MODULO 02 NEXT.PDF----------------------------------

PHYSICS
CAT B1+B2

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TABLE OF CONTENTS

1 Man ares " 7
11 NATURE OF MATTER 7
111.ISOTOPES, n
12. CHEMICAL COMPOUNDS, 2
131. PLASMA. - - -
132, SouD. -
133 LIQUID. 5
130.025 a 7 . 2 1%
14. CHANGES BETWEEN STATES 1
VAI CATALYST. E 15
2. MECHANICS 7
21, FORCES. MOMENTS, AND COUPLES. 2
211. CENTER OF GRAVITY. a 1
213. PRESSURE AND BUOYANCY IN LIQUIDS. = 2
22. KINETICS. - 30
221, MOTION 30
222. LINEAR MOVEMENT. € i. S 30
224. PERIODIC MOVEMENT 35
2.25 THEORY OF VIBRATION, HARMONICS, RESONANCE 36
226. VELOCITY RATIO. MECHANICAL ADVANTAGE AND EFFICIENCY. sa
23. DYNAMICS... a A 53
231. MASS AND WEIGHT. s
233.(®} MOMENTUM 62
24, FLUID DYNAMICS. 70
24). DENSITY. ss = 70
22. SPECIFIC GRAVITY... = = 70

243 VISCOSITY B

a.

44, FLUID RESISTANCE 5
45 STREAMLINING, so
3. THERMODYNAMICS. e
3). TEMPERATURE, 2
311. THERMAL EXPANSION/CONTRACTIO!
312. HEAT ENERGY UNITS,

32. THERMOMETERS. ss
21. NON ELECTRIC TEMPERATURE INDICATORS, es
HEAT DEFINITION. 97

4, SPECIFIC HEAT 98
35. HEAT TRANSFER. 99
352. CONVECTION cum a 2 on
353. RADIATION 105
361 IRSTLAW 04
362 SECOND LAW 04
571, BONES LAW... E 05
72. CHARLES LAW 107
3.73, GENERAL GAS LAW, 108
374 DALTON'S LAW. 108
375 IDEAL GAS LAW 108
3776. WORK AND EXPANDING CASES. 109
& ENGINE CYCLES, 09
381 CONSTANT VOLUME 10
58.2 CONSTANT PRESSURE. u
383 THERMAL EFFICIENCY. m
39. REFRIGERATION AND HEAT PUMPS na
391 LATENT HEAT ns
310, THERMAL ENERGY. 6
311, HEAT OF COMBUSTION, E ns
4 opmics. a
|. THE NATURE OF LIGHT 1
411.SPEED OF LIGHT, 8

43, REFRACTION 12
44, LENSES, 122
45. FIBER OPTICS, 12

4:51. CABLE CONSTRUCTION. 13

452 FIBER MODES. 124
53. TERMINATION AND SPLICING. 126
54. FIBER OPTIC DATA UNK. 128
VE MOTION AND SOUND

511. MECHANICAL WAVES. m
512 ELECTROMAGNETIC WAVES. E
51.3 SINUSOIDAL WAVE MOTION. 134
515. STANDING WAVES, A 15

522 SPEED OF SOUND,
523 PRODUCTION OF SOUND,

525 PIICHAND QUALITY = o
526. DOPPLER EFFECT

1. MATTER

Matter serves as the cornerstone of all physics discourse. It Is the substance from
les are formed: anything that occupies space, possesses mass and can
be detected in some manner by our senses. The Law of Conservation stipulates that
matter can neither be generated nor annihlated, but Re physical state can undergo:
transformation For instance. when liquid gasoline evaporates. blends with alt. then
combusts, it may give the impression that this piece of matter has vanished into thin
air and no longer exists. However although it no longer manifests as liquid gasoline.
the matter continues to exis in the guise of the gases emitted by the buming fuel

which al ent

1.1. NATURE OF MATTER

Every bit of matter is composed of atoms. An atom represents the smallest fragment
of matter that determines the unique attributes ofa substance. Over 100 isparate
coms with varying physical

characteristics. These diverse and unique types of matter are denoted as elements
-omposed into simpler substances without

kinds of matter exist, each constructed from

These elements resist being further d

surrendering their unique identities

‘Atoms from diferent elements bear similarities to each other as they comprise the
same basic components An atom possesses a nucleus, within which are subatomic
particles. One or more protons are found in the nucleus of all atoms, carrying a
positivo electrical charge. One or more neutrons also reside in the nucleus of all
‘atoms, but unlike protons, neutrons carry no electrical charge. Cicling around the
nucleus is another type of subatomic particle known as an electron, which carries a
negative electrical charge. Electrons are arranged around the nucleus in orderly
concentric rings referred to as shells. Fig1-1 portrays the fundamental st
components of atoms.

cure and

Typically. each atom has an equal number of electrons and ne
protons However, lts the quantity of these particles contained in each atom t
causes the elements to differ from each other. For instance. an atom of hydrogen.
the simplest element. has one proton. one neutron. and one electron. An atom of
‘Oxygen. on the other hand, has eight protons. eight neutrons, and eight electrons.
Copper boasts 29 of each of these subatomic particles and so on. The quantity of

subatomic particles that each atom contains determines the type of element it i
and its inherent properties. The mass of an atom correlates to the number of
characteristic subatomic particles that constitute the atom of each element.

Fig.1-1An atom and its sub-atomic particles.

Elements are assigned an atomic number according to the quantity of protons found
in their atom nucleus. Each element also possesses a distinctive 1.2, or 3 letter
abbreviation. The elements are arranged in à table known as the periodic table of
lements The table groups the elements by periods running horizontally and by
Fig

roups arranged vertically to ilustrate similar characteristics of the elemen

‘Atoms of the same or different elements may form a chemical bond
me element bond to form a molecule

molecule. When tao or more atoms of thos
of that element. However. when atoms of different
= properties and

form a molecule. the resulting molecule exhi

ments bond

characteristics that are entirely different from those of each individu
constitutes & For Instance, a water molecule. which is composed of two hydrogen
sos Rs own unique properties that are

atoms and one oxygen atom. poses

completely different from those of hydrogen or oxygen in isolation.

ELEMENTS

PERIODIC TABLE

|
|

(08/18/5118 18
een)

When atoms forge a bond to form molecules. they share electrons. The shell closest
tain
ed in the next o

to sctrons. Ifthe atom has more than

orbiting

two electrons, thay ar

the nucleus. This second shell can only accommodate eight electrons. If the atom

has more than ten electrons (2 in the first shell +8 in the second shell they orbit in

a third shell located even further out from the nucleus. This third shell & populated

h up to eight electrons and then a fourth shell stats to fi the element stil has

lus electrons. However, when the fourth shell contains eight electrons. the

number of electrons in the third shell begins to increment again until a maximum
of 8 is eeched. Fig 5)

She or Or Number

ere

Fig.13 Maximum number of electrons in each orbital shell ofan atom

The outermost shell of an atom whore the electrons are located. is referred to as the
valence shell. The number of electrons within this valence shell plays a significant

role in determining the chemical bonding propensity of the substance as well as

other properties such as electrical conductivity, When the valence shell is fully
the maximum count of electrons. it is deemed complete. and th
electrons exhibit a strong affinity for the nucleus. Materials exhibiting this teat are
chemically stable. A considerable amount of force is required to dislodge these
electrons from the valence shell of one atom and transfer it to another. Gien 1
electron movement Is synonymous with electric current, substances that have a

saturated vi

complete valence shell ae recognized as efficient insulators because they resist the
pessage of electrons or electric current. (Fig1-4)

le
‘oe
oo
Falun Neon Aron Kıypion

Fig. 14 Elements with (ul valence shells are good insulators.

ds. thoso that lack

Meanwhile, atoms with an incomplete valence shell. in other w

the maximum count of electrons in their valence shell the electrons are less tightly

bound to the nucleus. Such a material is chemically inclined to merge with other

10

AN.

unstable valence configuration and

trons in the valence shell, Multiple substances may
engage in el ading to the formation of à
yond. A covalent bond Is à mechanism through which atoms fulfil their

ectrons with other atoms, leading to the

formation of molecules

shells are capable of transitioning

Furthermore. electrons in income
froaly from

cases these are referred to as free electrons. As menti
ferred toas electric current or current low. Wher
from one atom or comp

€ valence shell of one atom or compound to that of another. In such

4 earlier, the displacer

ofeelectronsis re nelectrons can freely

transit und to another. the substance is identified as a

conductor. (Fig)

+
af
+
Aluminum — Copper Sived God

Figi2.5 The valence shells of elements that are common
‘conductors have one (or three) electrons

1.1. ISOTOPES

isotopes refer to the variants of the same element that have difering counts of
neutrons Due
lement possess dissimilar masses The ter
ulates and subseque

© this var « diferent isotopes of the same

‘mass’ refers to the amount of matter

an entity encap As dif

fferent neutron counts, ther weight
of E

protons The atomic number is determined la

inform Regardless, d
ey have
rotons I

same element share the same atomic nur equal count of

(e

Hydrogen-1 Hydrogen-2, Hydrogen-3,
mate number ‘deuterium ‘tritium
mass number 2 mass number: 3

Fig. 1-6 Isotopes of hydrogen.

isotopes provide an intriguing insight into the atomic universe. Despite being atoms

from the same element. they exhibit distinct physical properties, while their
Je feature stems from the fac

on count and identical

chemical attributes are almost the same, This u

that isotopes of a specific element share the same elec

Hydrogen, the most plentiful element, has three common isotopes Protium (IH) the
ron and no neutrons. Deuterium (2H), with ono
de mass of 2 Tritium (GH)

two neutrons has an atomic mass of 3 Protium and deuterium are stable isotopes.

1.2. CHEMICAL COMPOUNDS,

nt properties c

ls comprised of ave

s exhibit dite

‘chemical compounds are mi

formed a chemical bond. Com mpared to the

elements from which they originate. They be differentiated through a
chemical reaction. Compounds possess a unique ch u a fed
ratio of atoms of different elements that are chemic gether. It's

© confuse compounds with mixtures. Mixtures are atoms and
ther but
are closely related or depa

not chemically bonded. The
ident on the

Mixtures can usually be separated by

les that are physically mixed tog
properties of the indi

1.3. STATES OF MATTER

Matter manifests in four common states: solids, liquids. gases and plasma. À state of
1 physical condition of a substance Solids. liquids and

The compoundís) from wie

state of motion due to the heat energy in the material. The physical ta

is related to the degree of motion between these particles with solids having the

{m for the aviation maintenance professional.

ance ls derived do not change. respective of

Atoms and molecules that constitute a substance are always in

€ of matter

least motion and gases and plasma having the most

131. PLASMA

Plasma represents a distin
pos

ons in proportions that result in a relatively neutral
harge. ts particles are close enough together that

ionized gas comprising

fe ions and free e

lectively when
‘exposed to a magnetic feld. Plasma ls also electrically conductive, It is sustained
easly at the extremely high temperatures present in stars and as such is the most

inthe universe

13.2. SOLID

Matter is classified as solid when it possesses a definite volume and shape. The
molecules of a solid are tightly bound to each other. resisting any change in sha

or volume, Solids may be a red They aro
incompressible and do not contain enough movement ofthe molecules to permit a

ically or irregularly st

133, LIQUID

Liquid matter is characterized by molecules that have more energy and increased

movement. This causes the molecules to be able to flow and not take a rigid shape

he

such as a solid. Liquids conform to € of thei
ime of a liquid does not change significantly. Liquids are said to
id molecules are abi

closely packed enough that the application of pressure does litle to change the
volume, The molec sound enough to each other that surfa
ated. Surface tension prevents liquids from complete freedom of
‘expansion. It can be observed when a container is filed with a liquid
the brim yet the liquid does not spill ver.

shay container even thous

incompressible. Lo slide past each other. they are til

lightly over

AN.

13.4. GAS

Matter also exists as a gas. This type of matter contains even more heat energy and
movement in its molecules The bonding that causes surface tension ina liquid does
not exist ina gas A greater space between molecules exists. Gases take the shape of
their container but unlike liquids. gases are compressible. When pressure is applied
the molecules can be made to exist closer to each other. It is possible to put a gas
Inder

lo much pressure that it changes to a liquid state.

1.4, CHANGES BETWEEN STATES

Matter can change betwoon the states by adding o

moving energy. The chemical
composition of the material remains the same during all states of matter but the
energy level causes it to be a solid liquid. or gas. For exampl
milions of pairs of hydrogen atoms covalently bonded to a single oxygen atom
loosely held next to each other in a liquid state,

water is always HO.

When energy is remove
Cf the molecules is greatly reduced and they no longer have the energy to side past
Cone another as aliquid. The:

and water becomes ice, itis sill O. However the mation

same is true when heat energy is added to water. Water

vaporis formed as the motion of the molecules causes more freedom of movement

between molecules But the water existing as a gas (vapor) Is still formed from
milions of 4,0 molecules

‘The heat energy added or subtracted to a substance Is typically measured by
temperature. The higher the temperature of a substance. the more energy it
contains Heat always flows from hot to cold, These terms (hot and cold) express the
relative amount of energy present in the substance. They do not measure the
absolut

transfer of energy

amount of heat present. Without a difference in energy levels there is no

‘Adding heat to a substance does not always raise its temperature. When a substance
en a liquid changes i
This is calle latent heat. When a vapor condenses in

changes state. such as w

10 8 vapor, heat energy is absorbed

o à liquid. this heat energy is
given off. The temperature of a substance remains constant during its change of
state. All energy absorbed or given of the latent heat, is used for the change process

Once the change of state is complete. heat added to a substance raises the
temperature ofthe substance After a substance changes state Into a vapor. the rs
in temperature of the vapor caused by the addition of still more heat is called

A,

The temperature at which a substance changes from a liquid nto a vapor when heat

isadded is known as its boiling point This isthe same temperature at which a vapor
condenses into a liquid when heat is removed. The boiling point of any su

varies directy with pressure. When pressure on liquids increased. its boling point
increases and when pressure on aliquid isdecreased its boiling
For example, water boils at 100 °C (212'F) at normal atmospheric pressure (147 psi.
(When pressure on liquid water s increased to 20 ps. it does not boll at 100 °C. More
energy is required to overcome the increase in pressure It bolls at approximately 108

intalso decreases.

(© (2264 F1 The converse is also true. Water can also boll at a much lower
temperature simply by reducing the pressure upon k. With only 10 psi of pressure
upon liquid water it bolls at 90 © (194'F).(Fig-7

» »

Fig.1-7 Boiling point of water changes as pressure changes.

Vapor pressure is the pressure of the vapor that exists above a liquid that is in an
‘enclosod container at any

von temperature. The vapor pros

© dovoloped by

various substances 5 unique to each substance. Asubstance thatis sald to be volatile.
develops high vapor pressure at standard day temperature 15 'C (59 “FL This is
because the boiling point ofthe substance is much lower, The vapor pressure of any
substance varies directly with temperature

141. CATALYST

Acatalystis a substance that causes or accelerates a chemical reaction without itself
boing

ted. À two part epoxy mix is a good example of a catalyst. The main
ingredient is the epoxy resin itself The second ingredient. when mixed with the resin,

ox resin mix
The opposite ofa catalystis an inhibitor Inhibitors dow down reactions

causes the resin to harden faster and then remains as part of the

2.MECHANICS

2.1. FORCES, MOMENTS, AND COUPLES

Force isthe influence tending to change the motion of a body or produce stress ina
stationary body. The magnitude of such an influence on a moving body is often
calculated by multiplying the mass ofthe body by its acceleration, The effect of force
‘acting on a stationary body or structure ls stress There are diferent types of stress
which are discussed below. The forces acting on a stationary body are typically
measured in pounds ornewtons When force is applied some distance fram the point
at which the effects of the force are being considered, the force measurement
includes a distance component such as pound inches,

A force not only has a certain magnitude but it also has a specific direction Because
Of ths, forces aro fraquer ors. This Is evident in discussions on
aerodynamics (Module 08) and weight and balance (Module 07A} In both of those
disciplines its possible to consider forces that impinge on the aircraft around a
central point. In aerodynamics, the point is the center of lift. In weight and balance

y represented by v

‘computations the point is the center of gravity

A vector is represer the force is applied.
The longer the arrow, the greater the force. Using geometry, vectors representing

y pointing in a
direction that isthe resultant ofthe directional forces applied. An example of this is
ven later in section 222 Kinetics/spee

by an arrow that points in the direc

forces in different directions can be consolidated into a single vec

4 and Velocity

11 tuo equal forces act on the same point of a rigid body but in exact oppost
directions hore are no applied forces. When two
forces are equalin magnitude and in opposite directions but are applied to the body

hey cancel each other out itis as

parallel to each other, the forces are said to be coupled, As long as the coupled forces

are not applied at the same point. they produce a rotating force upon the body to
which they are applied. The resulta

known as torque. A moment is the distance between an applied force and a
reference point. But a moment

Int caused by the coupled forces is

pled forces is independent of any particu

reference point making it

AN.

211. CENTER OF GRAVITY

The center of gravity (CC) of
suspended from this

int for the arcraf An aircraft
1 a nase up or nose
of an altplane for any

cbje

attitude. The CG Is the point about

[An arm Is the horizontal distance that a part of the a
ed from a manufacturer sos

the product of a weight (force) multiplied by it

# or a piece of equior
called the datum. A

m The moment for a

s loc fled reference point

piece ofequipment installed on an aircraft isin facta torque value. measured in inch:

on-meters. Calculations aro performed using the weight of

various components and their respective distances to the aircraft datum in order to
ensure that the center of gravity of an aircraft remains unchanged or within an
acceptable range.

Mal
equipment. light
loading passengers. bag

enance personnel are required to incorporate center of gravity considerations

odified with new

remains within safe limits when
for proper weight and balance

to the center of gravityare discussed in Module O7A of this

98 and fuel. The proc

21.2. ELEMENTS OF STRESS, STRAIN, AND STRESS

Whenever an aireraf isin op ena

ion it experiences something called st

forces are applied to the alrframe and engine components. Reactionary force ins

the materials of the components counter the extemal forces. This Internal resistance

to deformation is known as stress. There are five major stresses to w

are subjected: (Fig21)

Tension

TENSION

force that tends to pull

A,

The engine pulls the areraft forward, but air resistance tries to hold it back

ner
<«— Y —

Fig. 2:1 The five stresses that may acton an aircraft and its parts.

The resultis material is
measured in pounds per square inch (psi) and is calculated by dividing the load fin
units of weigh pull the material apart by its cross-sectional area (in
distance squared)

sion. which stretches the airraft The tensile stren

COMPRESSION

Compression is the stress that resists a crushing force. (Fig2:18) The compressive
stress that tonds to

trength ofa material is also measured in psi Compression is

shorten or squeeze aircraft parts,

TORSION

Torsion is the stress that resists twisting, (Fig2IC) While moving the aircraft forward,

the engine alsa tends to twist it to one sde, but other airerat componente hold it on

»

course. Thus. torsion i created, The torsion strength of a material i its
twisting or torque.

