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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
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weather
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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
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--Stratopause
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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
"<$'-
N
eb '_
r adient]
-e _
I
Pt
/L,_,,_
"
D.e.c reasing
PrOssur
_
\_ve.-'_
/
_o
[low
pressure
<)o
,,9
along
_g-edge
highest
.,,,_'°e?b_
g "_-----'-77..vOSl_-I
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=
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IV = O)
.... _ _Ve Pr
_
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ess
Ure
_raclient)
Lowest
pressure
at shoulder
l
/
0_
(c)
Distance
Figure
airfoil
will appear
the
existence
sent
basic
real,
to be slightly
of drag
From
flow of air
Ideal
fluid
different
in several
principles.
viscous
29.-
The
point
is allowed
laminar
ure
and
30(a)
adjacent
of these
fluid
turbulent
turbulent.
shows
in straight-line
the
and
streamtubes
layers.
flow.-
flow,
are
flow the
the uniform
(laminas)
from
and then
Laminar
Fluid
There
In laminar
a laminar
layers
reduction
of the
past
assumption
in lift
few pages
is dropped
and
repre-
and a
to exist.
Real
Laminar
discussions
on, the inviscid
flow
an airfoil.
with an accompanying
forms.
this
flow about
along
the
flow
left
two different
fluid
moves
rectilinear
to right.
streamlines
need
Flow
types
in layers
flow,
The
not be in a straight
fluid
called
laminas.
consisting
laminas
indicate
of real
may
of air
Figmoving
be considered
the direction
line.
flow:
Figure
of movement
30(b)
shows
39
Infinitesimal
fluid layers
(laminas)
No distinct
layers
Fluid
exchange
free
w
l
Uniform
No fluid
exchange
between
layers
rectilinear
flow
(a)
Turbulent
moves
Adjacent
laminas
have same
Fluid follows curved
surface
speed
in laminas
flow
- Flow
left
to right
but
disorganized.
generally
is highly
(d)
profile
_b)
Fluid
layers
(lamina)
move
more
slowly
as one
approaches
the
surface
but
still
slide
over
one
another.
ofile
(c)
_'_
Laminar
flow
l
(e)
Figure
a small
segment
the curved
case
foil
surface,
lines,
of the surface
surface
for a real
smoothly,
fluid
layers
over
and turbulent
airfoil.
in laminas.
they move.
slide
Laminar
of a curved
to be discussed
the slower
the fluid
30.-
For
Figure
later.
30(c)
The closer
However,
one another
here
without
flow.
an ideal
shows
the
also,
fluid
the
the more
complex
fluid layers
as indicated
fluid being
flow follows
are
flow
to the
air-
by the stream°
exchanged
between
layers.
In turbulent
flow.
4O
Figure
30(d)
flow,
secondary
shows
random
a disorganized
motions
number
are
superimposed
of streamlines.
on the principal
They
are
evidently
not
fluid
layers
and
More
importantly,
ticles
speed
particles
rising
from
which
may
ments
(or
tance
above
wave
example
faucet.
Opened
But
Colorado
faucet
the
the
flow
flow
In some
cases,
rising
in the
less
parameter
and
flow
slide
In other
flow
the
air
in the
and
turbulent
out
out
room
is
and
disturbed.
flow
is the
column
water
-
turbulent
laminar
column.
In the
turbulent
both
dis-
laminar
in laminas.
confused
assume
fila-
some
between
in a cloudy
rocks
The
motion
in a clear
moving
smoke
filaments
is laminar.
eddying
par-
rapids.
a laminar
It will
and
turbulent
of factors.
appear
cases,
by
"naturally"
causing
question
turbulent.
in smooth
transition
smooth
in the
will
The
the
flows
may
a number
slower
this
speeds
over
surfaces
flow
gave
water
downstream
airfoil
flow.
which
the
may
upon
or
the
fluid
shows
The
when
moving
to the
which
rises
of laminar
speeds
turbulent
laminar
cigarette
slow
to another.
