Introduction to Aerodynamics of Flight

NASA

SP-367

INTRODUCtiON TO THE AERODYNAMICS OF FLIGHT

Theodore Langley

A. Talay

Research

Center

Prepared at Langley Research Center

Scientific and Technical Information NATIONAL AERONAUTICS

O_ce AND

1975 SPACE

ADMINISTRATION Washington,

D.C.

For sale by the National Technical Springfield, Virginia 22161 Price - $7.00

Information

Service

CONTENTS

FOREWORD

......................................

I. A SHORT

HISTORY

II. BACKGROUND The

The

OF FLIGHT

INFORMATION

Atmosphere

Winds

..........................

1

..........................

5

..................................

and Turbulence

Airplane

III. FLUID

lit

5

...............................

10

....................................

FLOW

13

...................................

25

The

Fluid

......................................

9.5

The

Flow

......................................

9.5

Ideal

Fluid

Flow

..................................

31

Real

Fluid

Flow

..................................

39

IV. SUBSONIC Airfoils

FLOW

EFFECTS

and Wings

Aerodynamic

...........................

.................................

59

...............................

84

of Airplane

...............................

91

Propellers

and Rotors

...............................

96

V. TRANSONIC

FLOW

Total

Drag

Devices

59

VI. SUPERSONIC The

FLOW

103

...............................

119

SST .......................................

Sonic

Boom

VII. BEYOND Hypersonic Lifting Space VIII.

................................

..................................... THE Flight

Bodies Shuttle

127

SUPERSONIC

...........................

.................................

131

....................................

133

................................

of an Airplane

131 131

...................................

PERFORMANCE

Motions

123

137

...............................

137

Class

1 Motion

...................................

137

Class

2 Motion

...................................

149

Class

3 Motion-Hovering

IX. STABILITY

Flight

AND CONTROL

.......................... ...........................

147 151

Stability

.......................................

151

Control

.......................................

169

V

APPENDIX

A -

APPENDIX

B - DIMENSIONS

APPENDIX

C - COORDINATE

BIBLIOGRAPHY

NOMENCLATURE

AERONAUTICAL AND

UNITS

SYSTEMS

................

..................... ......................

...................................

vi

181 187 193 197

FOREWORD

nings

The

science

but,

remarkably,

powered

airplane

decades

have

and no letup passing

of aerodynamics

ductory

the

subject

The

result

various

volume

was

modified

A thorough

the

reader's

interest

of these

as presented to pursue

objectives

herein. more

first

moon

to its

begin-

heavier-than-air

landing.

science

and technology

an interest,

the task

The

last

of aerodynamics

of education

Specialization

encom-

is indicated

of the author's

more

courses

set of notes

which,

of an intro-

at the NASA

Langley

a layman's

treatment

than

individual

teaching

on the

college

through

level.

the teaching

better.

with considerable It is hoped

specialized

aerodynamics.

°°.

111

few

education.

to provide

in many

notes

the

and technicians

illustrated the

of years

separated manned

semesters

was

as taught

to fulfill

revision

in the text

faced

thousands

is staggering. of any

to apprentices

qualitative,

first

in the

subject

of several

problem

but not the detail is a highly

the

has

who possess

of the

in aerodynamics The

from

is an essential

is a result

back

span

growth

those

aspects

knowledge

Center.

process,

resulted

For

life

Hawk

phenomenal

is in sight.

course

Research

at Kitty

witnessed

all the

This

only one human

flight

but a background

can be traced

that

education

up-to-date this

volume

in the

many

material will

has

stimulate

topics

of

of

I. A SHORT

The

theory

It probably through

began

the air.

to his gods What

is this

that

air

has

is a gas,

is the

culmination

with

man's

desire

man, to fly.

substance

called

weight

and

around

Through

influenced As a result intended

of these

to copy

But these

and the

the

designs

first

helicopter

ry man

did not imitate

ple and

took the

the two Montgolfier

popular Gradually,

his

remained

correctly

-

the drawing

a parachute.

it was

hot-air

from

1.)

balloon.

into the atmosphere.

Although

designs

lighter-than-air

mercy

of the winds

acquired

aerostat

small

proved

of

that

the

shape

air

of things

and designs

of the wing to fly.

machines being

designs

first

that

by man.

included

those

machine

to car-

in 1783

distinction

ballooning

became

not fly where

steering

Heavier-than-air

devices,

flight

by

of initiating

thereafter

and could and

princi-

Constructed the

were

supplied

flying

2.)

holds

that

movement

on the lighter-than-air

engines

devices.

other

(See fig.

the balloon

at the

principle

lift necessary -

The

based

France,

man was

the the

power

His

fig.

the notion

a basic

foresaw

it was

the muscle

(See

to question:

Pascal

ornithopters

board.

Instead

of a large

balloon

wing

and fly

attributed

conceived

and

produced

several

began

the principles

that

that

bird

with altitude.

came

concluded

of a bird's

of the

formed

da Vinci)

flight

individuals.

himself,

Aristotle

Bacon,

(Leonardo

he designed

the birds.

of man

Roger

reaction

actions

bodies

decreases

of bird

the

of many

philosophers

of floating

Galileo,

resulting

brothers

pastime,

law

studies

and

form

ascent

fly in it?

did not leave

for the

first

can man

and

works

into the heavens

air

man

action

to copy

to soar Greek

1500 one

studies,

of the

serious

pressure

Da Vinci

to the air

FLIGHT

But the

and its

his avid

others.

relative

unable

Men like

is compressible,

to come.

being

Archimedes'

vehicles.

In the years

the

prehistoric

ability

lighter-than-air

OF

of aerodynamics

Early

the

HISTORY

a

he willed. but they

was

still

years

as the

father

away. Sir George of modern

Cayley

aerodynamics.

glider

with a wing

of the

wing

flat cept

ones.

once

in his very

of inventors

tried

Meanwhile,

Lilienthal

was

successful

flights

before proved

which

and that designs

the basic flew

curved came

is generally

of his

servants

to use

surfaces with

the

flying crashing the

would use

engine

to his concept

acting

on a wing

produce

of dihedral

that

he built their

century,

death

in 1896.

and

built

lift force

an important

the

late

glider 1800's

a

and had

a German

named

flight.

He recorded 3 shows Today,

than con-

airplanes

Figure

a

importance

a man-carrying

of his own design.

of heavier-than-air

the

more -

During

to power

end of the nineteenth in gliders

recognized

He realized

as a passenger.

a steam

the

forces

successfully.

In 1853 it is believed

toward

successfully

Lilienthal

unit

day:

with one

success.

designs.

a tail

of attack

to this

flew

number

angle

(1773-1857)

He understood

and

Stability

used

which

of England

little Otto

over

2000

one of his this

form

of

Helicopter

Parachute

Figure

Figure 2

2.-

Montgolfier

1.- Designs

balloon

(1783).

of Leonardo

Figure

da Vinci.

3.-

Lilienthal

glider

(1896).

flying, are

now called

various

hang-gliding,

claims

Russians),

Americans

are

At the Smithsonian was

designing

wing

span

small

tandem

two propellers, Congress

1903.

flew

gear

On December

machine

improving

designs.

and

numerous

commonplace

propulsion

Samuel

spurred

have

II (1945)

of transonic, The

plane's

design.

pointed

both the

at Langley

Research

supersonic,

following

War

material

fitted

with a steam

Backed

to carry

during

October success

success

rapidly

1903.

in the airplane.

research

and hypersonic shed

future.

civilian

the

some

since

and German

light

a pilot.

Unfortu-

and December

Two world

of

swept

pushed

lifting

wars

combat

concepts wings

of aviation.

is being

transports,

from

Aerial

advanced Soon

sectors

driving

lay in continually

developed

I (1918),

engine

in a gasoline-

(1903).

advances

Langley

a 5-meter

by a grant

achieved

Their

was

"Aerodrome"

and

there

or the

Pierpont

successful

Langley's

Center

will

Samuel

most

twice

the way to the

military

Dr.

airplane

brothers

own design.

limited

dominated

shuttle.

it to crash

have

wars

His in 1896.

the Wright

Although

the Germans,

D.C.,

Aerodrome,"

and aerodynamics

War

Today areas

4.-

comeback.

French,

credit.

of the same

caused

by the end of World

end of World

"the

version

of their

Figure

the

1 kilometer

17, 1903,

engine-powered

Aviation

given

(the

airplanes.

over

failure

first

in Washington,

(fig. 4),

a full-scale

launching

their

generally

steam-powered

which

a substantial

flew

Institution

biplane

he built

nately,

is enjoying

as to who really

at the

and jet

(See fig. forward

bodies,

was

5.)

in the

and the

on the how and why of an air-

space

World

War

I (1918)

P-51 World

War

D II

(1945)

Modern

(1974)

Figure 5.- Designs showing advance of aeronautics.

4

II. BACKGROUND

As a background material

presented

required

background

for the in the

nomenclature

descriptions

of aircraft

this

A general

paper.

included. craft's aid

Appendix motion

This

discussions

the Earth's

in locating

surface.

further

Nature

of the

namely

air.

Air

ing the

Earth

-

imately keep dry

90 km, the

makes

vapor,

estimated together position air

up the

fluctuating

mixed

dust

near

the

sea

particles,

represent

total

can be made

to vary

problem

has

brought

other

TABLE

I.- NORMAL

DRY

ATMOSPHERIC

gas

(Ne),

although nitrogen the

areas

OF SEA

That

to light

in recent

by

(He), ethane

ozone

_O3) , sulfur (NH3),

krypton (CH4)

dioxide carbon

(Kr), , nitrogen (SO2'.,

monoxide

hydrogen

(H2)

oxide nitrogen (CO),

(N20), dioxide and

iodine

(NO2) (12)

,

a total of 0.003 Traces of each gas

for

local times

comby

than

volume

.031

taken

higher

markedly

percent

is

mon-

CLEAN,

Content,

are

of carbon

1962]

(CO2)

helium

the

LEVEL

formula

of clean,

variable,

and oxygen

the percentages

COMPOSITION

atmosphere,

highly

are

of approx-

in the table

gases.

pollutants

NEAR

composition

.934

(Xe) ....

ammonia

normal

fluid,

in all directions

20.948

xenon

will

surround-

Up to altitudes

78.084

dioxide

an airpaper

one

envelope

vapor,

(Ar)

Carbon

gaseous

dramatically

AIR

about

Not included

(02\

Argon

end of the

I.

of all

harmful

Standard

and

in

is also

to define

turbulence

(N2)

Oxygen

Neon

volume

in industrialized

Constituent

as used

presented.

gases.

Interestingly,

[U.S.

Nitrogen

Water

total

oxide, sulfur dioxide, and numerous in nonindustrialized areas.

the

The

in table

etc.

been

used

at the

atmospheric

is given

volume.

where

-

proportions.

of the

units

motion

is concerned

of several

general

same

level

99 percent

systems

atmosphere

bacteria,

at 0.41-percent

coordinate

aerodynamicist

and

and

and

Atmosphere

Earth's

winds

dimensions

bibliography

the

A contains

definitions

on the materials

a mixture

in nearly air

pollution

The

and represents

atmospheric

water

the

air

atmosphere.-

Appendix

and relative

The

The

paper.

scalars,

information

to examine

and represents

aeronautical

B discusses

the various

is urged

is basic

this

general

of vectors,

C describes

reader

information

both

Appendix

discussion

the

throughout

concerning types.

above

the reader

presented,

appendixes.

for the

aeronautical

material

INFORMATION

Above

about

to their

respective

oxygen,

helium, Based

"shells."

90 km,

and

then

homosphere. the heterosphere. most

common

are

the

troposphere,

ure

6 shows

the

temperature

man

lives

harmful ionosphere, outwards. spheric

also.

the

the

gravitation.

500 km),

the solar

becomes

a dominant

The aircraft

and

The

rocket

cal distribution sound lar

time

atmosphere.-

Since

or place,

a hypothetical

may be expected.

This

model

to be devoid

with

is assumed respect The

Europe

to the first

and the

ciled

and

Civil

Aviation

cially The

6

Earth

standard United

States.

Organization by NACA

extended

(that

solar

from

wind,

that

of dust,

moisture,

model

(ICAO).

This

and forms

5 km below

and,

of course,

indefinitely

region

subject

only to

the

extends

knowledge

the

of the

and

constant

speed

atmosphere.

vertiof

at any particu-

as an approximation The

vapor

Sun) all

calibrations,

density,

and water

than

small.

altimeter

remains

of the

(greater from

which

The

of the atmo-

altitudes

so forth,

standard

absorbing

to what air

in the

and to be at rest

or turbulence).

models

accepted

in 1952

7 shows

extends

is negligibly

be employed

as the

slight

and

never

is known

The

Fig-

developed.

of plasma

temperature,

must

here

orbits

at these

of pressure

design,

no winds

in free

however,

purposes

model

is,

order

to aeronau-

the outer

an "atmosphere"

atmosphere

atmospheric

an internationally

accepted tables

model

or layers,

layer

and

represents

particles

one has

as pressure,

the real

is called

Figure

of one or more

can move

and their

quantities

is the

exosphere.

not have

mesosphere

exosphere to note

For

performance

shell

in the stratosphere

ionization

of high-energy

of the

shell

In ascending

occurs

layer

in the

particles

so that

density

of such

is required.

The

(streams

or

shells

atmospheric

weather

ozone

It is interesting

influence

the

and

as we know it would

in which

atmospheric

wind

standard

Most

begins

is significant.

the

Sun.

life

region

the

shells.

important

the beneficial

It represents

constant

thermosphere,

most

region.

layer,

of

shells.

is the

radiation, known

where

to the

in the various

Without

layers,

distribution.

and temperature-defined

ultraviolet

strata,

is one way of distinguishing

composition-

out according concentrations

the gases.

with altitude,

mesosphere,

fly in this

constituents

varies

is the temperature

aircraft

atmosphere

way

composition

stratosphere,

a popularly

Earth's

is essentially

which

here solar

of all

the composition

troposphere

most

find high

two atmospheric

used

variation

It is the

or separate

are

composition

criterion

to settle one would

is the lightest

there

90 km where

both the

begin order

which

then,

Although

the

since

hydrogen

90 km where

Above

gases

In ascending

on composition, Below

tics

the different

densities.

were

developed

differences was

between

introduced

new ICAO the basis

to 20 km above

in the the

models

Atmosphere

of tables sea

in NACA level.

in both were

in 1952 by the

Standard mean

1920's

recon-

International was

report

offi1235.

With increased knowledgesince 1952becauseof the large scale use of highaltitude soundingrockets andsatellites, extendedtables above 20 km were published. Finally in 1962,the U.S. StandardAtmosphere (1962)was publishedto take into account

this

new data.

(1962)

is in agreement

range

but extends

able

data

For

all practical

with the ICAO

to 700 kin.

purposes, Standard

Uncertainty

the U.S.

Atmosphere

in values

Standard over

increased

Atmosphere

their

common

with altitude

as avail-

decreased.

Exos

}here

?, Satellites :

:

::

o %

:

):

:

:

.

:i

...-..:::::

:.......... !:.i: _i:. :_i;

::..

_:_

ij:::: ___::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 500 : ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

,D

c)

Thermosphere

2

x-15 :ii

ii;

Mesopause

_ 10__20

::)::i!ii::!ii::!::i:::ii!#.i::!ili:ii::i::iiii!ii ::;iii:_i::}:_i;ii!

!

;iiiiiiii!ii 80

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Mesos Meteorological

, [

Jhere

-...z.-__70 l ]

Meteors burn up

¢J

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,,,,',_

n:

/ , _,,,,,,, %,

,',' tAzom layer ,' " ' ,',,',, (absorbs solar ultra_mlet ,',:' radiation) ,'ilill'

ill

'

','Ii$

!iillillll

'7

| [

,' tl 'i' 'ill'

',''llll'_'"'

_

["'ili'

........ ! '

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Illl']

,,'i,',,,,,',,",'_,,,,I_',_,",',""'/,'_l, '','1i'7'','7/i///I ', ,_l 40

',,',',W/,_/'_' ,' _t' t'/',"'/J_'//' /IdWIIJYI' '/_l_i',"]'/',"]]/'_ "--', ' ' _ ' ...... _'_ ' "_ "'_ " f i / ' [' "/,_/f/'i//_ili//I/Stratosphere/ff/////i//////," I///i/l '!/////i_ _ t_ I , i /' " 30

:

::

Balloons ........ T ropopause ::-:: :-:-:-"."."

/toommerclal._t_ [ aire_r_

!.

'[li71]iitHii,l'_

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'"_,'"

I'_i!,,ti I_'_

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_ "-

, ,_

_ Light

laircr'_t

__..7 weather

North Pole

¢ ._ I ff.___[ ,/_l_

tSeaSea

Equator

Figure

6.-

Atmospheric

structure.

level

altitude

Geometric

altitude

pressure,

density,

U.S.

Standard

vs.

temperature,

speed

of

Atmosphere

sound 1962

100 /// 9O

8O ,Mesopause 70

@ o

6O

"

_

\\\

5O --Stratopause _J

*$

4O

O

_

J e_

30 ¢d

2O

i

-

Tropopause

10 f

150

200

250

300

K(temp) I

I

0

5

I

I

I

0 l 200

.5 I 250

N/m2(pressure)

kg/m 3_

m/sec

Figure

(density)

(speed

7.- Atmospheric

(Based 1962 .)

on U.S.

10

15 [:104

I

I

1.0 I 300

1.5 l 350

of sound)

properties

Standard

variation.

Atmosphere,

Troposphere

With the expansionof this nation's spaceprogram requirements, a needwas generatedfor information on the variability of atmospheric structure that would be used in the design of second-generationscientific andmilitary aerospacevehicles. Systematic variations in the troposphere due to seasonandlatitude had been knownto exist andthus a neweffort was begunto take those variations into account. The result was the publication of the most up-to-date standard atmospheres - the U.S. StandardAtmosphereSupplements(1966). Essentially there are two sets of tables - one set for altitudes below 120km andone for altitudes, 120km to 1000kin. The model atmospheresbelow 120km are given for every 15° of latitude for 15° N to 75° N and in most cases for January andJuly (or winter and summer). Above 120kin, models are presented to take into accountvarying solar activity. The older 1962model is classified in the 1966supplementsas an average mid-latitude (30° N to 60° N) spring/fall model. The 1962U.S. StandardAtmosphere is the more general model andit is useful to list the standard sea level conditions: Pressure, Po = Density,

Po = 1.225

Temperature,

Figure from

sea

level

these

parameters. In the

is seen first shows

with

altitude.

the lift

responded

type

(from

of continents

m/sec2

density,

merely

sea

level

linearly

217 K before

of variation.

Both curve

is directly

atmosphere.-

It would atmospheric

and oceans,

to indicate

and the

with

general

shells

are

altitude.

increasing

the

density

again.

Earth's

In the The

speed variation

also

importance

of

included.

atmosphere),

it

stratosphere speed

are

of sound

seen since,

it

of sound to decrease as will be

on the density.

be fortunate model

standard

and pressure

is of particular

dependent

and

the

to 10 to 20 km in the

at about

density

temperature,

atmospheric

decreases

The

to a standard

of pressure,

temperature-defined

on an airfoil

real

go = 9.807

It is intended

temperature

constant

a similar

The

ence

the

remains

rapidly seen,

to 100 km. The

K (15 ° C)

a o = 340.294m/sec

a multiplot

troposphere

that

kg/m 3

of gravity,

of sound,

7 gives

N/m2

T o = 288.15

Acceleration Speed

101 325.0

if the

but thermal rotation

Earth's

real

atmosphere

effects

of the

Sun, the

all

combine

to stir

corpres-

up the

9

atmosphereinto a nonuniform, nonstandardmass of gasesin motion. Although a standard atmosphere provides the criteria necessary for design of an aircraft, it is essential

that

"nonstandard"

performance

This nonstandard performance cussed in this section.

shows

in the real up in numerous

Winds Unquestionably,

the

considerable

attention

the

standard

atmosphere

that

the air

respect

mass

to the

is exceedingly motions winds) one

and affect

most

of late,

through

surface

of the

complex. (2) small-scale the

navigation

an airplane Its

motion

motion

and the

of which

some

effect,

also.

are

flies

motion

to the

is constantly is variable

performance

both in time

in

it is known

in a state

into two classes:

Large-scale

Although

Earth,

of motion and

with

space

and

(1) large-scale

motions

of the atmosphere

of an aircraft.

Figure

(or

8 illustrates

effect.

(a) Aircraft

heading

parallel

to AB.