SHEAR

Shear isthe stress that resists the force tending to cause one layer of a material to
slide over an adjacent layer. (Fig
to a shearing force. Usually. the

AD) Two riveted plates in tension subject the rivets
loss than its tensile or compressive strength. Aircraft parts especially scrows. bolts.

hearing strength of a material i ei

and rivets. are often subject toa shearing force

BENDING STRESS

Bending stress is a combination of compression and tension. The rod in Fig2-1E has
ich

been shortened (compressed) on the inside afthe bend and stretched on the ou
cof the bend,

An airplane in flight experiences a bending force on the wing as aerodynamic lit

Lies to raise the wing. This force of lit actually causes the skin on the top of the wing

to compress and the skin on the bottom of the wing to be under tension. When the
airplane ison the ground sitting on its landing gear, the force of gravity tries to bend
the wing downward, subjecting the bottom ofthe wing to compression and the tor
Cf the wing to tension (Fig2-2) During certification testing. an aircraft manufacturer
intentionally bends the wing up:

falling

¡down to make sure it can take the stress without

og Top is
vee
Wg Bom
uncer onsen Er

Fig.22Alrplane on the ground, wing under tension and
compression,

20

AN.

Strength or resistance to the extemal loads imposed during operation are the

principle design requirement in certain structures. How

ther characteristics in addition to and controlling the fve ms

‘engineers must consider. For example. coming airings.and similar part n
ject to significant loads requiring a high degree of strength. However, these parts

ay not be

must have treamnlined shapes to meet aerodynamic requirements such as reducing
drag or ai

Ifthe stress acting on an object is great enough it can cause
shape or to become distorted, One chara

ye object to change its
teristic of matter Is that it tends to be

elastic. meaning it can be forced out of shape when a force & applied, and then
return to its original shape when the force is removed, When an object becomes
is said tobe strained.

distorted by an applied force. the obje

On turbine engine test cells the thrust of the engine is typically measured by what
aro called strain gages When the force (thrust) of the engine is pulling out agains

sured and then translated into the

the strain gages the amount of distortion is me:

appropriate thrust reading.

A deflecting beam style of torque wrench uses the strain on the drive end of the
wrench and the resulting distortion of the beam to indicate the amount of torque

ae

Fig. 2-3 Deflecting beam torque wrench. measures
‘strain by distortion,

Elestietyis the ability ofa material to return to ts original shape after being effected
by a force such as stretching or bending. Examples of elastic materials include a
rubber bandera metal spring. The reasons for elasticity can be different for diferent.
materials. In metals. the atomic structure changes when force ls applied. When
forces are removed. the structure goes back to the original state. For rubber and
some other materials. elasticity is caused by the stretching of the atomic structure
when forces are applied

A flexible aircraft wing is a good example of elasticity in aviation. fit were not for the
ability of a wing to flex and return to its normal shape when stressed. it would be
much more likely to fall during turbulence. hard landings, or when under other
stresses. The opposite of elasticity is rigidity. Fig2-4)

Fig. 2-4 Elasticity ofa modern aircraft wing aids when absorbing of stress for
structural integrity and for passenger comfort.

21.3. PRESSURE AND BUOYANCY IN LIQUIDS

SURE

The pressure exerted on the bottom of a container by a liquid is determined by the
height ofthe liquid and not by the shape of the container. This can be seen in Fig2-
5. where three diferent shapes and sizes of containers are full of colored water, Even
though they are diferent shapes and have different volumes of liquid, each one has

2

‘ahoight of 231 inches, Because ofthis height each one would exert a pressure on the
bot

volume of 231 int (one gallon). One gallon of wa
pressure on the bottom is 834 ps.

‚m of 834 psi. The container on the left. with a surface ares of lin, contains a

er weighs 834 Ib, which s why the

Still thinking about F2 5 ifthe pressure was measured half way down. it would be
half of 34, or 417 psi. In other words. the pressure is adjustable by varying the height
of the column Pressure based on the column height of a fluid is known as static
pressure, With liquids. such as gasoline. it Is sometimes referred to as a head of
pressure, For example. ¡fa carburetor needs to have 2 ps supplied to its inlet (head
of pressurel this could be accomplished by having the fuel tank positioned the
appropriate number of inches higher than the carburetor

As identified in the previous paragraph, pressure due to the height ofa fluid column
is known as static pressure, When a fluid is in mation and its velocity s converted to
pressure, that pressure Is known as ram, When ram pressure and static pressure are
‘added together. the result is known as total pressure. In the inlet of a gas turbine
engine, for example, total pressure is often measured to provide a signal to the fuel
metering device or to provide a signal to gauge on the flight deck.

‘This same principle of pressure caused by a column of fluid applies to the earth's
“atmosphere, Air's a fui that has weight. This weight causes atmospheric pressure.
(On a standard day at sea level if square inch column of alr extending to the top
of the atmosphere is woighed. it hy standard day
atmospheric pressure ls sald to be 147 pounds per square inch 047 psi)

ould woigh 147 Ib. That is

Each container is filed with colored water to a height of 231 inches

Fig 2 5 Fluid pressure based on column height

Since atmospheric pressure at any altitude is due to the weight of air above it
pressure dec

‘an area at 15.000 fe would be les than the total
von.

ses with increased altitude. Obviously, the total weight ofair above

jeightof the air above an area at 10

Atmospheric pressure is often measured by a mercury barometer. A glass tube

somewhat over 30 inches in length is sealed at one end and then filled with mercury.

Its then inverted and the open end placed in a dish of mercury. Immediately. the
mercury level in the inverted tube will drop a short distance. leaving a small volume
f mercury vapor at nearly zero absolute pressure in the tube just above the top of
the liquid mercury column. Gravity acting on the mercury in the tube w

the mercury run out. Atmospheric pressure pushing down on the mercury in the

‘open container tres to make the mercury stay in the tube. At some point these two
forces (gravity and atmospheric pressure) wil equalize and the mercury wil sabilz
at a certain height in the tube. Under standard day atmospheric conditions the air
in a square inch column extending to th

square inch column of

pslisequal to 2992 "Hg when referring toa barometric reading. Fig2-6 demonstrates

mercury. 2992 inches tall also weighs 14.7 Ib, That is why 147

Mes

Ya j

Fig 2:6 Atmospheric pressure as inches of mercury

À second means of measuring atmospheric pressure is with an aneroid barometer
use on airplanes. Aneroid barometers (altimeters) are us

4 to indicate altitude in

flight. The pressure of the atmosphere is exerted against a thin metal aneroid
the pointer, Calibrations are made in thousands of feet rather than in

connected
Psior inches of mercury. For example the standard pressure at sea level is 20.92 "Ha,
or 147 pst

AL10 000 feet above sea level. standard pressure Is 20.58 Hg, or 1010 psi Atimeters
are calibrated so that IF the pressure exerted by the atmosphere is 1010 psi the
I point to 10 000 ft. Fig.27)

altimeter

Fig.2.7 An airplanes altimeter is an aneroid barometer.

A solid body submerged in a liquid or a gas weighs less than when weighed in free
space, This ls because of the upward force, called buoyant force, which any fluid
‘exerts on a body submerged in it An object wil lot if this upward force ofthe fluid
is greater than the weight of the object. Objects denser than the uid, even though
they sink readily. appear to lose a part of their weight when submerged. A person

an if a larger weight under water than he or she can possibly lift in the it

row can is filed to the
feighs 10 Ib.

‚mpletely submerged in the water and it weighs 5 Ib. The

The following experiment is illustrated in Fig2-8. The

spout with water. The heavy metal cube is first weighed in stil air and

itis thon weighed while co

difference between the two weightsis the buoyant force of the water As the cube is

The volume

erflow can the water's caught in the catch bucke
of water which overfiows equals the volume of the cube. (The volume of irregular
shaped objects can be measured by this method) If this experiment is performed

careful, the weight of the water displaced by the metal cube exactly equals the

buoyant force of the water. which the scale shows to be 7 Ib

2

= 7
E

Fig. 2-8 Example of buoyancy.

Archimedes (287-212 BC.) performed similar experiments As a result he discovered
that the buoyant force which a fluid exerts upon a submerged body is equal to the
weight of the fluid the body displaces. This statement is referred to as Archimedes
principle. This principle applies to all uids. gases as well as liquids. Just as water
‘exerts a buoyant force on submerged objects. air exerts a buoyant force on objects
submerged in it.

The amount of buoyant force avallabie to an object can be calculated by using the
following formula:

Force = Volume of Object % Density of Fluid Dis

wil float If the

If the buoyant force is more than the object weighs, the obj
buoyant force I less than the object weighs the object will sink For the object that

sinks its measurable weight wil be less by the weight of the displaced flu

Example: A 10: object weighing 700 Ibs Is placed in pure water. Will the object
joat? Ifthe object sinks, what & Its measurable weight in the submerged condition?
I the object floats how many cubie feet of is volume is below the water line?

Bu ce = Volume of Object X Density of Fluid Displaced
cn

Because the buoyant force is less than the object weighs. the object will sink The

difference between

weigh

e buoyant force and the objects weight

be its measurable

Two good examples o

uoyancy are a helium filed airship and a seaplane on floats.
Anaiiship is able to float in the a

nosphero and a seaplane is able to float on water
That means both have more buoyant force than weight. Fig 9is a De Havilland Tuán
Otter seaplane. with a gr

3 take-off weight of 12 500 Ib, Ata minimum, the floats on
this alrplane must be large enough to displace a weight in water equal to the
airplane's weight. Certification standards typically require that the floats must be 80

ded to support the alrpla

For this airplane. the ne:

jay izo ofthe floats would be calculated as follows,
Divide the airplane weight by the density of water.
Multiply this volume by 80%

2003 x 80% = 160277

2003 + 1602 = 3605 fe"

Fig. 2.9 De Havilland Twin Otter seaplane,

By looking at the De Havilland Twin Otter in Fig2:9, it is obvious that much of the
volume of the floats is out of the water. This is accomplished by making sure the
floats have at least 80 percent more volume than the minimum necessary

Some of the large Goodyear airships have a volume of 230 000 ft. Since the fluid
they are submerged in is air. t find the buoyant force of the airship. the volume of
the arship is multiplied by the density of air (076 SI IbAP For this Goodyear airship.
the buoyant force is17 597 lb. Fig2-10 shows an inside view of the Goodyear airship.

The ballonets are air chambers within the airship, Through the sir scoop. air can be
pumped into the ballonets or evacuated from the ballonets in order to control the
weight of the airship. Controlling the weight of the alrstip cor
positive or negative IR it has. Although the airship is classified as a lighter- than-air
aircraft it is in fact flown in a condition slightly heavier than air

ols how much

Fig. 2:10 Inside view of the Goodyear airship.

AN.

2.2. KINETICS

221. MOTION

The study ofthe relationship between the motion of bodies or objects and the forces
acting on them is often called the study of force and motion? In a more specific
ween velocity, acceleration, and distance is known as

sense, the relationship b

Kinematics

22.2. LINEAR MOVEMENT

Motion may be defined asa continuing change of position or
in which a body undergoes displacement When an object is at diferent points in
0 be in motion. and ifthe distance the

space at diforent timos that object is sad
object moves remains the same for a given period of time, the motion may be
jayshasa constant speed

à Thus an object inuniform motion al

In everyday conversation, speed and velocity are often used as # they mean the sam
thing. In physics
an object is moving. or how far the object will travel in a specific time. The speed of
he direction an object is moving, For example ifthe

ed refers

¡ey have definite and distinct meanings Sp he

an object tells nothing abo
jpplied that an airplane leaves
a speed of 150 mph, this information tells nothing about the direction in which the
the end of 8 hours it might be in Kansas City or fit traveled

York City

New York City and travels 8 hours at

in circular route. it could be back in Ne

Velocity is that quantity in physics which denotes both the speed of an object and
the direction in which the object moves. Velocity can be defined as the rate of
motion ina particular direction. Velocity is also described as being a vec

the:

‘vector being a line of specif length, having an arrow on ene end

length of the line indicates the number value and the arrow indicates the direction
in which that number is acting

Two velocity vectors such as one represer
representing the velocity of the wind, can be added together in what is called vector
analysis Fig2-11 demonstrates this with vectors “A” and 8" representing

Cf the airplane and the wind. and vector C* being the resultant. With no wind, the
speed and direction of th

accounting for thewind direction and speed. the airplane ends up fying at the speed

g the velocky of an airplane and one

the velocity

airplane would be that shown by vector “A” When

30

a.

and direction shown by vector"

Vector A = Ve of Aie

>

Fig. 2-1 Vector analysis for airplane velocity and
Wind velocity

Imagine that an airplane is fying ina circular pattern at a constant speed. Becaus:

of the circular pattern. the airplane is constantly changing direction which means

tho airplane is constantly changing velocity. The reason for this is the act thatvelocity
includes direction.

1 ravels is divided by the elapsed
will be miles per hour (mph). I the dis
seconds, the units of speed will be feet per second (
multiply by 1.467. Velocity ls calculated the same way.
must be recalculated every time the direction changes.

culate the speed of an object. the dista
is measured in miles and the time in hours. the units of speed
nce is measured In feet and the time in

convert mph to fps
y difference being it

A
Increased from 20 mh to 30 mph.

ration i defined as the rate of change ofvelocity Ifthe velocity ofan al
10 object has been accelerated. I the increas
in velocity is 10 mph in 5 seconds, the rate of change in velocity is 10 mph in

seconds, or 2 moh per second. If this were multiplied by 1.467. it could also be

express celeration of 235 feet per second per second fps). By

comparison. the acceleration due to gravity is 322 fps/s (9.8mpsk. To calculat

‘acceleration, the following formula is used

Velocity Final (Vf) = Veloctoy Initial (9)

Example: An Air Force FAS fighter is ¢ vances thi

throttos to full afterbumer and accelerates to 1 20%

ising at 400 mph, The pilot
mph in 20 seconds. What is the

average acceleration in mph’s and

In tho example just shown. the acceleration was found to be 587 pis Since 322
Tps/s is equal to the acceleration due to gravity, divide the F15s acceleration by 322
to find out how many © forces the pilot is experiencing, In this case, it would be 1.82
NEWTON'S LAWS OF MOTION

FIRSTLAW

Objects at rest tend to remain at rest and objects in motion tend to remain in motion
a the same speed and in the same direction, unless acted on by an external for
When a magician snatches a tablecioth from a table and leaves a full setting ofdishe

undisturbed, he is not displaying a mystic art: he is demonstrating the principle of

‚hen an airplane is brought to a

inertia, inertia is responsible forthe discomfon fel

AN.

sudden haltin the parking area and the passengers are thrown forward in ther seats
Inertia is a property of matter. This property of matter is described by Newtons fist

law of motion
SECOND LAW

When a force acts upon a body, the momentum of tha

edly Is changed, The rate of

change of momentum is proportional to U

€ applied force

dy that has great
momentum has a strong tendency to remain in motion and is therefore hard to stop.

For example. a train moving at evento

locity is dificult to stop because of its la

mass. Newton's second law applies to this property. Based on Newton’ second law.
the formula for calculating thrust Is derived, which states that force equals mass
times acceleration (F = MA) Eater in this chapter. it was determined that mass

equals weight divided by gravity a

scceleration equals velocity final minusvelocity

initial cvided by time. Putting all these concepts together, the formula for thrust is

Example. A turbojet engine is moving 150 Ib of air per second through the engine
The air enters going 100 fps

nd leaves going 200 fps. How much thrust in pounds

20

THIRD LAW

For every action there is an equal and opposite rea

Newton's third law of motion is often called the law of action and reaction This
means that if a force is applied to an object. the abject will supply a resistive forc

‘exactly equal to and in the opposite direction of the force applied. I is easy to see

how this might apply to objects at rest For example. as a man stands on the floor,
the floor exerts force against his fe

‘exactly equal to his weight But thislawis also
applicable whon a force is applied to an object in motion

Forces always o

In pairs The term acting force means the force one body exerts
ona second body. and reacting force means the force the second body exerts on the

firs

When an aircraft propeller pushes a stream of ar backward with a force of 500 Ibs.
the air pushes the blades forward with a force of 500 Ibs This forward
the aircraft to move forward. turbofan engine exerts a force on the air entering the
Inlet duct. causing it to accelerate out the

accelerating to the rear is the action. and the force inside the engine that makes it
happens the reaction. also called thrus

In duct and the tailpipe. The al

22.3, ROTATIONAL MOVEMENT

Circular motion à the motion of an abject along a curved path that has a constant
radius. For example if one end of a string is tied to an object and the other end is
held in the hand, the object can be swung in a circle. The object is constantly
lefected from a straight (linear) path by the pull exerted on the string. as shown in
Fig2.12. When the weight is a

int A. due to inertia it wants to keep mi

straight line and end up at point E, Because of the force being exerted on the string,
itis forced to move in a circular path and end up at point C

Fig.212 Circular motion.

AN.

The string exerts a centripetal force on the object and the object exerts an equal but
poste force on the string. obeying Newton's third law

‘equal to centripetal force. but acting In an opposite direction. is called
force. Centripetal force Is always directly proportional to the mass of 4
Circular motion Thus. ifthe mass ofthe object in Fig2-12 is doubled. the pull on the

motion, The f

ntrifugal

string must be doubled to keep the object in its circular path provided the speed of
the object remains constant

Centripetal force isinversely proportional to the radius ofthe circle in which anobject

ed and the speed remains constant. the pull
Con the string must be increased since the
pull the object from its linear path more rapidly. Using the same reasoning. the pull

ing in Fig2-12 is shor

adius is decreased. and the string must

fon the string must be Increased if the object Is swung more rapidly in its orbit

Centripetal force is thus directly proportional to the square of the velocity of the

object. The formula for cor reos:

Centnpetal Force = Mass Velocity’) + Ractivs

For the formula above, mass would typically be converted 1

weight divided by
‘gravity. velocity would be in feet per second, and the radius would be In feet

Example: What would the centripetal force bei a10 pound weight was moving in a
3% radius circular path at a velocity of S00 fps?

Centripetal Force = Mass Velocity") + Radius

Centripetal Force = 10 (500%) + 322 (3) = 2580010
In the condition identified in the example. the object acts like it weighs 2 588 times
more than it actualy does, it can also be sal

hat the object is experiencing 2 589

ce of gravity) The fan blades in a large turbofan engine, when the engine is

‘operating at maximum rpm. are experiencing many thousands of Gs for the sam

2.2.4, PERIODIC MOVEMENT

Periodic motion is evident during pendular motion and vibration. À pendulum i a
weight suspended from a fixed point so it can swing freely back and forth, The

mation is characterized by a few important variables. The period isthe time it takes

for the weight to complete one cycle of ms

It's dependent on the length of th

AN.

ficaly.the period varies directly with the square root

suspending rod or string. sí

suspending item (ie. a string or red), The period also
a

SFE which is the length oft

root of the acceleration of gravity. The follow

T=24
V8

Were

= length of the pendulum in feet or meters

endulums are unique in that the per
swings to and for even though it grad

y has resulted in pendulum mation to be the regul

y displaces less and less with each ensuing

fluid or an elast

Vibratio ie motion caused by oscillation of the parts of a
ld whose equilibrium has been disturbed. An electroma:
‘experiences vibration. Something that is vibrating has motion b
a central pain mies in an aircrat, vibe
estructive, Designengineers must design the aircraft to withstand or safely disipa!
luced by the engine. components or by the aircraft's move

‚ck and forth across

also b

any vibration pre

through the.

