Such checks are written into the aircraft main- tenance manual at the discretion of the aircraft design team, and were not called up on the BAC One-Eleven. Had they been necessary, then the sub-standard integrity of the incorrectly fitted windscreen would have been apparent. A full account of this accident, the events leading up to it and the subsequent safety rec- ommendations will be found on the Air Accident InvestigationBoardwebsite,10 from which some of the above account has been taken. The safety recommendations As a result of the above accident and subse- quent inquiry, eight safety recommendations were given. Briefly, these recommendations are as follows: • The CAA should examine the applicabil- ity of self-certification to aircraft engineer- ing safety critical tasks following which the components or systems are cleared for ser- vice without functional checks. Such a review should include the interpretation of single mal-assembly within the context of vital points. ish Airways should review their quality rance system and reporting methods, and ourage their engineers to provide feedback m the shop floor. ish Airways should review the need to oduce job descriptions and terms of ref- ce for engineering grades, including shift ntenance manager and above. ish Airways should provide the mecha- m for an independent assessment of stan- ds and conduct an in depth audit into work ctices at Birmingham Airport. CAA should review the purpose and pe of their supervisory visits to airline rators. CAA should consider the need for peri- training and testing of engineers to ensure ency and proficiency. CAA should recognize the need for cor- ive glasses, if prescribed, in association h the undertaking of aircraft engineering vities. CAA should ensure that, prior to the e of an air traffic controller (ATC) rating, andidate undertakes an approved course raining, that includes the theoretical and ctical handling of emergency situations. bove recommendations are far reaching provide an example of human factors ement, far removed from the direct main- ce activity, but very much impacting on ain of events leading to an accident or s incident. It is these complex interac- hat may often lead to maintenance errors made, with subsequent catastrophic con- nces. matter how sophisticated the policies rocedures may be, ultimately due to the nce of human factors, it is the integrity, de, education and professionalism of the dual aircraft maintenance engineer, that rs most, in the elimination of maintenance . Concluding remarks hoped that this short introduction into craft maintenance industry has given you an insight into the demanding and yet very rewarding work, offered to aircraft maintenance certifying staff. No matter at what point you wish to enter the industry, you will find routes and pathways that enable you to progress to any level, dependent only, on your own ambitions and aspirations. The training and education to reach the top of any profession is often long and arduous and aircraft maintenance engineering is no exception! The subject matter that follows may seem a long way removed from the environment por- trayed in this introduction and yet, it forms a vital part of your initial educational devel- opment. Therefore, you should approach the subjects presented in Chapters 2 and 3 of this book, with the same amount of enthusiasm and dedication as you will with the practical activi- ties you find yourself engaged in, when qualified to practice your profession. The non-calculator mathematics, you are about to meet, may seem deceptively simple. However, do remember that the pass rate is 75%, as it is for all your JAR 66 examina- tions. This is likely to be significantly higher than any other examination pass rate, you may have encountered up till now. It is, therefore, very important that you become familiar with all the subject matter contained in the following chap- ters, if you are to be successful in your future CAA examinations. There are numerous exam- ples, multiple-choice questions and other types of questions provided to assist you in acquiring the necessary standard. References 1. CAA-SRG Engineer Standards, papers 3–6 (May 2001). 2. Kingston University, Rationale for Aerospace Pro- grammes (May 2001). 3. CAA-SRG, JAR-66 Information for New Applicants Leaflet 2 Issue 16 (October 2001). 4. JAA Administration and Guidance Material (1999). 5. JAR-66 Appendix 2 Section 1 Levels (April 2002). 6. CAA-SRG JAR-66 Syllabus and Examinations No. 6 (issued 16/10/01). 7. CAA Corporate Information, page 1–3. (April 2002). 8. JAR-66 Certifying Staff Maintenance, page F1 (April 2002). 9. CAP715 An Introduction to Aircraft Maintenance Human Factors for JAR-66 (January 2002). 