momentum
a confused
turbulent.
occurrence
churns
to a turbulent
is to be
to the
fully
air.
is
that
sector
30(e)
smoke
identity;
up into
adjacent
such
up their
the
their
break
water
over
lose
flow
one
figure
distance
not
at low
depending
flow
do
closer
the
the
changed
some
this
brook
give
Consider
suddenly
slightly,
characteristic
be
particles
of a common
River
that
smoke
but
from
of monmntum
themselves.
cigarette;
open
of fluid
exchange
For
moves
In a mountain
an
moving
streamtubes)
Another
seen
fast
down
around
the
an exchange
is
a cigarette.
flow
be
and
slow
turbulent
flow.
is
there
up
and
there
In
a quantitative
a disturbance,
arises
1883,
in a laminar
as
Osborne
to how
of the
as
a laminar
one
Reynolds
indication
flow
can
laminar
flow
tell
introduced
in the
can
whether
a
a dimension-
to turbulent
transition.
Reynolds
strated
nar
the
fact
tube
under
colored
fluid
However,
flow
fluid
speed
of the
tank
speed.
of the
field.-
In his
circumstances
region
was
flow
injected
water
tube.
had
a long
The
tube
into
was
the
flowing
tube
through
its
identity
for
the
entire
speed
was
high,
the
filament
the
cross
section.
Reynolds
defined
a dimensionless
Reynolds
number,
to give
Reynolds
number
R
R - pVf
#
a quantitative
fig.
flow
The
experimental
outlet
Reynolds
in a tube
changes
setup
with
a stopcock
smoothly
into
the
the
flow
(See
the
at
the
through
experiments,
faired
flow
maintained
when
existed
certain
water
the
of colored
the
on the
a given
A large
to control
When
effects
over
31(a).
filament
that
that
to turbulent
in figure
the
number
tube
length
broke
the
demonfrom
lami-
is
illustrated
at
the
end
tank.
of
A thin
mouth.
was
of the
up
low,
the
tube.
into
filament
(See
the
fig.
of
31(b).)
turbulent
flow
31(c).)
parameter,
which
has
description
of the
flow.
since
been
In equation
known
form
as
the
the
is
(I0)
41
rI
]
[
,5
[
I
//
as
Valve,o control--,
[
[
/-Smooth
--
t/
I
Water
[
.........
z_/,/zz'z/zz'zzzzi//////
Reynolds
experimental
/
Water
level
drops
flow continues
[
--I
[] _ye
tank
-_--_ ....
fairing
t"
F
--
.
flow
. ,
Long
tuoe
speed
\
x
/
|
"°
Dye
in
[il;unent
flow
1_'_
Outlet
-NN
"_'
(a)
S
Low
remains
speed distinct
flow
(R
indicating
/ 2100)
throughout
laminar
- Filament flow
(b)
R
,%
-._
" 40000
__
(/
Figure
31.-
-
Filament
_-turbulent
breaks
up
flow
indicating
[
/
._-
,el
Dependence
l
of flow on Reynolds
number.
R - pVf
where
density
V
mean
of fluid,
velocity
characteristic
of viscosity
discussion),
the pipe
true
this
was
regardless
tion between
42
setup,
laminar
of fluid,
length,
coefficient
For
kg/m
m/sec
m
(called
simply
"viscosity"
in the
earlier
kg/m-sec
Reynolds
found,
as evidenced
of his varying
laminar
3
by using
by the distinct
combinations
and turbulent
water,
colored
of values
flow occurred
that
of
below
R = 2100
filament.
p,
for Reynolds
V,
This
f, or
numbers
the flow in
value
p.
was
A transi-
between
2100
and40 000dependingupon howsmooth the tube junction was andhow carefully the flow
entered the tube. Above R = 40 000 the flow was always turbulent,
as evidenced
by
the
colored
number
fluid
filament
(between
lence
since
2100
has
on the flow.