Vibratory motion is also known as harmonie motion. It is regular in nature. Vibration

ischarecterized by having a period. whichis the time it takes for a complete cycle of

mover: nd a complete cycle

The unit of measure for frequency is the hertz (Hz). One cycle per second s equal
e midpoi

Its frequency s the numberof times pers

also has amplitude, Amplitude is measured

ne hertz, Vibra

Cf the motion to the point of maximum displaceme:
the vibrating ‘amplitude of vibration will stead!

decrease as time goes on. However. the frequency of vibration will remain the same.

input energy Into

na musical instrument. it is the frequency that sets the pitch ofthe tone created
vihen the string is plucked. The amplitude is related to the loudness of the vibrati

The formula for computing
the same as that of a pendulum Instead of gravity supplying the force as with a

lod of a vibrating or oscillating object is virtually

Pendulum, some other force must be applied to create vibration. But the uniqueness
and a pendulum. Not
oscilator in electronics does have a means for steadily supplying extra energy to the

ofa st

ay frequency is shared by vibrating obje hatan

vibrating system and does not confor to this mode

m= mass in pounds or kilograms (Kg)

k= force in pound feet or dynes /em

When an objects forced to vibrate at its natural frequencies it vibrates ina manner

‚ch that a standing wave pattem is formed within the object Whether itis a guitar

string, or an air column, the medium vibrates in such a way that a
pattern results

anding wav

Each natural frequency that an object or musical instrument produces has its own

characteristic vibration pattern, These pet

ns are created at specific frequencies.

which are known as harmonics. For objects that vibrate in regular and periodic

fashion the harmonic frequencies are related to each other by simple whole number
ratios (Fig.

Fig. 2:15 The first three levels of harmonic vibration

All types of matter. regardless of whe

s a solid, liquid, or gas. have a natural
frequency at

at mattervibrate. ftv
al frequency, and one of thom sta

brate. can transterits wave

rate. This

fer of energy is known as

resonance red airplanes have an rpm range that

arded to avoid because spinning the prop at that mm can cause vibration
probloms. The diffculy les in the natural frequency of the metal in the prop. and
the frequency of ibration that will be set up with a particular tip speed for the prop.

ticularrpr stresses can be se

22.6. VELOCITY RATIO, MECHANICAL ADVANTAGE AND
EFFICIENCY

the distance travelled by th
in a simple machine. Fi
computation. As shown in Fig 14, beca

effort. compared to the

jon is not included in the

istance between the handle

stance of 00mm. causing

10 of 100 men. Thus, the ve

1. Similarly. an effort exerted of 100 Newtons for a distance of
moved a distance of100 mm

and the wheels the worker has pulled the handles up a
the wheelbarrows supporting legs to rise by a dist

ratio is measured
300mm:

Fig. 2:14 A100 Newton effort over 300mm yields a 300 Newton result over
100mm.

A machine is any device with which work may be accomplished. In application.

1. Machines are used to transform energy. asin the case of a generator

transforming mechanical energy into electrical energy

2. Machines are used to transfer energy from one place to another. asin the
ction gears transferring

examples ofthe connecting rods crankshaft, and re

Conergy from an aircrafts engine to its propeller
3. Machines are used to multiply force: for example. a system of pulleys may be

nables the load to be raised by

used to lit a heavy load, The pulley system
force that is smaller than the weight o
4. Machines can be used to multiply speed. A good example is the bicycle. by
ich speed can be gained by exerting a greater force
‘used to change the direction of a force. An example of this

coxerting the load.

5. Machines can b

ward force on one side of the rope exerts an upward.

use is the flag hoist. A dow
force on the other side. raising the flag toward the top of the pole

wer, the pulley. the wheel and axle.
basic principles in machines: the lever and the inclined plane, The pulley (block and
heel and axle. and gears operate on the machine principle ofthe leve

ane. An understanding

‘There are only sx simple machines They are th

the

inclined plane. the screw. and the gear. Physicists h

The wedge and the screw use the principle ofthe inclined
Cf the principles of simple machines provides a necessary foundation for the study
or mote simple machines.

of compound machines. which are combinations of

tements 3 and 4 under simple ma
to multiply force or to multiply speed. It cannot. however. multiply force and speed

As identified in 2 Ines. a machine can be used

at the same time. In order to gain one. it must lose the other. To do otherwi
mean the machine has moro power going out than coming in, and that is not
ison of th
our distance to the input distance. If

possible, In reference to machines mechanical advantage is a com

‘output force to the input force. or the ou ero

í a mechanical advantage in terms of force, there wll be a fractional disadvantage

advantage,

o. The following formulas can be used to cal

Mechanical Advantage = Force Out + Forcein

The simplest machine. and perhaps the most familiar one. isthe le
of a lever, with two people sitting on cither en

familar examp of a board and a

pivoting point in the middle. There are three basic parts in all levers. They are th
fulcrum °F: a force or effort“E and a resistance “R Shown in Fig2-15 are the pivot
point F (ulerum) the effort “E which is applied at a distance “L from the fulerum,
and a resistance R" which acts at a distance * from the fulcrum. Distances L' and

Resistance “R Elon “E

Fulcrum °F

Fig-215. First class lever.

The concept of torque was discussed earlier in this chapter, and torque is very much

involved in the operation ofa lever. When a person sits on one end of a seesaw. that
person applies a downward force in pounds which acts along the distance to th

center of the seesaw. This combination of force and distance creates torque, which

40

AN.

tres to cause rotatio

In the first clas lever, the fulerum is located between the effort and the resistance.

mentioned earlier. the seesaw is a good example ofa lever, and it happens to be

2 first class lever. The amount of weight and the distance from the fulerum can b

varied to suit the need. Increasing the distance from the applied ffo

compared to the distance from the fulcrum to the weight being moved. increases
the advantage provided by the lever. Crowbars. shears, and pliers are common

‘examples of this class of lever.

‘The proper balance of an airplane is also a good example, with the center of ifton
the wing being the pivot point (fulcrum) and the weight fore and aft of this point

being the effort a Jon calculating how much effort is required to

following formula can be used,

E) x Effort Arm (L) = Resistance (8) x Resistance Arm (0

What this formula really showsis the input torque (eff
nce arm). This formula and concept apply to
all three classes of levers. and to all simple machines in general

imes effort arm) equals the

output torque (resistance times resista

Example: A first class lever isto be used to lift a 500 1 weight. The distance from the

weight to the fulerum is 12 inches and from the fulerum to the applied effort is 60

inches. How much force is required to lift the weight

Effort (E x Bffort Arm (L)

Resistance (R) X Resistance Arm (D
Ex 60in = 500 x 12in
E = 50010 x 12in + 60,

The mechanical advantage of the lever in this example would be:

Mechanical Advantage = Force i

+ Fore in

An interesting thing to note with this example lever is ifthe applied effort moved

the weight on the other end would only move up 2 inches. The
weight being líted would
lof work Because a lever cannot

nly move one fith as far. The reason for this isthe concept

Lift times more weight. you will only move it 1/5 as fr as you move the effort
SECOND CLASS LEVER

The second-class lever has the fulerum at one end and the effort is applied at the
other end. The resistance is somewhere between these points. A wheelbarrow i a
100d example of a second-class lever. with the wheel at one end being the fulcrum.

10 oppose end being the applied effort. and the bucket in the

middle being where the weight or resistance Is placed. (Fig2-16)

lft

Resistance “A”

Fig. 216, Second class lever.

8

resistances with a relatively small effort The first-class low

fist: and second-class levers are commonly used to help in overcoming big

Depending on how close or how far away the weight is placed from the fulerum. the

first class lever can be made to gain force or gain distance, but not

time. The second-class lever can only be made to gain force
Example. The distance from the center ofthe whee! to thehandies ona wheelbe!
is 60 inches. The weight in the bucket is 18 inches from the ce
300 Ibs is placed in the bucket, how much force must be app

lied at the handles to

lift the wheelbarro

Effort (E) x Effort Arm (L) = Resistance (R) x Resistance Arm (0)

EX 60in = 30016 x 18in

AN.

E = 30010 x 19m + 60m
E = 901

= 33307333101

There are occasions when it is desirable to speed up the movement ofthe resistanc

‘even though a large amount of effort must be used. Levers that help accomplish this
min Fig2-17 the fulcrum is at one end of the lever and

the weight or resistance to be overcome is at the other end, with the effort applied

are third class levers. AS shor

at some point between. Third class levers are easly rec

gnized because the effort is
applied between the fulerum and the resistance, The retractable main landing gear
o is a good example of a third class lever. The top of the landing ge

here it attaches to the airplane, s the pivot pol à and brake assembly

at the bottom ofthe landing gearis

e resistance. The hydraulic actuator that makes
the gear retract is attached somewhere in the middle. and that is the applied effor

Fig. 217. Third class lever.

THE PULLEY

Pulleys are simpl form of a

heel mounted on a fixed axis and
supported by a frame. The wheel, or disk is normally grooved to accommodate a
rope, The wheelis sometimes referred to as a"sheave" (sometimes sheaf"). The fram
that supports the wheel is called a block. A block and tackle consists of a pair of
blocks Each block contains one or more pulleys and a rope connecting the pulley

f each block.

AN.

SINGLE FIXED PULLEY

A single fixed pulley is really a first class lever with equal arms. In Fig.2.18, the as
from point “R* to point °F’ is equal to the arm from point “F" to point “E* (both
distances being equal to the radius of the pulley), When a fest-class lever has equal
arms, the mechanical advantage is. Thus, the force ofthe pull on the rope must be
equal to the weight of the object being lifted. The only advantage of a single fxed

pulley is to change the direction of the force or pull on the rope.

\

Fig. 2.18. Single fixed pulley.

SINGLE MOVABLE PULLEY

A single pulley can be used to magnify the force exerted. In Fig2-19 the pullay is
movable. and both ropes extending up from the pulley are sharing in the support of
tho weight. This single movable pulley acts like a socond-clas lover. with tho offor
arm (EF! being the diameter of the pulley and the resistance arm (FR) being the

chanical advantage of two

radius of the pulley. This type of pulley would have a me

diameter of the pulley is double the radius of the pulley. In use, if

because
someone pulled in 4f ofthe effort rope. the weight would only rise off the floor 2 ft
Hehe w 100 Ib, the effort applied would only need to be 50 Ib. With this

fort will always be one-half ofthe weight being lifted.

type of pul

——

o.

o

\

=

Fig. 249, Single movable pulley.

pulleys, some of them fixed and so
ulleys the top two

A block and tackle is made up of multi
movable. In Fig2-20, the block and tackle is made up of four
being fixed and the bottom two being movable, Viewing the Figfrom right to left
four ropes supporting the weight and a fifth rope where the effort is
of weights supporting ropes determines the mechanical

.@ the mechanical advantage is four If

applied. The nu
advantage of a block and tackle, so in this

€ weight was 200 bs, it would require a 50 Ib effort to lift it

2 AN

Fig. 2-20. Block and tackle.

THE GEAR

Two gears with teeth on their outer edges, as shown in Fig2 21, act ike a fit class
lever when one ge athe drive
‘gear. and the other is called the driven gear. The effort arm is the diameter of the
{riven gear. and the resistance arm isthe diameter of the drive gear. Notice that the

drives the other. The gear with the input force sc

two gears turn In opposite directions (the bottom one clockwise and the top one
counterclockwise}. The gear on top (yal
and the gear on the bottom (blue) is 12 inches in diameter and has 60 teeth

wis 9 inches in diameter and has 45 teeth

Fig. 2-21. Spur gears.
Imagine that u
riven), The mechanical advantage in terms of force would be the effort arm divided
by the resistance arm or9+12, which 5075. This would actually be called a fractional

disadvantage. because there would be less force out than force in, The mechanical
advantage in terns of distance {rpm in this case) would be 12 +9, or 133. Thi

blue gear is driving the yellow one (blue is the drive, yellow is the

alysis
tell us that when a large gear drives a small one, the small one tums faster and has
less available force. n order to be a force gaining machine, the small gear need

turn the large one. When the terminology reduction gearbox is used. such as a
propeller eduction gearbox, it means that there is more mm going ln thanis coming

‘out The end result is an increase in force, and ul

imately torque.

Bevel gears aro usod to chango the plane of rotation, so that a shaft turning

horizontally can make a vertical shaft rotate. The sizeof the gears and their number

of teath detern

ine the mechanical advantage, and whether force is being increased
or rpm is being increased If each gear has the same number of teeth, there would
be no change in force or pm. (Fig2-22).

lemma AA A A a
ee ela

Fig2-23. Worm gear.

propeller. (2-24)

Sun Gear

Ring Gear Planetary Gear

Fig. 224, Planetary sun gear

GEAR RATIO

‘The velocity ratio and the gear ratio of a geared drive are essentially the same
A gear ratios calculated by comparing the number of
number of teet

thing
ona chive gear to the

h on the driven gear. The result isa ratio that brings into focus th

amount of mechanical advantage pr

4 ratio or velocity ratio can also be calculated. Instead of comparing the

er of teeth on the

gears, the rotational speed of each gear is considered

When

vo gears are used in an aircraft component, the rotational speed of each gear

is represented as a speed ratio. As the num

rotational speed oft!

of teeth in a guar decreases, the

gear increases, and vice-versa

the speed rat
two goats have a gear ratio of

then thelr speed ratio is

opposite) of the gear ratio. If

Example. À pinion gear with 10 teeth is driving a spur gear with 40 teeth. The spur

gear is rotating at 160 rpm. Determine the speed of the pinion gear

To solve for SP. multiply 40 » 160, then divide by 10. The speed of the pinion gear is

Example: the cruising speed of an aiplane is 200 knots and its maximum speed is
250 knots what isthe ratio of cruising speed to maximum speed?

First, express the cruising speed as the numerator ofa fraction whose denominator

Next. reduce the resulting fraction to its lowest terms.

‘The ratio of cruising speed to maximum speed is 45

‘Another common use of ratios sto convert any given ratio to an equivalent ratio w
à denominator of}. Example: Express the ratio 95 as a ratio with a denominator of}

R= 22 sine9 + 5 = 1then 2 =

‘Therefore, 95 isthe same ratio 351.81, nother words.9 to 5 le the same ratio 88 18 1

INCLINED PLANE

The inclined plane sa simple machine that facilitates the rabing or lowering ofheayy

objects by application of a small force over a relatively long distance. Some familiar

examples of the inclined plane are mountain highways and a loading ramp on the

mal airplane. like a Cessna 72. an inclined plane

dtoget tho airplane on the scales by pushing it. rather than jacking

IL A ramp can be seen in Fig2-25. where a Cessna 172 right main gear is sitting

lectronic scale, The airplane was pushed up the ramps to get ton the scales.

50

Fig. 2-25, Ramp in use with a Cessna 172.

With an inclined plane. the length of the incline is the effort arm and the vertical
height of the incline is the resistance arm. th of the incline is five times
greater than the height. there will be a force advantage. or mechanical advantage.
of five. The Cessna 172 in Fig2-25 weighed 1 600 Ib on the day of the weighing. The
ramp its sitting on is 6 inches tall resistance arm) and the length of the ramp is 24
inches (effort arm).

needed to push the alrplane up the ramps. use the same
en levers were discussed as follow

To calculate the for
formula introduced earlier

Effort (E) x Bffort drm (L) = Resistance (R) X Resistance Arm (0)
Ex 24in = 16001 x Gin
E = 6001b x Gin + 24in

Bolts, screws, and wedges are also examples of devices that operate on the principle
for example, has a spiral thread that runs around its

Of the inclined plane. À bol
circumference, As the thread winds around the bolts circumference, it moves a
vertical distance equal to the space between the threads The circumference of the
bolt is the effort arm and the distance between the threads is the resistance arm,
(Fig226)

AN.

Based on this analyss. it can be seen that a fine threaded bolt (more threads per

inch) has a greater mechanical advantage than a coarse threaded bol

Fig.2:26.A bolt and nut asan inclined plane.

THE WEDGE

A chisel is a good example of a wedge. A chisel might be 8 inches long and only Y
inch wide with a sharp tip and tapered sides The 8 Inch length isthe effr

the H inch width isthe resistance arm. This chisel would provide a force advantage

(mechanical advantage) of 16.

Mechanical efficiency is always a goal ofthe alreraft designer Efficiency refers to how
vall a machine uses input energy. Losses due to heat. fiction. defection and wear

be inefficient. A machine that minimizes these losses in said to
be efficient

Efficiency is measured in percentage. No machine can be 100% ef
calculate efficiency is with the following equation

lent A

Efficeney = Mechanical Advantage + Speed Ratio x 10

Another way to look at efficiency is as follows: Eificiency = Measured Performance
Ideal Performance

is sub-medule, force, work and one of the major factors th
causes machines to not be efficient. Fiction are examined

2.3. DYNAMICS

23.1. MASS AND WEIGHT

Mass is a measure of the quantity of matter in an object. In other words. how many

molecules are in the object. or how many atoms or to be more specific. how many

fons, and electrons. The mass of an object does not change regardless
niverse. and it does not change with a change of sta
mass of an object isto ade or take a

of where you take itin the

Mathema

ly. mass can be stated as follows:

Mass = Weight + Acceleration due to grav

The
Tos/s) An object weighing 322 pounds (bs) here on earth is sald to have a mass of

celerate of fs when a fore
standard atmospheric con:
22 Ib

eleration due to gravity here on earth is 322 feet per second per second (522

À slug is a quantity of mass that will
applied. In other words, und
qual to 52.2) a mass of one slug is equ:

of pol tions (oravigy

Weights a measure of the pull of gravity acting

Ih under the earths force of gravity. Becau

mass an obi

itis for the mass of an object to go away, the only way for an objec

be weightless is for gravity to go away;

utile and itappears that they are weightloss. Ev

though the shuttle is quite a few miles above the surface of the earth the force of
gravity has net gone away. an 5 are not weightless. The astronauts and
the space shuttle are in a state offre fal. so relative to the shuttle the astronauts
appear to be weightiess

Mathematically. weight can be stated as follows:

Weight = Mass X Gravity

Jower.or torque can be discussed, we must understand

vihat force means Force is the intensity of an impetus. or the intensity of an input
e apply à force to an object. the tendency will be for the object to

move. Another way to look

to bea force that initiates the process

For example. i

‘The unit for force in the English system of measurement is pounds. and in the metre
system it Is newtons. One pound of force Is equal to 4.448 newtons When wi
calculate the thrust of a turbine engine. we use the formula “Force = Mass

‘Acceleration and the thrust of the engine Is expressed in pounds The CE90-15
turbofan engine (powerplant for the Boeing 777-300), for example, has 115 000
pounds of thrust

Inertia is the resistance of an object to a change in its state of motion. including

changes t ts spced or direction. Inertia tends to keep an object moving ina straight

line and a constant velocity. Similary. inertia is the property. which needs to be

overcome before a stationary object may begin to move from lts present position.

Thus. an object will continue moving at its current velocity until some force causes
or direction to change. (Fig2-27)

more difficult
tobe pushed

Fig. 2.27 An object of greater mass has more inertia than a lesser abject.

The study of machines, both simple and complex is in one sense a study of the
hines transfer input energy.
work done by the

energy of mechanical work, This is true because all má

y the work done on the machine, to ou

ut energy. or the

Werk in the mechanic
a force acting through a measurable distance. Two Fact
‘movement through a distance. As an example, suppose a small

sense ofthe

rm is done when a resistance is overcome by
15 are involved: (1) force and

the snow. Two men push against it for a period of time, but the aicraft does not
move. According to the t

the aircraft By defnition. work is accomplished only when an object is displaced

nical definition. no work was done in pushing agains

some distance against a resistive force.

To calculate work the following formula is used:

fork = Force (E) x Distance (d)

In the imperial system. the force will be identified in pounds and the dis
in feet or inches. so the units will be foot pounds or inch- pounds Notice
the same units that were used for potential and kinetic energy.