Wind

drift

causes

_

to account

actual

flight

path

A

(b) Aircraft

yawed

into wind Figure

10

dis-

and one receiving

of the atmosphere.

with respect

may be divided

motions.

ways,

atmospheric

is motionless

Earth.

The

real

is the relative

which

be anticipated

and Turbulence

important

the air

atmosphere

with 8.-

angle Effect

of winds.

for wind

drift.

AC.

In figure 8(a) the pilot is attempting to fly his aircraft He sets motion

his heading

and flies

of the atmosphere

flight

path.

After

point

B if there

were

not taken

the winds,

into

the

pilot

in figure

8(b).

course.

Compensation

and the wind

This

velocity

Statistical been

wind

and

typical

velocity

should

flight

path.

should

the

had

change

with

drift

represent

In the consult

him

the aircraft

more

airports

at point

C.

to his intended the pilot

The

In order

out any

knowledge

wind

or less

drifting

to

winds,

which

to compensate

into the wind

of both

and

drift

speed

a standard

Again,

time

local

brought

B.

large-scale

crosswise

have

slightly

canceled

A to point

for

as illustrated

of the aircraft

the aircraft's

off

velocity

to the ground.

curve.

of wind

himself

point

(representing

blowing

would

off course.

of horizontal

case

are

which

finds

requires

values

statistical

pilot

have

respect

B but winds

ground)

pointed

would

for

point

time

forced

have

at any particular

cal average. pilot

flight

no winds, account,

for

to the

required

average

calculated

one such

relative

the

were

directly

from

curve.

in the case place

then,

for wind

than

conditions

of altitude

Figure

of a real

will vary rather

as a function

9 represents

atmosphere,

considerably use

from

a statistical

and forecasts

have

the the

real statisti-

curve,

along

the

his intended

3O

2C

J

o

3

10 J

J

J

J

i

i

I

f

i

I 100

50 Maximum

Figure

9.-

A typical USAF

wind speeds, m/see

statistical Handbook

maximum

wind

speed

curve.

of Geophysics. 11

The small-scale motion of the atmosphereis called turbulence (or gustiness). The responseof an aircraft to turbulence is an important matter. In passengeraircraft, turbulence may cause minor problems such as spilled coffee and in extreme cases injuries if seat belts are not fastened. Excessive shaking or vibration may render the pilot unableto read instruments. In casesof precision flying such as air-toair refueling, bombing, andgunnery, or aerial photography,turbulence-induced motions of the aircraft are a nuisance. Turbulence-inducedstresses and strains over a long period may causefatigue in the airframe andin extreme cases a particular heavy turbulence may causethe loss of control of an aircraft or evenimmediate structural failure. There are several causesof turbulence. The unequalheating of the Earth's surface by the Sunwill causeconvective currents to rise and make the plane's motion through such unequalcurrents rough. On a clear day the turbulence is not visible but will be felt; hence,the name "clear air turbulence (CAT)." Turbulence also occurs becauseof winds blowing over irregular terrain or, by different magnitudeor direction, winds blowing side by side andproducing a shearing effect. In the case of the thunderstorm, one has oneof the most violent of all turbulences where strong updrafts anddowndrafts exist side by side. The severity of the aircraft motion causedby the turbulence will dependupon the magnitudeof the updrafts anddowndrafts and their directions. Many private aircraft have beenlost to thunderstorm turbulence becauseof structural failure or loss of control. Commercial airliners

generally Figure

lences

fly around 10 illustrates

liquid

will

real

flight

atmospheric

or vapor

affect

cipitation

form,

an aircraft that

for the

path

comfort

and

of an aircraft

less

dense

than

dry

air

less

dense

than

dry

air.

safety

through

Air

density

of an aircraft standard is important

air

degrees.

and

physical

depends

atmosphere

does

a pilot

consequently

in the

of their

passengers.

the various

upon

humid

the

pure

dry

turbu-

true

such

caused

air

(air

in the air,

standard with

and

the forms

of pre-

on the wings,

Water

containing

requires

atmosphere

as icing

by hail.

in either

vapor

water

a longer

is

vapor)

will

take-off

dis-

be

air. in the lift,

temperature

a local

dry

is familiar

an aircraft

factor

not indicate

to contact

damage

dense

important

Water

performance

of this,

more

in the

Everyone

aircraft

Because

is a very

and

for

than

and

of moisture.

for

affect

in fog or snow,

in humid

is that

is not accounted

in varying

visibility

tance

effect

can adversely

zero

12

the

storms

described. Another

its

such

and conditions

airport

drag,

pressure

and

engine

locally.

at a particular

for the

local

power Since

time

atmospheric

output the

and place, conditions.

it

.,i..t..,.

;i? iL !iLk ?¸

Ii ii

71 ii iiii

?iii?iiiii!i!i iiiiii j'iiiiiN

iiiiiii!!iii!iii!_!:i:i_i:!:i:i:i:i:i:i:i_i:!:i:i:i!iiiiiiii!iiii!ii!i!iii!i!i!iiiii!:i:i:!:i:!:i Figure I0.- Flight path of an aircraft through various forms of turbulence. Relatively stable air exists above thunderstorms. From

the

hence,

must

local

temperature

take-off The

local

zero

his

standard

and

distance pressure

altimeter

pressure

readings,

power

is important

pressure

sea-level

pressure

and engine

output

density

in aircraft

to local

using

measured

if he is to obtain

may

be obtained

and,

may be determined. pressure

altimeters.

sea-level

accurate

altitude

A pilot

pressure

rather

readings

above

than

to

sea

level. Although nonstandard still

the preceding atmosphere

remains

discussion

on aircraft

as a primary

considers

design

reference

in the

The Basic known

airplane.-

as airplanes.

its application physical

makeup

several

surfaces, considered

basic landing later

Fuselage.the

controls

attention

Before

it would

of a typical

gear,

preliminary

the design

many

standard stage

effects

of a

atmosphere

of an aircraft.

Airplane be centered

into any be well

mainly

discussion

on that

class

of aerodynamic

to consider

in some

detail

view

an airplane

of aircraft theory

and

the overall

airplane.

11 demonstrates components

will

proceeding

to airplanes,

As figure into

Our

only a few of the

and performance,

in exploded as follows:

and powerplant(s).

form,

fuselage, The

wing,

tail

aerodynamics

may be resolved

assembly of these

and control components

are

in the discussion. The

necessary

body for

of an airplane

is called

operating

controlling

and

the

fuselage.

the

airplane.

It houses It may

the

crew

provide

and space

13

_Controt

_

.

ge3.r

Figure cargo

engine ture

and passengers

may be housed of the

generally mission

airplane

since

the

many

provides

sectional

shape

of the wing

planform

shape

of the wing,

airplane Figure

mission 13 illustrates Tail

the

assembly

collection

(1) the vertical and pitch.

14

and

(2) the

Figure

of the

is known

compromise

the shapes control

stabilizer

(fin) and

stabilizer

with

force

airfoil

numerous

forms

to the

air.

overall

struc-

to it.

It is

with the

in figure

12.

Lift is The cross-

The airfoil

in the

section depend

airplane

shape, upon the design.

used. assembly

provide

(appendage)

The tail

a tail

represents

assembly

directional

provide that

vary

on the fuselage

airplane.

which

attached

Designs

section.

often

which

are

an

the basic

of an airplane.

respect

The tail

rudder

In addition,

as illustrated

of the wing

of the

and elevator the

endless,

necessary

surfaces.rear

drag.

lifting

and placements

at the

14 illustrates

as the

components

to reduce are

sorts.

is, in one sense,

large

wing

and placement

of structures

horizontal

of various

the principal

the best

and

other

variations

action

components.

The fuselage

as possible

and the

dynamic

airplane

armaments

of the

as much

The wing

from

Basic

in the fuselage.

to be performed

obtained

11.-

and carry

streamlined

Wing.-

y

t

_n

for

assem

longitudinal assembly

consists

stability

in yaw,

stability may

of

take.

in

/

|

B-26B

Twin-engine

bomber

WWII

/

l

%

P -47N

Albatross

Flying

boat j/_-

- /

I

,

(+

Long

Figure

range

8-engine

12.- Various

/

B-52G

bomber

fuselage

designs.

15

Wing

Wright

L

P-36

(Subsonic)

F-51

(Subsonic)

F-104

(a)Examples

Brothers

(Supersonic)

of airfoilshapes.

Figure 13.- Wing shapes and placements.

16

Rectangular straight wing

Tapered

straight

Rounded or straight

Slightly

elliptical wing

swept

Moderately

Highly

wing

wing

swept

swept

wing

Simple

Complex

(b) Examples Figure

of wing 13.-

wing

delta

delta

wing

wing

planform.

Continued. 17

High-wing

Mid-willg

Low

(c) Examples

of wing

Figure

13.-

Elevator

_

H orizo Rightfinnal

_

. '

_

Fin

,vertical

_ [t,l'lZdlntitl

Nl:t|)lltZ_l"

evatlw -

_

fin

tail

V-butl(,r

Figure 18

stabiliz(,ri

//

__'_._.._._

s ta hi, i zter -

Twin

placements.

Concluded.

Rudder --_

14.-

-wing

Tail

assembly

fl}:-t._il

forms.

Included used or

for

attitude,

right)

trol

is

the

provided

heavy,

small

pilot

and

ailerons

wing

or

ailerons

lift

Spoilers

operating

at are

of roll

control.

a simple

aileron

large

airliner.

jet

it is at

rest

may

fixed

be

absorbing

or

gear

arrester modern-day

installation

The

landing or

include are

attitude

and

a more

or

in water,

use

oil

or

skis

for

snow

Figure

they

may

control

of most

to

cushion

and

floats

17 shows

for

blow

the

and

takeBy

alternate

form

and

figure

16 shows used

on

airplane

landing.

a

while The

attached

gear

to shock-

Special

carrier

gear

used

an

of landing. For

wing

quickly.

the

are

rudder,

of the

wing

and

the

surfaces.

arrangement

of the

nose

without

landing

surfaces

water.

several

left)

wing.

elevators,

provide

_tirplanes

the

the

for

take-off

or

rudder,

wishes

supports

the

of the

edges

complicated

during

edge

to move

an airplane

undercarriage,

and

wheels

air

wing,

right

pilot

trailing

generally

to the

(2) to maintain

primarily

on

are

con-

if it is too

move

necessary

used

lift

the

gear,

The

used.

the

of the

airplane

the

Pitch

elevator,

condition,

and/or

are

the

left

types

of

landings,

arrangements

found

on

airplanes.

or

power

propeller,

With plant

(or

turbojet,

turboprop,

engine's

rotating

and

piston

on an

in unaccelerated

face

forces.

exceptions

some

Body

forces

force

or

and

the

a thrust

of the

many

force varied

are

two

flight. on

plant

the

Surface

engines

They body

from

forces

general

termed

because

engine

types

the

ram

(and

are

jet,

the

pulse

jet,

of a reciprocating by

placements

a distance. act

as

energy

types be

a thrust-producing of the

engine

accomplished

engine

may

main such

the is

possess consists

The

Converting

into

act

must

power

reaction

engine.

steady

airplane

accessories.

There

weight.

The

related

airplane.or

an

flight.

rocket

crankshaft

body

gravitational

the

type),

and

18 illustrates Forces

few

to sustain

if present),

reciprocating

Figure

flap

ground

Power_plants.device

to reduce

15 illustrates

on

(3) to help

leading They

sides

inserts

setting

effort

fin.

wing

trailing

the

to the

which

the

cruise

controls, of the

to the

outer

(1) to balance

of the

on both

surface

particular

pilot

parts

the

airplane

elevators

(rolling

in a stable

on the

used

that

hooks

are

whatever

the

retractable.

struts

landing

at

devices

the

control

to fly

airspeeds.

gear.on

hinged

reduced

and

Landing

near

of an airplane

the

attached

by the

generally

heavy

Figure

provided

located

pivoted

independently

is

surfaces

(turning

generally

control

relieve

or

is

down)

moving

control

which

functions

or

thus

Yaw

Roll

whose

hinged

to increase

or

those

stabilizer.

pressures

and

are

up

all

control.

auxiliary

maintairting

are

rudder

ailerons

rudder,

the

off.

the

heavy,

elevator,

drag

by the

surfaces

tail

Flaps

and

airplane

are

aileron

surfaces

horizontal

by

tabs

and

lift,

to the

Trim

control

provided

(nosing

attached is

in the

the

propeller.

possible.

of forces as For

that

body

forces

the

airplane

of contact

may

between

act and this

on

a

suris

the

the

19

RuddE Elevator

(all-movir

Spoiler

-- Flaps

Spoiler Flaps

(a) Control

Rudder

_

surfaces

Side

on F-4B

Phantom.

view

_-T_\ Rudder

-_

_

Aileron

\_

.-_

Aileron

_ tab

_ "_

AHeron-_

Figure

2O

15.-

surfaces Main

.

Speed---,I 'el

trim

(b) Control

J

control

on T-28B. surfaces.

,

aJleron

Left

Right

(a) Simp/e Outboard

Outboard

Inboard

aileron

flap arrangement.

aileron

flap

aileron

/ Inboard

flap

(b)Jet airlineraileron and flap assembly on Wing. Figure 16.- Flaps and ailerons.

2!

gear

Arrester hook

Main gear

(a) Tricycle

gear

-

nose

wheel,

two main

wheels.

•

(b) Conventional

gear

-

tail

wheel,

two main

_

wheels.

Skids

(c) Unconventional Figure

29.

gear 17.-

-

skis,

Landing-gear

skids, forms.

or floats.

_Tail wheel

Reciprocating or turbo-engine propeliors

]

Jet

engine

Starfighter

Single engine F-104

Phantom

Twin engine

_

Three engines

F-4

Trident

Four engines

Multi engine

Figure

18.-

Power-plant

placements.

Lift

Thrust

=-

Weight

Figure 19.- Forces on an airplane in normal flight. 23

medium

and the body,

and thrust, Basically,

the

other

the

four

Weight: fuel

Thrust: propeller, along

Drag: the

the wing.

In the

this

of the

at a uniform

velocity.

conditions.

To maintain

equals

They

generally

drag

arise

are

because

concern

arise.

This

all

thrust,

the

surface

lift,

payload,

decreases.

propulsive

so forth,

Weight

drag, forces.

and drag.

and the

It represents

situation

this

system

fuel.

acts

Since

in a direc-

is used,

engine

It may

be taken

is the thrust.

(except

for

vertical

of air the

from

the

aerodynamic

take-off

around

of the

driven to act

airplanes).

the airplane,

component

Weight

force

the

flight

along

or can be easily

of the

dynamic

are

the

travel

disposition

around line

the

major

resultant

aerody-

airplane

but is

physical

of flight.

in straight

of the

the lift

the

four

equals

attributes

forces

controlled.

of the

airplane

through

now in some

in which detail.

the

lift and

level under

flight these

and the

of an airplane.

and

manner

and

the weight,

determined

movement is the

will

situation,

and thrust

known

is considered

flow of air

an airplane

19 shows basic

of aerodynamics subject

weight,

itself,

by the flow

arises

Figure

the drag.

major

24

force

flight

are

Lift,

of flight.

resultant

simplest

thrust

line

and

airplane

from

Again,

component

engine, of the

to the

are

the weight

of whatever

is generated

normal

on an airplane,

airplane

flies,

force

resulting force

the

force

axis

acting

surface.

Earth.

rocket

the longitudinal

and the airplane

on an airplane

airplane

driving

jet engine,

portion namic

includes

of the

the air

forces

weight

center

This

main acting

The

Lift:

between

forces

as the

the

is,

three

The

is consumed

tion toward

that

But lift and the air. drag

forces

The

III. FLUID FLOW The Fluid Viscosity.- There are basically three states of matter - solid, liquid, andgas. H20 is commonly called "ice" in the solid state, "water" in the liquid state, and "water vapor" in the gaseousstate. Assume onehas a piece of ice andside forces are applied to it (called shearing forces). Very large forces are neededto deform or break it. The solid has a very high internal friction or resistance to shearing. The word

for internal Liquids

a solid. ers, air

friction

and gases

Imagine

faster

that a shear force internal friction. under

have

extremely

gory

of fluids,

mary

interest

But it will be shown important

effects

that

with

speeds

involved

150 m/sec, throughout into

motion

air

another

Even not great.

may

be treated

the flow).

air.

one that small

in terms are

extent,

may

For

be treated

subsonic

as incompressible

At higher

speeds

the

effects

the

Air,

cate-

of pritheories,

friction)

has

drag. is, density

generally

increases

highly

over

an airplane

(that

is,

under

incompressible

as incompressible

flow

air.

solids

or is "inviscid."

(or internal

(that are

possess

than

and in some

viscosity

compressible but liquids

also

viscous

gases.

viscosity

of air

of lift and

they

Under

zero

viscosity

the fact

low viscosities. than

lay-

with the

However, that

from

to these

in general,

small

has

applied

more

large.

differently

that,

viscosities

a relatively

very

of the layers

times

higher

provided below

no change

the

flow

about

in density

of compressibility

must

be taken

account.

The Pathlines ways

fifty

One concludes

possess

-

are

indicates

have

gases

are

fluids

fluids

this

to some

the

behave

layers.

whereas

fluid even

the water

is about

than

All fluids

gases.

than

to deform

has

on an airplane

pressure)

compared

relative

generally

Compressibility.increasing

sustained

one

is generally

they

and

viscous

as a perfect

since

forces

in aerodynamics,

it is described

value

If shear

high viscosities liquids

to be fluids

temperatures,

more

its

or air.

be applied

normal

Ice is 5 × 1016 times

for a solid

of water

over

must

and

considered

a substantial

sliding

Water,

are

two layers

one discovers layers

is viscosity

-

the

and

streamlines.-

Lagrangian

approach

standpoint,

one particle

is chosen

time.

line

The

traced

ple is a transmitting

out by that ocean

buoy

A fluid and the

Flow

flow may Eulerian

and it is followed one particle shown

in figure

be described approach.

in two different From

as it moves

is called 20(a).

Lagrangian

through

a particle Its

the

position

space

pathline. has

been

with An exammarked

at

25

6-hour intervals over a period of several days. The path observed is the particle pathline. In order to obtain a clearer idea of the flow field at a particular instant, a Eulerian approachis adopted. One is looking at a "photograph" of the flow. Figure 20(b) showsthe surface oceancurrents at a particular fixed time. The entire flow field is easily visualized. The lines comprising this flow field are called streamlines. ,'_ + 48

hrs

f /

t_t+ Particle pathline

_-_._

42

hrs

/

it+

36 hrs

] ., _1+ 30 hrs 2_i

Coast

+ 24

Buoy position at 6 hour intervals

hrs

/_+ 18 hrs ! + 12

hrs

I

•_/+

6 hrs

J

_

0 hrs

(a) Particle

pathline.

Streamlines

Flow

at + 6 hours

Coast

(b) Streamlines. Figure

26

20.-

Particle

pathline

and

streamlines.

It is line.

important

A pathline

streamline

presents

of whether

particle

Stsady fluid

calls

direction or

if its

velocity

does

not

house of time

time.

wind

and

consider a windy later.

pattern

If,

this day One

sees

is different;

however,

at the

figure instant

each

21(a)

that

this

flow

the

streamlines

is

Particle pathlines and streamlines

(a)

it blows

constantly

speed

direction

flow

or

of a fluid

in the the

presents and

is

There

changing

their

On

a windy

from

the

day

the

many

and

is

this

fluid.

about

flow

a

an instant

areas

position

-

in the

(of air)

wind

is steady

constant

the

a

same

object

points

flow

are

question

in understanding

an

shows

a

next.

changes,

all

fluid

21(b)

The

considered

remains at

a streamwhereas

time.

about

flow

same the

figure

unsteady. are

same

flow."

be

of time

the

of a "steady

point

velocity

ever

and space

a fixed

importance

the the

at

and

Of basic

stands

manner

that

further, at one

concept he

direction)

require

are

pathline

in time

particles

flow.-

the

if where

In a similar

(speed

of many

unsteady

a particle

particle

streamlines

is

speed.

necessarily

on

and

between

of a single

of motion

with

steady

unsteady.

To

differences

trace

an object

at a constant

"gusty"

flow

compared about

the

line

pathlines

flow

the

to the the

movements

person

to note refers

where shape

the with

for this flow are not equivalent.

Streamlines

at

time

t 0.

y

(b) Streamlines Figure

21.-

Unsteady

flow

at time

t 1.

of air

about

a house. 27

Figure house)

22 shows

in a wind

At time

t1

develops

further

flow appears through

the

a nicely

tunnel.