The
numerical
and
be the
Additionally,
water
airfoil.
Thus,
different
for
several
the case
million.
low Reynolds
turbulent.
The
The
flows
viscous
forces
number
arise
the fluid's
number
flow the
whereas
in high
inertia
steel
through
dropped
the liquid;
another
Reynolds
number
An example
ball
case
and turbulent
flow,
flows
of low Reynolds
are
number
about
would
numbers
a particular
number
flows
an
be far
of
body,
are
mostly
(ii)
friction
viscous
are
Dust
flow.
very
flow and high
flow
small
(called
oil.
These
relative
ball
settling
flows
in the
flow will
to the
flow)
falls
the
laminar.
air
In a high
of aircraft,
between
is a
slowly
through
are
flight
contrasts
number
inertia
forces
Stoke's
The
particles
interesting
Reynolds
The
In a low Reynolds
are
silicon
experienced
Some
fluid.
with the viscous
number
large.
number
of the
forces
of heavy
as typically
present.
length.
way:
compared
the
a container
such
flows
at Reynolds
to acceleration.
negligible
of a low Reynolds
number
Reynolds
an airfoil,
forces
forces
flows
forces
experiment
flow
For
turbu-
the chord
air
operate
evident.
another
of a low Reynolds
into
viscous
and high
induced
For
called
whereas
are
Reynolds
particular
and turbulent
resistance
are
edge
airfoils
that
of the pipe.
trailing
of the internal
natural
forces
Reynolds
forces.
small
because
diameter
however,
= Inertia
Viscous
for this
laminar
Typically,
be viewed
transition
experiment
between
laminar
may
number
forces
represent
inertia
are
the
the effect
are
and
in the Reynolds
that
indicates
is the
the leading
trends,
fact
transition
f
number
general
number
Reynolds
chosen
of an airfoil.
Reynolds
The
used
transition
The
variable
for the
between
was
the
given
length
distance
up quickly.
40 000) was
values
the characteristic
would
are
breaking
laminar
the
results
be demonstrated
shortly.
Surface
body
immersed
laminar
rence
this
roughness
point.
surface
is seen
in a flow field
to turbulent.
of turbulent
As the
flow will
An airfoil
roughness
effects
surface
is increased
to go turbulent
further
on the flow
is that
surface
move
field.-
it causes
is shown.
along
In each
and the Reynolds
upstream
in each
effect
the flow
roughness
upstream
The
near
increases,
the
succeeding
case.
the body
the point
airfoil.
number
of surface
Figure
case
is held
The
roughness
to go from
of first
Reynolds
occur-
32 illustrates
the degree
fixed.
of a
of
The
flow
number
and
43
surface roughnessare not independentof eachother and both contribute to the
determination of the laminar to turbulent transition. A very low Reynoldsnumber
flow will be laminar evenon a rough surface and a very high Reynoldsnumber flow
will be turbulent eventhoughthe surface of a bodyis highly polished.
Pressure
transition
from
the static
pressure
gradient
effects
laminar
to turbulent
increases
flow will be amplified
with
downstream
will
tend
up to the
point
region.
Beyond
static
before
of maximum
the
pressure
the
flow will
point
Recall
that
of maximum
The
Another
important
laminar
gradient
distance,
over
If the
thickness
in the
static
flow
(or
the
flow field.
pressure
decreases
out and the
static
pressure
will be encouraged
shoulder
in the
in a laminar
flow will damp
an airfoil
A laminar
factor
disturbances
result.
in a laminar
thickness.
increased.
trailing
with downstream
disturbances
laminar.
field.-
flow is the pressure
and turbulent
distance,
to remain
on the flow
decreased
in this
of the airfoil)
flow now is hindered
and
may
flow
the
go turbulent
edge.
_ran.
Laminar
_._tion
v_
Tran.
sition
SY_ly
rough
mrwu
_//_
,,///7-
r
v_
v_
Figure
44
32.-
Surface
roughness
and
flow field.