In the SI/Movic System, the force ls identified in newtons IN) and the distance in
meters. nt units being joules. One pound of force is equal 104.448 N
and one meter is equal to 328 feet. One joule & equal to 136 feb

Example: How much work is accomplished by jacking 2 150 000-Ib Albus A320
airplane a vertical height of 3 R7 (Fig2-23

= Force (P) x Distance (D

= 15000018 x 4fe

Example: How much work is accomy
bar and a Boeing 737-800 airplane
hangar? The force on the tow bar ls 5 000 Ib

ished when a tow tractor ishooked up toa t
sighing 130 000 lbs is pushed 80 R Into the

In this last example, notice the force does not equal the weight ofthe airplane. This
is because the airplane Is being moved horizontally and not lifted vertically. In
Virtually all cases, it takes less work to move something horizontally than it does
lift it vertically. Most people can push their car a short dis

theie car and lift it off the ground,

nce if It runs out of gas

but they cannot get und

ss

Fig, 2-28, Airbus À 320 being jacked,

POWER

‘The concept of power involves the previously discussed topic of work, which was a
force being applied over a measured distance. but adds one more consideration
time. In other words how long does it take to accomplish the work Ifsomeone asked
the average person if he or she could lift one million pounds feet off the ground
tho answer most assuredly would bo no. This person would probably assume that he
or she isto lift it all at once. What if he or she is given 365 days to lift it. and could lft
small amounts of weight ata time? The work involved would be the same, regardless
‘of how long it took tif the weight. but the power required sdifferent. Ifthe weight
is to be lifted in a shorter period of time it will take more power

‘The formula for power is as follows

‘The units for power will be foot-pounds per minute, foot pounds per second, inch
pounds per minute or second, and possibly mie pounds per hour. The units depend
Con how distance and time are measured

Many years ago, there was a desite to compare the power of the newly evolving
steam engine to that of horses. People wanted to know how many horses the steam
engine was equivalent to. Because of this the value we curently known as one
horsepower (hp) was developed, and itis equal to 550 foot pounds per second (Fe
lbs). It was found that the average horse could lit a weight of 550 Ibs, one foot off
the ground. in one second, The values wo use today. in order to convert power to

ss

»
tip = 378 me pon peros (nt =)

To convert power to horsepower divide the power by the appropriate conversion
based on the units being used.

Example: What

would be needed, and horsepower, to raise the GE-90
turbofan engine into position to instal it on a Boeing 777-300 airplane? The engine
weighs 19 000 Ibs and it must be lifted 4 ft in2 minutes

Power = Force x distance + tim

9000 lbs x 4 fe + Zmin

Mp= ia

I need to be powered

The hoist that will be used to raise this engine into position wi

i their arms for the necessary 2 minutes.
TORQUE

Torque is very interesting concept and occurrence, and its definitely something

that needs to be discussed in conjunction with work and power. Whereas work is
along a distance Torque is something that creates twisting and tries to make

If we push on an object with a force of 10 Ib and it moves 10 inches in a straight line
vie have done 100 in-Ib of work By comparison. ifwe have a wrench 10 inches long
mon it with a force of 10 lbs. at

that ison a bolt. and we push do, ue of 100 in

is applied to the bot Ifthe bolt was already tight and did not move as we pushed
on the wrench the torque of 109 in- would still exist

Even though the formula looks the same as for calculating work recogniz

that the distance value in this formula isnot the linear distance an object moves, bu

rather the dis led

ce along which the force isap

Notice that with torque nothing had to move. because the force Is being applied
along a distance and not through 2 distance. Notice also that although the units of

work and torque appear to be the same, they are not The units of work
pounds. and the units of torque were pound inches, and that is what differentiates

inking about how engines work both piston

Torque is very important when

engines and gas turbine engines Both types of engines create torque in advance of

boing able to create work or power. With a piston engine. a force in pounds pushes

down on the top of the piston and tries to make it move. The piston is attached

the connecting rod. which isattached to the crankshaft atan offset. That offset would

be like the rench discussed gerer, and the force acting along tha

ength of the
length is whatcreates torque. (Fig2-29)

Tora = $6004

A7 bit

Paso

}
Fig.2:29Piston engine and torque.

For the cylinder in Fig.2-29. there isa force of 500 lbs pushinadewnon the top of the
piston. The connecting rod attaches to the crankshaft at an offset distance of 4 in
The product ofthe force and the offset distance is the torque, in this case 2 000 in
te,

In a turbine engine, the turbine blades at the back of the engine extract energy from
the high velocity exhaust gases. The energy extracted becomes a force in pounds
Pushing on the turbine blades which happen to be a certain number of inches from
the centre ofthe shaft they are trying to make rotate The number of inches from th
turbine blades to the centre of the shaft would be like the length of the wrench
discussed earlier

Mathematically, there ls a relationship between the horsepower of an engine and
the torque of an engine.

AN.

The formula that shows:

s relationship is as follows
Torque = Horsepower X 5252 + rpm

Example: A Cessna AR has a Lycoming 10-360 engin

hat creates 180 horsepower

0 rpm. How many pound-fest of torque is the engine producing

Torque = 180 x 5252 + 2700 = 3501b—

23.2 ENERGY

Energyis typically defined as something that gives us the capacity to perform work
e feel full of energy is probably indicating that
N a let of work Energy can

As individuals, saying that
porfa

classified as one of two types

POTENTIAL ENERGY

Potential energy is defined as being energy at re

or energy that is stored. Potential
energy may be classifed into three groups: () that due to position. 2) that due to
tion of an elastic body, and (3) that which produces work through chemical

à an airplane raised off the ground sittin

Con jacks are examples of the fist group. a stretched bungee chord on a Piper Tr:
Pacer or compressed spring are examples of the second group. and energy in
aviation gasoline food, and storage batteries are examples of the third group.

To calculate the potential energy of an object due to its position. as in height the
following formula is used:

Energy = Weight x Height
A calculation based on this formula will produce an answer that has units of foot
pounds (fs) or inch- pounds nibs). which are the same units that apply to work
Work. which is covered laterin this Sub-Module is described as a force being applied
over a measured distance, with the force being pounds and the distance being feet
cr inches Itcan be seen that potential energy and work have a lot in common.

Example: Boeing 747 weighing 450 000 pounds ne
so maintenance can be done on the landing gear. How

ds tobe raised 4 feet inthe air

much potential energy does
the airplane possess because ofthis raised postion?

60

Potential Energy = Weight Height
PE = 450 0001 x 4f

PE = 1900000

As mentioned previous. aviation gasoline possesses potential energy because of ts
chemical nature. Gasoline has the potential to release heat energy. based on its
British thermal unit (BTU) content One pound of aviation gas contains 18 800 BTU
ef heat energy. and each STU is capable of 778 fe y 778
by 18 900. we find that one pound of aviation gas is capable of l 704 200 fs of

bs of work. So if we mul

work. Imagine the potential energy in the completely serviced fuel tanks of an
airplane

KINETIC ENERGY

Kinetic energy is defined as being energy in motion. An airplane rolling down thi

runway or a rotating flywheel on an engine are both examples of kinetic enero
Kinetic energy has the same unis as potential energy. namely foot pounds or inch
pounds To calculate the kinetic energy for something in motion, the following

formula is used

To use the formula, we will show the mess as weight + gravity and the velocity of the
object will bein feet per second, This is necessary toend up with units infos

Example: A Boeing 777 weighing 600 000 lbs ie moving down the runway on ts take:

ff roll with a velocity of 200 fps. How many foot pounds of kinetic energy does the

airplane possess(Fig230)

Kinetic Energy = ¥ x 600 000 + 322 x 200%
KE = 372 670000 /t—tb

Fig2:30. Kinetic energy (Boeing 777 taking off)

TOTAL ENERGY

ned, the mechanical energy of an object can be the result of
motion (kinatie energy] andor its stored energy of post

ion (potential energy) The

total amount of mechanical energy is simply the sum of the potential and Kine

As stated previously. mechanical offic

y requires the actual performance of a
machine to be as close as possible to the ideal performance of that mac
addition to frictional losses. many machines fil to convert some of the input energy

19 heat loss. An engine. for example, loses significant heat energy
> the various parts ofthe engine. Not only docs the combustion
be maximized. transfer of the energy released must occur with
task fora heat engine because the
engine. which Is turning due to heat energy from combustion is always cooler than
the heat of combustion and will eonstanty act as a heat sink. The most eff
engines operate at around 50% efficiency with the average e
35% efficiency.

through conduction

Cf the fue! need to

the least amount of heat loss. Ths is a sign

ing at 25

233.(B) MOMENTUM

Newton's third law. for every action there is an equal and opposite reaction’. is most
hen associated with the forces involved in jet engine

thrust. It also applies to

momentum and the action of objects that are interacting. There is always an equal
sste direction when one obje
were to colide first
‘opposing force on Object 1. And. the momentum of the objects will be affected by
the applied force because force affects acceleration (Force = Mass » Acceleration)and
Velocity). Thus. the force on
different in

upon another, So if Object 1

fer

second obj

accel
both objects will be equal but the!

ation affects momentum (Momentum = Mas

accelerations will be affect

CONSERVATION OF MOMENTUM

In the above paragraph even if Object 2is sta
toit Object 2 will begin to accelerate thus giving it momentum. Object 1 already had
momentum which is affected by its interaction with Object 2. In this and all other

lonary when Object 1 applies a force

similar cases. momentum is conserved. The momentum of each object changes bu

the total momentum of both objects remains the same

ject 2 will accelerate. and Object 1 will decelerate but the total momentum of
both objects remains the same. Thiss the momentum conservation principle

IMPULSE

ider

ch

Therefore. by substitution

Mass x Change in Velocity

Using symbols. this is F= M

By multiplying both sides ofthe equation by

Fx EM x AV, or,as stated above, by definition: Impulse = M x AV

By definition: Momentum = Mass + Velocity, Therefore It is logical to realize that

AN.

Mass x AVelocity = aMomentum

Thus. in a collision, for example. a force is applied for a certain amount of time and

the object will experienc lso experienced

causes a change in the momentum of y

considered. The total momentum of both obje

Gyroscopes and the gyroscopic effect play a large role in aviation - from the
propellers effects on the behaviour of the aircraft to the use of gyroscopes in
An understanding of basic gyroscopic principles given in this section

"Pob

=>
a a a a

Fig. 2.51. Gyroscopes.

A mechanical gyroscope. or gyto. Is comprised of a wheel or rotor with lts mass
around its
speeds (Fig2 314) Different mounting configurations are available for the rotor and

imeter. The rotor has bearings to enable itto spin at high

axle, which allow the rotor assembly to rotate about one or two axes per

ndicular
to lts axis of spin. To suspend the rotor for rotation. the axe is frst mounted in a
supporting ring (Fig2 316)

If brackots aro attached 90" around the supporting ring from where the spin axle
attached, the supporting ring and rotor can both move feely 360° When in this
configuration. the gyro ls said to be a captive gyro. It ca only one axis

dicular to the axis of spin, (ig2 FC)

The supportingring can also be mounted inside an outer ring. The bearing pol

the same as the bracket just described. 90° around the supporting ring from where

the spin axle attached. Attachment of a bracket to this outer ring allows the rotor

rotate in two planes while spinning. Both of these are perpendicular to the spin axis
Cf the rotor. The plane that the rotor spins in due to Rs rotation about its axle Is not
counted as a plane of rotation:

A gyroscope with this configuration. two rings plus the mounting bracket. Is said
gyro because itis free to rotate about two axes that are both perpendicular

bea fe
to the rotors spin axis (Fig2 SID) As a result. the supporting ring with spinning gyro
‘mounted inside is free to tum 360" inside the outer ring.

Uniess the rotor of a gyros spinning, It has no unusual properties itis simply a wheel
Universally mounted, When the rotor is rotated ata high
the gyro exhibits 8 couple of unique characteristics. The fist & called gyroscopic

speed and due to its inertia,

figidlty. or rigidity in space. This means that the rotor of a free gyro always points in

the same direction no matter which way the base of the gyros positioned. (Fig2-32)

Fig. 2-32. Once spinning. a free gyro rotor stays oriented in the same position in
space despite the position or location ofits base

Gyroscopic rigidity depends upon several design factors

1. Weight: For a given size. a heavy mass is more resistant to dist
alight mass
2. Angular velocity. The higher the rotational speed, the greater the igiity oF

5. Radius at which the weight is concentrated: Maximum effect is obtained from a

mass when its principal weight is concentrated near the rim, rotating at high

ss

4, Beating fiction: Any friction applies a deflecting force to 8 gyro minimizing
boating fiction keeps deflecting forces at a minimum,

This characteristic of gyros to remain rigid in space is exploited in the attitude
indicating instruments and the directional indicators that use gyros

Precession is a second important characteristic of gyroscopes By applying a force to

the horizontal axis of the gyro, a unique phenomenon occurs. The applied force is
resisted. Instead of responding to the force by moving horizor
yro moves in response about its vr Stated another way. an applied force
to the axis of the spinning gyro does not causo the axis to tit Rather. the gyro
responds as though the force was applied 90° around in the direction of rotation of
the gyro rotor. The ayro rotates rather than tits (Fig2-33)

jour 3 axis the

ictable cor
instrument. The rigidity in space and precession character
must always be considere:

red precession of a gyroscope ls utilized in a tum and bank

les of gyroscopic action
when objects of ary appreciable mass are rotating.

Fig. 2-38. When a force is applied to a spinning gyroscope. it reacts as though the
force came from 90° further around the rotor in the direction itis spinning. The
plane of the applied force, the plane of the rotation, and the plane in which the
9910 responds (known as the plane of precession), are all perpendicular to each

‘other.

In calculating work done, the actual resistance to be overcome is measured, Ths is

not necessarily the weight of the object being moved, (Fig2-34) A900 Ib loadis being
pullod a distance of 200 ft This does not mean that the

ork done (force » distance

is 180 000 ft-lbs (900 Ib + 200 ft. This is because the person pulling t
working against the total weight ofthe load, but rather against the rolling friction of

ne load is no
the cart. which may bo no more than 90 lbs.

Friction is an important aspect of work. Without fiction it would be impossible
walk. One would have to shove oneself from place to place, and would have to bumo
le to stop at a destination. Yet friction Is liability as well as an
and requires consideration

‘against some obs

hen dealing with any moving mechanism.

In experiments relating to friction, measurement of the applied forces reveals th:
there are three kinds of fiction. One force is required t
another required to keep the body moving at constant speed. Also. ater.

start a body moving. while

in motion. a definitely larger force is required to keep it sliding than to keep it rolling.

Thus. the three kinds of friction may be classified as

1 Starting
2. Sliding fiction. and
3. Rolling fi

STATIC FRICTION

When an attempt is made to slide a heavy object along a surface. the object must

fist be broken loose or started. Once in motion. it sides more easily. The "breaking
loose" force's, of course, proportional to the weight ofthe body. The force necessary
to start the body moving slowly ls designated ‘F This is the normal force pressing
the body against the surface (usually ts weight) Since the nature of the surfaces
rubbing against each other is important they must be considered, The nature of the
surfaces is indicated by the coefficient of s

letter "kz This coef

sting friction which s designated by the

nt can be established for various materials and is often

published in tabular form. Thu

when the load (weight of the object) is known,
starting fiction can be calculated by using the following formula

ba = Fore + Dein
onza

Foxe 800.

se uy

Y

Po

Fig. 2:34. The effect of fiction on work.

For example, ifthe coeficient of sling friction of a smooth ron bl
horizontal surface is 03 the force required to start a 1b block would b
Ib block 12 lbs

‚ck on a smooth

3 bs:a 40

Starting fiction for objects equipped with wheels and roller bearings is much smaller
than that for slding objects Nevertheless. a locomotive would have cifficulty getting
a long train of cars in motion all atone time, Therefore. the couples between the cars

to have a few inches of play. When starting the train, the
hed together Then, with a quick
fret car is et in motion This technique is employed to avercomy

engineer backs the engine until all the cars are pu

start forward the

the static fiction of each wheel (as well as the inertia of each car) It would b
impossible forthe engine tostartall ofthe cars at the same instant for static friction,
which is the resistance of being set in motion would be greater than the force
‘exerted by the engine. Once the cars are in motion however, static friction is greatly
reduced. and a smaller force Is required to keep the train in motion than was

required to startit
SLIDING FRICTION

Sliding friction is the resistance to motion offered by an object sliding over a surface
It pertains to fiction produced after the object has been set in motion and is always
less than starting friction. The amount of sliding resistance is dependent on the
nature of the surface of the object. the surface over which it slides. and the normal
force between the object and the surface. This resistive force may be computed by
sing the folowing formula

AN.

In the formula above.“F isthe resistive force due to fiction expressed in pounds: N
is the force exerted on or by the object perpendicular (normal) to the surface over
which it slides: and m° (mul is the coefficient of sliding fiction. On a horizontal
surface. Nis equal to the weight ofthe object in pounds. The area ofthe sliding object
‘exposed to the siding surface has no effect on the results. block of equally
wood, for

{does not enter into the equation above.

seured

‘ample, will not side on ary one side easier than another. Therefore. area

ROLLING FRICTION

Resistance to mation is greatly reduced if an obje
The force of frction for objects mounted on wheels or roller i called rolling friction

‘mounted on wheels or rollers.

This force may be computed by the same equation used in computing sliding
friction, but the values of my will be much smaller For example, the value of for

er tires on concrete or macadam is about 002, The value of “mn for roller

bosrings ls very small. usually ranging from 0.001 t0 0.003 and is often disregarded,

Example: An aircraft with a gross weight of 79 600 Ib towed aver aconcrete ramp.

What force must be exerted by the towing vehicle to keep the airplane rolling after
F = mW

COEFFICIENT OF FRICTION

Coeffcient of friction ls a value that shows the relationship between the force of

seen two objects and the normal reaction between the objects that are
involved. It is a value that is sometimes used in physics to find an objects normal
force or frictional force when other methods are unavallable

The coefficient can be two different things It is ether the coofficiant of static friction
the coefficient of kinetic fic

The coefficient of static fiction ithe friction force

0 objects when neitherofthe objects is moving, The coefficient of kinetic

friction isthe force between two objects when one object is moving orif both objects

are moving against one anothe!

The coefficient of fiction depends on the objects that are causin
is usually between O and 1 but can be greater than L A value of O means there is no

friction. The value

friction at all between the objects. This is only theoretically possible as all objects in
the real world will have some fiction when they touch each other. A value of! means

is equal to the normal force. À value more than one just means

that fiction is stronger than the normal force. An material such as rubber for
example, can have a coefficient great

an one. The coefficient of fiction can al
bbe changed by the mass and speed of the moving object

2.4. FLUID DYNAMICS

241. DENSITY

The density of a subs

use in the Imperial system of measurement is cubie foot
itis 1 eubie centimes

ance à its weight per unit volume. The unit volume selected for

(env!) Therefore. density s expressed in pounds per cul

Albi] or grams per cubic centimetre (gfem:

To fin the density of a substance, te weigh

* and vo
is then divided by its volume to find the weight per unit volume, For example, the

¡me must be known ts weight

liquid which fils a certain container weighs 1 4976 lb. The container & 4 # long. 3 f

ide. and 2 ft deep. Its volume is 24 (4 ft x 3ft x 2/1). 24 of liquid
4876 lb, then 1 weighs 14976 + 24 or 62.4 Ib, Therefore. the:
24 Ib/ ft. This is the density of water at 4 °C (Celsius) and is usually used as the
standard for comparing densities of other substances. In the metric system. the

fensity ofthe liquid is

ter is glem’. The standard temperature of. Cis used when measuring
of liquids and solids Changes in temperature will not change the weight
of a substance but will change the volume of the substance by expansion or

density of
the densi

contraction thus changing its weight per unit volume,

‘The procedure for finding density applies to all substances however. itis necessary
to consider the pressure when finding the density of gases. Pressure is more critical
han measuring the density of gases than i Is for other substances. The density of a
905 increases in direct proportion to the pressure exerted on it. Standard conditions
for the measurement of the densities of gases have been established at O °C for
temperature and a pressure of 760 mm of mercury (Hg) hiss the average pressure
of the atmosphere at sea level) Density ls computed based on these conditions for
all gases

2.4.2. SPECIFIC GRAVITY

It is often necessary to compare the density of one substance with that of another

For this purpose, a standard is needed. Water is the standard that physicists have

70

chosen to use when comparing the dersities of al liquids and solids For gases. ais
ndard for gases.
lo. Thus, specific gravity is calculated by

commonly used. However. hydrogen is sometimes used a:

comparing the weight of a definite volume of the given substance with the weight

of an equal volume of water. The terms “specific weight” or
-ometimes used to express this ratio

The following formulas are used to find the specific gravity of liquids and solids.

fie Gravity = Pen of the substance

Density of water

The same formulas are used to find the density of gases by substituting air or

hydrogen for water

Is not expressed in units but as puro numbers For example, if a
liquid

Specific gra

ions 08 times

certain hydraulic fluid has a specific gravity of 02.1 fe of
92 lb.