10. UK Air accident investigation branch (AAIB). www.dft. gov.uk/stellent/groups/dft_accidentinvest_page.hcsp P A R T 2 cientific fundamentals This page intentionally left blank a p t e r 2 Mathematics eral introduction hapter aims to provide you with a sound ation in mathematical principles, which nable you to solve mathematical, scientific ssociated aircraft engineering problems at echanic and technician level. Mathematics ded into two major parts: Non-calculator matics, which covers all of the mathemat- d down in Joint Aviation Requirements 66 Module 1, up to the level appropri- r aircraft maintenance category B certify- chnicians. The other part of mathematics ther mathematics (Chapter 3), which in pinion of the authors, is necessary for rough understanding of the physics and cal principles that follow. A second objec- f Further mathematics is to provide the matical base necessary for further aca- and professional progression, particularly ose individuals wishing to become Incor- ed Engineers, after successfully obtaining ategory B license. start with some elementary arithmetic. In ular, we review the concepts of number e laws that need to be followed, when car- out arithmetic operations, e.g. addition, ction, multiplication and division. The tant concept of arithmetic estimates and ation techniques involving various forms mber are also covered. While revising the mental principles of number, we consider explicit numbers and literal numbers (let- in order to aid our understanding of not arithmetic operations, but also the alge- operations that will follow later. Decimal ers and the powers of 10 are then con- d, after which fractional numbers and the ulation of fractions are covered. algebraic content of JAR 66 Module 1 roduced with the study of powers and ents (indices) of numbers. This, together with your previous knowledge of fractions and fractional numbers, will provide you with the tools necessary to manipulate algebraic expres- sions and equations. The essential skill of trans- position of formulae is also covered. This will be a particularly useful mathematical tool, when you study your physics and electrical principles. We finish our study of algebra by consider- ing binary and other number systems and their application to simple logic circuits. In our study of geometry and trigonometry, we start by looking at the methods used for the graphical solution of equations and other func- tions. This section clearly lays out the idea of graphical axes and scales. We then consider the nature and use of the trigonometric ratios and the solution of right-angled triangles and the cir- cle. The nature and use of rectangular and polar co-ordinate representation systems, for finding bearings and angles of elevation and depression are then considered. We finish our study of non- calculator mathematics with a study of the more important theorems of the circle, together with some geometric constructions, considered par- ticularly useful to solve engineering problems, in particular, as an aid to engineering drawing and marking out. In our Further mathematics (Chapter 3) we build on our initial study of algebra by consid- ering more complex algebraic and logarithmic expressions, functions and formulae. We will use our basic knowledge of graphs to repre- sent more complex algebraic and logarithmic functions and to solve equations and engineer- ing problems, which involve these functions. In addition, we will briefly introduce the concept of complex numbers, which will be found par- ticularly valuable for those wishing to pursue an avionic pathway. Our further study of trigonometry will include the use of trigonometric ratios to solve engineering problems involving measurement. we introduce and use a variety of statis- methods to gather, manipulate and display fic and engineering data. We will then der the ways in which the elementary rules culus arithmetic may be used to solve ems involving simple differentiation and ation of algebraic and trigonometric func- Finally, we use the calculus to solve some ntary engineering problems, which involve of change and the summation of areas and es. rder to aid your understanding of mathe- , you will find numerous fully worked ples and test your understanding exercises, d throughout this chapter. In addition, typ- ample JAR 66 license questions are given end of this chapter. tant note: Only very familiar units, such ss, weight, pressure, length, area and vol- re used in this part of the mathematics. etailed study of units appears in the chap- n physics and electrical principles (Chap- and 5, respectively), where their nature se is fully explained. Some of the JAR estions, found at the end of this chapter, e the reader to have some understanding ts, which may be gained by studying other ns of the book (in particular, Chapter 4). N-CALCULATOR MATHEMATICS ntroduction entioned earlier, this part of the mathe- has been written explicitly to cover all of labus content laid down in JAR 66 Mod- It can thus be studied independently, by only wishing to gain the knowledge neces- o pass the Civil Aviation Authority (CAA) nation for this module. wever, in order to offer the best chance cess in the JAR 66 physics and electri- nd electronic principles modules and as paration for further study, the authors, ly recommend that you should also the further mathematics contained in er 3. 2.2 Arithmetic 2.2.1 Numbers and symbols It is generally believed that our present num- ber system began with the use of the natural numbers, such as 1, 2, 3, 4, .... These whole numbers, known as the positive integers, were used primarily for counting. However, as time went on, it became apparent that whole num- bers could not be used for defining certain mathematical quantities. For example, a period in time might be between 3 and 4 days or the area of a field might be between 2 and 3 acres (or whatever unit of measure was used at the time). So the positive fractions were introduced, e.g. 12 , 1 4 and 3 4 . These two groups of numbers, the positive integers and the positive fractions, constitute what we call the positive rational numbers. Thus, 711 is an integer or whole num- ber, 14 is a positive fraction and 234 3 5 is a rational number. In fact a rational number is any num- ber that can be expressed as the quotient of two integers, i.e. any number that can be written in the form