All cases
at same
Reynolds
number.
If
vided
real
the
The
boundary
the
background
fluid
flow.
force
is
referred
previously
33
a body
immersed
cous
caused
forces
to show
the
-
that
drag
over
to the
fluid,
the
the
fluid
Pressure
normal
of the
strongly
forces
and
are
help
vehicle.
that
act
also
present.
Hydrostatic
the
proin a
subsonic
and
create
has
immersed
flight
This
dependent
roughness,
./._-
Real
is
forces
lift
low-speed
surfaces
and
discussion
on a body
during
pressure
fluid
foregoing
produced
surface
viscous
ideal
is
force
number,
in addition
The
force
flow
Reynolds
modify
how
skin-friction
in a moving
which
drag.-
aerodynamic
by viscous
to as
shows
skin-friction
important
mentioned
Figure
and
needed
An
shear
force
layer
on
factors
gradients.
everywhere
normal
It is
real
shear
the
pressure
is
fluid
these
to
vis-
drag.
pressure
at rest
forces
to surface
._
___-_-- Static-pressure
forces
flmd
in
Figure
Consider
approaching
stream.
surface
the
plate,
figure
flow;
If the
with
the
the
fluid
velocity
velocity
34
flow
were
V_
which
33.-
Pressure
shows
a very
ahead
of the
ideal,
that
as
distribution
shown
a
is,
(that
the
flow
viscous
forces.
thin,
smooth
plate
parallel
of the
plate
is
fluid
would
inviscid,
is,
fluid
and
leading
in figure
real
edge
the
34(a).
variation
At all
points
of velocity
to the
a uniform
simply
along
as
free
slip
over
the
surface
one
moves
the
of
per-
45
pendicularly
drag
away
would
result
In a real
fig.
34(b).)
the surface)
if the
fluid
fluid,
This
of a body,
from
of the fluid
constant
value;
Within
in the
case
is changing
layer
and an internal
friction
the body.
cumulative
ary
The
there
effect
drag
Initially,
the
leading
layer
also
is steady
downstream,
as more
and more
reached
on the plate
becomes
a turbulent
fluid
There
from
the
one
moves
is slowed
is no slip
at the
surface
boundary
layer
total
tendency
in a turbulent
boundary
slower
moving
fluid
the
near
and
difference
up more
quickly
will be shown
as
is greater.
in figure
away
flow,
directed
thickness
further
is
turbulent
important
builds
moves
thickens
a point
for
as shown
fluid
of
As one
layer
transition
boundary-layer
of the
the wall
layer.
as the downstream
the two profiles
layer
layers
and the bound-
Eventually,
velocity
layer.
a drag
boundary
Another
where
surface
flow
As is usual
plate.
that
This
the
of the
the
by comparing
to the
undergoes
as well
fact
can be seen
reenergize
layer
is the
condition
particle
a laminar
friction.
34(b).)
of fluid
a
drag.
laminar
layer
although
This
the
boundary
and the
(See fig.
boundary
the wall,
a laminar
becomes
is to produce
one has
the
as the boundary
extends
forces
(See
the body
layer
to as skin-friction
boundary
layer.
The
between
friction
by internal
laminar
No
at the surface
from
A the velocity
is known
friction
to act
in the
from
value
hence,
down
Voo.
surface.
that
away
V_.
velocities
these
-
is
internal
continues
the
point
of the plate,
layered
where
at some
is referred
motion
laminar
away
of all
edge
boundary
is a random
motion.
and
moves
value
relative
force
viscosity
this
This
of
to the
It states
As one
to a constant
are
value
adheres
condition.
until
is present.
This
near
no-slip
plate
zero
on the plate.
further
there
of a flat
from
of fluid
is zero.
increases
constant
(inviscid).
thin film
important
gradually
the boundary
force
a very
very
be a uniform
frictionless
B, the flow velocity
velocity
the velocity
were
however,
is the
point
would
from
34(c).
the wall
to produce
to
important
consequences.