At time

tunnel

tO

is started

at time

unchanged

an unsteady

"streamlined"

t2

and

transient

not the

same.

From

appear

fixed

in position

with

t3

downstream

line

at time

t 5.

The

moves

particle

t3

pathline

time

that

is,

onwards

respect

a steady

along with

the

and no air the body;

pattern

When

the

pathlines

streamline

the flow

starts,

and

A particle

is flowing.

at time

flow

t 3.

The

it passes

streamlines

flow is established.

body. that

to the bluff-shaped

about

a constant t 5.

particle

to the

coincides

flowing

reaches

and

(as opposed

is not running

begins

finally t4

state;

time

the tunnel

and air

at time

body

are

Streamlines

P

shown

as shown

on a stream-

at times

t4

and

streamline.

====2,.i

Tunnel

at

time

t o

Tunnel

at

t 1

r

Tunnel

at

t 2

Tunnel

......

flow:

Figure

are

equivalent

for

flow visualization. Rotational

the

28

elements

and

the

means

that

Lagrangian

at each

Particle

22.-

and irrotational of fluid

:,:::

'_:"

_'_

Tunnel at t 5

Steady

this

t 3

.........

Tunnel at t4

Summarizing,

at

Unsteady

point

of view

Fluid

:

Streamline

and steady

for a steady

flow.point

pathline

flow is the

flow

in the flow have

flow.

a particle same

as the

can be rotational no net

pathline

angular

and

Eulerian

streamline approach

or irrotational. (spin)

velocity

If about

constant velocity.

It is irrotational.

remains

irrotational

limited

to a small

flow may

still

if zero region

near

be treated

basic

streamlines fluid nent.

ideas

along

Taken

Fluid

flows

locity

varies

with

the

as shown

24(c).

uniform

at each

stated,

tube,

distance

they

airfoil

One

section,

effects

it

are

Most

of the

flows

the

tube

temperature,

section

for the

the

convey

laws

the

flow to be one

that

stream

value since

are

velocuniform

as indicated it varies

made.

flow properties

tube.

The ve-

streamline

dimensional"

arise, of mass

and

is perma-

or channel.

varying

since

only

In addition

must

also

be

dimensional.

forces

mass

tube

larger

of

tube

an "average"

observations

of conservation

facts

individual

imagine

and other

how aerodynamic

an even

actual

a bundle

stream

to the

"one

where

the

a pipe

the

shows

of as a stream

through

can easily

to aid in under-

24(a)

flow,

comprise

to represent

density,

are

tubes

is considered

along

employed

Figure

of steady

according

24(b).

then

velocity

They

the

viscosity

can be thought

water

in general,

in figure

to understand

be considered. Simply

for example,

The

cross

streamline

of stream

often

flow.

In the case

section

pressure,

In order

Each

at the cross

the particular

about life,

and in its wake.

argument

of a one-dimensional

flow.

it as,

across

passes In real

of the airfoil

A simplifying

the bundle

through

to velocity,

surface

it as if in a tube.

of velocity

in figure

is that

together,

ity variation, value

flow.-

of a simple

flows

the

airflow

is assumed.

as irrotational.

One-dimensional standing

As the

viscosity

energy

two basic and

principles

conservation

can neither

must

of energy.

be created

nor

destroyed. For sidered ered

introductory

purposes,

to be inviscid steady

simplifying

and incompressible

assumptions (and hence,

are

made.

"perfect").

The

The

Fluid

Many

infinitesimal

form

thickne_ Fluid velocity

_

_

duct

Stream.tube

boundary)

(outside

streamlines

t/ in

(a) Stream Figure 30

velocity out

streamlines

(actually

24.-

Stream

tubes

tubes. and one-dimensional

flow.

is con-

flow is consid-

and one dimensional.

__.,__

fluid

the points, the fluid flow is said to be irrotational. wheel

immersed

rotating, figure

the 23(b),

in a moving motion

fluid

as in figure

is irrotational.

the flow

If the

One can imagine a small paddle

23(a).

wheel

If the wheel

rotates

translates

in a flow,

without

as illustrated

in

is rotational.

(a) Irrotational

(b) Rotational

flow.

flow.

Ik

(c) Inviscid, Figure

According initially the

airfoil

to a theorem

irrotational, section

23.-

flow about

Rotational

and irrotational

of Helmholtz,

it remains shown.

irrotational

The

irrotational. flow far

ahead

assuming In figure

an airfoil.

zero

flow.

viscosity,

23(c),

of the airfoil

if a fluid

an observer

section

flow is

is fixed

is uniform

to

and of 29

/-Transverse

velocity ion

_

__'--

Ave ra4Ie

veloeit

y

luidvelocity

(b) Real

velocity

flow

--

profile.

One-dimensional velocity profile

idealized

--} (c) (e)

One-dimensional Figure

24.-

Ideal The tion but

continuity

of mass has

in a system.

a constriction

tube.

is

areas

A 1

in the

and

cross

A2,

sections pipe

nor

is

equation

states

that

the

fluid

value

at

creation"

any -

station cross and

(Mass

2 per section

the

that

rate)

fluid

being

mass unit

flow

1 = (Mass

V1

a statement

uniform

in diameter

25(a). under

and

This the

be

is

2 have the

called

average

pumped

in through

the

sides.

The

unit

time

In fact,

this

there

is an

or

assumption

"mass

flow

accumulation

is violated.

Simply

assump-

flow is

time.

a venturi

stated

assumption

1 per

ends,

cross-sectional

A further

station

conserva-

at both

previously

1 and V2

of the

flow).

passing

rate)2

is

in figure fluid,

is

Stations

Let

examined

steady

which

the

(one-dimensional

in the

passing

as

Flow equation

indicated.

respectively.

no leaks

mass

ends

assumed

direction

Fluid

a pipe

the

profile.

Concluded.

continuity

Consider

it is

flowing

The

between

Furthermore,

tions,

these

equation.-

flow

must

rate"

speeds

that

there

continuity equal

must

of mass

at are

be -

the

fluid

the

same

"mass

stated,

(1)

31

where Mass This

equation

rate

reduces

the

fluid

reduces

x Area

x Velocity

(2)

to

PlA1V1 Since

= Density

(3)

= P2A2V2

is assumed

to be incompressible,

p

is a constant

and equation

(3)

to AlV 1 = A2V 2

This

is the

simple

dimensional be valid

continuity

flow as long

(4) equation

with no leaks. as average

By rearranging

for

inviscid,

incompressible,

If the flow were

values

equation

of

Vl

and

viscous, V2

the

across

steady,

statement

the

one-

would

cross

still

section

are

used.

(4), one obtains

A1

(5)

V 2 - A2 V1

Since

A1

is greater

greater made,

than V 1. This is a most that the flow speed increases

decreases the

equation,

highest

narrowest

part

of the

The

that

the

fact

venturi

tube. than

spaced

streamlines

indicate

regions Bernoulli

32

speed

speed

constriction

flow is composed

this

with the

than

at the

ends.

at the

station called

a constant 25(c)

of the throat,

the

streamlines

The

indicate

shows

Figure

Hence,

regions

the

is

25(b)

picture.

part.

V2

under the assumptions and the flow speed

speed

remains

that

It states, decreases

commonly

AV

of high-speed

is inviscid,

Figure flow

it can be concluded

result. the area

is reached

increases.

's theorem

important where

a larger

product

wide

fig. 25(a)),

increases.

In the area

in the

fluid

as before,

(see

of the streamline

and the

the

area

the

together

A2

indicating

interpretation the

the

constriction

nuity the

where

than

distance

conclusion of low-speed

flow

In fact,

of smallest the throat along

shows

must

and

of the

This

is at tube.

of flow allows

streamline crowd

an

pattern

in

closer decreases

speaking,

widely

closely

spaced

streamlines

Assume

a fluid

flow which,

flow. -

the

conservation

incompressible, of several

energies.

of energy.-

steady, The

and one dimensional. kinetic

energy

arises

The

energy

because

at

conti-

venturi

streamlines

relatively

arrow

by the

area.

a tube the

between

is that,

longer

in

of the

directed motion of the fluid; the pressure energy is due to the random motion within the fluid; andthe potential energy is due to the position of the fluid abovesome referencelevel. Bernoulli's theorem is an expression of the conservationof the total energy; that is, the sum total of these energies in a fluid flow remains a constant along a streamline. Expressed concisely, the sum of the kinetic energy, pressure energy, and potential energy remains a constant. If it is further assumedthat the fluid flow is horizontal (as, for example, airflow approachingan aircraft in level flight), then the potential energy of the flow is a constant. Bernoulli's theorem reduces to Kinetic energy + Pressure energy = where the

the

energy

theorem

constant per may

unit

includes

the

volume,

one obtains

be expressed

constant

in terms

value

Constant

(6)

of potential

the dimensions

energy. of pressure

If one and

considers

Bernoulli's

of pressure.

I Station 1 I

Ca)

' > (b)

increased

Figure

25.-

Venturi

flow

tube

speed

and

continuity

principle. 33

The kinetic energy per unit volume is called dynamic pressure q andis deter1 AV2 where p and V are, respectively, the fluid flow density and mined by q=_p speedat the point in question. The pressure energy per unit volume (due the

static The

pressure

of the fluid

constant

energy

Bernoulli's

per

equation

Dynamic

and is given unit

pressure

the symbol

volume

reduces

to random

is called

motion

within

the fluid)

is

p.

the

total

pressure

Pt"

to

+ Static

pressure

= Total

(7)

pressure

or

1 _V 2 _p + P : Pt

For rotational from streamline usual

case

same

constant

flow the total pressure Pt is constant along a streamline to streamline as shown in figure 26(a). In an irrotational

considered

the

static

for

value

Bernoulli's of the flow,

airflow

less

the

pressure. such

approaching

everywhere

equation

the

pressures

(8)

states static

There

that

as shown

their

that

total

in figure

fluid

an_t the less

a simple

remains

the

total

pressure

is the

26(b).

in a streamline

pressure; exists

an aircraft,

but may vary flow, the

the

exchange

flow,

speed

the

of the flow,

between

the same.

the greater

the

the

greater

and

static

the other

must

dynamic

As one increases,

speed

decrease. Pressure pressures

in a flow

hollow

bent

tube,

measurement and

The

to rest

the

total pitot

tube.

pressure tube

Figure facing This

the tube

instrument everywhere.

34

are

a pitot

at the

tube

"stagnation

since

22(b)

shows

static

the

Except pressure

of holes

which

fluid

the

static

rest

fluid

another

fluid

a simple to a pressure tube

divides

entrance up to flow

at the stagnation

to zero

when

the

point

is

flow stagnates.

device.

been

point,

dynamic

flow about

at the

of the

hollow

have

and

is connected

pressure

reduces

acts

static,

up immediately

be connected

at the stagnation of the

dams

the

measuring

flow about

and may

shows

while

a total-pressure

tube

how total,

inventor,

pressure

and a number

a static

its fluid

equation

the fluid

flow is closed

27(a)

point"

the dynamic

therefore,

as before.

after The

By Bernoulli's

is called

us now examine Figure

instrument.

is,

The

Let

measured.

called

readout

comes

around the

measurement.-

tube

drilled

normal

fluid

now the end

into the

to a pressure the

except

measuring

is parallel

to the

tube's

tube's

side. readout

to the tube surface.

Since

Pt, 1 _

Pt,2

Pt,4

(a)

Rotational

flow.

Total

pressure

varies

from

streamline

to streamline.

Pt,1 /"'_"_

Pt,1

/""'_

Pt,1

_/

__

..7

Pt,1

t/

Pt,1 _ Pt,1

Pt, 1

_'I_

/

Pt,1

_J

_

_

Pt,I

(b) Irrotational flow.

Total pressure Figure

pressure

must

be continuous,

26.- Total-pressure

The

opposite pressure

flow speed nected

measuring

and static pressure

the dynamic

pressure,

measuring

a combined

ends of a pressure

can be calculated.

directly to an airspeed

display the aircraft airspeed

everywhere

in flow.

variation.

normal

to the holes is communicated

device.

pitot-static tube. readout

is measured.

defined as

Pt,l

static tube, therefore, with the holes parallel to the

flow direction, is a static-pressure 27(c) shows

constant value

the static pressure

into the interior of the tube.

Figure

same

1 _pV 2.

By

When

properly

connected

instrument,

the difference

Bernoulli's

equation this difference is

If the fluid density

p

between

to

is known,

total

the fluid

In actual use on aircraft, the pitot-static tube is conindicator which, to the pilot.

The

by proper

gearing, will automatically

device is sometimes

mounted

forward

35

_ Total

p_

Smalll --_hoes

p..

" Sta.:--/

--"Jl--

pressure entrance

T

T To

pressure readout instrument

To

pressure readout instrument

(b) Static

(a)Pitot tube.

Total_1

1/

pressure

.... _rarzc pressure

tube.

I'll

-

g _

/I II I! !l

M

!

Outer

tube

static

pressure instrument

communicates to

readout

Middle tube communicates total pressure to readout instrument

(c) l>itot-static Figure on a boom sible,

extending

Returning

discussion

Bernoulli venturi

equations tube.

ing the tube then

may

The

of figure

may static

be used

is a greater

28 holes

tube

to the

have 27(b)

within

which

is a liquid

such

at the

static

tap

the

equal

pressure

are

36

reference indicated

static

level.

pressure.

by a decrease

These

pressures

or increase

the

fluid

the fluid above

in the level

along

flow

enter-

pressure

pressure. similar

in the In fig-

to the

are

a tube static

continuity

distribution

holes -

When pressure,

the

of static tube

manometer"

static

But static

earlier,

static

venturi

as pos-

condition).

free-stream

free-stream

alcohol.

free-stream

as closely

the static-pressure

of the

to a "U-tube as colored

introduced

Any variation

the

the walls

measuring,

undisturbed

value. than

its

the free-stream

tube

of the

the

connected

called

to describe

to measure

equals

(also

pressure

value

devices.

to insure

of the venturi

into

taps"

at some

flow

drilled

and are

nose

as a reference

"static

measuring

be used

or lesser

been

Pressure

airplane

approaching

the

ure

the

the undisturbed

and

tube

from

27.-

tube.

static

commonly

called

having

a U-shape

pressure

measured

levels

or below of fluid

in the

the

tube

free-stream

in the tube.

are

[nviscid,

P_oyV_

_

incompressible

I

free-strea_ static pressure

_I r

andvetocity

I

manometer

Station

St'ttic

_/I

tap

Station 2 (throat)

_

_

_ __

q

pressure,_ q Static pressu P

Figure Figure and

static

station

2

the

throat

tion

the

28 shows

taps

to measure

V2

is greater

also

is the

total

flow).

static block

pressure diagrams

is less

where and

flow.

indicates static The

follow

achieved

continuity

1

as seen

V1

in the venturi

pressure

2 using

equation

This

reaches

pressure airfoil

is also the

than

tube.

and

fluid,

the

-

the

at

speed

By Bernoulli's

flow (assuming

Pt

in terms

at

equa-

irrotational

of the static

and

(8), namely,

P2 = Pl

dynamic

The

the liquid

free-stream

in an ideal

previously

speed

(9)

(fluid

pressure,

conclusion

demonstrated

the

the

=pt

of high-speed

throat

since

of manometers

equation

tube.

in the

the total

V1

for as the

the venturi

and a set

By the

everywhere

+p2

than

Pl'

tube

2

in the region

lower

of a real

speed

1 and

flow.

is incompressible)

hence

must decrease to maintain a constant value below the venturi tube show this interchange

decreases

as one

mum

than

all along

low-speed

at station

1 =_p2V2

is greater

P2

that

is constant

tube

of a venturi

pressure.

at stations

V2

Venturi

setup

can express

+pl

that

pressure

Pt

lplV122

Since

pressures

static

highest

one

pressures

complete

than

pressure

Therefore,

dynamic

the

28.-

re,UUlll]

flow

fluid.-

following

speed

level

liquid

has

risen

pressure.

increases,

the

of total pressure Pt" of dynamic and static from

this

increases levels above At the

is that

in the of the the

throat

the

region

The static of

manometers

reference this

level

is the mini-

is the highest.

To supply section

flow and by the

static

drawn

speed,

it follows

a point

expands

of reference the previous

in the discussion

discussions

to

of venturi

37

flow to the ideal fluid flow past an airfoil. Figure 29(a)showsa "symmetric" (upper and lower surfaces the same) airfoil operating so that a line drawn through the nose and tail of the airfoil is parallel to the free-stream direction. The free-stream velocity is denotedby Vo_ and the free-stream static pressure by Po_. Following the particle pathline (indicatedby the dotted line andequal to a streamline in this steady flow) which follows the airfoil contour, the velocity decreasesfrom the free-stream value as one approachesthe airfoil nose (points 1 to 2). At the airfoil nose, point 2, the flow comesto rest (stagnates). From Bernoulli's equationthe static pressure at the nose, point 2, is equal to the total pressure. Moving from the noseup along the front surface of the airfoil (points 2 to 3), the velocity increases and the static pressure

decreases.

airfoil,

point

lowest

value.

By the

Beyond to 4, the point

this

point

velocity

as one

comes

Beyond

the trailing

reached

and the

and 29(c).

Note

particularly

ent).

This The

parallel fect

rear

defies

forces

parallel

a fluid

by the

and

is zero

for this

If, however,

the

symmetry

results. Air

continuity

and

of zero

lift is determined

distribution

38

intuition

components

metrical.

force

a planar

no matter

This

viscosity.

Bernoulli

pressure

particular

fluid. principles

case

the

upper

since

at an angle and lower

and

the

It possesses still

apply

section

main

gradi-

and the

operating

drag

in a peris.

This

It is the

of the static-pressure of the rear

between pressure to the

free

surfaces

airfoil

surface

in the

world.

of the airfoil. and lower

distribution

is sym-

stream,

no longer

With

always

the upper

slight The

the pressure exists

of the airfoil

viscosity. real

of

pressure

paradox.

surface

function

station

of the airfoil

on the

the

in fig-

gradient)

direction

components

forces

veloc-

case.

as D'Alembert's

difference

is tilted

desirable

airfoil

on the front

static-pressure

between

is not a perfect and

of the

pressure

the orientation

The

direction

airfoil

is very

is known

shown

(up to the

fluid

is

These

are

free-stream

what

value

(a positive

in the real

For

the

surfaces

pressures

direction.

to the free-stream

balance

increasing

to the

zero

streamline

edge,

pressure.

pressure.

(a negative

3

at the trailing

free-stream

static

pressures

norma]

is always

the

its

points

to the total

of the airfoil

as the force

physical

of assuming

surfaces

until

on the

pressure

of the airfoil,

equal

until

point

the static

increases

pressure

will be of importance

and

surface

the center-line

decreasing one has

free-stream

the drag

result

The

has

rear

to free-stream

front

the thickest

value

increases

for

on the

reaches

pressure static

returns

surfaces

is defined

to the

seemingly

one

relationship lift

fluid,,

exactly

that

thickness), on the

the

speed

pressure

the

static

with

the flow

as one

its highest

along

distributions

29(b)

whereas

and the

edge

ity and static-pressure

maximum

acquired

moves

to rest

static

equation,

has

decreases

4, the flow

ures

continuity

3, the velocity

and a lift

section.

modification, airflow

over

the an

speed static

lowest pressure

mu

mu

v_ ®

Zero

speed

High

pressure

_

....

(al

spee_ High

(Total

pressure

(Tot

pressure)

al pressure)

v4

g

P_

\

/

_'x_

_"

_reatcr

\

than

\

\

cce,_'"

>

Leading edge

(b)

Trailing edge

(V = O)

Leading-edge

Traili

highest

pressure

I

P Increasing

Pt

1) : .\_x_

e pressure

(posing

"I

(a) Total

aircraft

shocks.

e,

$

F-84

h_

(1949)

X-15

_

(1964)

0._ i- _ F-100

(1954)

f

/

e_ b_

/

.= 0.4 e.

x 0.6

I 0.8

i 1.0

Mach

number

(b) Improving Figure The question value

closer

really

suggests

engine

thrust

delaying Mach

88.-

as to whether

is the ability before

the transonic

to 1).

(1) Use

of thin

airfoils

(2) Use

of sweep

(3) Low-aspect-ratio (4) Removal

may

the drag-divergence

delay of novel

aerodynamic

to fly at near-sonic

wave

closer

large

drag

rise

flight.

characteristics.

subject

encountering

number

transonic

Supersonic

one

to 1 is a fascinating

I 1.2

wave

velocities drag.