Specife gravity and density are independent of the size of the sample under
nd depend only upon the substance of which itis made. See Fig2-35
for typical values of specif gravity for various substances

consideration

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man ise) cod 1"

Mercury 136 Platinum 215

Fig, 2.35. Specific gravity of various substances.

A device called a hydrometer ls used fo

ring specific gravity of liquids. This
glass tube. (Fig 2-36) The
A rubber suction bulb draw
¡se the float and

device consists of a tubular glass float

the liquid up into the container. There must be enough liquid to

prevent it from touching the bottom. is weighted and has a vertically

graduated scale. To deter ale is read at the surface of th

ne specific gr
h the float is immersed. An indication of 000 is read when the foat is
immersed ina liquid of greater density. th

the float sinks.

liquid in

An example of the use ofthe termine the

ic gravity of th

loc aicrak battery. When a battery ls discharged, the

bo (battery liquid) in

calibrated float immersed in the electolyte will indicate approximately 1150.
indication of a charged battery is be

1510 actually represent 1.150, 1275, and 1310. The electrolyte in a dischar
is 115 times denser than water. and in a charged battery 1275 to 13 times denser

275 and 1310, The values | 150.1 275.

sed bol

I I

Fig.2:36.Hydrometer for checking battery specific gravity.

2.4.3, VISCOSITY

tant properties of any Auid is its viscosity. Viscosity is internal
resistance to flow. A liquid such as gasoline that has a low viscosity flow easily. wil

(One of the most impor

a liquid such as tar that has a high viscosity flows slow. ll fluids have viscosity. While

synamics. as air
the nature of th

‘easier to see in aliquid. gases. such as air. also have viscosity. In aer
the ai ao

flows over the surfaces of an aicraf. the viscosity
flow

Viscosity increases as temperature decreases, A satisfactory liquid for a given
hydraulic syst

valves. and pistons, but it must not be so thick that & offers res

Im for example, must have enough body to give a good seal at pumps.

ce 10 flow. leading

to power loss and higher operating temperatures. These factors add to the load and

viscosity that is too low alsoleadsto rapid
ts or of parts that have heawy loads.

Lo excessive wear of parts. Afluid
cof moving p:

Maintaining a functional viscosity throughout the operating temperature range is
also an issue in lubricating syst index isa numb

effect of temperature changes on the viscosity of lubricating oil À low viscosity index
¡fes a relatively large change of viscosity during temperature variations A high
Viscosity index indicates the fuid experiences small changes in viscosity as

ms. Aviscosi the

The instruments used to measure the viscosity of a liquid are known as viscometers
or viscosimoters. Several types of viscosimeters are in use today. The Saybalt
Viscometer measures the time required. in seconds for 60 millilitres of the tested
fluid at 100 °F to pass through a standard orifice. The time measured is used to
om sit. in Saybolt universal seconds or Saybolt furol seconds

Fig237)

ess the fluids vise

eating Unit Liquid Bath Thermometer

où

= Resenoir
=> ce.
Container :

Fig. 2-37. Saybolt viscosimeter

2.4.4. FLUID RESISTANCE

A fluid, by definition, is any substan
confined or restricted, Liquids and gases are both classifed as fluids an

8 that is able to flow if it not in some way

doen actin

a very similar way. One significant difference comes into play when a force Is applied

to these fluide, In this case. liquids tend to be incompressible. and gases are highly
compressible. Many of the principles that aviation is based on, such as the theory of
lift on a wing and the force generated by a hydraulic sys
‘quantified by using the la

om, can be explained and

of fluid mechanics

The foundations of modern hydraulics and pneumatics were established in 1653

when Pascal discovered that pressure set up in a fluid act equally in all directions.
This pressure acts at right angles to containing surfaces

I pressure in the fluid ls caused solely by the ffluid's height. the pressure

thew

lis ofthe container is equal at any given level but It is not equal if the

om is compared to the pressure halfway down. The concept of
the pressure set up in a fluid, and how trelates to the force acting on the fluid and

the surface area through which tacts Is Pascal law.

In Fig2 5 fa piston is placed at the top of
down on the piston, additional pressure will be created in the liquid Ifthe additional

he cylinder and an external force pushes

pressure is 100 psi. this 100 psi will act equally and undiminished from tho top of th
cylinder al the way tothe bottom. The gauge at the bottom will now read 108 34 psi

and if a gauge

re positioned halfway down the cylinder, it would read 10417 psi

(100 plus half of 834) Pascal: law. when dealing wi

th the variables of force. pressure.

and area. is dealt with by way of the following formula.
In this formula, the force is in units of pounds, the pressure Is in pounds per square

inch (psi) and the area is in square inches By transposing the original formula, w
have two additional formulas, as follo

Pressure = Force + Area

and

and com vay to remember
relationship between the variables. is with the tia
variable

Jas for Pascals lave, and the
le shown in Fig238, IF the

up. what remains is

for Is covered up. the

he remaining tu

variables shi

F on the top and

he“P on the bottom meaning force
vided by pressure

Fig. 2-88, Force, an

pressure relationship,

The simple hydraul

system in Fig2-39 has a S-lb force acting on a piston w
in sur

4 on Pascals aw, the
plied divided by the
pressure of 10 psi is present even

rea of the piston or 10 psi As shown in Fig2-39, the
ere in the fluid

om @

the force a

10 psi

©

Piston Area = Hin?

Pressure = Force + Area
Pressure = 5 + Y
Pressure = 10 pl

Fig. 2:30. Pressure created in a hydraulic system.

AN.

The hydraulic sys
Fig2-40,
si The iy

in Fig2-40 sa tie more complex than the one in Fig252. In

input force of 5 Ib is acting on a % in? piston, creating a pressure of 10

t cylinder and piston is inder wh
aSin* piston. The pressure of 10 by the input piston pushes
in the second cylinder, creating an output force of 50 pounds.

hcor

the piston

Force = 50 Ib

Piston Area
Sine

Force = Pressure x Area
Force =10 psi x 5 in?

10psi

10psi

Fig. 2-40. Output force created in a hydraulic system.

More often
force, wi
and the input force, as discussed earlier in this chapter. is known as mechanical

ite Filmen ota Hera qee I era lange tie

Fig2-40, the input forces Siband the

The relationship between the output fore

advantage

The mechanical advantage in Fig2-40 would be 50 divided by or 10, The follo
formulas can be used to calculate mechanical advantage

Mechanical Advantage = Force Out + Forcein

Mechanical Ad

Earlier in this char hines. such as levers and gears were

discussed. it was ider no machine allows us to gain work The same

tatement holds true for a hydraulic system. that wo get no more work out of a

a.

hydraulic system than we put in. Since work is equal to force times distance. if we
ain force with a hydreulic system, we must lose distance. We only get the same work
ut if the system is 100 percent efficient,

In order to think about the distance that the output piston will move in response to

nent ofthe input piston the volume of fluid displaced must be considered!
In the study of geometry. one leams that the volume of a cylinder is equal to the
cylinders surface area multiplied by its hoight.So when a piston of? in? moves down
ina cylinder a distance of 10 inches. it displaces a volume of fluid equal to 20 In! (2
in? «10 in}. The 20 in’ displaced by the frst piston is what moves over to the second
¿ylinder and causes its piston to move,

jo-piston hydraulie sys
and the distance moved is shown by the following formula.

Input Piston Area (Distance Moved) = Output Piston Area (Distance Moved)

In essence, this formula shows that the volume in is equal to the volume out. This

concept ls shown in Fig2.41 where a small input piston moves a distance of 20

piston only moves a distance of} inch.

inches. and the larger outpu

Example: A two piston hydraulic system. like that shown in Fig2-41. has an input
piston with an area of int and an output piston with an area of 15 in?

Distance Moved = 1 in

Input Piston Area = H in?

Piston Area (distance)
in? (20 in) = 5 in (distance)
5+5 = Distance
Distance = 1 in

4 and the input piston moves 30 inches What is th
db

= 50006

Mechanical Acta

AN.

Part of understanding Pascals law and hyttraulcs involves utilizing formulas and
recognizing the relationship between the individual variables. Before the numbers
are plugged into the formulas, it is often possible to analyze the variables in the

system and come to a realization about what is happening.

For example. look at the variables in Fig 2-41 and notice that the output piston is 20,
times larger than the input piston [5 in’ compared to 4 in), That comparison tells us

that the output force will be 20 times greater than the input force. and also that the

output piston will only move half as far. Without doing ary formula-based
calculations, we can conclude that the hydraulic system in question has a
dvantage of 20,

2.4.5. STREAMLINING

When a fluid encounters a particular obstacle to flow around, be it the wing of an
aircraft or @ curve in a hydraulic system line. a gradual curved surface enables the

possibility of smooth flow which is free from turbu
to speed up to negotiate the obstacle smo

velopment on the upper sur

lence. Fluid particles may be able

ly without tumbling. This smooth flow

is essential for low pre:

ce of à wing, Known as

streamlining, the gradual shaping of areas where fluids must flow reduces the
compression of gases and temperature of liquids in areas where turbulent flow may

‘otherwise result

MORESSIBILITY

In fluid dynamics, compressibility is a measure of how much the volume ofthe fluid
changes as a response of pressure changes. Generally, gases are considered to b
compressible. while liquids are incompressible,

The main diference between compressible and incompressible fluids is that a force

applied to a compressible fluid changes its density whereas a force applied to an

incompressible fluid does not change it to a meaningful degree. in normal
temperature and pressure conditions, the volume or the density of a gas does not
change. However. they can easily with even small changes in temp

directions causing the molecules ofthe gasto collide with greater frequency, The

80

collisions give more time for thegas molecules tointeract. and more atraction forces
ur between molecules. These attraction forces reduce the motion of gas

BERNOULLIS PRINCIPL
Bernoull's principle explains the action ofa liquid flowing through the varying cross
‘gradually decreases to a minimum diameter inits centre section. A tube constructed
in this manner is called a ‘venturi or"ventufi tube” Where the cross-sectional area is
decreasing. the passagenay is referred to as a converging duct As the passageway
starts to spread out. itis referred to as a diverging duct

‚bes. In Fig2-42 a tube is shawn in which the cross

As liquid (uid) flows through the ventun tube. the gauges at points “A: “Band °C

re ofthe liquid. The venturi
in Fig2-42 is used to illustrate Bernoulli's principle. which states that: The static
Pressure of a fluid liquid or gas) decreases at points where the velocity ofthe fluid
increases provided no energy is added to nor taken away from the fluid. The velocity
Cf the alr iskinetic energy. and the static pressure of the airs potential energy

are positioned to register the velocity and the static

In the wide section ofthe venturi (points A and ofFig2 42] the liquid moves at low
velocity, producing a high static pressure. as indicated by the pressure gauge. As the
tube narrows in the centre. lt must contain the same volume of fluid as the two end

pressure than that at points À and C, as indicated by the velocity gauge reading high

and the pressure gauge reading low.

In this narrow section, the liquid moves at a higher velocity, producing a om

A good application of Bemoulis principle is in a float: type carburettor. As the air
ws through the carburet
where the static pressure Is reduced, The fuel in the carburettor, which is under a
ro, flows into the lower pressure vonturl area and mixes with the a

1 on its way to the engine, It goes through a ventur

higher pre

Bernoull's principle is extremely Important in understanding how some of the

systems used in aviation work. including how the wing of an airplane generates lift

Cor why the Inlet duct of a turbine engine on a subsonic airplane is diverging in shape.
The

bottom surface. The curved top surface acts Ike half of
middle of a ventur As the al flows over the top of the wing, the air speeds up. and
its static pressure decreases. The static pressure on the bottom of the wing is now

Ing on a slow-moving airplane has a curved top surface and a relatively

he converging shaped

greater than the pressure on the top, and this pressure difference cre

the wing. Bemou
depth in Module 08 - Basic Aerodynamics.

principle and the concept of lift on a wing is covered in great

a

Velocity Pressure Velocity Pressure

Velocity Pressure

Fig. 2-42. Bernoulli's principle and a venturi

he total pressure ofthe airflow remains the san
nego
ses tomoveover the curved surf

ton of the curvature of a venturi or wi

«sure increases. Dynamic pressure ls associated with the kinetic energy in the

Expressed as an equation:

3.THERMODYNAMICS

‘Thermodynamics is the branch of physical science that deals with the relations
between heat and other forms of energy.

3.1. TEMPERATURE

Temperature is a dominant factor affecting the physical properties of fluids It is of
particular concern when calculating changes in the state of gases. The four
temperature scales used extensively are the Celsius the Fahrenheit. the absolute or
Kelvin. and the Rankine scales. The Celsius scale is constructed by using the freezing
and boiling points of water. under standard conditions, as fix

100. respectively, with 100 equal divisions between. The Fahrenheit
the freezing point of water and 212 as the boiling point. and has 180 equal divisions
between. The absolute or Kelvin scale is constructed with its zero point established
25 minus 275°C, meaning 275" below the freezing paint of w:
the other fixed points of the scales are shown in Fig3-1

10) a73__ |) 212) pure water Bots

o 2 E AAA
en fo 4% Po oecerhoton
Censos a Aosta
Zar
Cobos Kl Fatt Rankine

(centigrade)

Fig. 3-1. Comparison of temperature scales.

AN.

When working with temperatures. always make sure which system of measurement

s being used and knowhow to convert from one to another. The conversion formulas

Degrees Fahrenheit = 18 Degrees Celsiss)+

Degrees Celsius = Wogrees Fahrenheit -32)+ 58
Degrees Kelvin = Degrees Celsius
Degrees Rankine = Degrees Fahrenheit + 460

calculations the Rankine scale is commonly u

Fahrenheit to abso it readings above zero,
160" plus 72°. or 532° absolute. If the Fahrenheit reading is bel

actod from 460" Thus -40 °F equals 460" minus 40° or 420° absolu

be stressed that the Rankine scale does not indicate ab

olute temperature readings

in accordance with the Kelvin scale, but these conversions may be

calculations of changes in the stato of gases

The Kelvin and Celsius scales are SI scales used extensively in scientific work
Technical. manu

ls may use these scales in giving directions and operating

311. THERMAL EXPANSION/CONTRACTION

‘Thermal expansion takes place In solids, liquids, and gases when they are heated

Bocaus

en heated and contract when cooled:
ong

the molecules of solids are much closer together and are more

attracted to each other, the expansion of solids when heated is very sight in
comparison to the expansion in liquids and gases. Tho expansion of fluids ls
discussed in the study of Boyles law. Thermal expansion in solids must be explained
in some detail because of its close relationship to aircraft metals and materials

Because some substances expand more than others it is necessary to measure

ally the exact rate of expansion of each one. The amount that a u

length of any substance expands for a one degree rise in temperat

e is known as

the coefficient of linear expansion for that substance. The coefficient of linear

‘oxpansion for various materials is shown in Fig3 2

Era “Fee Cas
Aluminum 25x 10%
Brass or Bronze 19% 10%
Brick 9x10*
Copper 17x 10%
Glas Plate) 9x10*
Glass (Pyrex) 3x10
los 51x 10%
Iron or Stet 11x 10%
Lead 29% 10%
Quartz 04x10°
Siver 19% 10°

Fig. 322 Coefficient of expansion for various materials

To estimate the expansion of any obj as a steel rai. is necessary to know
three things about tits length the rise In temperature to which It issubjected. and
ts coefficient of expansion. This relationship Is expressed by the equation:

Expansion = (coefficient) x (length) x (rise intemp.

x sel ie =10-6

The coefficient

of expans
Expansion = (11 x 10 — 6) x (9 feet) x 34

int, when added to the original

od 9.003 566

length has only increased by 31000 of an inch,

The increase in the

math of the red is relatively small, but if the rod

here it could not expand freely there wo exer

designing airframes. powerplants or related equipment

AN.

31.2. HEAT ENERGY UNITS

‘The Si unit used to express quantities of heat energy is the joule. Two different non

Si units are used to express quantities of heat energy. They are the calorie and the

BTU. One calorie is equal tothe amount of heat required to change the temperature

of gram of water 1deg

e Celsius.

‘This term “calorie” (spelled with a lower-case c) is 11000 of the Calorie Ispelie with

a capital C) usedin the measurement ofthe heat eneray in foods One BTU is defined

3 the amount of heat required to change the temperature of Ib of water 1 degree

Fahrenheit (VF) The calorie and the gram are seldom use tion

in discussing avi

maintenance, The BTU. how

ever. Is commonly referred to in discussions of engine

thermal efficiencies and the heat content of aviation fue

A device known as the calorimeters used to measure quantities of heat energy. For

‘example, it may be used to determine the quantity of heat energy available in 1
pound of aviation gasoline. given weight of the fuel is burned in the calorimeter

and the heat energy & absorbed by alarge quantity of

water and the increase in its temperature, itis possible to compute the heat yield of

the fuel. A definite relationship exists be
relationship has been established and verified by many experiments which show

One BTUof heat energy « 778 fi

One pound of aviation gasoline contains 18 900 BTU of heat energy. Since each BTU
is capable of 778 ft Ib of work. Ib of aviation gasoline & capable of 14 704 200 feo

of work

3.2. THERMOMETERS

A themome The temperature of

à temperature measuring instrumé

humerous items must be known for an aircraft to be operated property, Engine
carburettor mixture, inlet air. ree alr. engine cylinder heads. heater ducts. and
exhaust gas tempera =
monitoring, Many ot

y

ro of turbine engines are all items requiring temper

peratures must also be known Different types of
nd present temperature information,

321. NON-ELECTRIC TEMPERATURE INDICATORS

The physical characteristics of most materials chang

temperature. The changes are consistent. such
ficient of expansion of different materials variesand

each material. Most everyone is familiar with the liquid mercury

eter. As the ten

passage that has:

that expansion The

sven exposed to changes in

traction of

expansion or

liquids. and gases. The:

feof the mercury
ted scale upon it to read the temperatur

ssoclated with

A bimetallic thermometer à very useful in aviation The temperature sensin
lement of a bimetalic thermometer is made of two dissimilar metals ti
together. Each metal expands and contracts at a different rate when temper
changes. One end of the bimetallic strip is fixed, the other end is colled. A pointer is
attached to the colled end which is set in the instrument hous
bimetallic sip is heated, the two metals expand. Since their expansion rates differ
and they are attached to each

expande faster than the other. M

bonded

ati called end tres to uncoll

dial face of the instrument. When the temperature drops the metals contract at
front rates which tends to tighten the coll and move the pointer in the oppos

rence at ended metas th
dada cocino e pasion,

Fig. 3-3 A bimetallic temperature gauge works because of the dissimilar

coefficients of expansion of two metals bonded together. When bent into a coil,

cooling or heating causes the dissimilar metal coll to tighten, or unwind, moving
the pointer across the temperature scale on the instrument dial face

ing bimetallic temperature gauges are often used in li
perature or outside air temperature (OAT). In this application. a

protrudes through the wind

cllecting Shield of the aircraft to be exposed to

ip in the instrument head is

the atmospheric ar. The coiled end of the bimetall st
inside the windshield where it can be read by the pilot. Figures 3-3 and 3-4)

A bourdon tube ls also used as a direct reading non. electric temperature gauge in

simple, light aircraft. By calibrating the dial face of a bourdon tube gauge with a

re. The basis for oper

consistent expansion of the vapor produced by a volatie liquid in an enclosed ares.
This van
such a volatie liquid and connecting it to a bourdon tu

indication of the rising and falling vapor pressure due 1

ressure changes directly with temperature. By filing a sensing bulb with

1 dial face in degrees Fahrenheit or Celsius. rather than psi, provi
placed in
capillary tube connects

ration of

a temperature reading. In this type of gauge. the sensing bulb is
needing to have temperature O. measured. A lo

ourdon tube in the instrument housing, The narrow diameter of the capillary
at the volatile liquid is lightweight and stays primarily in the sensor

nes measured this way.