The
Reynolds
Reynolds
number
viscosity),
Reynolds
zero.
number
increases
the boundary
number
Thus,
the
at the
wing
surface
It is clearly
in this
46
layer
region.
of the
evident
This
less
wing
that
gives
never
that
than
the flow
slowly.
at the
thickness
a centimeter.
tremendous
to the
on the
boundary
speed
However,
surface
layer.
As the
and/or
even
decreasing
though
of the body
the
the
must
be
disappears.
a typical
to hundreds
rise
more
the velocity
layer
to note
effect
by increasing
thickens
large,
boundary
is generally
an important
(caused
becomes
It is interesting
craft
has
Yet,
of m/sec
shearing
of the boundary
the
velocity
at the outer
forces
skin-friction
(internal
drag.
must
edge
layer
vary
on an airfrom
of the boundary
friction)
must
zero
layer.
be acting
v_
v_
Flat
)late
(a) Inviscid
flow along
a flat
plate.
v_
v.
B_-oundary_
layer
thickness
[......._j
|
BW_
v_
Laminar
layer
" [--_
thickness
tilickncss
_
I"_
plate
botmdal_ "__]
layers
Turbulent
layer
(b) Viscous
_rl
_l I
flow along
a flat
boundary
_
:1
(/
Steetl, er
Laminar
Turbulent
layer
boundary
taycr
(c) Comparison
Figure
airfoil
foil surface
and
the
originally
free-stream
slightly
same
in a real
modified
fluid.-
energy
of laminar
Figure
p_
29.
apply.
purposes
fluid
Again
case.
flow.
flow in a real
fluid.
The
The
all practical
the
the
same
real
fluid
ahead
velocities
and
maximum
on along
flow
free-stream
flow field
a stagnation
and the pressure
reaches
its
pressure).
From this point
and
and turbulent
35 illustrates
in figure
profile
exchange
boundary
Boundary-layer
pressure
and for
as for the ideal
edge of the airfoil
(total or stagnation
34.-
considered
static
/
plate.
I__z/
The
Flat
l
point
value of
the airfoil,
the
velocity
of the
static
occurs
over
airfoil
airV_
is only
pressures
are
at the leading
Pt at this point
the picture
changes.
47
Sh¢,ulder of airfoil maxh_mm
speed
outside
,a[ Ihe llI)w_d_l'vh_yer
_
I
/
_--
/--Note
/
-- _-
Flow
laver
.
outside boundary
is in_is(id
flow
'
",':
Turbulent
--
boundary
layer
(S_alled flow)
Figure
35.-
wake
Real
fluid
greatly
exaggerated.
on the upper
As noted
because
very
the
much
pressure
and will
the
pressure
present.
This
shoulder
just
came
that
the
forces.
push
layer
continues
dient
and viscosity
pletely.
that
The
the
to rest
from
is the
outside
pressure
the
and
same
acting
to the surface
boundary
begins
of it the
as
flow acts
surface
layer.
This
and thus
layer
to form
on the
boundary
up to the
feels
acts
this
with distance
as if
static
grows
and a laminar
in thickness
particles
condition
the
distance
before
the trailing
shoulder
pressure
the
character
a turbulent
of the flow
boundary
for the flow,
trailing
edge
surface,
pressure
Pushing
stalled
rear
short
than
in the
ideal
flow
present,
is reached.
the static-pressure
distance).
changes
of reaching
the
the
in the ideal
boundary
pressure
flow stops
trailing
fluid
viscous
laminar
turbulent
an unfavorable
point,
The
and the
and the
This
and at some
stopping
edge
gradient
layer.
against
before
slower
with viscosity
with downstream
unfavorable
downstream.
has
to the
is
When
previous
at some
the
layer
flow
the airfoil.
moving
because
The
boundary
along
are
favorable
downstream).