a/b where a and b represent any inte- gers. Thus 25 , 8 9 and 1 are all rational numbers. The number 1 can be represented by the quo- tient 11 = 1, in fact any number divided by itself must always be equal to 1. The natural numbers are positive integers, but suppose we wish to subtract a larger natural number from a smaller natural number, e.g. 10 subtracted from 7, we obviously obtain a num- ber which is less than zero, i.e. 7 − 10 =−3. So our idea of numbers must be enlarged to include numbers less than zero called negative numbers. The number zero (0) is unique, it is not a natural number because all natural numbers represent positive integer values, i.e. numbers above zero and quite clearly from what has been said, it is not a negative number either. It sits uniquely on its own and must be added to our number collection. Key point The natural numbers are known as positive integers. o the natural numbers (positive integers) ve added negative integers, the concept o, positive rational numbers and nega- atural numbers. What about numbers like This is not a rational number because it t be represented by the quotient of two rs. So yet another class of number needs to luded, the irrational or non-rational num- Together all, the above kinds of numbers tute the broad class of numbers known as umbers. y include positive and negative terminat- nd non-terminating decimals (e.g. ± 19 = 11 ... , 0.48299999, ±2.5, 1.73205 ...). eal numbers are so called to distinguish from others, such as imaginary or com- numbers, the latter may be made up of real and imaginary number parts. Com- umbers will not be considered during our of mathematics. y point ional number is any number that can be essed as the quotient of two integers, i.e. a/b e a and b are any two integers. hough we have mentioned negative num- we have not considered their arithmetic ulation. All positive and negative num- re referred to as signed numbers and they he arithmetic laws of sign. Before we con- these laws, let us first consider what we by signed numbers. nventional representation of signed num- shown below, with zero at the midpoint. ve numbers are conventionally shown to ght of zero and negative numbers to t: −4 −3 −2 −1 0 +1 +2 +3 +4 ··· number of units a point is from zero, dless of its direction, is called the abso- alue of the number corresponding to the on the above number system when points awn to scale. Thus the absolute value of a ve number, or of zero, is the number itself. the absolute value of a negative number is the number with its sign changed. For example, the absolute value of +10 is 10 and the abso- lute value of −10 is also 10. Now the absolute value of any number n is represented by the sym- bol |n|. Thus |+24| means the absolute value of +24. Which is larger, |+3| or |−14|? I hope you said |−14| because its absolute value is 14, while that of |+3| is 3 and of course 14 is larger than 3. We are now ready to consider the laws of signs. Key point The absolute value of any number n is always its positive value or modulus and is represented by |n|. The laws of signs You are probably already familiar with these laws, here they are: First law: To add two numbers with like signs, add their absolute values and prefix their common sign to the result. This law works for ordinary arithmetic num- bers and simply defines what we have always done in arithmetic addition. For example, 3 + 4 = 7 or in full (+3) + (+4) =+7. After the introduction of the negative num- bers, the unsigned arithmetic numbers became the positive numbers, as illustrated above. So now all numbers may be considered either pos- itive or negative, and the laws of signs apply to them all. Does the above law apply to the addition of two negative numbers? From ordinary arith- metic we know that (−7) + (−5) =−12. This again obeys the first law of signs, because we add their absolute value and prefix their common sign. Second law: To add two signed numbers with unlike signs, subtract the smaller absolute value from the larger and prefix the sign of the number with the larger absolute value to the results. So following this rule, we get for example: 5+(−3) = 2; −12+9 = −3; 6+(−11) = −5 and so on. numbers written without signs are, of e, positive numbers. Notice that brackets been removed when not necessary. rd law: To subtract one signed number another, change the sign of the number to btracted and follow the rules for addition. example, if we subtract 5 from −3, we 3 − (+5) =−3 + (−5) =−8. w what about the multiplication and divi- f negative and positive numbers, so as not our the point the rules for these operations mbined in our fourth and final law. rth law: Tomultiply (or divide) one signed er by another, multiply (or divide) their ute values; then, if the numbers have like prefix the plus sign to the result; if they unlike signs, prefix the minus sign to the refore, applying this rule to the multipli- of two positive numbers, e.g. 3 × 4 = 12, 8 = 96 ... and so on, which of course, is e arithmetic! Now applying the rule to the plication of mixed sign numbers we get 3 × 4 =−12, 12 × (−8) =−96 ... and so e can show, equally well, that the above elds similar results for division. mple 2.1 the fourth law to the following arithmetic ems and determine the arithmetic result: −4)(−3)(−7) = ? (b) 14/−2 = ? −6)(−2) = ? (d) −22/−11 = ? this example we apply the fourth law ice, (−4)(−3) = 12 (like signs) and so (−7) = −84. /–2 applying the third law for unlike signs mediately gives −7, the correct result. ain applying the third law twice. 