32.2 ELECTRICAL TEMPERATURE INDICATION

nme: mper yy commen in aviation. The

jems can be found on many types of aircraft

The use of electricin suring
following measuring and indication sys
10 more suitably measured by one or another type of

Fig. 5-4, A bimetallic outside air temperature gauge and lts installation on alight
aircraft

Principle parts of the electrical resistance thermometer are the indicating

instrument, the temperature sensitive element (or bulb] and the connecting wir

and plug connectors, Electrical resistance thermometers are used widely in ma
measure carburettor air, oll, ree ar temperatures, and more. They

70°C t0150°C

types of airra
are used to measure low and medium temperatures in

changes. This is the pn etmometer operates.
Typically, the electrical resistance of a metal increases as the temperature rises

‘cle upon which a resistance

Various alloys have a high temperature-resistance cooffciont. meaning their

90

resistance varies significantly with temperature. This can make them suitable for use
in temperature

hich temperature needs to be messured, Its connected by wires to a resistance
measuring device inside the cockpit Indicator. The Instrument dial is calibrated In
degrees Fahrenheit or Celsius as desired rather than in ohms Asthe temperature to
ben
measuring indicator shows to what extent

sing devices The metal resistors subjected to the fluid or area in

measured changes. the resistance of the metal changes and the resistance

A typical electrical resistance thermometer looks like any other temperature gauge.
Indicators are available in dual form for use in multiengine aircraft. Most indicators
are self-compensating for changesin cockpit temperature. The heat-sensitive resistor
is manufactured so that it has a define resistance for each temperature value within

its working range. The temperature sensitive resistor element is a length or winding
made of a nickel/ manganese wire or other suitable alloy in an insulating material
‘The resistor is protected by a closed-end metal tube attached to a threaded plug
with a hexagonal head. (Fig3 5) The two ends of the winding are brazed, or welded,
to an electrical receptacle designed to receive the prongs of the connector plug

Fig. 55, An electric resistance thermometer sensing bulb,

The indicator contains a resistance measuring instrument. Sometimes it uses a
modified form of the Wheatstone bridge circuit. The Wheatstone-bridge meter
operates on the pri f balancing one unknown res

resistances. A simplified form of a Wheatstone bridge circuit is shown in Fig 6.

or against other known

a

ig
£
A

Fig. 3:6. Internal structure of an electric resistance thermometer indicator
features a bridge circuit. galvanometer, and variable resistor, whichis outside the
indicator in the form of the temperature sensor.

Three cqual values of resistance [Fig3-SA 8, and C) are connected into a diamond

shaped bridge circuit A resistor with an unknown value (Fig3-6D) is also part of the

Circuit. The unknown resistance represents the resistance of the temperature bulb of
the electrical resistance thermometer system. A galvanometer is
ireuit at points X and Y.

When the temperature the resista

of the bull to equal that of the other

resistances, no potential difference exists between points X and Y in the circuit
Therefore, no current flows in the galvanometer leg of the circuit Ifthe temperature
of the bulb changes. its resistance also changes. and the bridge becomes
unbelanced causing current to flow through the galvanometer In one direction or

the other, The galvanometer pointer is actually the temperature gauge pointer. As
moves against the dial face calibrated in degrees It indicates temperature. Many

indie

tors are provided with a zero- adjustment screw on the face of the instrument

‘This adjusts the zeroing spring tension of the pointer when the bridge is at the

balance point (the position at which the bridge circuit is balanced and no current
flows through the meter)

Another way of indicating temperature

thermometer is by using a ratiometer. The W 1e-bridge indicatoris subject to

errors from line voltage fluctuation. The ratiometer is more stable and can deliver
higher accuracy. As its name suggests. the ratiomet
thermometer measures a ratio of current flow

The resistance bulb sensing portion of the ratiometer electric resistance

Jed above. The circuit contains a
variable resistance and a fixed resistance to provide the indi
branches for current fl

thermometer is essentially the same as descr

y, Each has a coll mounted on either side of the pointer
assombly that is mounted within the magnetic field of a large permanent magnet,
Varying current flow through the: whieh
react with the larger magnetic field of the permanent magnet. This interaction
rotates the pointer against the dial face tha

Celsius. giving a temperature indication (Fig377

is causes different magnetic fields to form.

3 Is calibratod in degrees Fahrenheit or

‘The magnetic pole ends of the permanent magnet are closer at the top than they
€ magnetic fel lines of Aux bete
be more concentrated at the top. As the two coils produce t
stronger field interacts and pivots downward into the weaker. less concentrated part
of the permanent magnet field. while the weaker coll magnetic feld shifts upward
tow sd flux field of the large magnet. This provides a
balancing effect that changes but stays in balance asthe coll field strengths vary with
temperature and the resultant current flowing through the coll.

are at the bottom. This causes seen the pole

heir magnetic fields. the

ré the more conce

ji

Fig. 3:7.A ratiometer temperature measuring indicator has two coils. As the:
‘sensor bulb resistance varies with temperature different amounts of current
flow through the coils. This produces varying magnetic fields. These fields
interact with the magnetic field of a large permanent magnet. resulting in an
indication of temperature.

For example, ifthe resistance of the temperature bull is equal to the value of the

AN.

Fixed resistance (R}. equal values of current flow through the calls, The torques.

caused by the magnetic field each coll creates, are the same and cancel any

mover vertical
position. ithe bulb temperature increases. its resistance also increases, This causes
the current How through coil A circuit branch to increase. This creates a stronger
magnetic fold at coil A than at coll B. Consequently. the torque on coll A increases.

netic field. At the
same time. less current flows through the sensor bulb resistor and coll B.causing col
B to form a weaker magnetic field that is pulled upw
1 the permanent magnets magnetic field. The pointer stops rotating when the
fields reach a new balance point that is directly related to the resistance in the
sensing bulb The opposite ofthis action would take place if the temperature of the

ger magnetic field. The ind

‘and it is pulled downward into the weaker part of the large m:

heat-senstive bulb should decrease

Ratiometer temp

ature measuring systems are used to measure engine oll, outside

air. carburettor alt. and other temperatures In many types of altcraR. They are

especially in demand to measure temperature conditions

important. or large variations of supply voltages are encountered

A thermocouple is a circuit or connection of two unlike metals. The metals are
touching at two separate junctions. If one of the junctions Is heated to a higher
voltage is directly proportional to the temperature. So. by measuring the amount of
electromotive force temperature can be determined, A voltmeter is placed across

the other. an electromotive force Is produced in the circuit This

the colder of the two junctions of the thermocouple. It is calibrated in degrees

Fahrenheit or Celsius. as needed, The hotter the high temperature junction thot

he higher the

Fomotive force produced. and

junction) becomes, the greater the el

temperature indication on the meter. (Fig3-3

PR E
©"

Fig 3-8. Thermocouples combine two unlike metals that cause current flow
When heated

Thermocouples are used to measure high temperatures Two commen applications
are the measurement of cylinder head temperature (CHT) in reciprocating
and exhaust gas temperature (EGT) in turbine engines. Thermocouple leads are
made from a variety of metals. depending on the maximum temperature to which
they are exposed, Iron and constantan. or copper and const
CHT measurement Chromel an

ngines

stan, are common for

alumel are used for turbine ECT thermocouples

The amount of voltage produced by the dissimilar metals when heated is measured
in milivolts. Therefore, thermocouple leads are designed to provide a specifi

amount of resistance In the thermocouple circuit (usually very
length. or cross-sectional size cannot be altered without compensation fer the

change in

resistance that would result Each lead that makes a connection back
+ be made of the same metal as the part of the thermocouple

it is connected. For example, a copper wire is connected to the copper
€ hot junction and a constantan wire is connected to the constantan

portion of

The hot junction of a thermocouple var
‘Two commen types are

es in shape depending on its application
he gasket and the bayonet In the gasket type, two rings of
the dissimilar metals are pressed together to form a gasket that can be installed
under a spark plug or cylinder hold down nut. In the bayonet type. the metals come

togetherinsice a perforated protective sheath, Bayonet thermocouples fit into a hole
er wall in a cylinder head. On turbine engines. they are found mounted on the
turbine inlet or outlet case and extend through the case into the gas stream. Note
that for CHT indication, the cyinder chosen for the thermocouple installation is the
ne that runs the hottest under most operating conditions, The location of this
Gylinder varies with diferent engines. (Fi93-9)

os

o ate Toe Mere

gn Spa ru re

Fig. 5-9. cyinder head temperature thermocouple witha gasket type hot
Junction is made to be installed under the spark plug or acylinder hold down
nut ofthe hottest cylinder (A) A bayonet type thermocouple ls installed in a bore
inthe cylinder wall (8)

on of the thermocouple circultis inside the Instrument case. Since the

the diference in temperatur
between the hot and cold junctions it is necessary to co

jensate the indicator

‘anism for changes in cockpit temperature which affect the cold junction. This
isaccomplished by using a bimetallic spring connected to y
When the leads are disconnected from the ind
area around the instrument panel can be read

indicator mechanism,

Fig. 310. Typical thermocouple temperature indicators.

3.3. HEAT DEFINITION

Heat is a form of energy. is produced only

he conversion of one of the other
formsof energy. Heat may also be defined as the
any sub

ao as follows:

total kinetic energy ofthe molecules

ance. Some forms of energy which can be comuerted into heat energy

chanical Energy. This includes all methods of producing increased motion

of molecules such as fiction impact of bodies, or compres

ion of gases

gs converted to heat energy when an
electric current flows through any form of resistance suc

electric ight. or an electric blanket
Chemical Energy. Most forms of chemical reaction comert sto

‘energy into heat. Some examples are the explosive effects ofgunp

the burning of oil or woed, and the combining of oxygen and grease
ant Energy, Electromagne
inen they are absorbed by the bodies they strike such as x-ray,
infrared rays
Nuclear Energy Energy stored in the nucleus of atoms is released during the

jt rays. and

process of nuclear fission in a nuclear reactor or atomic explosion
The

un. All heat energy can be directly or indir

traced to the nuclear

‘occuring in the sun.

When a gas ls compressed, work Is done, and the gas becomes warm or hot
Conversely. when a gas under hig

pressure is allowed to expand, the expanding gas

rk was converted into energy in the form of heat:
cond case heat energy was expended, Since heat ls given off or absorbed
enh

there must be a relationship bet

eat energy and work. Also, when two surfaces

are rubbed together. the friction develops heat However. work was required to cause
the heat. and by experimentation. it has been shown that the work required, and the
‘amount of heat produced by ft al. Thus, heat can be regarded se

2 form of energy

According to this theory of he

as a form of energy, the molecules. atoms. and
rons in all bodies are in a continual state of mot

In a hot body, these small
particles possess relatively large amounts of kinetic ©

oy. but in cooler bodies they
have less. Because the small particles are given motion. and hence kinetic energy
work must be done to slide one body

ver the other. Mechanical energy apparentiy
is trensformed. and what we know as heat is really kinetic energy of the small
molecular subdivisions of matter.

3.4. SPECIFIC HEAT

f heat to produce the same temperature change in ag

nass of thi

substance Each substance requies a quantity of heat. called ks specific heat
capacity to increase the temperature of a unit ofits mass 1'C. The specific heat of a

bstance ls the ratio of its specific heat capacity to the specific heat capacity of

rater Specific heat is expressed as a number which. because itis.

and applies to both the Imperial and the S/metric systems

It is fortunate that water has a high specific heat capacity The larger bodies of water

th koop the air a

solid matter on or near the surface of the earth at a
fairly constant temperature, A great quantity of heat is required to change the

emperature ofa large lake or river. Therefore, when the temperature falls below that

f such bodies of water they give of large quantities of heat. This eps th

face of the earth from changing rapidly, The
specific heat values of some common materials are listed in Fig3 11

Matera Specie Heat

teat 001
Mercury 0033
Brass am
Copper 0.005,
Iron o Stoo! ons
Gas 0.195
Aland oser
Alıminum ore
water 1000

Fig 3-1 Specific heat value for various substances.

Spe

nee is considered in a constant volume or a con

nding the volume so that pressure can remain the same. The t

1st often experience referenc

3.5. HEAT TRANSFER

4 from one location to anothe
ods are conduction. convection.

There are three methods by which heat is transfe

y from one substance to another. These three me

and radi

351. CONDUCTION

Heat transfer always takes place by areas of high heat energy migrating to areas of

low he by conduction requires that there be physical contac:
between an object that has a large amount of heat energy and one that has a smaller
amount of heat energy,

Everyone knows from experience that the metal handle ed pan can burn

the hand. A plastic or wood handle, however, remains rel
isin direct the pan. The metal transmits the heat more casí

wood because it is a better conductor of heat Different materials conduct heat at
different rates. Some metals are much better c ys of heat than others
jpper are used in pots and pans be
rapidly. Woods end plastics are used for handles beca

Aluminium ar

8 they conduct h

eat very

Fig3 12 Illustrates the diferent rates of conduction of various metals. Of those listed
silver isthe best conductor and lead isthe pe
and aluminium are used in pots and pans be:
interesting to note that silver, copper. and aluminium are a
of electricity.

rest As previously mentioned cop

use they are good conductor. lt is

110

100

si
ñ
i
ai
»
° |
i

Fig, 312. Heat conductivity of various metals.

Liquids are poorer conductors of heat than metals. Not

shown in Fig3113 is not melting rapidly even though the water at the top is boiling.

100

AN.

The water conducts heat so pootly that not enough heat reaches the ice to mel

steam
ng \
Water
\
ke à
N
Meal ing to Keep
Ice From ising

Fig. 3-18. Water asa poor conductor.

conductors of heat than liquids. Its possible to stand quite
Inducter. Since

al without being burn
conduction isa process whereby the inc
actual contact gases with molecules spaced further apar

rease in molecular energy is passed along

the point of applicat
agitated. These m
agitated
throughout the substance. Because molecules are farther
solids the gases are much poorer conductors of hea!

of the heat source, the molecules become violently

ecules strike adjacent molecules causing them to becom

nis process continues until the heat energy ls distrib
R in gast

Materials that are poor conductors are used to prevent the transfer of heat and are
& A wooden handle on a pot ora soldering iron serves as a heat

insulator Certain materials, suc

e as finely spun glass or asbestos are particularly poor

heat conductors, These materials are therefore used for many types of insulation

352. CONVECTION

hestistransferre nent ofa heated fl
25 oF quid), For example an incandescent light bulb will when heated. becom

Convection isthe process yw y mos

increasingly hotter untl the air surrounding It begins to move. The motion of the air

is upward. This upward motion of the heated air cartes the heat away from the hot
light bulb by convection Transfer of heat by convection may be hastened by using a
ventilating fan to move the alr surrounding a hot object. The rate of cooling of a hot
electronics component. such as the CPU in a computer. can be increased If It is
ided with copper fins that conduct heat away from the hot surface. The fins
provide large surfaces against which cool air can be blown

Ac

section process may take place in aliquid as well asin a gas. A good example
Of ths ls à pan of water sitting on the stove. The bottom of the pan becomes hot
because it conducts heat from the surface it i in contact with. The water on the
bottom of the pan also heats up because of conduction. As the heated water starts
to rise and cooler water moves in to take its place, the convection

recess begins.

When the circulation of gas or liquid is not rapid enough to remove sufficient heat
fans or pumps are used to accelerate the motion of the cooling material. In some
installations, pumps are used to circulate water or oll to help cool large equipment
In airborne installations electri fans and blowers are used to aid convection.

An aircraft air-cooled piston engine Is a good example of convection being used to
transfer heat. The engine shown in Fig3-14 Is à Continental 10-520. with six heavily
finned air-cooled cylinders. This engine does not depend on natural convection for
cooling. but rather forced air convection coming from the propeller on the engine.
The heat generated inside the engine finds its way to the cylinder cooling fins by
conduction. meaning transfer within the metal ofthe cylinder. Once the heat gets to

the fins. forced air flowing around the cylinders caries the heat away

Fig. 314, Alrcraft piston engine cooled by convection.

AN.

353. RADIATION

Conduction and convection cannot wholly account for some of the phenomena

‘associated with heat transfer

For example, the heat one feels when sitting in front of an open fire cannot be
transferred by convection because the air currents are moving toward the fre It

cannot be transferred through conduction because the cond

cthity ofthe aris very

small and the cooler currents of air moving toward the fire would more than

‘overcome the transfer of heat outward, Therefore, there must be some way for heat

to travel across space other than by conduction and convection.

The existence of another process of heat transfer is sil more evident when the he
from the sun is considered. Since conduction and convection take place only

through some medium. such as a gas ora liquid heat from the sun must reach the

‘earth by another method. since space is an almost perfect vacuum. Radiation is the

ne given to this thd method of heat transfer

The

er “radiation” refers to the continual emission of energy from the surface ofall
bodies, This energy Is known as radiant energy

Is in the form of electromagnetic

waves, radio waves, or x-rays, which are all alike except fora difference in h

These waves travel at the velocity of light and are transmitted through a vacuum
more easily than through air because air absorbs some of ther. Most forms of energy
can be traced back to the energy of sunlight. Sunlightis a form of radiant heat energy

that travels through space to reach tho earth. These olectromagnetic heat waves ar

absorbed when they come in contact with nontransparent bodies, The result is that
the motion of the molecules in the body is increased as indicated by an increase in
the temperature of the body.

The differences between conduction, convection, and radiation may now be
considered, First. although conduction and convection are extremely slow. radiation
takes placo at the speed of light. This fact is evident atthe time of an eclipse of the
of the light. Second, radiant heat may pass

ing off ofthe heat from the sun takes place at the same tl

without heating it For example. the glass through which the sun's rays pass. Third
A may travel in roundabout routes,

in a straight line. For example. radiation can be cut off

although heat transfer by conduction orconwect
radiant heat always tra

laced between the source of heat and the body to be protected,

105

3.6. THERMODYNAMIC LAWS

‘The principle of conservation of energy can be sta

destroyed. Alternately. this can be thought of as the total energy in an
The first law of thermodynamics isan application
a created or destrayed. I states

.d as: energy can be neither

Isolated system remains const

of the fa

energy cannot whee

nge in

intemal energy of a system is equal e work
done. In other words, there isa finite amount of he

If increases. itis be dd from outside the system. If it appears

e heat added to the system minus y

(energy) in any closed system,

hen the temperature decreases, that energy is accounted for by

is done by the system.