There

(or equivalently,

These

include

of the wing

forward

Mach

designs. with are

increasing

the

What

same

a number the

number

to a

this

available of ways

of

drag-divergence

or back

wing

of boundary

layer

and vortex

generators

109

(5) Supercritical These

methods Thin

are

to the

is used,

the flow

Thus,

The

square

wave

of the

speeds

one

area-rule

technology

now discussed

airfoils:

portional

foil.

and

may

individually. drag

rise

associated

thickness-chord

around

the

airfoil

fly at a higher

free-stream

one

reaches

the drag-divergence

of using

thin wings

are

that

are

tural

speed

support

shows the

range

and they

members,

the

airfoil

sections

have

increased,

(fig.

89(b))

was

high and

used

to achieve

lift.

landing

mishaps

were

of using

a thinner

the drag

divergence

Mach

reduce

the

shock

waves

reduces

It was effects

confirming One section

(t/c

chord

that

been

are

number

(at which

a sonic

delayed

to higher

values.

Figure has

flow has

92(a)

of sweep

longer

reduced.

as the

sweep

of sweep

than

(See fig. more

time

point

92(b).)

appears)

93 shows

a modern however,

to adjust

and

jet

employing

stability

ratio

airflow If the wing

a thinner

to

airfoil

The, critical

accomplish forward

new

of thickness

Mach

and handling

airfoil

encounters

situation.

will

of sweep.

section.

the drag-divergence

airplane

in the

the

it

data

a thinner

with

using

to the

or sweepback

Additionally,

the wing

maximum

and

of the

experimental

airfoil

flow over

One is effectively

in which

that

delay

formation

using

is shown

a typical The

the

may

to a high degree

wing

previously.

particularly 90 illustrates

sweep

number.

a straight Notice

penalized

in particular,

91 shows

as effectively

Sweepforward

disadvantages,

Mach

no sweep

A, the same

was

As

F-104

but was

Figure

that

of a wing

to the wing.

angle

section

results.

effect

decades.

value.

Figure

from

struc89(a)

The

airplane

will delay

to a higher

numbers.

is swept

In figure

to some

sections has

the

perpendicularly

is now swept airfoil

view

as a wing

wing

tanks,

three

Notice,

who proposed

A swept flow

drag.

in the

Figure

drag

pilots.

to a greater

in 1935

all Mach

of this

disadvantages

fuel

decreased. wave

untrained

transonic

is delayed

Busemann

over

reduced).

approaching

number

in transonic

drag result

may

on the

past

airpoint

produced)

wing.

the

have

speed

among

of compressibility.

wave this

common

over

possible

landing

a sonic

(wing

pro-

section

thicker

The

of lift

a thicker

ratios

for the

number.

structure

than

minimum

the

section

Adolf

encountered

the

etc.)

airfoil

before

(in terms

U.S. fighters

the

As a result,

the effect

Sweep:

by three

number

less

the thickness-chord

designed

with low subsonic

effective

stations,

those

Mach

can accommodate

armament

speeds

less

flow is roughly

If a thinner

than

Mach

and before

subsonic

(t/c).

will be less

appears

they

with transonic

ratio

Mach

number

are

these

desired

sweep.

Forward

characteristics

at low

speeds. A major

disadvantage

wing,

and the boundary

roots

for

II0

sweepforward.

of swept

layer

wings

will thicken

In the case

is that toward

of sweepback,

there the

tips there

is a spanwise for

sweepback

is an early

flow along

the

and toward separation

and

the

Chord

Thickness

_-r

_ZZZZzzz_-

Very

(1940' s)

F-86

(1950' s)

F-104

T (a) Changes

P-51

in airfoil

(1960' s)

sections.

thin wings

(b) F- 104G airplane. Figure

t/c =

89.-

Thin

airfoils.

.18

t/c= .o6

O

I 0 Mach

Figure

90.-

I I,

A .5

Effect

of airfoil

i 1.0

number

thickness

MUD , drag

I ,i

on transonic

divergence

Mach

drag.

Lift = 0;

q = Constant;

number. III

0.10 0° Sweep

10 1/2 ° Sweep

I

0.05

40 ° Sweep

I 49

0

.7

.8

.9 1.0 1.1 Mach number

Figure

91.-

Effects

transonic

drag

of sweep

on wing

coefficient.

(b) Swept wing

(a) Unswept wing

I

1/4 ° Sweep

Chord

v_

[-

Figure

112

92.-

Sweep

reduces

Chord

swept

effective

[

thickness-chord

ratio.

Figure 93.- HFB 320Hansa Jet with forward sweep. stall of the wing-tip sections andthe ailerons lose their roll control effectiveness. The spanwiseflow may be reducedby the use of stall fences, which are thin plates parallel to the axis of symmetry of the airplane. In this manner a strong boundarylayer buildup over the ailerons is prevented. (Seefig. 94(a).) Wing twist is another possible solution to this spanwiseflow condition.

Stall

fence

Wing

(a)

__.....-%_

Mig-19

_

_

Vortex

generators

(b)

Figure

94.-

Stall

fences

and vortex

generators. 113

Low aspect ratio: The wing's aspect ratio is another parameter that influences the critical Mach number andthe transonic drag rise. Substantialincreases in the critical Machnumber occur whenusing an aspect ratio less than aboutfour. However, from previous discussions, low-aspect-ratio wings are at a disadvantageat subsonic speedsbecauseof the higher induceddrag. Removal or reenergizing the boundarylayer: By bleeding off some of the boundary layer along an airfoil's surface, the drag-divergence Mach number can be increased. This increase results from the reduction or elimination of shock interactions betweenthe subsonicboundarylayer andthe supersonic flow outside of it. Vortex generators are small plates, mountedalong the surface of a wing and protruding perpendicularly to the surface as shownin figure 94(b). They are small wings, andby creating a strong tip vortex, the generators feed high-energy air from outside the boundarylayer into the slow moving air inside the boundarylayer. This condition reduces the adverse pressure gradients andprevents the boundarylayer from stalling. A small increase in the drag-divergence Mach number can be achieved. This methodis economically beneficial to airplanes designedfor cruise at the highest possible drag-divergence Mach number. Supercritical and area-rule technology: One of the more recent developmentsin transonic technologyanddestined to be an important influence on future wing design is the NASAsupercritical wing developedby Dr. Richard T. Whitcomb of the NASA Langley Research Center. A substantial rise in the drag-divergence Mach number is realized.

Figure

95(a)

-

beyond

the

layer.

Figure

(supercritical arated

boundary

same tion

Mach

number.

and strength

shock-induced even

shows

The

of the

This

critical

shocks

has

operating

number)

shows

is greatly

closer

decreased.

represents

with

near

airfoil which

to the

trailing

edge.

increase

Mach

and

operating

surface

critical

1 region

shocks

upper

The

a major

the Mach

its associated

the supercritical

a flattened

to a point

delay

airfoil

Mach

95(b)

airfoil

separation

up to 0.99.

a classical

sep-

at the

delays

the

forma-

Additionally, number

in commercial

the

is delayed airplane

performance. The surface new

curvature

of the supercritical

supercritical There

First,

wing

are

by using

subsonic drag

two the

cruise

divergence without

higher

at lower

lift

has

same

speeds.

camber

penalty.

the

its lift.

Because

at the

ratio, the

transonic

supercritical This

airfoil

of the flattened

However, trailing

of the supercritical

thickness-chord 1 before

wing

lift is reduced.

increased

numbers,

a drag

the

advantages

Mach

Mach

gives

airfoil,

main

near

to be used

114

of a wing

to counteract

airfoil reduces

this,

the

edge. airfoil

the supercritical drag

upper

rise.

as shown airfoil

in figure

permits

Alternatively,

permits

a thicker

structural

weight

96.

high

at lower wing and

section

permits

I

trong shock ---.

_

Separated

(a) Classical

boundary

l_ayer

airfoil.

Weak shock

_Smaller

separated

boundary

layer

( (b) Supercritical Figure

95.-

Classical

and

airfoil. supercritical

airfoils.

( _M

15"{

cruise

r_ _9

Thickness-chord

Figure Coupled Dr.

Richard

transonic

to supercritical T. Whitcomb

airplanes

Basically, obtained

96.-

when

and area

the

Two uses

technology of NASA

later

ruling

that area

nal axis

can be projected

into a body

changes

in cross

along

area

against

body

section position,

its

Research

minimum

the resulting

Or, curve

concept

Center flight transonic

distribution

of revolution

length.

wing.

"area-rule"

to supersonic

states

cross-sectional

of supercritical

is the

Langley

applied

ratio

in the early

which

is smooth.

developed 1950's

by

for

in general. and

supersonic

of the airplane

if a graph

also

is smooth is made

along and

drag the

is

longitudi-

shows

no abrupt

of the cross-sectional

If it is not a smooth

curve, 115

then the cross section is changedaccordingly. Figure 97 presents the classic example of the application of this concept- the Convair F-102A. The original Convair F-102A was simply a scaled-upversion of the XF-92A with a pure delta wing. But early tests indicated that supersonic flight was beyond its capability becauseof excessive transonic drag andthe project was aboutto be canceled. Area ruling, however, savedthe airplane from this fate. Figure 97(a) showsthe original form of the F-102A andthe cross-sectional area plotted against bodystation. Notice that the curve is not very smoothas there is a large increase in cross-sectional area whenthe wings are encountered. Figure 97(b)showsthe F-102A with a coke-bottle-waist-shaped fuselage and bulges addedaft of the wing on each side of the tail to give a better area-rule distribution, as shownin the plot. The F-102A was then able to reach supersonic speedsbecauseof the greatly reduced drag andentered military service in great numbers.

Bulges

_ o_

Nose

[eal

____

Body

(a) YF-102A

station

before

capable

of cruising

critical

wing

cross-sectional

is used. area

at Mach

/-Indent.fuselage

ruling

has

this The

of F-102A

been

around

98 shows Notice

Body

/Actual

station

(b) F-102A

Area

numbers

that the shape is near optimum. near-sonic Mach number.

ll6

ruling.

concept

Figure plot.

Nose

97.-

the area-rule

_

_

Tail

area

rear_

Ideal

Actual

Figure Recently,

at

the curve shocks

applied

0.99.

to design

area

ruling.

a near-sonic to area

obtained

now is completely and drag

after

airplane.

In addition

configuration

Tail

divergence

transport

ruling,

and the

a super-

resulting

smooth

and

are

delayed

indicates to a

--'-_-.

/--

smooth

Completely

surve

e_

/

o

\

t

I

%

/

\

/

Body

Figure

98.-

\

station

Near-sonic

transport

area

ruling.

117

118

VI. SUPERSONIC

The

previous

through

proper

directly

applicable

supersonic

design,

wave

three

dimensions,

extends

will

back

wing

loss

exist

back

Mach

behind

that

cone

has

dominant.

They

include

high

of attack

The

is designed

cruise,

it would is the

and how,

also

are

drag

in the

it was

shown

that

a bow

1.0.

(See

swing-wing

lift,

airplane

does

the

is the

advances

and reduced not have

efficiency,

airplanes

added

weight

employing

solving

plotted

airplane. speed

problems

span

and

regimes,

it is evident

One

major

of the also.

sweep

Figure

drag

advan-

numbers. transonic

For and

swept

and

the

are ratio),

wing

for equal

that total

drawback mechanisms. 103 shows

an airplane

supersonic

102 shows

number

not necessarily

over

a straight

of trailing-edge

Figure Mach

delta

or low aspect

cruise

Although

role,

the

disadvantages.

wing

against

individually. and complexity

these

wing

or swing-wing.

for the Mach

the disadvantages

subsonic

a straight

can in a multimissioned

other

are

sweep

respective

these

of a large

in fact,

Mach

effectiveness

for example,

to combine

and,

however,

of

swept

of minimizing

(due to small

most

supersonic

at higher

in the interest

drag

over

qualitatively

wing

numbers,

As long as

a highly

rapidly

Mach

to compensate

higher

of even

101 shows

or delta

Mach

maximum

swept-wing

capability

than

a swept

edge

to increase

Figure

wing

In

as it

the

the advantage

swept at still

leading

drag

primarily

for the variable

in their

a simple

that

flow

100) has

88.)

cone)

numbers.

is subsonic

(fig.

fig.

(a Mach

Mach

But,

the

high induced

for

wing

than

total

over

be advantageous

and

configurations

the

used

of aerodynamic

straight-wing

area

to be multimission,

logic

a measure

A delta

At subsonic

straight-wing

which

airplanes

used

99 demonstrates

there

in sweepback.

has

been

drag.

ical

rise

wave

in shape

increasing

cone,

preferable.

wing

wave

airplane

techniques

above

Figure

with

Mach

wing

causes

supersonic

angles

back

may approach

becomes

a straight

a cone

the

greater

condition

(no sweep)

better

drag

minimum

formation,

is in reality

of the airplane.

experienced

Sweepback

This

of the

to fly with

numbers

low drag.

but also

the This

flaps.

on the transonic

Mach

swept

and relatively

numbers,

tage

Many

of shock

for free-stream

increasingly

angle

wing

mainly

airplane

discussion

the nose

of lift usually

wing.

the

the bow shock

is swept

the wing

to the

from

becomes

sweep

centered

it may be delayed.

in designing

returns

shock

the

has

regime.

If one

cone

discussion

FLOW

design. (L/D)max,

an optimum to the

an airplane speed of the

optimum with

regime,

a

be

swing-wing But technolog-

a variety

of modern

a swing-wing.

119

In addition may

also

slender,

be

to low-aspect-ratio

minimized

cambered

by

employing

fuselages

minimize

wings

at

supersonic

speeds,

thin

wings

and

area

drag

and

using

also

improve

supersonic ruling. the

Also

spanwise

wave long, lift

distribution.

Conical

bow

M_=

shock

F-100D

1.3

Conical

bow

1_=

shock_

2.0 English Lightning

Figure

120

99.-

Mach

cone

and

use

of sweep.

drag

F-106

Figure

100.-

Delta-wing

airplane.

wing __

Straight

Swept ', /

¢)

St raight-wi ng

Swept-back advantage

__

1.0

J

I

1.5

2.0 Mach

Figure

101.-

Wing

as functions

design

drag

of Mach

number

coefficients

number.

121

25

2O

15

,-1 10

_

!

0

1.0 Mach

Figure

102.-

Variation

of

,_'l,-Ji

(L/D)ma

x

Optimum swept wing

!

J

2.0

3.0

number

with

Mach

number.

Variable

¢_::!

Mirage

III

G

F-14A

Figure

122

103.-

Modern

variable-sweep

airplanes.

sweep

airplane.

The SST On June 5, 1963in a speechbefore the graduating class of the United StatesAir Force Academy, President Kennedycommitted this nation to "developat the earliest practical date the prototype of a commercially successful supersonictransport superior to that being built in any other country in the world .... " What lay aheadwas years of development,competition, controversy, andultimately rejection of the supersonic transport (SST)by the United States,and it remains to be seenwhether the British-French Concordeor Russian TU-144 designs will prove to be economically feasible andacceptableto the public. NASAdid considerablework, starting in 1959,on basic configurations for the SST. There evolved four basic types of layout which were studied further by private industry. Lockheedchoseto go with a fixed-wing delta design; whereas, Boeing initially chosea swing-wing design. One problem associatedwith the SSTis the tendencyof the noseto pitch down as it flies from subsonic to supersonic flight. The swing-wing can maintain the airplane balance andcounteract the pitch-down motion. Lockheedneededto install canards (small wings placed toward the airplane nose (fig. 104(a))to counteract pitch down. Eventually, the Lockheeddesign useda double-delta configuration (fig. 104(b))and the canards were no longer needed. This design proved to have many exciting aerodynamic advantages. The forward delta begins to generatelift supersonically (negating pitch down). At low speedsthe vortices trailing from the leading edgeof the double delta (fig. 105(a))increase lift as shownin figure 105(b). This meansthat many flaps and slats could be reducedor done awaywith entirely anda simpler wing design was provided. In landing, the doubledelta experiences a ground-cushion effect which allows for lower landing speeds. This is important since three-quarters of the airplane accidents occur in take-off andlanding. Figure 106showsthe British-French Concorde wing

called

low- speed

and

the Russian

the ogee subsonic

TU-144

wing.

prototypes.

It, too,

uses

They

use

the vortex-lift

a variation concept

of the

double

for improvement

delta in

flight.

-Canards lble

delta

I i

(a) Lockheed

(b) Lockheed

CL-823. Figure

104.-

Lockheed

double

delta.

SST configurations. 123

(a) Vortices

on double

delta

wing.

Nonlinear coefficient vortices

Angle

(b) Lift Figure Ultimately, U.S.

SST competition.

from

one

design.

The

engines

were Despite

cal advances

124

with

Major

moved the

increase

Lifting

design cruise

the

size

changes

was

evolution

of the

were

lift-drag

of double

design

107 shows The

due to vortices.

vortices

a swing-wing

designs.

supersonic

attack

coefficient

105.-

Figure

of the NASA

requirements.

faces.

Boeing

of

incorporated

ratio

wing.

selected

grew into

as the winner design

the

from impinging

the

exhaust

advantages

previously

quoted

for

in time.

Because

airline

Boeing

6.75

a swing-wing

of the

originally

to meet

increased

aft to alleviate

did not appear

delta

of this

airplane

further

in construction

excess lift due to on wing

derived payload

2707-100

to 8.2 and the on the concept,

of the

rear

tail

sur-

technologi-

swing-wing

mech-

Russian

Figure

i06.-

British-French,

Y I

Figure

10'/.-

'

TU-144

and Russian

_

Evolution

of Boeing

SST airplanes.

Model

733-197

Model

733-790

Model

2707-100

Model

2707-300

SST design. 125

anisms

and beefed-up

tion of payload Figure

resulted.

107 shows

continuing

into advanced

cruise

M = 2.7,

configurations

with

at the

NASA

126

at

transports

a cruise

108.-

speed

-

Research

Langley

problems

the B2707-300.

to cancel

in the

of

incurable

but to adopt a fixed-wing

and Russian

M = 2.2 to 2.4,

Langley

Figure

States

Concorde

supersonic

and TU-144

tested

adopted

led the United

the British-French

placement,

had no recourse

configuration

factors

Concorde

design

due to engine

Boeing

the final

and environmental While

structure

the

United

States.

Center

advanced

is shown

cruised

analyzed.

in figure

SST design.

is still

Whereas,

design

are being

economic,

in 1972.

fly, research

and the Boeing M = 3.2

concept.

Political,

project

TU-144

in reduc-

108.

the at One

such

Sonic One

of the

commonly

referred

to a description A typical one

of the

tail

(See fig.

as shown. above pressure place

The

and

on the

pressure

a final

in one-tenth

with

resulting

coming the

ground,

recompression

shocks

some

is felt

leading from

appear

and edges,

the air-

to be "N"

below The

return

(bow shock)

wing

pressure.

is

supersonically.

as an abrupt

and heard

must

distance

decompression

to atmospheric

transport

one

flying

changes

pulse

and is felt

boom,

one at the nose

pulse

by a rapid

or less

sonic

off the canopy,

main

this

any supersonic

an airplane

waves,

pressure

followed

of a second

about

shock

waves

facing

To explain

formation

to merge

To an observer

atmospheric

boom."

Shock

tend

109.)

"sonic

two main

shock).

etc.

of the problems

shock-wave

generates (tail

nacelles,

plane.

objectionable

to as the

airplane

off the

engine

more

Boom

shaped

compression atmospheric

total

as a double

change jolt

takes

or boom.

airplane Bow shock Tail shock

underpressures Overpressures with distance

decay and

-Underpressure

Overpressure

"N"

Figure 109.- Sonic-boom The such

sonic

boom,

as airplane

angle

spheric

turbulence,

overpressures

or the overpressures of attack,

atmospheric

will increase

sectional

area,

decrease

with

will

altitude,

with increasing

decrease

increasing

conditions,

with

Mach

increasing

that

shaped

generation.

cause

them,

cross-sectional

altitude,

are

area,

and terrain. airplane

pulses

controlled Mach

As shown angle and

of attack first

by factors

number,

atmo-

in figure and

increase

110, the

crossand

then

number. 127

1 f

O9

o

6

0 Angle

of

Cross-sectional

attack

area

1

Altitude

Figure Turbulence the impact

away and

travel from

they

on the

to nothing

the

airplane ground

Orthogonals shock

normal

may

and produce

(normal

that

of the flight the

multiple

the

speed

of sound

in which will

directly

beneath

waves

locally

-Supersonic airplane

by

Stratosphere _/;(_?:S_)_:

_W ropopau

s e t///_i:_:_/(

_

Boom on

Troposphere

heard _

,I

ground

_Maximum boom

Figure

111.-

Refraction

of shock

waves.

increases

point the

a superboom.

to

booms

the overpres-

at some

It is interesting

of shock

lessen

overpressures.

cause

path. set

thus

may

they

is felt

and

waves)

refracted

128

the

the directions

and

boom

concentrate

profile

amplify

profile,

that

sonic side

"N" wave

and buildings

case

number

overpressures.

in fact

atmospheric

strongest

on either

the

may

111 shows

in this The

hand,

by terrain

Figure

refracted

sonic-boom

smooth

other

In a normal

altitude. are

supersonic

intersect

affecting may

overpressures

the Earth.

decreases

a turning

or,

aftershocks.

with decreasing sures

boom

of the

post-boom

Factors

in the atmosphere

of the

Reflections

110.-

Mach

curve

airplane to note where

that

or

Perhaps

the greatest concern expressed about the sonic boom

public. The effects run from structural damage

is its effecton the

(cracked building plaster and broken

windows) down to heightened tensions and annoyance of the citizenry. For this reason, the world's airlines have been forbidden to operate supersonically over the continental United States. This necessitates, for SST operation, that supersonic flightbe limited to overwater operations. Research for ways in which to reduce the sonic boom continues.