5(−6) = 30 (unlike signs) and (−30)(−2) = 60. 22/−11 applying the third law for like sign ves 2, the correct result. se of symbols ave introduced earlier the concept of sym- o represent numbers when we defined al numbers where the letters a and b used to represent any integer. Look at the symbols below, do they represent the same number? IX; 9; nine; +√81 I hope you answered yes, since each expression is a perfectly valid way of representing the positive integer 9. In algebra we use letters to repre- sent Arabic numerals such numbers are called general numbers or literal numbers, as distin- guished from explicit numbers like 1, 2, 3, etc. Thus a literal number is simply a number repre- sented by a letter, instead of a numeral. Literal numbers are used to state algebraic rules, laws and formulae; these statements being made in mathematical sentences called equations. If a is a positive integer and b is 1, what is a/b? I hope you were able to see that a/b= a. Any number divided by 1 is always itself. Thus, a/1 = a, c/1 = c, 45.6/1 = 45.6. Suppose a is again any positive integer, but b is 0. What is the value of a/b? What we are asking is what is the value of any positive inte- ger divided by zero? Well the answer is that we really do not know! The value of the quotient a/b, if b= 0, is not defined in mathematics. This is because there is no such quotient that meets the conditions required of quotients. For exam- ple, you know that to check the accuracy of a division problem, you can multiply the quotient by the divisor to get the dividend. For example, if 21/7 = 3, then 7 is the divisor, 21 is the div- idend and 3 is the quotient and so 3 × 7 = 21, as expected. So, if 17/0 were equal to 17, then 17 × 0 should again equal 17 but it does not! Or, if 17/0 were equal to zero, then 0 × 0 should equal 17 but again it does not. Any number multiplied by zero is always zero. Therefore, division of any number by zero (as well as zero divided by zero) is excluded from mathematics. If b= 0, or if both a and b are zero, then a/b is meaningless. Key point Division by zero is not defined in mathematics. When multiplying literal numbers together we try to avoid the multiplication sign (×), this is because it can be easily mistaken for the letter x. instead of writing a×b for the prod- two general numbers, we write a ·b (the otation for multiplication) or more usually b to indicate the product of two general ers a and b. mple 2.2 let the letter n stand for any real num- hat does each of the following expressions ? n= ? (b) n× 0 = ? (c) n× 1 = ? + 0 = ? (e) n− 0 = ? (f) n−n= ? 0 = ? n= 1, i.e. any number divided by itself is ual to 1. × 0 = 0, any number multiplied by zero is elf zero. × 1 =n, any number multiplied or divided 1 is itself. + 0 =n, the addition of zero to any number ll not alter that number. − 0 =n, the subtraction of zero from any mber will not alter that number. −n= 0, subtraction of any number from elf will always equal zero. 0, division by zero is not defined in athematics. ommutative, associative and butive laws l know that 6 × 5 = 30 and 5 × 6 = 30, so ue that when multiplying any two num- ogether, the result is the same no matter the order? The answer is yes. The above onship may be stated as: roduct of two real numbers is the same no r in what order they are multiplied. That = ba this is known as the commutative multiplication. hree or more real numbers are multiplied er, the order in which they are multi- still makes no difference to the product. ample, 3 × 4 × 5 = 60 and 5 × 3 × 4 = 60. elationship may be stated formally as: product of three or more numbers is me no matter in what manner they are grouped. That is, a(bc)= (ab)c; this is known as the associative law of multiplication. These laws may seem ridiculously simple, yet they form the basis of many algebraic tech- niques, which you will be using later! We also have commutative and associative laws for addition of numbers, which by now will be quite obvious to you, here they are: The sum of two numbers is the same no mat- ter in what order they are added. That is, a+b=b+ a. This is known as the commutative law of addition. The sum of three or more numbers is the same no matter in what manner they are grouped. That is, (a+b)+ c = a+ (b+ c). This is known as the associative law of addition. You may be wondering where the laws are for subtraction. Well you have already covered these when we considered the laws of signs. In other words, the above laws are valid no matter whether or not the number is positive or neg- ative. So, for example, −8 + (16 − 5) = 3 and (−8 + 16) − 5 = 3 In order to complete our laws we need to con- sider the following problem: 4(5 + 6) = ? We may solve this problem in one of two ways, firstly by adding the numbers inside the brackets and then multiplying the result by 4, this gives: 4(11) = 44. Alternatively, we may multiply out the bracket as follows: (4 × 5) + (4 × 6) = 20 + 24 = 44. Thus, whichever method we choose, the arithmetic result is the same. This result is true in all cases, no matter how many numbers are contained within the brackets! So in general, using literal numbers we have: a(b + c) = ab + ac This is the distributive law. In words, it is rather complicated: The distributive law states that: the product of a number by the sum of two or more numbers is equal to the sum of the products of the first number by each of the numbers of the sum. Now, perhaps you can see the power of alge- bra in representing this law, it is a lot easier to remember than the wordy explanation!