now,
becomes
the
an assisting
appear
both this
layer
shoulder,
It would
is too much
reached
layer
edge.
point,
to thicken
flow
But the
the fluid
(increasing
boundary
at all.
is an unfavorable
transition
layer
layer
layer
however,
against
quickly
boundary
flow is laminar
boundary
moves
thin and
outside
decreasing
The
at the trailing
At the
boundary
48
(pressure
to rest
come
the
of the airfoil
This
must
layers
to it.
surface
is unfavorable
particles
ber
respond
laminar
flow
surface
a boundary
the static
pressure
not present
case.
As the
gradient
were
the airfoil.
flow will
of boundary
lower
plate,
is very
Also,
static
through
is reached,
fluid
flow along
layer
fluid.
by the
exists
up along
Thickness
of the flat
boundary
of an ideal
front
gradient
speeds
ideal
that
layer
Over
the
This
is transmitted
boundary
Bottom
in the example
is determined
pressure
the
earlier
like
an airfoil.
surface.
of viscosity.
airfoil
flow about
edge.
fluid
gracom-
(Rememcase.)
of
This
stall
point
outward
moving
point
and
away
known
into
back,
eddies
is
the
airfoil.
and
around
it.
The
the
airfoil.
Figure
airfoil
36(a)
surface
separation
pressure
force
field
acting
stream
(See
of forces
allel
net
is
result
drag.
the
center-line
shearing
fig.
front
forces
tion
of the
ideal
fluid
of the
The
in the
net
force
due
This
(internal
now
to the
is
friction)
static-pressure
35 is
on
fluid
case
that
the
rear
this
to the
boundary
on
the
to the
the
surface
par-
surface.
The
called
pressure
drag
Additionally,
free
airfoil.
due
the
pressure
to the
modificalift
from
the
case.
_[deal
....
_k
p _'
'"
x
[
leadim,
]
edge,
fluid
Real
_---
fluid
.......
/
.
_
"
1
.
/
distribution
edge
_reatlv
inodified
Separatmn
Distance
OCCURS
here
fluid
(a) Airfoil
Pressure
equal
airfoil
upper
surface
to
static-pressure
alld
stream
opp_,site
(no
Figure
conll)ollents
equal
7
-
no
Net
component
pressure
36.-
drag).
Real
(c)
fluid
effects
flow
distributions.
These
free
alon_
near
in
real
case
forces
parallel
fluid
PressuJ'e
trailing
0
(b) Ideal
up
cancellation
front
rear
in the
tile
the
to the
and
skin-friction
a decrease
that
of the
distribution
layer.
at
parallel
on the
pressure
behind
static-pressure
surfaces
acting
away
occurs
symmetry
acting
field
wake
Note
net
of
to flow
the
shoulder)
the
actually
distribution
case
force
causes
called
separation
(up to the
flow
forced
once
in addition
distribution
is
but
asymmetric
in the
region
this
a region
the
large
fluid
flow
is
disrupting
case.
exceeds
a drag
is
fluid
acting
real
tile
real
static-pressure
direction
air
from
This
static-pressure
ideal
that
is
starting
the
airfoil
canceled
however,
very
line,
around.
figure
case
with
In the
surface
in
a line
this
which
dead
shown
not
along
turning
air
fluid
are
All
Beyond
tile
streamline
and
36(c).)
as
modified.
free-stream
(See
before
ideal
differences
is a drag
nose
outside
compares
destroyed.
to the
flow
of eddies
Now,
stalling.
"dead"
region
opposed
36(b).)
the
point.
is
represents
greatly
on the
flow
Thus,
the
is
exactly
fig.
and
and
point,
separation
the
toward
whirlpools
the
the
flow,
upstream
from
as
Real
fluid
on
an
airfoil
lonR'er
downstream
Pressure
(net
pressure
drag).
airfoil.