129

130

VII. BEYOND

THE

SUPERSONIC

Hypersonic Hypersonic although

flight

no drastic

magnitude

have

research

been

waves

shocks, the body

in today's

leading

surfaces

sufficient

the

112 shows

wing

for effective

are

being

ure

113 shows

Although

commercial

ciple

that

the

pulsion

This

Because tering landing ballistic

from

for example,

flight

does

away

the

with

the

normal

of

metals

or methods

wing

that

of the of sweepback.

is used.

placed

so that

they

if shielded

will be ineffective.

that

exhibited

airplane control

strong

heating

Otherwise,

they

airplanes

shows

surfaces

cost

with

and safety,

distance. little

knowledge

much the

of this

highly

swept

out on the wing

that

The

waves

moving

parts

landing

engine the

the

studies

design.

Fig-

have site.

for

that

on the

prin-

combustion

in

designs

to maneuver reentered Large

the

an efficient

recognized crew

works

air

field.

long been

the

realized, for

Economically,

in this

it has

enable

speeds.

represents

Bodies

over

being

necessary

and

Lifting

Up to now spacecraft control

ramjet

compress

continuing

would

from

(HST).

at hypersonic

shock

is also

be found

is a long way

engine.

many

NASA research

must

problem

is the ramjet numbers

a great

entries

to operate.

transport

major

Mach

of the

spacecraft

them

the basic

hypersonic

prospect

method.

part,

degree

design

about

has

they

most

temperature

a high

be strategically

craft

that

the

materials

must

reentry

hypersonic

is another

at high

engine.

most

The

by using

research

angle

Aerodynamic

required.

hypersonic

by NASA to obtain

a proposed

Propulsion promising

across

flight

NASA X-15

Dynasoar

a high

speeds.

control.

conducted

most

modified

X-20

Secondly,

a flat-plate

fuselage,

two proposed

The

and the

tips

ratio,

pressure

flow by the

philosophy.

delta

lift-drag

dynamic

For

new

of this

at these

the body.

flight

5

NASA X-15

at such

be reduced

for hypersonic

approaching

Figure

may

and the

back

therefore are

Mach

speeds

about

hypersonic

effects

To date,

increase.

melt;

beyond

encountered

in nature.

sustained

quickly

wing

a good

trail

temperature

For

would

to obtain

Control

design

problem.

of the airplane

Additionally,

from

a drastic

are

layers

turbulent

this.

and spacecraft

by a body

highly

at speeds

to define

problems

the boundary

the high-temperature

edge

encounter

are

airplanes

can withstand

evident

formidable

undergoes

is a major

are

as flight

only by rockets

with

layers

the air

defined

generated

interact

boundary

used

achieved Several

the shock seriously

these

flow changes

airplane.

First, may

is arbitrarily

Flight

the

pro-

of reencraft

to a

and followed

near

recovery

forces

and 131

Figure 112.- Examples of hypersonic designs.

°

Figure operations been

involved

spacecraft. because

132

were

usually

in designing They

of their

113.necessary. aircraft

are called body

Proposed

shapes.

lifting

hypersonic

Starting

in the late

that produce bodies,

transport

more

for they

lift have

1950's, than

sport

(HST). however, drag

no wings

NASA has

and yet resemble but obtain

lift

Figure teristics

114 shows

and flight

the NASA Ames advantages

The

of the shapes

qualities

of this

Research

of stability

speeds.

four

Center

lifting

10+ and,

top and a flat

a flat

bottom.

pointed

belly.

two since

Rebuilt

with

at Mach

a rounded

The

it now has

handling

in contrast

developed

to the

the

Center

M2 vehicle,

X-24A

is very

it, like

a double-delta

at

at subsonic

Research

although

charac-

and combines

ratios

Langley

Marietta

type

belly

lift-drag

rounded

the

M2 vehicle

a rounded

NASA

Martin

it is more

as the X-24B,

The

with high

trim

sesses

the previous

topped

speeds

by the

optimum

to evaluate

concept.

developed

to provide

from

is flat

tested

body

shaped

shape

unusual

at hypersonic

HL-10

being

is it pos-

different

the HL-10,

planform

and

in has

a more

nose.

Northrop

M2-F3

Northrop

HL-

10

Martin

Martin

X-24B

X-24A J

Figure The sonic

lifting

speed

bodies

ranges

of more

advanced

benefiting

from

being

to show

Lifting

flight-tested

how control

vehicles. this

114.-

are over

research

is the

Space

cost

method

settled

is shown

rockets

engines

is the actual

Shuttle

represents

of delivering

upon

solid-fuel stage

Space

in figure

and a large

to complete part

and

of the

States'

vehicle

into

may

generation

low super-

aid in the

of vehicles

orbit.

to go into

commitment

to and

booster

nonrecoverable

the boost total

The

ratio

and

landing

primarily

Shuttle

payloads

l15(a).

subsonic

Shuttle.

the United

returning

the

lift-drag

of a new

Space The

exploring the

Representative

bodies.

stage

external The orbit

from

and

orbit.

consists

fuel orbiter

to developing

tank stage

return

The

basic

a lowdesign

of two recoverable used

by the

shown to Earth

orbiter

in figure

llS(b)

to a controlled

133

Liquid

fuel

_.-Delta-wing-

orbiter

(a) Space Shuttle.

udder

Cargo bay _

(b) Orbiter. Figure landing.

Aerodynamic

mission

when

from

subsonic

ated

with the

staging

The must

boost

and landing

hypersonic landing capability

about

30 °.

range

and

l15(b))

this

2000

km.

This

high

and landing

entire

are

range

some

solid-fuel

is an area like

uses

a conventional with this

a double-delta

and

still

orbiter

the

reenters

of attack

part

for orbiter

Mach

on the

concern.

of the

The There

has

as well

orbiter are

vehi-

numerous

mission.

configuration a good

vehicle,

numbers.

lift-drag

to optimize ratio

a side-to-side

the atmosphere

is used

associ-

by parachutes,

airplane.

wing

provide

capability,

angle

of great

acting

of the

numbers

problems

pressures boosters

stages

of Mach

unique

both at low and high

associated

The

boost

of dynamic

of the

land

lift-drag

designs.

the

The

There

mission

characteristics

of about -

of the

problems

(fig.

With

evident.

considerations

research

phase.

recovery

to deorbit

flight

as the

Shuttle

about

is covered.

the

phase

orbiter

are

such

control

be able

The

134

phase

Space

is centered

pressures

to supersonic

aerodynamic

attack

dynamic

aerodynamics,

as stability

cle

interest

115.-

to concentrate

in the range

at a high the

the

angle

maximum

of

aerodynamic tection

heating

on the underside

is provided.

a reaction

control

control

yaw)

and

become

effective.

In the system, elevons

is deployed

challenge

to aerodynamic into

(combined

to slow

the unknowns

reaches

but as the

On landing,

parachute further

upper

of the vehicle

the the

research

elevators rudder

pressure and

splits

attitude

builds,

ailerons

to control

to come

The Space

thermal

Shuttle

and is a stimulus

pro-

is controlled

the vertical

open to act as a speed

to a stop.

for years

of high-speed

the greatest

of the atmosphere,

dynamic

orbiter

where

pitch

by

tail

(to

and

roll)

brake

and a

represents for

a

probing

flight.

135

136

VIII. PERFORMANCE In the earlier discussions, the conceptsof lift anddrag were explored extensively to discover howthese forces arise. With these basic ideas in mind, it is relatively easy to follow the results of the application of the fundamentalforces on a complete airplane. As indicated earlier, there are four basic forces that act on an airplane - these include lift, drag, weight, andthrust. Additionally, in curved flight another force, the centrifugal force, appears. Performance, to be consideredfirst, is basically the effects that the application of these forces have on the flight path of the airplane. Stability and control, considered later, is the effect that these forces have over a short term on the attitude of the airplane itself. For performance purposes the airplane is assumedto possessstability and a workable control system. Motions of an Airplane Figure 116illustrates the various flight conditions encounteredby an airplane. All the motions may be groupedinto oneof three classes: (1) unacceleratedlinear flight, (2) accelerated and/or curved flight, and (3) hovering flight. Performance of an airplane is a very broad subject and much could be written on it alone. In the interest of brevity, therefore, only the simplest, but probably the most important, aspects of airplane flight are considered. Class 1 Motion Straight flight

may

and

occur

it is usually dition

been

Figure

altitude,

The weight. ities

to the along

the

this

combining

system

seen

thrust

must

it with

surface

that

plane. lift

equal

must

the the

plane

this may

condition

in the

for

design

and

simplicity

equal

weight.

and

important

of an airplane.

level

level since

This

con-

flight

path

will be made. flight.

it is assumed

the flight

straight

it is very

comments

straight

For

Although

flight,

additional

and for

The that

to be horizontal,

tile thrust or constant

To fly at constant

velocity

(unac-

the drag.

of the airplane

examines

which

condition

the

force

flight).-

of the total

but some

horizontal

(cruise

section

on before

Earth's

velocity If one

over

a small

flight

the standard

touched

it is easily

celerated)

over

117 shows

is horizontal acts

only

unaccelerated

considered

has

always

level

must

be sufficient

statement

closely,

fly straight that

Lift

to produce

it says

and level. = Weight,

that

there

Expanding one

a lift

equivalent

is a range equation

to the of veloc-

(25) and

obtains

137

1 Weight = _ p_V_2CL If it is assumed one

easily

decreases, Minimum CL,max, flight a small

observes which flying that

that may

speed

is,

is limited value

that

near by the

of

CL

(36)

S

the weight,

air

as the velocity

be accomplished for

straight

the stall thrust

V_

available a small

p_,

The

and

increases,

by a decrease

and level

angle.

and hence

density

flight

occurs

wing

when

flying

the engine.

angle

area

the wing in the

maximum

from

wing

the wing for

condition

Maneuver (or combat)

Descent turn

_Unaccelerated, [III]ffm]Accelerated

Figure

138

116.-

Airplane

flight

flight

direction linear

and/or

conditions.

flight curved

CL

is operating

straight

of attack.

Indicates

constant,

of attack.

Maneuver (or combat)

_lP

are

lift coefficient angle

speed

This

S

flight

also

and requires

at level

In conclusion, at low speedsto fly straight andlevel the airplane angle of attack is large (fig. l18(a)) whereas for high speeds the airplane angle of attack is small (fig.

118(b)).

Lift

Thrust Flight

F-106

path

horizontal to ground

Figure

117.-

Weight

Straight

and level

flight.

Lift

Low

(a) Straight

Need to

less

angle

generate

Horizontal

level

-

Flight

path

Figure

dive. flight

It has path.

118.-

unaccelerated

systems been The

Speed

ascent

for the

cases

assumed

that

climb

speed

lift

(b) Straight

the force

= Drag.

low speed.

High

Straight,

Thrust

of attack

same

z

and

= Weight;

or descent

and

level

high speed.

effects

on straight

and level

(climb)

or descent

(dive).-

of an airplane the

-

speed

thrust angle

in a straight,

line is given

lies by

along +_

flight.

Figure

119 illustrates

constant-velocity the

free-stream

or

->,, respectively.

climb direction

or or

If the

139

+ y

(Horizontal

_

Weight

t (a) Climb,

unaccelerated.

J J

J

Horizontal

(b) Dive, Figure forces

are

summed

weight

force

parallel

is resolved L=W

119.and

unaccelerated.

Unaccelerated perpendicular

ascent

to the flight

into two components.

cos

y=

W cos

and

One

descent. path,

To maintain weight maintain

weight for 140

a straight

perpendicular

(-y)

climbing

velocity

the forward component

constant

(-y) =D-

to the

a constant

retarding

sin

along

velocity.

motion the

flight the

path thrust

of the flight

(eq. must

airplane.

path

helps

the

(Climb or dive)

(37)

(Climb)

(38)

(Dive)

W siny

(or diving)

that

obtains

T = D + W sin y T =D +W

it is seen

flight (37)). equal

path,

the

In the the

In the the thrust

lift

case

drag case

equals of the

plus

the

component

of

climb

condition

to

a weight

of the dive

by reducing

(39)

the

component

condition

the

drag

component

The conclusion velocity ation from the

and

use

of a car

where

slowing car

less

sin Lift

_, = 0

(39). and

= Weight

_, = 90 °, and vertically tical

climb,

thrust

to dive

in going

speeding

It is interesting (38), and

one

one must

down

from

is that

First, cos

is equal

This

the

lift

Horizontal

equals

yields

the

drag

cos

plus

zero

the

/

flight,

at constant

is analogous

thrust)

gas"

cases the

previously (T = D).

y = 0.

Thus,

airplane

weight

This

condition

(L = 0).

This more

up on the

special

= Drag

and

(apply

to climb

to the

to prevent

(use

less

of the

use

thrust)

situ-

the

car

to prevent

a hill.

three level

Thrust

sin _, = 1

"let

and

thrust

velocity.

gas"

down

to examine

_, = 1.

to the

and

going

in straight

an increased

it the

up a hill

(L = W) and hence

use

at constant

"give

up when also

must

climb

angle

derived Secondly

of equations

V is zero,

conditions in a vertical

the thrust

necessary

(T = D + W). is shown

Also,

in figure

(37), hence

that climb to climb for a ver119(c).

= 90 °

Thru

Weight

Drag_

(c) Unaccelerated Figure

119.-

vertical

climb.

Concluded.

141

The equals

final

zero.

lift and

condition

to be discussed

It is therefore

drag

with the

simplified.

is gliding

necessary

to balance

Equation

weight.

flight.

In gliding

flight

the aerodynamic

(37) remains

unchanged

the thrust

reaction

forces

but equation

of

(39) is

In a glide L = W cos

(40)

yg

(41)

D = W sin Vg as shown

in figure

L _ D

If one

120(a).

tan

drag

ratio

is a measure

sess

the greatest

to keep

the

lift-drag

ratio

range.

glide

angle

pilot

to raise

range

ratios

them

aloft. with the

of the flight

is a maximum.

maximum

For

This

but unless

this

excellent

For

a particular

angle

smallest

the result

is then

the

is

of attack,

a steeper

glide

(increase

the

of the

airplane.

the

maximum

lift-drag

angle for

of attack

posrely

on

120(b),

to try

the descent

for which

glide

is less

It is a natural

ratio,

they

in figure

minimum ratio

of attack)

lift-

(not to be confused

the lift-drag results.

since

as shown

of attack

The

Sailplanes

design

of the airplane

angle

and hence

is the maximum.

is a particular

angle

angle,

ratio

airplane,

of attack There

glide

aerodynamic

nose

gives

the

efficiency

with

angle

hence,

airplane

that

the lift-drag

path).

any other

is increased; the

when

of the aerodynamic

varies

angle

this means

is obtained

lift-drag

currents

ratio

language

range,

air

this

(41),

_g

gliding

glide

(40) by equation

(42)

maximum

the

equation

1

In nonmathematical

with

divides

angle

and the

tendency

to get

and

for

a

maximum

will be steeper

instead.

Class Class cases

2 accelerated

of take-off,

landing,

Take-off.the

instant

leaving

(50-ft)

142

obstacle.

may

transition

the

and

curved

begins

its take-off continuous

be considered distance,

flight

is considered,

constant-altitude

of an airplane

it is under

needed (2) the

and

take-off

airplane

the ground,

off distance distance,

the

The

motion

2 Motion

to the

of accelerated time

acceleration. to consist

and

(3) the

for the

banked.turn.

is a case roll

specifically

of three climbout

it begins (See fig. parts: distance

motion. its

From

climbout

121.)

The

(1) the

ground-roll

over,

say,

total

after take-

a 15.25-m

Lift

Flight

'L

path

Weight

\

cos

_,g

W sin _,g

(a) Unaeeelerated

glide

conditions.

12.0

3O

_or%_=_u_=_e p_

--.4

_Jl _

r_

o_ 2O

e

0 0

_ 10

0

)

/

I

-4

0

I' 4 u,

(b)

Glide

Figure

J 8

angle

J 12

a,, 16

20

24

-'JO

|

28

of attack

aerodynamic

120.-

j

Glide

characteristics.

characteristics.

143

Figure Figure weight, sum the

122 shows

drag,

of the

(about

attack, friction

pressure

(thrust build.

the

the

lift quickly

forces

drop

as the landing

gear

stall

velocity,

the

nary

equations

for

the

the

frictional

force

is equal

to zero

(eqs.

to the

landing

net force

acting

due

to the

of the

ground

retarding

force),

in a horizontal stall up.

velocity The

weight,

its

(37) and

(38))

Acting

safety)

the airplane airplane's

usually apply

f

increases some

decreases

I

_Rolling

velocity.

The

ordi-

SA.AB

A-37

Viggen

II/I/I/I11 resistance

Weight

Figure

144

122.-

Forces

acting

during

take-off

greatly the

//11

Rollins

Rolling

above

////

resistance

point of

20 percent

case.

I

lift

velocity

Z'-_ ///I/

and

the ground.

drag

are

the net

angle

//"

,,,,t

drag

at which

at constant

L

to accelerate

is reached

about

in this

The

the airplane leaves

total

gear.

under

until

increases

to thrust,

lift and

the velocity

end of transition,

climbout

roll,

attitude for

pitch

and

and the

At the

begins

In addition

total

at liftoff,

is retracted.

roll.

no winds).

airplane

the

ground

(assuming

remains

exceeds

climb

during

distance.

zero

or pitched

airplane

take-off

At the beginning

airplane

above

acting

direction

is still

is "rotated"

Total

is a rolling

exceeding

The

10 percent

airplane

there

the runway.

as dynamic

and drag

the forces

in a horizontal

down

acceleration

the

lift,

forces

airplane

zero

and

121.-

ground

roll.

The roll

total

distance

is important

Additionally, aborted

the

The

drag

and

pilot

take-off

distance there

retard

use

rocket-assisted

a transitory periods.

airplane's will

Landing.vertical

an airplane

will

touchdown

and

Under and

that

they

are

the

The

not be considered,

ground

conditions

lift equals

the weight.

advantageously

maximum

lift

take-off

may

be

high lift to increased

an optimum

These

form

setting

may

units

acceleration the

flap

airplanes

also

represent

for

short

of a catapult,

or two. down

phase

at the lowest

and its

the two terminal

possible

associated

phases,

techniques

namely,

the

rollout.

touchdown

used

takes

of touching

but only

the

of its

purposes.

contribute

Some

of high

of a second

approach

start

design

and other

also

distance.

method

consists

velocities.

of flaps

is usually

a means

in a matter

which

distance.

minimum

this

for

the

to a stop.

they

There

provide

carrier,

is achieved

and horizontal

to a landing

the

an aircraft

from

since

take-off

off in the

and

speed

use

from

required

by the use

to their

the

to take

m (50 ft)

for deceleration

acceleration.

in thrust

Landing

maximum

exists

minimize

units

speed

the

15.25

of runway

may be reduced

the

On board flying

know

is a limit

which

increase

to clear

the amount

runway

However,

an airplane

where

should

sufficient

for

the airplane

and determines

so that

devices.

for

it is assumed The

previous

to decrease

coefficient

that

the

discussion

the landing

and decrease

the

vertical

velocity

about

velocity.

landing

is near

flaps

indicates

Indeed,

velocity

zero

they

as indicated

that

increase by equa-

(35).

tion

Figure They

are

The

rolling

dition

123 presents

the

same

This

near

lift

thrust

negative. thrust

the

This

drag

ure

therefore,

stop.

