Aircraft Engineering Principles
Roll-Royce RB211-524 Engine fitted to a Boeing 747 Aircraft
Aircraft Engineering Principles
Lloyd Dingle
Mike Tooley
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ght © 2005, Lloyd Dingle and Mike Tooley. All rights reserved
ht of Lloyd Dingle and Mike Tooley to be identified as the
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ght, Design and Patents Act 1988
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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
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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
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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
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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!