361. FIRST LAW

The first law of thermodynamics essentially eliminates the possibilty of a per

n machine. Any machine that produces work does so through conversion of
of which is finite either within the system or it is added from

tside the system However. the concent conveyed concerning the ability to transfer

energy Is invaluable in physics. Application of energy where and wi

on it is needed
makes aviation posable,

362. SECOND LAW

The second lawof thermadynamics states: heat always flows from hot objects to cold
objet
and included all types of energy. There is a tendency towards an equilibrium of

hat is from high energy toward low energy. Actually, this law is universal

‘energy throughout the universe. Related isthe tendency toward high entropy, whieh
is basicaly randomness or high disorder.

‘The second law of thermodynamics guides the technician when understanding
‘due to heat and friction. Much of the inefficiency of an engine is
Jue to heat energy behaviour as stated by the second law. Note that while this

movement of energy is continuous and relentless. some measures can be taken to
keep it under control and favourable, In other casos, the transfer of heat is

manipulated to take advantage ofthis phenomenon,

3.7. GAS LAWS

The simple structure ble to mathematical

of gases makes them readily adapte
analysis from which has evolved a detailed theory of the behaviour of gases. This

called the kinetic theory of gases. The theory assumes that a body of gas is composed

identical molecules which behave like minute elastic spheres spaced relatively far

The degree of molecular motion is dependent upon the temperature of the gas.

Since the molecules are continuously striking against each oth

and against the

-ontginer, an increase in temperature with the resulting increase in
molecular motion causes a corresponding increase in the number of collisions
between the molecules. The increased number of collisions results in an increase in
pressure because a greater number of molecules strike against the walls of the
Container ina given unit of time.

I the container were an open vessel the gas would expand and overflow from the
container. However. if the container is sealed and possesses elasticity (such as a

and. For instance.
when making a long drive on a not day. the pressure in the tires of an automobile

er balloon) the increased pressure causes the container to

1d a tre whien appeated to be somewhat “soft” in cool morning

5 these have been explained and set forth in the form of laws pertaining to gates
and tend to support the kineti theory

jear normal at a higher midday temperature. Such phenomena

371. BOYLES LAW

As previously stated, compresibilty is an outstanding characteristic of gases The

English scientist Robert Boyle, was among the frst to study this characteristic that
od that when

fect measurement he discover

he called the "springiness of ar” By di

the temperature of a combined sample of gas was kept constant and the absol
pressure doubled. the volume was reduced to half the former value. As the applied
absolute pressure was decreased, the resulting volume increased. From these

bservetions. he that for a constant tem

ture the product of the
are of an enclosed gas remains constant (Fig 3-5

Boyle’ law is normally stated. The vo

o of an enclosed dry gas varios inversely with

its absolute pressure, provided the temperature remains constant The following
formula is used for Boyle's law calculations. Remember. pressure needs to be in the
absolute.

105

Force Pushing Down on Gas

o”...

Iran, oss Constant

Fig. 315. Boyle's law example,

AP = v2r2

pen is unde
y pressure be!

500 psi. IF the volume is redu

= mzopsia

The useful applications of Bo

and life vests (2) the
the compressed air

o used to inflate

M the carbon dioxide (COS) b

compressed ong ¡ding

brakes and shock absorbers: and (4) the use tanks

jh altitude fying

37.2. CHARLES LAW

The French scientist, Jacques Charles. provided much of the foundation for th

modern kinetic th He f

dand indirect

to the change in the absoluto temperature. provided the pressure is held

Asa formula this law is

o
112 = veri
(Charles law also works ifthe volume is held constant, and pressure and tempera

ase. the formula would be as follows

For this second formula, pr

Example: 15 7 cylinder of oxygen is ata temperature of 70 F anda pressure of 750

The cylinder is placed in the sun and the temperature of the oxygen increases

to 40 'F What would be the new pressure in psig

= 600 degrees Rankine

7647 (600) + 530

37.3. GENERAL GAS LAW

By combining Boyle’ and Charles ingle expression can be derived wh

ja which

states all the information contained in both. The f used 10 exp

When using the general gas law formula, temperature and pressure must be in the

Example: 20 ft of the gas argon Is compressed to 15 1
temperature of 60 °F and a pressure of 1 000 psig. After being compressed. its

F. What would its

new pressure be in sig?

s Fahrenheit 550 degrees Rankine

37.4. DALTONS LAW

If a mixture of

or more gases that do not combine chemically is plac
hroughout the total space and

lle its partial pressure. This reduc

ixed 9

discoverod by Dalton, an English physicist and is

of each gas is reduced to a lower valu

he pressure ofthe isequal to the sum of

the partial pressures Thi

set forth in Daltons lave “A mixture of several gases which do not react chemically

exert separately if each were allowed to occ

375. IDEAL GAS LAW

The ideal gas aw is used to describe the state ofa gas under a given set of conditions

such as temperature. pressure, and volume, Scientists and designers use this for a

thorough analysis of the behaviour of g hat gases are ideal
that is that the molecules are perfecty uniform and simply coli
but do not iat sides all of the

th other. Theret

he temperature. This dk

The law es

nergy to be the kinetic er

re. any change in energy within the

system also cha es not or is not actually the case when

377.6. WORK AND EXPANDING GASES

Work can be done by expanding gas In fact, this is how energy in fuel is extracted in
air and burned. The

expanding gas
forcing thom downwa

4 from combustion in a reciprocating
cd This

The rotating crankshaft tums the propeller In a turbin

ngine act u

otates the crankshaft throug

ing

ingine. the expanding gases

from combustion are directed through the turbine wheels T

nis rotates the engine

reduce thrust in the

«e remaining gas pressure expelled rearward

forward direction

In an adiabatic. or
volume that

lated system. when work is performed by expanding gases. the
jy increases but ng decrease in
no energy a adiab

he gases © there is a correspor

ded to the system since
ld be calculated using the
mpressed instead of expanded
Jolume would increase the pressure of

the values of pressure. temperature and vol
5 formula shown above. Ifthe gases.

the gas and increas

nal system is one in which temperature remains the same. When

regarding expanding gases in such a system, the pressure and volume must vary

inversely to each other. As volume increases (expansion of the gas) the pressure of
hold that if 4

sein an isothermal system

€ volume of the

the gas must decrease. Again. the opposite would

gases decreases the pressure ofthe gases i

3.8, ENGINE CYCLES

AN.

3.81. CONSTANT VOLUME

me

cle through which a reciprocating engine operates ls knovm as the Otto eye

rant volume of fuel air mixture being

onstant volume cycle owing to a co

burned du
Fig36

3 each cycle (2 revolutions of the crankshaft). Consider the diagram in

Vevoume
p= Prose

‘constant Volume recess

4 / pattem

Power Soke

Gumbusten Process

eat ejection
=

Fig3.16. Constant volume engine cycle of a reciprocating internal combustion
engine

This isthe beginning of the intake stroke of the
€ volume and the pressure are at a minimum near atmospheric

yele begins at the point labelle
cycle. Bot
prossuro, Between points | and 2, the piston is dr

n cut of tho cyiindor and th

suction caused by drawing

the pistonout ofthe cylinder pulls the fuel-air mis

nto it The compression stro

begins at point 2. The piston rises up in the cylinder reducing the volume but
increasing the pressure of the gas charge significantly. At point 3 on the graph, the
intake valve and the exhaust valve are closed À constant volume ofgasis held in the

combustion chamber as a spark from the spark plug lg

nites the mature

For the short duration that the fuel-air charge is
the piston passes.

Jurned. the volume remains

energy released by buming the fuel causes a sharp increase in
ints 3 to 4) The

when

p dead centre in the cylinder and the power stroke begins at
point 4. Between points 4 and S, the pressure from the burned fuel-air mix

pushes the piston down transferring mechanical energy to the rotating crankshaft in

point 5, the exhaust valve opens. Quickly the pressure is reduced to

‘atmospheric between points 5 and 6 Residual heat Is given off and during the

‘exhaust stroke between points 6 and 1. the piston moves back Into the cylinder

Pushing all of the exhaust gas out thus returning the volume (and pressure) in the
cle again,

the process At

engine to their minimum values to begin the:

Notice that there is an area on the graph created by graphing the cycle. This
represents the work done by the engine. For the purposes of this discussion. no
accommodations have been made for the inefficiencies inherited in engine

‘operation due to heat loss and fiction. The actual work done by the engine would
ver included.

appear on the graph as a smaller area if these loss

3.8.2. CONSTANT PRESSURE

A constant pressure engine cycle occurs in a turbine engine The Brayton cycles th
name given to the thermodynamic cycle of a gas turbine engine to produc
This is a variable volume constant-pressure cycle of events and is commonly called

thrust

the constant pressure cycle. A more recent term is “continuous combustion cycle

The four continuous and constant events are intake, compression. expansion

neludes power] and exhaust. These cycles are discussed as they apply to a gas

ambient pr
the intake at an increased pressure and a decrease in volume, At the compressor
om the intake slightly above
ambient. and a slight decrease in volume. Air enters the compressor where it is

Jure and a constant volume. it leaves

In the intake cycle air enter

t an increased pressus

section, air is received

in volume. creates by the mechanical action of the compressor. The next step.
expansion, takes place in the combustion chamber by buming fuel. which expands
the air by heating it

ut a marked incr

The pressure remains relatively constant b se in volume takes

place The expanding gases move reanvard through the turbine assembly and ar

converted from velocity energy to mechanical energy by the turbine. The exhaust

section, which ls convergent duct, corwerts the expanding volume and decreasing

pressure of the gases to a final high velocity. The force created inside the engine &
al and opposite re

keep this cycle continuous has an ‘on (thrust) to move the

aircraft forward,

A,

383. THERMAL EFFICIENCY
Any study of engines and power involves consideration of heat as the source of
Power. The heat produced by the buming of gasoline in the eylindk
‘expansion ofthe gases inthe cylinder. and this in tum. moves the pistons and creates
mechanical energy. It has long been known that mechanical work can be converted
into heat and that a given amount of heat contains the energy equivalent of a certain

rs causes à rapid

amount of mechanical work Heat and work are theoretically interchangeable and

bear a fixed relation to each other. Heat can therefore be measured in work units (or
‘example, Rib) as well as in heat units, The British thermal unit (BTU) of heat is the
quantity of heat required to raise the temperature of 1 pal Vis

ical work À pound of petroleum fuel. when burned

4 of water

equivalent to 778 f-Ibof mecha
with enough air to consume it completely (heat of combustion). gives up about 20
(000 BTU, the equivalent of 15 560 000 feb of mechanical work. These quantities
‘express the heat energy of the fue in heat and work units respectively

The ratio of useful work done by an engine to the heat energy of the fuel It uses.
‘expressed in work or heat units is called the thermal efficiency of the engine. If two
, the engine that converts into work the

similar engines use equal amounts of fu

greater part ofthe energy in the fuel (higher thermal efficiency) delivers the greater
amount of power. Furthermore, the engine that has the higher thermal efficiency has
loss waste heat to dispose of to the valves, cylinders, pistons and cooling system of
the engine. high thermal efficiency also means low specific fuel consumption and

nce at for. Thus. the practical

therefore. les fuel for a flight of a given dis

importance of a high thermal officioney is throofold, and it constitutes ono of tho

most desirable features in the performance of an aircraft engine.

Cf the total heat produced. 25 to 30 percent is utilized for power output 15 to 20

percent is lost in cooling (heat radiated from eylinder tis
lost In overcoming fiction of moving parts; and 40 to 45 percent is est through the
‘exhaust Anything that increases the heat content going into mechanical work on

fiction and pumping losses, or which reduces the

ad fins] 5 1010 p

the piston. which reduces th
‘quantity of unburned fuel or the hea
efficiency

lost to the engine parts increases the thermal

The portion of the total heat of combustion that ls turned into mechanical work
depends to a great extent upon the compression ratio. The compression rato is the
ratio of the piston displacement plus combustion chamber space to the combustion
chamber space, as mentioned earlier. Other things being equal. the higher the
‘compression ratio is. the larger isthe proportion of the heat energy of combustion
turned into useful work at the crankshaft. On the other hand, increasing th

compression ratio increases the cylinder head temperature. This is a limiting factor

because the extremely high temperature created by high compression ratios causes
the material in the cylinder to deteriorate rapidly and the fuel todetonate instead of
burning at a controlled rate

The thermal efficiency of an engine may be based on either BHP or indicated

horsepower (HP) and is represented by the formula

The formula for brake thermal efficiency is the same

value for bhp is inserted instead of the value for HP.

Example: An engine delivers 85 BHP for a period of hour and during that time
onsumes 50 pounds of fuel Assuming the fuel has a heat content of 8 800 BTU per

Pound, find the thermal eficiency ofthe engine:

Brake thermal efficiency = 02501 23 percent

Reciprocating engines are only about 34 percent thermally efficient that Is. they

mechanical energy

3.9. REFRIGERATION AND HEAT PUMPS

Previously, the second law of thermal dynamics: energy always flows

Id Since this is the
must be used in order

0 low energy or. from hot to se. means

of energy tx

‘cabin of an alreraft on a hot day.
thi

Since the elevated ambient temperature outside the alreraft is what

‘The replacement air comes from ambient alr which is known to be too hat

business and general av
y. Fig 17

ing is used on older transport category aireraf and on many

jon aircraft This is the same type of air conditioning in your

1 oF refrigera

menus | SOE

onsocan ON

ttit

ory
Pte

Um ese per

ih Tempura
i Prose ape

Fig. 5-17.Invaporcycle air conditioning, heat is carried from the cabin to the
‘outside air by a refrigerant which changes from a liquid to a vapor and back

again

from the cabin air into à liquid refigerant. Due to the additional energy. the liquid

changes into a vapor. The vapor is compressed and becomes very hot It is removed

from the cabin where the very hot vapor refrigerant transfers its heat energy to the
cooler outside ar. In doing so. the refrigerant cools and condenses back Into a liquid.

The refrigerant returns to the cabin to repeat the cycle of energy transfer

391. LATENT HEAT

(One of the keys to the operation of an air conditioning system is latent heat. Adding
heat to a substance does not always raise lts temperature. When a su
changes state. such as when a liquid changes into a vapor. heat energy is absorbed.

This heat enorgy absorbed to chango stato is called latent heat. When a vapor

condenses into a liquid, this latent heat energy is given off

The temperature of a substance remains constant

ing its chango of st
energy absorbed or given off the latent heat. is used for the change of state process
After the change of state is complete, heat added to a substance raises the
temperature of the substance

When a liquid changes state and becomes a vapor. the process is known as
evaporation. The heat energy absorbed to change from liquid to a gas is known as
thats, changing froma

25 to a liquid. the heat energy given offs sometimes known as the latent heat of

the latent he Ifa substance is condens!

fvaporiat

fusion. Substances have characteristic amounts of energy required to change state.

They also change state at diferent temperatures. The boiling point of substance is

the temperature at which the substance changes state from a liquid to a vapor. The
boiling point changes with the amount of pressure applied to the substance.
Roigerants used in air conditioning systems typical boll at vey low temperatures.

Another device that moves heat e

y a heat pump. A heat pump isa device that

moves heat energy from one location to another. It is typically used for moderate
temperature adjustments. Like a vapor cycle alr conditioner. the second law of

thermal dynamics is used to advantage. A circulating refrigerant absorbs heat from

a warm area and moves # to a cooler area where it is released Usually. a heat pump
Isreversibie o that heat can be
area becomes hot and the normal area to be cooled requires to be heated,

ed from the ares that was heat sink when that

3.10. THERMAL ENERGY

All matter not existing at ab
f

locules ofa substa

alone

25°C.

3.11, HEAT OF COMBUSTION

ical value that
fuel Heat of
per pound

foreach partícula

1093 joules per kilogram:

4.OPTICS

4.1. THE NATURE OF LIGHT

Light is a form of electromagnetic radiation It is part of the wide spectrum of
radiation that surrounds us at all times. Visible light is a relatively
small part ofthe spectrum (Fig 4"

>

Fig. 4:1, Radio waves are just some of the electromagnetic waves found in space.

411. SPEED OF LIGHT

Light Is a type of wave. As in the case of al wave motion. the wave moves with a
definite speed. The speed of light (cs exactly 299 792 458 meters per second which
is 186 282 4 miles per second. It should be noted that this is the speed of ight in a
vacuum, The passage of light through matter reduces this speed, Materials have a
refractive index In} which isthe speed of light (c) in a vacuum dlvided by the speed
Cf light through the material (y. The refractive index of ar s 1000 29, The refractive
index of water Is 135 and approximately 16 for glass. This means that light travels
ver through water than air and slower throug}

lass than water

The wavelength ofvisbie ight is usually measured in,
IA =10-10m Various colors of visible ight have chara

all the Angstrom (A)
critic wavelengths. They also
have characteristic frequencies since the frequency of light « wavolength = speed of
light. With symbols this is written £2 = ¢ FI lists various colors of light and their
respective wavelengths.

4,2. REFLECTION

Reflection is a change in direction of alight w

strikes a different media

ion is called sp

s a material that suppresses the propaga

à of the light wave o

ws the passage of light such as water or glass. Specular
reflection is shown in Fig4-2.

N D

Fig4-2. Specular reflection

the normal. The light striking the mirror forms an angle of incidence (i)

jected from the mirror also forms a
called the angle of reflection (Ar) It is a law of
is equal to the angle of refection

¡thor laws of reflection are; the incidenc

‘ay, the reflective ray and the normal at the point of incidence lie in the same plane.

and the reflected ray and the incidence ray are on opposite sides ofthe normal.
Reflection can occur off of a plane surface such as 2 typical fat mirror or piece of
glass It can also cecur off of a curved surface. When reflection occurs of of af

surface, is sald to form a mirror image. When occurring off of a curved surface the

image may be magnified or demagnified

Most curved mirrors are spherical. They can be convex (bulging outward toward the
light source) or concave (bulging inward away from the light source} À conwex mirror
reflects light outw
view. Corwex mirrors are commonly used as passenger sido rearview mirrors on
automobiles. A concave mirror focuses light when it reflects. The image it reflect
depends on the distance away from the surface. Generally. a concave mirror is used

fard and demagnifies the image. I also provides a wider field of

0 that it magnifies the image. It can be found in telescopes and in make-up mirtors

to gain a close look at one’s face. Fig 43)

+—
Er E
$

Fig. 4-3.Refection pattems of ight on a concave and convex mirrored surface.

120

43. REFRACTION

Retraction is the phenomenon observed when light changes direction due
passing through a medium in which it travels at an altered speed. When light enters
a slower medium at an angle. its frequency remains the same. This is established at
the source ofthe light But as soon as part ofthe Incoming light ray reaches a slow

ed and the light bends towards the normal line.