Another

which

is opened

mechanical across to large

may

more

flight

structural

ground

roll

braking

deck.

Deceleration

applied.

For

normal

reversible

landing

the thrust

deceleration used

acting

is exceedingly

maximum

carriers,

on the

force

the

airplane swift

drag.

and

airplanes,

is the

The fig-

it to a

parachute

landing

brake

a cable

the airplane

is

or

From

to slow

engaging

the

The

is retarding.

usual

con-

to "dump"

propellers

airplane

airplanes

this

is increased.

pitch

on the

by military

aircraft hook

for

direction.

touchdown.

and military

by using

the flaps

used

after

force

rollout.

operation

are

air

commercial

and

safe

into the

as the

the landing

magnitude

on the wings

by setting

On board

their

Spoilers

for large

device

during

rebounding

during

of the arresting

for

are

friction

usually

is a net

at touchdown. form

from

rolling

be increased

favorite

except

is accomplished

there

in the

the

or,

on an airplane

as the brakes

airplane

the

For

airplane 123,

the

condition

reversers.

acting

end of the rollout.

increases is zero

forces

the take-off

is greater

to prevent

condition

engine

as during

friction

occurs

airplane

the

is

laid

is subjected

forces.

145

Rolling

resistance

and

brakes

Rolling

resistance

and

brakes

Weight

Constant-altitude plane

are

cases

in a straight

include

One

of the

altitude

the

basic

In the

line.

previous

in that

same

line

path

force,

is proportional

By Newton's

third

force,

the

called

law

that

tight

turns.

R

horizontal

reaction

lift

must

146

flight

paths.

These

in combat

and aerobatics.

heading

is the constant-

flight-path

of an airplane,

an acceleration

law

the force

line

force.

due to a

acquire will

be supplied

toward this,

required

to maintain

the

centrifugal

force

sig-

continue

in

opposite

is given

an air-

the center

to perform

by the body,

added

To maintain

required

force

The

they

in a straight

by an external

that

is a reactive

accelerations

But in a turn

in motion

upon

force.

the

entering

turn

are

banked wings that

force.

occur

Thus,

a banked

curved

massive

called

of

centrip-

curved the

flight.

centripetal

by:

_

also.

flight

must

airplane

From

to the

When

horizontal.

component path. turn

This

equation

at high

executed

resolved

in the

this

airplanes

in a properly

a constant-altitude lift

of the

path.

it is the horizontal

the total turn.

for

at an angle to bank

velocity flight

of forces

the

For

is the

or curved

disposition

to maintain

weight.

Voo

forces

it is seen

needed

the

of the

lift on the

centrifugal equal

a body

of the airplane,

the wings

resultant

when

of curved

of an air-

(43)

124 shows

force

the

116, not all motions

maneuvers the

to the acceleration

centrifugal

components,

centripetal

turns,

to change

acted

second

is the radius

that

the

unless

there

mass

the highest

Figure

causes

landing.

mVoo 2 R

is the

particularly

cases

insignificant.

law,

centrifugal

FC -

sees

after

in figure

ample

of motions

were

requires

etal

and

required

first

By Newton's

curve,

are

and descending

discussions

curve.

m

acting

As shown

There

of flight

the

where

Forces

turn.

in a curved

altitude

turn.-

By Newton's

motion plane

banked

climbing

of direction

nificance.

123.-

maneuvers

banked

change

Figure

speeds

turn. This

into vertical of lift

one

that

in

Notice angle and is the

force

is balanced

by

the vertical

component

of

be increased

to maintain

constant

t

I ] Vertical compone,_t i of lift

I i I

I [ I $

I i Lift

I I I

I I I

t I Horizontall component of lift

I Centrifugal force

Weight

Figure

124.-

Forces

in a properly Horizontal

The the

smaller

the

angle

must

be.

to hold

the

airplane

banking

component

turning

radius This

flight.

has

In hovering

sphere. whole, and

3 motion

As that

such, is,

weight,

no

must

Thrust By vertically

properly as

shown

flight this lift be

been

and

drag

balanced

or

is

required turn.

is

in no

motion

greater

the

to produce

of the

= Weight;

in a turn, enough

condition;

aircraft

with

reaction

in figure

velocity

a large

flight

In equilibrium,

shown

lift

the

horizontal

in figure

lift

125.

of the

remaining

Hence,

of hovering

respect

forces the

that

for

to the

atmo-

aircraft

on

forces, hovering

the

thrust flight,

= Weight controlling

larger

Flight

aerodynamic

forces. as

the

to a special

no

Vertical force.

3 Motion-Hovering

assigned

there results

is

turn.

= Centrifugal

in the

Class Class

banked

lift

(44) the

thrust,

the

126.

The

chief

aircraft advantage

may

be

of such

made

to rise

aircraft

and

is their

descend ability

147

/ Thrust

of engines

/

Weight

Figure

125.-

Hovering

flight.

of

airplane

Thrust

= Weight.

Thrust

_

Thrust

Weight

Thrust Vehicle

> weight rises

Weight

Thrusq Vehich

Figure

148

126.-

VTOL

ascent

and

descent.

< weight descends

to land and take-off in small spaceswithout the use of long runways. Sincethey land andtake-off vertically they are called VTOL aircraft. They have the addeddistinction of being able to perform at high speedsas a conventionalairplane in flight. This is why helicopters, althoughcapableof hovering flight, are usually not included in this grouping. They are, at present, incapable of the speedsandmaneuvers of conventional airplanes. The first conceptsto be tried were three "tail sitting" airplanes, the Lockheed XFV-1, the Convair XFY-1, and the RyanX-13 Vertijet as shown in figure 127. The first

two used

thrust

needed

VTOL

airplanes

turboprop-powered

landing

and the

concept

tried

the

wing

whereas

the X-13

were

the tricky

engines

conventional

For

simplicity present-day

down

four

main such

to use

level

flight.

rotating

flight

Lockheed

exhaust

behind

nozzles

as shown

is supplied

XFV-

body

over

required into

vertical

with these

in the

conventional

take-off

The

and

flight.

in a conventional

to the horizontal.

separate

powerplants

But this

added

This are

used

in figure

127.-

uses

The

sense

next

but tilt

LTV-Hiller-Ryan

XFY-

Early

to each

Harrier

(fig.

the concept the

Control

in the wing

take-off

and

flight

regime.

128(b))

exhaust

tips,

is one

of "vectored from

at low flight

1

VTOL

vertical

weight

to deflect

128(c). jets

for

dead

Siddeley plane

Convair

Figure

problems

main

the

an aircraft.

by reaction

I

The

of the aircraft

the Hawker

aircraft.

to supply

maneuvering

aircraft

the vertical was

propellers

jet powered.

piloting

and efficiency,

to directly

in hovering

the

was

VTOL

was

the entire

from 128(a)

concept

best where

to tilt

to keep

in figure

Another ing and

need

was

and

XC-142A

contrarotating

nose,

Ryan

and

land-

of the

thrust" vertically

velocities

and

tail.

X- 13 Vertijet

airplanes. 149

Wing. tilts down

(a) XC- 142A.

(b) Harrier

GR MKI.

Forward

Transition

Hover

(c) Example Figure

150

128.-

flight.

VTOL

concepts.

flight

IX. STABILITY

The chapters

subject been

acting

of stability

kept

this

control

CONTROL

of an airplane

has

in the

background

so as not to complicate

and

the related

performance

on an airplane

consider

and

AND

subject

in view

of the presented

throughout the

the

study

considerations.

previous

of the forces

It remains

now to

material.

Stability Simply scribed

defined,

flight

conditions.

all

condition. The

For

equals

subject

the drag,

on it must

as in figure

and there

are

of it, of an airplane

of a pilot

is considered

to be in equilibrium

and level

or lack

is the ability

of stability

and moments

straight

is the tendency,

Control

an airplane

the forces

flying

stability

to change

be zero.

For Then

no net rotating

the airplane's

flight

first.

for a particular

129(a).

to fly a pre-

flight

example,

the

condition, consider

lift equals

moments

acting

the

of

an airplane

the weight,

on it.

sum

the

thrust

It is in

equilibrium. Now,

if the airplane

is disturbed,

noses

up slightly

(angle

If the

new forces

and moments,

tendency

to nose

diverge

from

to hold fig.

129(c).)

tion,

up still

that

tend

to bring

initially

of motion

and

level

that

the airplane

after (fig.

An airplane control

by working

to do this. statically necessary

unstable may the

An airplane and

increase,

produce

a

is statically

unstable

and its

If the initial

tendency

of the airplane

has

neutral

forces to its

static

and

stability.

moments

equilibrium

is statically

nose

return

130(a).)

This

are

straight

The case, (fig.

of this stable

stable,

motion

will is

(See generated

by the

and level

airplane

noseup,

condi-

of decaying

is said nose

condition

oscillatory

continue to have

up and down

three

overshoot

equilibrium

Or it may

it may

it may undergo

overshoot,

former

type

stable.

elevators

to change

down,

to its

of straight

motion

to nose

up and

neutral

dynamic

with

to a

increasing

indicates down

there-

stability magnitude

130(c)).

be dynamically

dynamically

except

in equilibrium.

airplane

it back

It may

amplitude. in the worst

and be dynamically

and

129(b).)

if restoring

is dynamically

or,

is no longer

by the angle-of-attack

the airplane

eventually

(See fig.

at a constant 130(b))

that

and

flight.

turbulence,

stable.

with time.

degree,

by atmospheric

the airplane

the airplane

hand,

If it is assumed

smaller

the

(See fig.

On the other

it is statically

forms

caused

position,

example,

increases),

further,

equilibrium.

the disturbed

airplane

of attack

for

unstable

in this design

last

has

poor

can be flown

the equilibrium

and instance. flying "hands

flight

still

be flyable But,

qualities.

if the

ideally,

pilot

he should

An airplane

off" by a pilot

uses not need which

is

with no control

condition. 151

Lift = weight Thrust = drag No net moments --

--

n_=======dm_

....

(a) Equilibrium

flight.

I

lq _

j

Statically unstable divergent

Equilibrium Disturbed moments increase disturbed condition

(b) Statically

unstable

airplane. No

moments - airplane holds disturbed

condition

4

Disturbed

Equilibrium

(c) Neutral Figure

static

129.-

Statically to return

stability.

Static

stable, airplane

stability.

dynamically to equilibrium

stable moments - oscillations

tend decay

Equilibrium

(a) Statically Moments tend but oscillations

and dynamically

to return do not

airplane decay

to equilibrium

.... ......"t-5-----'')----

Equilibrium

(b) Statically

stable;

Moments but

tend

neutral

towards

oscillations

Equilibrium

are

dynamic

stable;

stability.

equilibrium

[

divergent

"_/

(c) Statically

\\_/

dynamically

Figure 130.- Dynamic 152

stable.

unstable.

stability.

_

Longitudinal motion,

stability

lateral

stability

and

and

control

control

relates

tional

stability

and

control

relates

tional

stability

are

closely

interrelated

referred

to as lateral Longitudinal

of lateral

is concerned

with

an airplane's

to an airplane's

to an airplane's and,

rolling

yawing

therefore,

motion.

the two are

pitching motion,

and direc-

Lateral

and

sometimes

direcsimply

stability.

stability.-

and directional

Since

longitudinal

stability,

stability

it is discussed

can be considered

first.

Consider

med" to fly at some angle of attack, _trim" This statement in equilibrium and there are no moments tending to pitch the

independent

an airplane

"trim-

says that the airplane is airplane about its center

of gravity. Figure forces

131(a)

acting

are

shows the

how pitch

weight

through

dynamic

center,

and the

thrust

airplane

usually

is very

close

example

it lies

above ter

or below

of gravity

It is seen whereas the

in this the

needed

center

shown

in figure

"trimmed"

thrust

line.

aerodynamic

and thrust

a nose-up

tail.

are

to the

needed.

The

13 l(b).

both contribute If these

It is evident

horizontal

tail

control.

total

that

acts

equilibrium moment

cen-

of gravity.

each

wing

other

source

and the

tail,

only

the balancing

is

arm

can from

relatively moment

the

the airplane

out,

pilot

long moment

condition,

about

the

moments

moment

of the

lie

about

nose-down

as a small

supplies

may

and the center

another

of the In this

line

moments

of the horizontal tail

alone.

do not cancel

Because

center

To fly in a particular The

them

at the aero-

center

thrust

The

between

the horizontal

angle.

The

above.

moment.

aerodynamic Thus,

case,

The

lift and drag

of the wing

of gravity.

the distance

the lift

The

center

center

in this

lift by elevator

to a particular

as

elevator center

is

of

is zero. If the

airplane

the trim

to the

is statically

angle

equilibrium

of attack, atrim.

stable moments

against

the

angle

negative

moments

moments

rotate

of attack. rotate the

Now the curve different

nose

are

the

nose

up for

of the

down

angles

generated to express

the center statically

Of course,

of figure

components

in a longitudinal

It is customary

as a coefficient of moment about Figure 132 shows the longitudinal

the

the

not be in equilibrium.

of gravity

forces

the

the

times

contributes

or negative

small

from

that

the horizontal lift

gravity

case

of gravity,

to the aerodynamic above

for an airplane.

center

of gravity;

forces

is achieved

the

along

of and

center the

drag will

-

achieve

the are

airplane

the

in back

equilibrium

that the

tend

then

if disturbed

to return

moment

the

away airplane

nondimensionally

of gravity, or (Cm)cg. (See eq. (27).) stable case of the moments plotted

there for

is no moment angles

below

132 is a composite airplane,

sense,

of attack

at the trim above

angle

of attack;

atrim'

and positive

curves

caused

atrim" of all the

for example,

moment

the wing,

fuselage,

tail,

by

and

153

k Thrust

LLift

I ]

momj

Thrust

E

oment Drag

Weight

moment

(a) Net

moment

pitches

for

Tail

moment

= Resultant

tail

of thrust,

and

drag

thrust.

Figure

First,

the

stability ure

horizontal

134, if the

is moved

(point

C in fig.

neutrally

of point

has

A), the pilot

tail

the

range

of gravity

a great

static

are

effect

stability.

of the aerodynamic If the

sufficiently,

there

is a point,

curve

is moved

and the

is moved

maximum

becomes

airplane

forward

to generate lift large

the

back

on the static

neutral this

(point

toward

enough

135(a)).

the nose

force With There

are,

of the

point

airplane

is

D in fig.

134)

unstable. too far

on the tail power

in fig=

center

of gravity

is longitudinally

coefficient. (fig.

center

horizontal;

further

important.

As shown

forward

slope,

is relatively

has

facts

stable.

not be able the

fundamental

airplane

of gravity

of gravity

to achieve

Some

is statically

moment

positive

will

equilibrium.

is sufficiently

center

if the center

center=of=gravity

154

where

If the

curve

of attack

the

--I

lift,

Pitch

the entire

of gravity

toward

131.-

of the center

the airplane

134),

stable.

moment

Likewise,

angle

center

force

condition.

qualitatively.

and hence,

A or B), then

airplane

this

position

of the wing,

(points

the

133 shows

down.

moments

(b) Equilibrium Figure

airplane

(forward

to raise

off the usable however,

the

_9 Positive

moments,

_< _trim

b_

i Zero

¢9

i

[

moments,

_ I" _trim

_

Angle

of attack, ot

,4

atrim _9

Negative

moments,

a > atrim

i 0

E & C9

Figure 132.- Longitudinal staticstabilitymoments

as a functionof angle of attack.

\

v

_\_

,,+°+

.+oo

h_

\ \

_

_,o,,__ae_t_O

c9

i 0

I

__"

Angle of attack

_9

trim--'

O I h_

_\_

Complete \_

_tatically

\

airplane stable)

\ \ \

Figure

133.-

Longitudinal

static

stability

components. 155

Destabilizing

monmnts

/---> +

Center

i,J

O v

of gravity

at D

/

_9 %

5

_

0

Neutral

¢/

_

/_

Angle

of attack,

o,

Stable (equilibrium) condition

_9

_,_ _b_Bl_)

I

_

Center

factors

engine-on

thrust

considerations) airplane

loaded.

For

example,

airplane

was

loaded

side

the

range

the

center The

airplane plane

gravity

static

156

ground

the

effects

there or the

135(b).

usable

are cargo

The

that

an airplane

in flight

factor

horizontal

tail

controllable

curve.

of gravity

static with

By design stability.

The

of the airplane). further of the

away

as close

with respect

so that

from

wake

tail

of gravity

designed

and

because

center

of gravity

unstable.

The

contributor

give case,

the

center

The

tail

its

a more that

the fell

out-

location

of

to the

of gravity efficiency

efficiency

the downwash

complete

statically

the

distance

and slipstream

tail,

and other

airplane.

will

normal

include

center

crashing

the

moment

to 100 percent to the

the actual

became

Of course,

airplane.

to the airplane

it is made Finally,

as is the

flaps,

is carefully

in a stable

horizontal

(assuming,

stability respect

main

A larger

tail

is important. the

is the

These

gear,

airplanes

then

stability.

range.

To insure

airplane

Positions ol center of gravity

static

landing

of transport

shifted

limits.

D

(including

range,

cases

C

center-of-gravity

is an important

location

effects.

the usable

B

and unstable

of gravity

center

enhances

neutral,

in figure

within

of usable

a smaller

aft of the

tail

falls

moment than

and

as shown

of the

Stable,

reduce

effects

at A

Neu!ral

nloments

134.-

which

of gravity

Destabilizing

A

additional

at B

,e,

_

_///

Figure

"

from it is,

factor of the

stable

horizontal

tail

the

center

the

more

depends

engine,

the

of it

on the

and power

as possible from

airlies

wing

for most is of

Unstable; _off

< _-Center xx nmst

of gravity between

lie

these

limits

(a)

Ground

Unstable power

;

on

7.

mal_

Center must these

,,iq_

of gravity lie between limits

(b)

Figure considerable

importance.

it leaves

a wing.

deflected

air

turbed,

it will

degree

to which

the

stability

vertical

location

figure

and hits

angle

that

For

shows

range.

how the

results

in the

air

and the

affects this

it is exposed

the

reason,

is deflected

wing

the horizontal-tail

of attack

directly

airplane.

such

of air

center-of-gravity

reaction

plane.

downwash tail

to as little

If the

angle

effectiveness.

the horizontal

tail

downwash

force

also

downward

when

or lift.

This

airplane

is dis-

changes.

The

Hence,

it will

reduce

is often

located

in a

as possible,

as shown

in

136(b). Dynamic

airplane. ]ect

its

it changes

of the

136(a)

deflection

rearward

change

Usable

Figure

This

flows

135.-

Again,

in detail.

interest

longitudinal

with

this

is a very

Basically, regard

stability

there

to an airplane

is concerned

broad are

subject two primary

attempting

with the and no attempt

motion

forms to return

of a statically

is made

to treat

of longitudinal to an equilibrium

stable this

oscillations

subof

trimmed

157

Lift

_

(a) Downwash

_

_

Downwash angle at tail

_

of wing.

Horizoa_ F- 101A

_

,_

li

Downwash

(b) High Figure

flight

condition

tion which

after

being

is a long

fig.

137(a).)

can

control

the

drag

this

is.

as shown

it is poorly

oscillation

The

effort.

pilot

attempts

time

where

he may

instability

that

oscillation

occurs

"out

if the

and is influenced

by the

the

may

airplane

plane

that

occur. Insofar

aerodynamic condition under"

158

Proper

elevator

increases

of the

and be extremely

short

with

are

stable

period,

the

because

free.

This main

if a coupling

damped

pilot

of the

angle

may

pilot's

induce type

effect

free

if a

reaction dynamical

of short

"porpoising"

is vertical the

with no

slow

A second the

of attack

worsen

and thus,

is called

generally the greater

quickly

oscillation of the

between

(See

it is,

out very

forces.

The

term mode,

accelerations elevator

of

and air-

here.

effects

are

concerned,

as the airplane stability

damps

the oscillation,

left

is essential

the static

highly

of oscilla-

path. The

variation

oscillation

balance.

wing

more

to destructive

out of hand

design

the

mode

flight

can be an annoyance.

of a control

lead

as compressibility center

this

of phase"

elevators

get

and

its natural

eventually

is the phugoid

is a short-period

it out by use

get

may

form

on tail.

of the airplane's

although

Usually,

with

to damp

damped

effects

first

oscillation

oscillation

137(b).

However,

The

himself

second

in figure

pilot

slow

tail.

Downwash

disturbed.

period,

Often,

136.-

horizontal

to such

in a steep

dive.

goes

the rearward supersonic

an extent

that

the

movement

is most

evident.

airplane

may

of the This "tuck

Slow Axis remains to

of

ris("

airplane tamgent

flight

_111(1 fall

and

of

elmnging

:lJl'p|alle

spevds

Minimum

speed

path

_I _lx i tl/tl

(a) Phugoid

nl

speed

longitudinal

oscillation.

Short period anglt,-of-attaek variation

(b) Short-period Figure

This answer

condition

to this

goes

moment

due

to lift

advantage The

would

and the

strong

viding

trim When

Figure

at supersonic

turned

downward

apply

so that bility,

yaw

negative

yawing

vious

condition

it has

neutral further

shows observes

the

moment

generated

is shown

in figure

directional away

the variation a positively

from

"tuck

nose-up

arrangement

has

an

is beneficial.

The

at supersonic

speeds,

(flaps)

at low speeds

by pro-

to trail

in the free

under."

Additionally,

stream

at

should

ideas

involving

by convention, a negative

139(b).

equilibrium,

the

of canards the wing

139(a).

coefficient as a directionally

condition, To have

if the

for tips

staare

sideslip

holds

is to increase is directionally with

sideslip

stable

an airplane

flies

directional

sta-

is disturbed

sideslip angle

stability

static

airplane

a positive

If the airplane tendency airplane

longitudinal

equilibrium

be generated

for

a pair

forward.

in figure

If the

line

config-

center

It has

center

stability.

sloping

wing

an additional

control

XB-70.

In the usual

of yawing-moment

for

aerodynamic

of the basic

or alternatively

of fuel

drag.

as shown

moment

double-delta

This

can be allowed

the aerodynamic

is zero

tailplane

American

Many

range.

One

by a transfer

to develop

high lift devices

canard

North

the

SST.

lift.

of the

from

stability.

yawing

angle

shift

to prevent

stability.-

a positive

airplane

to the

rearward

include

of the airplane

minimum

to keep

solutions

oscillations.

regard

of gravity

and a rear

moments

speeds

with

and supersonic

for trim

the

center

to the

not used,

the yaw angle

nose

rearward

to directional

negative

tion,

transonic

generate

Directional also

in the

138 shows

bility

the

oscillation. longitudinal

previously

Other

at the

the

of dynamic

discussed

placed

nose-down also

types

is to move

of a canard

uplift. lift and

been

of contributing

use

canard

Two

supersonic.

or canards

added

zero

has

problem

as the airplane uration

137.-

longitudinal

angle

excursion. its disturbed the

/3 and a The

Here,

pre-

position,

disturbed

unstable. angle.

to a

posiFigure

140

one

case.

159

Canards

Folded down wing tips

Figure

(a) Equilibrium

138.-

XB-70

airplane.

condition

of zero

yaw.

Figure 139.- Staticdirectional stability.

160

\ (+) Sideslip angle Positive

yawing

moment

tends

decrease disturbance

to

sideslip

\ (b) Sideslip Figure

disturbance.

139.-

Concluded.

(÷)

Sideslip

Positive

T

]

a_

remS°t °mreing

(÷)

&

• (-)

Sideslip

angle

/

0

s /_Negatlve /

_

J restoring

(-)

o Sideslip

Figure

140.-

Directional

(÷) ._,,. angle

stability

curve.

161

The

fuselage

directional

and the vertical

tail

As figure

141 shows,

stability.

t.ion at a sideslip

angle

tends

the

to increase

component

of static

sideslip arm

disturbance;

of gravity

stabilizing

moment size

that

dition.

The

quately

covered

usually

has

a low aspect

results

and

a catastrophic

here.

of a dorsal

at large

sideslip

effectiveness

or ventral

tail

of the

of rudder

offset

to a zero

that

however.

The

Adding

more

provides

a stable

bomber

before

tail instability

vertical

yawing

and

con-

be ade-

vertical

result.

a

or yaw

cannot

occur,

area

moment

produces

sideslip

factors

main

due to the

by the tail)

that

is the

of attack

should

a B-17

This F8F pilot

angle

at the

can be very

Bearcat,

a carrier

to counteract

tail

moment

after

influences

add to the directional

stability

whereas,

contributing

reason

Lateral undergoing moments

for

choosing

stability.tend

that

to reduce

addition

bank

stability

with

to this

will

influence.

from This

lateral

stability

static

wing

detract

wings.

_, it generates the

high-

problem. A sweptback

wing

angle

degree

during

sweptforward

and restore

large

a certain

sidewash

moments.

to possess

it to some angle

by the

a destabilizing over

static

require

a solution

wings

the

direc-

As shown

in aircraft

a sweptforward

is said

rolls

induced

on the

slipstream.

reduces

would

the yawing

sweptback

the bank

that

pronounced

are

it is by itself

An airplane

a disturbance that

since

influence

to the

plane,

propellers

of sweep

stability

tail

the yaw

degree

directional

velocity

effect

Contrarotating

The wing's

is a destabilizing

a rotational

a sidewash

Grumman by the

airplane

imparts

tail.

take-offs.

total

tail

If a stall may

142 shows

vertical

multiplied

on many

condi-

a moment

of vertical

back

stalling.

generate

at an angle when

useful,

divergence

of a typical

and it also

The

the

are

to prevent

Figure

propeller

engines.

will

airplane

is dependent

sideslip

143 it produces

powered

the

observations

ratio

will

center

in

is in a disturbed

The

placed which

components

fin extension.

stability,

in figure

tail

fin extension

A tractor tional

to move

Some

angles.

When force

to aerodynamic

of the vertical

by use

of a dorsal

tends

alone

is, it is unstable.

a side

of airplane

influential

an airplane

fuselage

stability.

it generates

the two most when

the

that

directional

disturbance,

(center

8, in general

are

if after

forces

equilibrium

is a

and

flight

condition. Dihedral shows some flight,

a headon dihedral the

turbance lift vector the airplane

162

is often view angle

lift

rotates

one

to the

wing

to improve

that

horizontal.

by both wings

and

to move

as a means

of an airplane

produced

causes

used

to drop

there sideways

has

relative

is a component in this

dihedral

Under just

lateral

the

equals

Figure

the wings

are

where condition

shown,

the weight.

to the other

The

Now,

as shown

of the weight

direction.

stability.

acting

airplane

144(a)

turned

in straight assume

in figure inward is said

up at and level

that 144(b).

which

a disThe

causes

to sideslip

and

V_

Sideslip angle

Airplane to some

Fuselage produces

is disturbed sideslip

angle

side force destabilizing

arm

moment

Moment

Fin and

rudder

arm

force

produces stabilizing moment

Figure

141.-

Directional

stability

moments.

163

Small

Large Dorsal

Figure

142.-

Improving

fin

fin

and

and

rudder-_

rudder

fin

directional

stability.

Grurrlman F8F-1 Bearcat

Figure

164

143.-

Slipstream

effect

at tail.

_-_

Di:e ralT--

---_

Dihedral angle

(a)

Velocity component due to sideslip

Weight !_ _

(b)

L1

____///

////// Figure

the

relative

free-stream

sideslipping. bank

angle.

closer will

If the From

to the experience

There

results

figure

144(c). The

airplane

geometric (that

a greater a net

position design,

is

as

angle

force

and

of the

wing

shown

L 2

is

now

effect on lateral stability.

in a direction

laterally

stable,

considerations, is,

>

Total relative freestream (main component along longitudinal axis) (c)

direction

sideslip

L1

144.- Dihedral

airplane

Component of weight acting to cause sideslip

toward

also

in figure

than tending

has 145,

wings

free-stream

of attack moment

moments when

the

toward

an

the

contributes

arise

that

have

dihedral,

velocity), raised

to reduce

impact

which

on the

wing the

and bank

lateral

airplane

tend

hence

lateral

to the

the

the

hence angle

to

reduce

the

wing

stability. stability,

the

lower

greater as

is

wing, lift.

shown

in

A high-wing whereas

a

165

Low-wing

placement

is destabilizing

High-wing

Figure low wing

placement

counteracted

has

sweep

swept-wing

velocity

normal

tends

to diminish

noted

that

the combination

bility

and

some

airplanes

to lessen

the

The airplane presented gravity, ish

by the

lizing

moment

plane decrease

166

these

up that

of partial

detrimental

the

the

a small

overall

the

than

may

amount

may

sideslip

will away

from

moment

a

the

a sideslip.

arises

that

It may be

too much

of anhedral

When

experience

to equilibrium. produce

be

stability.

146 shows.

and a roll

airplane

effect

lateral

the wing

sideslip

and sweep

this

as figure

toward edge

return

(wings

lateral

turned

stadown

stability. and vertical

In a sideslip, and vertical side

tail

there tail.

147, there

If the

because use

use

fuselage

If the

is below

will further

increase

that

also

of the direction span effects.

flaps.

tend

may

contribute

will be a side

is a roll

force

moments

arise

and the

lateral

in figure

set

Destabilizing a sideslip

will

fuselage

angle.

toward

and

the

stability

leading

stability.

However,

to improve

lateral

of dihedral

on lateral

in roll.

the wing

wing

angle

stability.

as shown

the bank

bank

of the

lateral

promote

on the

the

effects

dihedral

laterally

placement

effect

to the wing's

lift is generated

is stabilizing

of wing

is sideslipping,

More

slightly)

Effect

more

will help

airplane

placement

a destabilizing

by including

Wing

higher

145.-

laterally

side

moment the the

center bank

to increase

of the

slipstream

Added

dihedral

force

to or detract

force acts

caused above

generated

that

of gravity,

by the the

tends

there

from

the

area

center

of

to dimin-

is a destabi-

angle. the bank

angle

of an airplane

for a propeller-driven or sweep

again

may

in air-

be used

to

/_normal

¢

Figure

Cross stability roll

effects

are

causes

exists

gives

rise

divergence,

to the

a yaw

the yawing continue

yaws

moments until

important

the

into that

airplane

lateral

the

a yaw

motion

static

dynamic

motions

stability.

earlier,

of an airplane

causes

stability

motions

lateral

and directional are

such

that

a roll

motion.

Thus,

and lateral

static

stability

observed:

directional

a

crossand

divergence,

roll.

divergence or rolls

and

aids

As mentioned

stated,

directional

and Dutch

sweep

effects.-

motion the

three

Directional

Wing

Briefly

between

spiral

airplane

and dynamic

interrelated.

motion

coupling

146.-

is a result a sideslip

arise

continue

is broadside

of a direetionally so that

side

forces

to increase

the

to the

relative

unstable on the sideslip. wind.

airplane. airplane This

(See fig.

are

When

the

generated,

condition

may

148(a).)

167

er

of g rav i t Y _Js --

- _tLmaa! Side _ml_eZa!in_g

force

I

I

I

o ravity

Side

force

/

Point

v-_

of side-force

[ _,L

Laterally destabilizing

application I

moments

!

( Figure

Spiral

divergence

but not very this

case

the

plane

negate

stable

when

this

sideslip

spiral

airplane

angle

increases

away

the wake

fins,

of the

stability

wing

exhibiting

disturbance

although

travels

angle.

and the fig.

stability

is very

stable

airplane

with

the

force

side

faster,

airplane

directionally

no dihedral. tends

generates

No lateral

continues

to turn

more

stability

In

lift,

is present

to turn

into

to the

148(b).) of both directional

is strong, as the

The

stability.

whereas

airplane

airplane

the directional

yaws

wags

its

divergence

in one tail

stability

direction,

from

side

the to side.

effect. primarily

at high angles

and increasing

bank

occurs,

that

finned

characteristics

in a countermotion. this

wing

(See

The lateral

illustrates

Ventral

spiral.

on lateral

sideslipping,

outer

a higher

is a motion

If a sideslip

149(a)

The

a large and

to still

bank

divergence.

rolls

Figure

168

roll

The

example,

wind.

and tail

by an airplane

is in a bank

in an ever-tightening

is weak.

eral

for

airplane

will

roll

of fuselage

is characterized

relative

roll.

Dutch and

the

airplane

Effects

laterally;

into the

and the

147.-

the

used of attack,

directional

to augment are

also

stability

the vertical beneficial to reduce

fin which in decreasing

the

effects

may be in the lat-

of Dutch

roll.

Initial flight path

_

Insufficient

directional

stability

(a)

Di_

_

divergence (airplane may yaw broadside

\ to \

\stabilily, oor atera \

I

_

Airplane

(b)

Spiral _ divergence

--,_

in sideslip

1

(Bank angle increases and causes greater greater sideslip)

Figure

disturbed

148.-

._

Original

and _:_flight

Directional

and

condition

spiral

divergence.

Control Control, change alter

an airplane

the airplane's the lift The

vide

whether force

the rudder discussed

on the

familiar

longitudinal

flight

to provide later.

Figure to the

control

pilot's

point

of view,

are

shown

or unstable,

It is brought

to which

(in pitch),

directional

150 shows surfaces

conditions. surface

controls control

is stable

they

are

in figure

the ailerons control

about

15.

They

to provide

(in yaw).

Some

basic

control

system

is by use

of the

control

stick

the

control

stick

ability

by the

use

of a pilot

to

of devices

that

attached.

a simple

if he pulls

is the

back,

include

the elevator

lateral

control

other

control

as operated and rudder the

elevator

(in roll), devices

by a pilot. pedals. turns

to pro-

From

and

are

His

link

the

upward

169

Tail-wagging

"Dutch roll"

k

(a)

Disturbedcondition

Undisturbedcondition

_------Ventralfins to improve (b)

directional

stability (as well as augment the vertical fin)

Figure

(fig.

151(a)).

surface about

This

and the

a downward

airplane

of the

control

shown

in figure

camber ing

of the

in the

170

the

other

pedal

This

wing.

pressure

produced.

in the

and

condition

toward

which

to the

the

wing

This

forward

the

then

the

rudder (the

of one camber

control pedals

left

pedal

the

pitches

up

will comes

lift to

roll

pushed.

deflect

the

other

motion

down

as

it increases the

about

rudder. the

moment

A side the

while than

was

back),

a nose-up

and

wing

airplane

horizontal-tail

upwards.

aileron

more

stick

entire

produces

of one

produces

causes

to the

in turn,

airplane

movement

roll.

camber

This,

reduces One

Dutch

a negative

of gravity

151(b).

direction

right

is

results

results.

Applying pushes

gives

lift

center

stick

moment

axis

movement

149.-

rudder

other its

the and

a roll-

longitudinal

If the deflects

pilot to the

..

Elevator

control

"--

__roncontrol

control

I

Figure right.

As shown

and a tail

force

and hence,

in figure to the left

the airplane

Control

the larger

is fitted,

the greater

faces

possess

151(c),

greater

the

Basic movement

A moment

is a measure

control

control

control

system.

increases arises

that

the vertical yaws

the

tail

nose

camber

to the right

right.

control

the

this

results.

turns

effectiveness

general,

150.-

surface

of how well is with respect

effectiveness. effectiveness

Also, than

a control to the

surface entire

does surface

high-aspect-ratio

low-aspect-ratio

its

to which

control surfaces.

job.

In it

sur(See

fig. 152.)

171

(b) Aileron

control.

Beagle

(c) Rudder Figure

172

151.-

Control

control. surface

operations.

206

Z.1

_ntrol

surface

//

._V

larger

with

_V"

Smaller

control

effectiveness

Greater

Figure Balanced

controls.-

flow,

a pressure

to its

original may

only

the

must

to insure

forces

required.

the

of the

the

face

tending

effort

controls

are

that

even

and, are

has

Mass

balance of the

effect

a sense

surface

at will,

is used

artificial

in the

balance

surface

the

are

the

shown.

air

that

hence

force

deflection The

strikes

force,

that

aft of the

control

design,

the pilot-

sur-

must

be exercised

so that

to move

them)

lest

unwittingly

control

systems is used

is incorporated

the

pilot

of today's or not, into

the

airplanes

the pilot-felt the

controls

so

controls.

in front may

surface

back

care

balance feel

control

to reduce

By careful

aerodynamic

surface

be small

deflection.

The

control

should

the

needed

fluid

but the forces

counteracts

However,

effort

the

Not

distribution,

surface

into

design.

of aerodynamic

This

surface

surface

a pressure

In fact,

and a control

control

creates

whether

which

the

Balance

to its destruction.

surface

the

is deflected,

reduced.

is employed

upon

not tire.

further.

of feel

to force

the surface

(little

small.

tends

surface

when

the control

light"

a control

to hold a particular

two forms

of the hinge

is considerably

the pilot

dynamic

so that

surface

power-operated

vent flutter

does

is set

the airplane

forces

pilot

the

entire

to

effectiveness.

up that

depending

respect

effectiveness

deflects

necessary

to deflect

153(a)

not "too

overcontrol

control

the

to reduce

supplied

force

In figure

forward

turn

a pilot

not be small

be able

that

Control

will be set

The

or may

surface

surface

helps

are

distribution

pilot

enough

hinge

Whenever

position.

deflection

152.-

control

nOW

of the hinge

occur that

line

of a control

due to accelerations deflects

about

surface

to pre-

on the airplane.

on its own may

lead

It is a

to dynamic

173

Area

forward

Area Me-

109

forward

of hinge;

_1_,_

F

(a) Horn

balance.

(a) Inset

Mass-balance

balance.

weight

! " Balanced" moving-surface

hinge

, J

_

n

rfa

_Movi g-su | weight

ce

_

weight

(b) Mass-balanced Figure

instability

of the

ity near

or forward

ward

primary

Tabs

to the primary

downward

moment,

to move

balance Trim

the

tabs

are

or manually

steady

used

They

surface long

are

and

set

tabs

movement.

important may

stick

by the pilot.

set

are

used

forces.

If the

tab will

they

and are

stick

forces

are

very

they

insure the

154(b)

edges

of the

(2) to trim. propor-

to assist

the

pilot

wishes,

in

for

as the

a force,

powerful

elevator

hence

at the trailing in action.

for particular

shows

for-

and

upward

that

lead

balances.

and

placed

airplane

of grav-

opposite

create

to zero

when

Figure

mass

pilot

deflect

up will

arms

since

small

up to move

Because

center

by adding

(1) to balance

set

be set

surface

at the trailing

They

the balance

pilot

tabs

by using placed

are

down.

balance.

control

two purposes:

moment

very

Trim

the

153(b),

distribution

to reduce

flight.

operated

down,

mass

be accomplished

surfaces

in reducing

pressure

possess

conditions.

in holding

surface

control

may

in figure

balance

and

and the

This

serve

154(a),

and

is to move

control

the elevator

tabs

line.

Tabs

surface

to move

solution

auxiliary

control

control

deflects

174

are

in figure

the

Aerodynamic

or as shown

As shown

example,

flight

line

surfaces.

moving

The

of the hinge

control

tional

edge,

airplane.

of the hinge Tabs.-

153.-

weight.

chosen

the pilot

will

is on the

ground

a deflected

not tire

control

Tab t- Balance Fixed

surface

__

"m':'_

_

surface

otal Main surface

"-_ ___

surface

_ _

f--_

' ' Fixed

force Tab geared proportional

/

_

_._

deflection

__osite

force

(a) Balance

helps

move

._-,_

surface_*

control

Trim

tab-placed

_----/-----_position

O_',_"_,..._ _,_2_ot--_,_ "_._"__]__

by

/_

airplane it holds particular

_

_-/ " _._..________.__. without Mom_ced by M(_ment produced by trim tab to counteract control surface to control surface return to undeflected morn ent position

(b) Trim

tab

operation.

154.-

Balance

and

Figure

plane

will

control

the trim

continue

surface

control the

control outlined

advantages.

butterfly

"dump"

condition

When

new setting devices.-

They

Included

are

and

a new

about no pilot

control

effort.

tabs.

the

hinge

effort

deflection

when

line

to zero.

is required is needed,

The

to hold the

trim

air-

the tab

must

(if adjustable).

Some

above.

moments

or

is on the grounda control in a fixed position pilot

trim

in a fixed

pilot

control

are

devices

used

do not fall

in unusual

spoilers,

flight

all-moving

into the

conventional

circumstances

or for

surfaces,

reaction

added

controls,

and

tail.