The amount of bend depends of the speed af light through the medium The slower

have a refractive index which compares the

As previously mentioned, mater

speed of light through a vacuum to the speed of light through the material
higher the refractive index, the slower the speed of light through the material

Using information about how light will pass through a n
production of optic lenses. Snell's Law provides a mathematical equation fo

determining the angle that light will reftact when passing from one medium

In this equations ny I the index of refraction of
f refraction of the second medium through with the light will pass and bend. The

angles are measured from the normal

4.4, LENSES

Because light can be directed at diferent angles using various mediums, lenses are
leveloped to focus light so that itis beneficial, Eye glasses aro mado so that the
incoming light will be corrected so that lt Focuses the Image of the object being

A lens can be defined as any device that transmits and refrac

lonses are constructed to focus electromagnetic

es that are not visible light such
as microwaves A lens can be simple, causing a single ref
compound

sisting of more than one simple lens. Compound lenses are used to

refine the focus and eliminate aberrations. An aberration in optics is the failure of

ays to converge at a single focus point because ofthe limitations or defects in the

in to the direction and focus of light passing through it. (Figa 4).

Sieve Pcs Me Pci Berea

Fig 4-4 A sample of different shaped lenses.

st

from the lens is convex. a lens that curves into the lens is conca

lenses (non spherical.

AN.

4,5. FIBER OPTICS

Fiber opties is h of optical technology concerned with the transmission of

light through fibers, Electrical data is converted to optical signals and sent through
‘optical fers at the speed of light. The transmission of data through optical fibers
offers wide bandwidth. ight weight. and freedom from elactromagnetic influence.
ige

Fig. 45, Fiber optic cable bundle.

451. CABLE CONSTRUCTION

A fbe

surrounded by a glass Jackot layer

ptical p

contribute 0
o prevent light that leaks out of one fiber from entering

material
another. (Fig 6)

iyi the fiber

but optical loss increases gr

ery fle

Fiber cable can bo
toa radius smaller than around
ound around a spool. Some fiber optic cable
‘and also to protect the cable

against rodents and

a h glass

increase strengt

Strength
Member

Cladding

/

Outer

Jacket /

Coating cons

Fig. 4-6. Construction of a fiber optic cable.

452. FIBER MODES

Single-mode (or mono-mede) fiber has a core diameter less than about ten times
the wavelength of the pror ight an ly a single signal at a
time. Most single-mode fiber is designed for of the
light spectrum,

Fi
In multi-mode fi

2 core diameter greater than 10 n multimode fiber

+. multiple rays of light are guided along the fiber core by the
n of the cladding surrounding the fiber, Each light pulse cares its
‘own piece of data and is transmitted through the cable at

feront

tointerfere with
the cladding at angles greater than the cr
that meet the boundary ata lower angle are rota

ther pulses traveling through the same cable. Rays that reflect fr

angle are comple s
into the cladding. and do not
nd 4-8

convey ight or information along the fiber. Figures 4-7.

Gladding

‘|

adding

Fig. 47. Propagation oflight through a multimode optical fiber.

1 In fiber optics. also known as transmission loss. ls the reduction in

ty of the light beam as it travels through the fiber medium. Attenuation is
ing and
limiting the transmission of a sig

¡ed by

5 large di
into limiting attenuation It has been said that IF ocean

ae nees, Much research has gone

fiber. one could see alt

1m of the Marianas Trench in the

way to the bot
000 feet

Fig. 48, laser bouncing through an crie rod illustrating the reflection of ight
ina multimode optical fiber

A,

453. TERMINATION AND SPLICING

Optical fibers are connected to terminal equipment by optical fiber connect

(Fi94 9) Standard connectors provide a physical contact where the mating surfaces
touch each other at an angled surface to achieve the lowest possible attenuation
and reduced reflections.

A fiberoptic connector is basically a rigid cylindrical barrel sur
that holdsthe barrel in its mating soc

the fiber end and inserting

nded by a sleove
‘Atypical connector is installed

into the rear of the connec

by preparing
dy, Quick set adhesive
is usually used to hold the fbersecurely, and a stain relleris secured to the rear. Once
the adhesive sets the fbers end is polished toa mirror finish Various polish methods

aro used, depending on the type of fiber and the application For single-mode fiber

fiber ends are polished with a sight curvature that makes the mated connectors
touch only at their cores This is called a physical contact (PC) polish. Such
‘connections have an PC connections, but greatly reduce back

from the angled surface leaks out oft

1, because light that rete 1 fiber

Fig. 4-9. Fiber optic cable connections into a data panel.

Optical fibers may be connected to each other by connectors or by splicing; that i.

pining two fixers together ta form a com

splicing method is known as arc fusion splicing. which melts the fiber ends tog
ith an electric ae. For quicker fastening jobs a mechanical splice can also be u

ous waveguide. The generally acce

In fusion splicing. th
fiber ends are stripped

Jo cable ends are fas
heir protet

ned insid

a splice enclosure and the
coating and outer jacket. The ends a

vs

cleaved with a precision cut
inspected via a magnified view screen to check the cleaves
splice. The splicer then emits a small spark at the gap to burn off du
Then the o larger spark that fuses the ends together permanently
The optical loss due tothe splice is measured by directing light through the cladding
{en one side and measuring light leaking from the cladding on the other. A splice loss
optical clarity under 01 dB 5

are placed in the splicer. The spl
efore and after the

and moisture.

Mechanical spices a
the need for stripping. careful cleaning and pı
aligned and held together by a sleeve. often using a clear gel that enhances the

se hit

loss and are less robust than fusion splices. especially if the gel is used. (Fig4-10).

| Mechanical Splicing | FusionSplicing |

Just a mechanical ligament device 1. Two fer ends are signed and then

2. Hold the fer ends in a precisely faved together with heat or lec
algnec positon. ar

3. Sul two separate fers Not 2. Two for become continous

Fig. 4:10. Mechanical and fusion splicing techniques.

Mi

used fiber optics for heads up displays. (Fig.l)

tary aircraft hav

The Boeing 777 uses some fi
systems and expanded use of fiber optics is promised. Some basic advantages of
fiber optics for data transmission includo

system Performance
Greatly Increased Bandwidth and Capacity
Lower Signal Attenuation (Loss

mune to Neise (Electromagnetic

in ference) and RedioFrequency
Interference
No Crosstalk

Lower Bit Error Ra

E

Signal Security
Difficult To Tap
Noneonductive Ek
No Common Ground Required

Freedom From Short Circuit and Sparks
Ind Weight of Cables
nrironmental Protection

OR.

e Signals)

Resistan ion and Corrosion

Temperature Variation

Important deterrents are high cost and the reliability of connectors in the harsh
aviation operating environments

Fig. 6-1 Fiber optic heads up display.

454. FIBER OPTIC DATA LINK

ta link is the name given to the system of components that u
which converts the

rs forthe transmission of data. Data is Input to a transmit
electric signals into optical signals and directs them into the fiber. The transmitters
drive circuit converts the electric signal to an optical signal by varying the electric
rough the light source. LEDS (lg

two common light sources employed. A secure, reliable and durable connector is
required to join the transmitter and the fiber. At the remote end of the fiber, another
Connector joins the ber to a receiver. The receiver transforms the optical signal back
into an electrical signal for use.

current rq diodes) and laser diodes are

ed. the cost and availabilty of easy to manipulate, reliable and durabl

imited the use of

the demand for high perfomance, bandh

ings free f

electromagnetic interferer use In alteraft

While many exp de fiber optics

dat work addressing the shor

fiber optic trans of sireraft operation (

landing gear. flight controls. system operations. etc.) may someday be performed

with fiber optic data links. (Fig. 4-12)

Fig. 612. Typical components ofa fiber optic data link

5.WAVE MOTION AND SOUND

5.1. WAVE MOTION

In physics a wave is an oscillation accompanied by a transfer of energy. Frequency
rofers to the addition of time, Wave motion transfers energy from one point to
‘another, which displace particles of the transmission medium-that is with little or
no associated mass transport. Waves consist, instead, of
around almost fixed locations

511. MECHANICAL WAVES

A mechanical wave is a wave that is an oscillation of matter. an
energy through a medium. While waves can move over long distances. the
movement of the medium of transmission (the material) is limited. Therefore, the
ing material does not move far from its Initial position. Mechs
transport energy which propagates in the same direction as the wave. Mechanical
saves can be produced only in media which possess lasticty and inertia

therefore transfers

A mechanical wave requires an intial energy input. Once this energy Is added, the
wave travels through the medium until al its energy is transferred. In contrast
electromagnetic waves require no medium. but can still travel through one,

An important property of mechanical waves is that their amp
in an unusual way, ba
this gets comparable t

rudes are measured
isplacement of the medium divided by its wavelength When
such as harmonic generation may

‘occur, and I large enough, may result in chaotic effects. For example, waves on the
face of a body of water break when this dimensionless amplitude exceeds 1
resulting ina foam on the surface and turbulent mixing, Some of the most common

nity. significant effect

‘examples of mechanical waves are water waves, sound waves and selsmic waves
‘There are three types of mechanical waves transverse waves longitudinal waves. and

To see an example. move an end of a Slinky
and right. as opposed tc
wave. although itis an

An example of
of water. (Fla:

Fig. $-2. Example ofa surface wave would be waves in a pool. the ocean any
other body of water.

‘There are two types of surface waves Rayleigh waves and Love waves

Rayleigh waves, also known as ground roll are waves that travel as ripples similar to

saves on the surface of water. A Love wave isa surface waves having horizontal waves

the direction of movement. They usually travel faster
nplitude

that aro shear or transverse

than Rayleigh waves and have the largest
512. ELECTROMAGNETIC WAVES

‘The second main wave type, electromagnetic waves, do not require a medium

Instead. they consist of periodic oscillations of electrical and magnetic felds which

are generated by charged panicles. and can therefore travel through a vacuum,

‘These wave types include radio waves, microwaves, infrared radiation, visible light.
and gamma rays.

ultraviolet radiation x

A clectromechanical wave can be transverse, where a disturbance creates
Cfcillations that are perpendicular to the propagation of energy transfer. or

fection of energy
propagation. While mechanical waves can be both transverse and longitudinal all
electromagnetic waves are transverse In free space,

longitudinal where the oscillations are parallel to the

153

513. SINUSOIDAL WAVE MOTION

une that describes a 3

As
oscila

wave or sinusoid is à mather

Aine wave is a continuous wave. (FigS-3)

€ when added

‘The sino wave is important in physics because
fine same fr
y, The hur:

this prop car waves as sounding clear

ions of a single frequency w

Sf

Fig. 5-3. sine wave isa steady wave with repeating amplitude and frequency.

‘Sine Wave

514. INTERFERENCE PHENOMENA

Wave inter ls the effect of er more waves moving on

mbining
cting paths. The effect is of combining the amplitudes of each

I both waves are of the same frequency and phase (they move at the same rate) the
sducing constr

reinforced ive interference, However if the two

amplitudes a
example. f vo stones are dropped In a pool of water. w

ing comp

8 occurs where they combine

results where the crest of one colncides with the crest of the other

Interferer
hav
pulsating frequency called a beat results when the wavelengths are slight!

g different wavelengths or frequencies The effect is a cı

different

cling in opposite dir

ons produce standing

5155, STANDING WAVES

A standing wave (or stationary wave) is a wave in which its peaks do not move

spatially. The amplitude of the wave at a point in space may vary, but its phas

remains constant. The locations st which the amplitude is smallest are called nodes.
and the locations y

the amplitude is greatest are called antinodes

Standing waves were frst noticed on the surface of liquid in vb

ting container.

I occurs because the medium is movin
a result ofinter

¡aves traveling in opposite directions.

The most common cause of stand

ing waves is resonance, in which standing

occur due to interference between waves reflected back and forth at the sam
frequency. For waves of equal amplitude traveling in opposing directions. there is no
net propagation of energ

5.2. SOUND

Sound has been defined as a series of disturbences in matter thet the human esr
can detect This def which are beyond the
transmission and reception of sound. These are the source, a medium for carrying

4

tion can also be applied to disturbance

range of human bearing, There are

ee elements which are necessary #

the sound. and the detector Anything which moves back and forth (vibratos) ar

production a

ransmission of sound is the ring of a bell When
is transmitted

struck and begins to vibrate. the particles ofthe medium (the surround

with the bell also vibrate. The vibraio

disturba

le of the medium to the next, and the vibrations travel in a wave

the medium until they reach the ear, The eardrum. acting as detector, is set

in motion by the vibrating particles of air. and the brain interprets this vibration as

the sound of the bell.

521. SOUND WAVES

Sound waves are m

best be understood by first considering water v

. When an object is thrown into

ool, a series of circular

Im the disturbance. In Fig5-4 such

waves are seen from a top perspective, with the waves traveling out from the center

succession of crests and troughs. The wavelength is the distance from the crest of

fone wave to the crest of the nest. Water waves are known as transverse waves

€ water molecules is up and down or at right angles to the

direction in which the waves are traveling. This can be seen by observing a cork on

bing up and down as the waves pass by

Y 7

Pau Vos Pour bet poe
ring ouate tno enor
et out
Tour

Fig. 5.4 Relationship between sound and waves in water.

Sound travels through matter in the form of longitudinal wave motions Th

are called longitudinal waves because the particles of the medium vibrate back and

When the tine of tuning fork moves in an outward direction the air immediately in

front of the tine is compressed so that ts momentary pressure is raised above that at

other points in the surrounding medium, Because air is elastic, this disturbance is

from the tine in the form of a

transmitted progressively in an outward dire
compression wave. (Fig 5-5)

Css

tote

i)

Fig. 5-5. Sound propagation by a tuning fork.

moves in an inward direction, the ar in front ofthe tine is

When the tine returns a
rarefied so that ts momentary pressure is reduced be
:bance is transmitted in the form of a rarefaction

surrounding medium. This dist
(expansion) wave and follows the compression wave through the medium,

inet motions: (1) The wave itself moves

The progress of any wave involves tuo di
forward with constant speed. and (2) simultaneously, the particles of the medium

that convey the wave vibrate harmonically. Examples of harmonie motion are the

of a clock pendulum. the balance wheel in a watch. and the pi

reciprocating engine. As the longitudinal sound wave progresses out from its sure
another pattern can be discemed 90 degrees to the longitudinal wave. This
transverse amplitude wave is sinusoidal as the vibration varies between maximum

and minimum amplitude,

es overlap or combine they demons
phenomena, If the waves arrive at the listener in phase, they will enhance and the
sound disturbance is larger. Ifthe waves arrive out of phase, they will partially cance!

When two or more sound w

inctive interference pattern of large and then small repe:

ach other out A di
disturbances s heard. Sound cancaling headphones take advantage of
eadset. an outof phase interference

interference phenomena. As sound reaches th

wave is created. It is broadcast in the set so that the original sound wave and the

broadcast wave intorfore and the wave disturbance is reduce to nearly nothing

5.2.2. SPEED OF SOUND

In any uniform medium, under given physical conditions. sound travels at a definite

d.In some substances the velocity of sound is higher than in others, Even in the
same medium under different conditions of temperature, pressure, and so forth the
velocity of sound varies Density and elasticity ofa medium are the two basic physical
properties which govern the velocity of sound

In general. a difference in density between two substances ls sufficient to indicate

which one will be the faster transmission medium for sound. For example, sound

travels faster through water than it does through alt at the same temperature.
nding
‘example among these exceptions involves comparison ofthe speed of sound in lead

However. there are some surprising exceptions to this rule of thumb. An outst

and aluminum at the same temperature. Sound travels at 16 700 fpsin aluminum at
20 C. and only 4050 fps in load at 20

(©. despite the fact that lea
such exceptions is found in the fact, mentioned at

6 much more dense than aluminum. The reason for

2 that sound velocity depends

con elasticity as well as density.

Using density as a rough indication of the speed of sound in a given substance, it can
be stated as a general rule that sound travels fastest in solid materials, slower in
liquids, and slowest in gases. The velocity of sound in air at 0°C (32 "F)is 1 087 fps and
increases by 2 fps for each degree Celsius of temperature rise (1 fps for each dogreo
Fahrenheit)

In the study ofairer

at fy at supersonic speeds. itis customary to discuss speed
(760 mph) at 15°C (59 °F. The term
Mach number has been given to the ratio of the speed of an aircraft to the speed

in relation to the speed of sound of 1223 lp!

of sound. in honor of Ernst Mac
level is 1 225 kph, an aircraft fying at a Mach number of 12 at sea level would be
traveling at a speed of 1223 kph » 12=1 467 kph.

iontst. If the speed of sound at sea

5:23. PRODUCTION OF SOUND

‘Sounds produced when something vibrates. The vibrating body causes the medium.
{water air ete) around it to vibrate, Vibrations in air are called traveling longitudinal

faves, which we can hear Sound waves consist of areas of high and low pressure

ompressions and rarefactions. Fig5-6 is a traveling wave. The shaded bar
above it represents the varying pressure of the wave, Lighter areas are low pressure

AN.

{rarefactions) and darker areas are high pressure

the wave is highlighted in red, This pattern repe:
one meter long. The wavele
Frequency
meters per second at standard temp
frequency s determined by speediivavete

indefinitely
th and speed of the
1 Sound, Since so

ure and pressure. speed isa
In Tnelor
he wave is its amplitude. The amplitude dete

int Thus.

he wavelength the

the pitch. The height ines how

loud a sound wil be Greater amplitude means th

sound will be louder

isin

Fig. 5-6. The various components of a sound wave.

524. SOUND INTENSITY

Sound int

nsity is measured in decibels. with a.
One decibel (dB) isthe smallest chang ity the human ear
can detect. A faint whisper would have an intensity of 20 dB. end a pneumatic drill
Ould be 80 dB. The engine on a modern jetliner at takeoff thrust, would have a
sound intensity of 90 dB when heard by someone standing 150 ft away. A110 dB
noise. by coms swice as loud as the jetliners engine. Fig5-7
he sound intensity from a variety

son. would sound

different sources

i
H

ety emo te
same
Fu

cevvsse

Fig. 57. Sound intensity from different sources.

525. PITCH AND QUALITY

The term "pitch" & used to describe the
recognizable diference bet
piano is a difference in piten. The pi

received per second. which in

of
compressions and rare

Im. is determined by

the vibration frequency of the sounding source. A good example of frequency is the
noise generated by a

ot the fan in the front
es à low freque

of the engine creates a high frequency sound. and the hot

sound,

ngs the sound waves spread outin all directions and the soundlis heard
ball is struck lightly the vib

and the sound is weak. A stronger

are of small ampitu

greater am

and the réa

is greater when y

e.the
of the vibrations of the sound

saves. As the distance from the source increases the energy in each wave spreads

As the sound wave advances, variations in pressure occur at all px

ns the more intense the

transmitting medium. The
nd to the square of the pressure variation
regardless ofthe frequency. Thus. by measuring pressure changes. the intens!
sounds having different frequencies ean red directly

wave, The intensity is

ties of

Note that if

the wave will rever

‘medium in has bound
‚hen it hits the boundary and travel back in the dire
e of the boundary and the frequency and wavelengths of

lependent on the distar

the sound waves.

52.6. DOPPLER EFFECT

When sound is coming from a moving object. the objects forward motion add

the frequency as sensed from the front and takes away from the frequency as sensed

from the rear. Thischangein frequency is knownas the Doppler ef

ct. and itexplains
why the sound from an airplane seems different as it approaches comparec

it sounds as it flies overhead. As it approaches it becomes both loud

55 and pitch both decrease not

pitched. sit Mies away.

airplane is fying at or higher than the speed of soun
ut ahead of the airplane, because the airplane catches up|
leave. The sound energy being created by the airplane piles up. and attach

I not be able to he
energy is actually traling behind the airplane. When
heard, it will be in the form of what is called a sonic boom

lane. As the airplane approaches. a person sta

ground

it until it gets past the

se sound of the airplane

[
3 IT

N

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