Spoilers, or

to reduce

to fly in this

for the

Other

set

deflection.

be readjusted

categories

tab

surface

tab operation.

r--/g

with

in the

direction

Tab

surface

but

surface

_

Fixed

to deflect to the control

the

previously lift on a wing

discussed

gliders

to vary

the

reduce

lift quickly

lift-drag to prevent

with

by altering ratio the

respect

the

pressure

for altitude airplane

to subsonic

from

control

flow,

distribution. and on airliners

bouncing

into

the air.

are

used

They

are

to reduce useful

on landing But,

they

on to

are 175

also useful in lateral (roll) control. At low speeds,ailerons are the primary lateral control devices. At high speeds,however, they may causebending momentson the wing that distort the wing structure. At transonic speedscompressibility effects may limit their effectiveness. Spoilers may be used to avoid these disadvantages. As shownin figure 155by reducing the lift on one wing, the spoiler will cause a net rolling momentto roll the airplane aboutits longitudinal axis. Control effectiveness may be increased by increasing the chord length of the control surface relative to the entire surface to which it is fitted. The limiting case is the all-moving control surface. Whereas the conventional control surface changed lift by a changein camber, the all-moving control surface controls lift by angle-ofattack variations. Examples are to be seenon the horizontal-tail surfaces of the F-4 Phantomand the F-14A airplanes (fig. 156). By being able to changeits angle of attack, the all-moving surfaces can remain out of a stalled condition. The conventional control surfaces are considerably less effective at high speedswhere compressibility effects are dominant. The all-moving horizontal tails may be movedindependently as well to provide lateral control. At low dynamic pressures aerodynamic control surfaces becomelargely ineffective becauseonly small forces and momentsare present. Under these conditions, reaction control devices may be used. These are small rockets placed at the extremities of the aircraft to produce the required momentsnecessary to turn the airplane about eachof its axes. At zero or low speeds,the Hawker Harrier VTOL airplane uses reaction rockets placed in the nose, wing tips, andtail as shownin figure 157. *Large

lift

lift

z ....

_-

f_

Ailerons Spoiler

up

to

dump

one

speed

Figure 176

155.-

Lateral

wing-

used

lateral

control

control

used

lift at

on

as

high device

with spoilers.

low

speeds

,G

All moving "stabilator"

F-4

/

_

\

_

Phantom

all-moving

control

surfaces

Tomcat

_"

Figure

156.-

control

Examples

_

J[

_

The North of such the

American

low air

same

reason

manner,

The trol

lems

its

since claimed

stability.

Shuttle

(fig.

are

the

reduced

used

use

roll

control

yaw,

up or down,

thruster

control

reaction

thruster

control

system.

reaction

controls

surfaces

were

reaction

controls

(fig.

variation

of the

is an interesting

weight

surfaces.

when

it flew

useless

at altitudes

(fig.

158(a)).

158(b))

for

In

the

same

attitudes.

functions

of the pitch, To pitch

will

and

159(a))

it combines

in cross-coupling

dynamic

aerodynamic

yaw,

Roll

All-moving surfaces

thrust

Harrier

the

pitch, tail

Hawker

Engine

plane

Space

A

V Pitch

/------_

rocket

that

the

butterfly

system

advantages

X-15

density

to change

157.-

_,_

/

Roll control thruster

Figure

of all-moving

\

of the vertical

and drag. and both

roll

and horizontal

However, motions

control

conventional

there and

surfaces

are

reduced are

tall. increased

conThe pro-

directional

moved

up or down

177

together moved

(fig.

This influence

brief the

a compromise airplanes, final

159(b)).

in opposite

arbiters

To yaw

directions introduction

design

or left equal

to stability

of an airplane.

to often the

right through

conflicting

compromises

the

and control

It must more

has

shown that

As one frequent.

Cost

and

many

lr

Roll

(a) X-15

(b) Space Figure

thrusters

reaction

Shuttle 158.-

wings

controls.

reaction Reaction

on

Yaw

controls. controls.

thrusters

are

that

design

competition

h thrusters

called 159(c).

factors

towards

of design.

_

are

in figure

the final

moves

___c

1'/8

as they

as shown

be stressed

parameters.

become

"ruddervators"

deflections

is at best

multimissioned are

the

Butterfly or "V" tail

Bonanza

(a)

(b)

Both elevators airplane pitches

Both elevators airplane pitches

down; down

up; up

(c) I Right rudder; airplane yaws

Figure

Left rudder; airplane yaws

right

159.-

Butterfly

tail

left

operation.

179

180

APPENDIX

AERONAUTICAL

NOMENC

General aircraft

any

machine

heavier

aerodyne

that lift

airplane

(aeroplane)

Definitions

air)

a subset

fixed-wing

the

science ous

that

aerodynamic

class

support

are

heavier

deals

and

of the

in relative

of aircraft chiefly

than

specifically,

reaction

that

fluids,

bodies aerostat

from

aircraft,

by the dynamic aerodynamics

heavier

of aerodynes,

of the

from

air

air

air,

and deriving

forces

acting

its

driven

is supported its wings

of air

and other

on bodies

with

buoyancy

which

against

motion

lighter

or

forces

air,

with the

being

by the

a mechanically

than

motion

lighter

action

being

chiefly

(whether

to be supported

or by dynamic

of aircraft

in flight

device

designed

by bouyancy

class

LATURE

or weight-carrying than

either

A

respect

than

to such

air

derived

when

gasethe fluids

and deriving

from

its

aerostatic

forces airship

a subset

of aerostats,

specifically,

a propelling system direction of motion aerostatics

the

aeronautics

the

and with

an aerostat a means

of controlling

science that deals with the equilibrium and of bodies immersed in them science

and

art

of designing,

provided

the

of gaseous

constructing,

and

with

fluids

operating

aircraft

Aircraft Figure airships

160 presents

(dirigibles)

sketches nonrigid

of the aircraft (blimp):

envelope,

types

defined

a lighter-than-air

or skin

or reinforced internal

Types

that

craft

is not supported

by stiffening.

pressure

herein.

of the

Its gas

shape

with which

having by any

a gas

bag,

framework

is maintained

by the

it is filled.

181

APPENDIX

semirigid

A

-

(sometimes

envelope

Continued

blimp):

reinforced

a dirigible having

by a keel but not having

its main

a completely

rigid framework. rigid:

a dirigible having

in an envelope

several

supported

gas bags or cells enclosed

by an interior rigid framework

structure. an airplane designed

amp_bi_

to rise from

and alight on either water

or land a rotary-wing

autogyro

aerodyne

flight by air forces through balloon

material

than-air.

It is an aerostat having

currents

in which

is lighter-

without a propelling system. or supporting

surfaces,

one

the fuselage

(hull) is especially

flotation on water into air

that keep it aloft

a type of rotary-wing

approximately a light frame,

an aerodyne

from

whose

liftand forward

airfoils mechanically

thrust

rotated about an

vertical axis covered

to be flown in the wind

which

the shape

aerodyne

usually of wood,

and designed body

gas which

airplane flown by being manipulated

are derived

lifting

of the craft

of silk or other light, tough,

filled with some

two wings

to provide

an engineless

kite

the motion

its

the other

a type of airplane designed

helicopter

made

nonporous

located above

glider

throughout

the air

an airplane

flying

rotor is turned

resulting from

a bag, usually spherical,

biplane

boat,

whose

derives

most

with paper

or cloth

at the end of a string

or all of its liftin flight from

of its fuselage, the wings

being essentially

nonexistent monoplane

an airplane

ornithopter

a type of aircraft achieving from

parachute

having

its chief support

consisting of a canopy

basically produces

of a falling body

182

or supporting

surface and propulsion

the bird-like flapping of its wings

a cloth device, which

but one wing

a drag

and suspension

lines,

force to retard the descent

APPENDIX paraglider

a flexible-winged, recovery

pusher

airplane

an airplane

rotary-wing

aircraft

a type

airplane

with the

an airplane

airplane

are

which

short

VTOL

vertical

V/STOL

an airplane

for use

or propellers

rotating

the devices

incorporated

with

take-off

is supported

or blades

in a

aft of the

main

which

about

used

air

wholly

a substantially

to obtain

stability

or in ver-

and

or propellers

forward

of the

surfaces

and landing

take-off

in the

in the wing

the propeller

supporting

STOL

designed

vehicles

propeller

in which

an airplane main

vehicle

launch

surfaces

by wings axis

control tractor

for

of aerodyne

part tical

Continued

kite-like

system

supporting

tailless

A -

and landing has

both

airplane airplane STOL

and

VTOL

capabilities

Amphibian Grumman

srihgii'pd

Rigid

SA-16A

Albatross

airship

,_,,, °""

_-_

_----

Autogyro

Biplane

_Balloon

Bristol

Figure

160.-

Examples

of aircraft

F2B

types.

183

APPENDIX A - Continued

Flying

boat..-----------_*

Shin

Meiwa

PX-S

Glider

Schweizer

1-23

Helicopter

Sikorksky

CH-3C

Kite

HL-IO

_

Lifting

body

7..-

Flapping

wing

ornithopter

Figure

184

160.-

Continued.

APPENDIX

A -

Continued

Paraglider Parachutes

Modified

ring-sail

Disk-Gap-Band

aircraft .q____Rotary-wing

Bell

XB-42

Jet

Ranger

Tailless airplane

airplane Tailles_

Tractor airplane Boeing

Figure

377

Stratocruiser

160.-

Continued.

185

APPENDIX

A -

Concluded

and landing airplane (STOL) Short take-off

DHC-6 win

Vertical and airplane

Figure

186

160.-

Concluded.

Otter

take-off landing (VTOL)

APPENDIX

DIMENSIONS

There

is a fundamental

represents

the

definition

of the particular matter the

scheme

present

edge

in a lump

of a book

A unit

in kilograms

or slugs

on the

system

choice

of units

of the book

its

rather

to denote has

than

are

called

ture.

are the

They

four

basic

may

property

which For

dimension

arbitrary

A dimension

remains

example,

of mass

scheme

mass

of matter

and the

length

of the

selected.

independent

the quantity

and the

kilometers

book

that

used

in the

physical

the

is,

to denote

lump

of size

of

magnitude

may

in meters

quantity

meters

the

of metal

expressed

Usually

to be employed,

basic

and units.

of length.

be expres-

or feet

to be measured

or feet

to measure

influthe

length

or miles.

Basic There

dimensions

the

of units

UNITS

measure.

the

particular,

Thus,

ences

the

used

the

depending

between physical

the dimension

property.

AND

of an inherent

of metal

represents

of a physical sed

has

difference

B

dimensions

or primary

Dimensions

of general

dimensions

be abbreviated

by using,

interest

and

are

to aerodynamicists.

length,

respectively,

mass,

time,

M,

T, and

L,

These

and

tempera-

8.

Derived Dimensions The tities

dimensions

expressible

derived times

of all other

in terms

or secondary a length

namics

and

The tended

or

their

arc

of the basic

dimensions. L 2.

A list

dimensions

measure

circle

central

divided

may

in table

Angular

Measurement of a circle

by the radius,

measure

is dimensionless

but is assigned

ally

one

express

in degrees

about

57.3 °.

The

less means that units to another.

the

fact

the

angle

that

numerical

both

area

common

included

angle

radian value

that

of an angle

These

of quan-

are

may

be represented

quantities

encountered

known

as

as a length in aerody-

II.

is defined

as the ratio

is,

of two lengths.

a ratio

a special

by noting

measure

to be combinations

dimensions.

example,

more

this

may

be found

or primary

For of the

are

of the

of the

quantities

name

that

does

of radians.

an angle

and degree

from

are

sub-

Thus, Addition-

of 1 radian

measure

not change

of the

equals

dimension-

one system

of

187

APPENDIX B - Continued Systemsof Units There are two basic engineering systems of units in use in aerodynamics. They are the International Systemof Units (SI) andthe British Engineering Systemof Units (B.E.S.). In 1964the United StatesNational Bureau of Standardsofficially adoptedthe International Systemof Units to be used in all of its publications. The National Aeronautics and SpaceAdministration has adopteda similar policy and this is the system of units used in this report. Table II lists the SI and B.E.S. units for both the basic dimer_._ionsand some of the more commonaerodynamic quantities. Vectors and Scalars Vectors are quantities that haveboth a magnitudeand a direction. Examples of physical quantities that are vectors are force, velocity, and acceleration. Thus, when one states that a car is moving north at 100kilometers per hour, with respect to a coordinate system attachedto the Earth, oneis specifying the vector quantity velocity with a magnitude(100kilometers per hour) and a direction (north). Scalars are quantities that have a magnitudeonly. Examples of physical quantities that are scalars are mass, distance, speed,and density. Thus, whenone states only the fact that a car is moving at 100kilometers per hour onehas specified a scalar, speed,since only a magnitude(100kilometers per hour) is given (that is, no direction is specified). To represent a vector on a diagram, an arrow is drawn. The length of the arrow is proportional to the magnitudeof the vector and the direction of the arrow corresponds to the direction of the vector. Figure 161showsthe side view of a wing called the airfoil cross section (or simply airfoil section). Two aerodynamic forces are knownto act on the section: lift and drag. They are vectors andmay be drawn to act through a special point called the center of pressure discussedin the text. In the first step a scale is chosenandthe force magnitudesare scaled. The secondstep is to place the vectors at the center-of-pressure point in the directions specified from the physical definition that lift always acts perpendicularly to the incoming velocity of the air V_ and drag always acts parallel to andawayfrom the incoming velocity of the air. : Vectors may be addedtogether (composition) to form onevector (the resultant) or one vector may be broken down (resolution) into several components. In figure 161 the lift and drag havebeen composedinto the resultant shown. The resultant can be resolved back into the lift anddrag components.

188

APPENDIX

TABLE

B - Continued

II.-SYSTEMS

OF

UNITS

Units Quantity

Basic dimensions SI

B.E.S.

Length

L

meter

foot

Mass

M

kilogram

slug

Time

T

second

second

Temperature

0

oc

(relative)

OF (relative)

K (absolute)

OR (absolute)

Units Quantity

Derived

dimensions SI

B.E.S.

Area

L2

meters

2

feet 2

Volume

L3

meters

3

feet 3

Velocity

LT- 1

meters/second

Acceleration

LT-2

meters/second

Force

feet/second 2

feet/second

MLT-2

newton

Pressure

ML-IT-2

newtons/meter

2

pounds/foot

Density

ML-3

kilogram/meter

3

slugs/foot3

Kinematic

L2T - 1

viscosity

Momentum

MLT-

1

newton-

Energy

joule

ML2T-3

watt radian

2

feet2/second

second

Power Angle

pound

meters2/second

ML2T-2

2

pound-second foot-pound foot-pound/second

or degree

radian

Angular

velocity

T-1

radians/second

Angular

acceleration

T-2

radians/second

2

Moment

of inertia

ML 2

kilogram-meter

2

or degree

radians/second radians/second slug-fl

2 2

189

APPENDIX

B -

Continued

Assume:

Lift

= 400

Drag

newtons

= 100

newtons

v_ Incoming velocity

free-stream vector Airfoil

I

I

100

200

section

I 300

I 400

Magnitude

i 500

I 600

1 700

N

scale

I I i

Step 1 Set magnitude of vectors

Lift

= 400

newtons _J

-I

I 100

Drag

I I

newtons

I

J

I

--i

Re sultant O

Step 2 Set directions of vectors

°/ II

v.

Center

of pre

Figure

161.-

Vector

representation.

Motion Motion is the movement

or change in position of a body.

respect to a particular observer. One may adopt two points of view.

Motion is always with

Consider the flightof an aircraft through the air. First an observer fixed in the air sees the aircraft

approach at velocity Voo. (See fig. 162(a).) On the other hand an observer fixed on the aircraft sees the air (or observer fixed in air) approach him at velocity V,o from the opposite direction. (See fig. 162(b).) The two observers read the same

magnitude

of velocity (thatis, speed) but indicate opposite directions. In many cases, for example, in the use of a wind tunnel, the second point of view is adopted where the aircraft or airfoilis fixed in the tunnel and air is forced to flow past it. (See fig. 162(c).)

190

APPENDIX B -

Observer in

Concluded

fixed air

(a) Observer

fixed

in air.

r

Observer fixed on aircraft

(b) Observer

Wing

",:::Top

fixed

on aircraft.

in tunnel

of tunnel'

Observer' stationary with respect to wing/

(e) Wind-tunnel

operation over Figure

-

wing

wing 162.-

fixed

in place

with velocity Relative

and

air

placed

/

in motion

V_. motion.

191

192

APPENDIX

COORDINATE

A point in space point

is considered what

is known

point

is then

located

vector its

from

three

nate

components

They

are

in space

along

employing

the

Cartesian

system

the

X,

Y, and

right-handed

Earth-axis

system,

of units

tail

rectangular

the

along

body-axis

each

(See

known

which

con-

unknown

of the three

as a

may

be resolved

fig.

163(b).)

Three

coordi-

generally

used.

axes,

and the

are

wind-axis

into

system. y-

_

axes

Additionally,

origin

Cartesian system,

The

The

163(a).

at the

axes.

lines

system.

in figure

is set Z

point.

perpendicular

coordinate

is shown

whose

it to a known

mutually

the number

This

at random

systems,

of three

as a rectangular

origin.

SYSTEMS

by referencing

origin

by specifying

the

oriented

be located

to be the

stitute

measured

may

C

)onent

COIE

Origin

° X

r

Point

(a) Location

system point

and second

-

along

fingers

Z

in a right-hand

coordinate

Right-hand axes

Z

of a point

rectangular

Z

P

(b) Location

system. X,

rectangular

Y,

thumb,

in a right-hand

Cartesian

system.

first

of right

of a vector

Resolution

coordinate into

components.

hand,

respectively. Figure

163.-

Rectangular

Cartesian

Earth-Axis In the Earth-axis X

and

Y

pointing east. ure 164.

axes

system

the

lie in the geometric The

Z-axis

points

Earth

system.

System

is considered

plane down

coordinate

of the

toward

the

Earth, center

to be fiat X

and nonrotating.

pointing

of the

Earth

north

and

as shown

The Y in fig-

193

APPENDIX C - Continued X_t Lie in geometric y_) Earth's surface E }

p- Nonrotati.ng

Figure

164.-

Earth-axis

Body-Axis In the that

the

tudinal

X-axis axis

craft

aircraft.

points

Z-axis The

Roll:

Pitch:

nose

The

is perpendicular of the

point

aircraft

system

the

system

out of the X

is taken

to define

axis

is oriented

and is coincident

is directed to both

entire

it is useful

Cartesian

of the

Y-axis

system.

System

the rectangular

out of the

origin

At this

pitch,

system

of the aircraft.

and the

downward.

roll,

body-axis

plane of

and

right

Y

axes

to be the

the important

with wing

such

the longiof the air-

and is directed

center

angular

of gravity displacement

of the terms

and yaw. the airplane

rotates

positive

is defined

roll

the

right

wing

the

airplane

the

Z-axis

about

its

longitudinal

as the Y-axis

axis

turning

(that is, toward

the

X-axis). Z-axis,

A that

is,

drops. rotates

turning

about

the

Y-axis.

toward

the

X-axis,

the

Z-axis.

A positive that

is,

pitch

the nose

is defined

as

of the airplane

rises. Yaw:

the

airplane

X-axis

turning

(clockwise

194

rotates

when

about

towards viewed

the Y-axis, from

above).

A positive that

is,

the

yaw is defined nose

moves

as the

to the right

APPENDIX

The figure

body-axis

system

and

the

C -

concepts

Continued

of roll,

pitch,

and

yaw

are

illustrated

in

165.

YB

XB

Roll

Yaw

ZB

Figure

165.-

Body-axis

Wind-Axis In the is

at the

center

oncoming airplane

The

Y-axis

Y-axis

of gravity

and is

The

system

ure

166(b)).

of the

airplane the out

then

X-axis of the

is termed

the

The The

to the to both

motion also right

X

X-axis

Z-axis

X-axis

the

of the

and

in the

geometric

lies

in the

plane

The

simplified

Z-axis wind-axis

rectangular points

lies

and

is

wing. the

System origin

aircraft. vector.

perpendicular

perpendicular

so that points

system,

velocity

is

of interest

motion)

wind-axis

free-stream

the

lems

general

system.

is Z

Cartesian

into

in the

directed

the

166(a)).

plane

of symmetry

of symmetry.

This

again

plane

system

in the and

of the

of symmetry

generally

(fig.

is

direction

plane

axes

system

of

downward. In many (no

means

prob-

yawing that

the

of symmetry.

is illustrated

in fig-

195

APPENDIX

C - Concluded

Yw

Zw Relative the

(a) General

wind

plane

of

not

in

symrnetry//_

wind-axis

)'7 jc/Xw

(i" system.

Z-axis

in plane

of symmetry.

Yw

f

(b) Simplified

wind-axis

system.

Figure

196

166.-

X

and

Wind-axis

Z

axes system.

in plane

of symmetry.

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