49
Figure 36(d)showsfiguratively the lift anddrag for an airfoil producing lift in
both an ideal andreal fluid case. One sees the effects of viscosity - the lift is
reduced anda total drag composedof skin-friction drag and pressure drag is present.
Both of these are detrimental effects.
x\\\\\
t
\\\\\',
\\*._-4
"_\
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\\_\\
X\.
_. N\
......
,.\_
\\
\\--_ \\"
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= ,
<
.....
\\,,X \\
_
"_
_\\\\-,
(d)
Viscosity
effects
Figure
It should
ited
be
to an airfoil
of the
these
aircraft
noted,
section,
to one
in detail
but
the
the
result
effects
this
of the
strongly,
similar
degree
In summarizing
are
very
or
will
drag.
The
extent
that
drag
arises.
Effects
of air
and
the
normally
body
is
being
flat
has
the
flow
plate
placed
small
a smaller
for
drag
has
been
evident.
the
reduced
on
the
the
all
the
the
viscosity
effects
because
pressure
lift
lim-
components
text
drag
causes
was
other
of this
airplane
that
net
discussion
scope
total
is disrupted
the
field.
37
Four
flight
higher
and
is still
from
that
five
of the
bodies
of subsonic
to the
pressure
The
the
The
smaller
of the
flat
bodies
to treat
is
discussed.
of a real
fluid
flow
a boundary
layer
and,
of viscosity
to the
is
are
number
reduced.
The
next
has
drag
is
operating
a large
the
cylinder,
result,
operating
fluid
at Reynolds
(R = 104
to
the
wake
with
the
105).
flow
num-
The
fifth
at the
same
occurs,
dra_
is a little
pressure
some
effects
drag.
separation
skin-friction
separation
skin-friction
plate;
in a real
(R = 107).
flow
than
placed
aircraft
boundary-layer
cylinder.
but
shows
Reynolds
component.
of the
plate,
Also,
previous
of "streamlining."
A large
wake
beyond
The
field
broadside
edge.
the
observes
fluid.
airfoil.
occurring
when
one
flow
in the
a much
shoulders
than
50
plate
a relatively
case
already
at
noted
Figure
encountered
at the
number,
before
resultant
operating
The
effects
of streamlining.-
bers
points
the
It is
be
of the
a skin-friction
considers
although
are
another.
an
Concluded.
processes
hence,
section
that
discussion,
viscosity
a pressure
36.-
on
drag
Reynolds
in this
larger
Overall,
of streamlining
case,
in this
the
are
total
Hehtl
Separationpoint
R
_
] ) I';IL'
105_
Flat
]D,
Separation
R _
lye
f(lrce
--_
plate
_Br(adside)
point-
105
R
_
10 5
R
= 10 4
-Separation
)aration
point
point
Skin-friction
cl rag
Pressure
drag
Figure
Also,
at the same
boundary-layer
streamline
37.- Effects of streamlining
Reynolds
separation
shape
may
and the wake
eliminating
exposed
to the
flow
is
Even
more
due
and
more
to the
thus
has
a greater
fact
that
area
One
may
There
assume
is ahnost
is the dominant
One
Oper-
component
large reduction
This has been accomplished
drag has been
increasing
streamlined
over
which
body
the
boundary
has
more
layer
and
in
by
only
can explain that the increase
the
no
then that a
separation.
noticeable is the very
streamlined.
siml)le
shape.
numbers.
of boundary-layer
drag since the sMn-friction
slightly as the bodies became
drag
small.
with the cylinder or plate.
the pressure
skin-friction
is very
the skin-friction drag now
drag is very small.
overall drag compared
Reynolds
is a streamlined
be defined as the absence
ating in the condition shown,
the pressure
number
at various
in
area
may
act.
51
Finally,
in figure
1/10
the diameter
drag
as the
early
could
of the
monoplane
and
fifth
points
shown
downstream
This
the
previously
discussed
and
the actual
better
measure
next
section
flow outside
a car
force
to wade
along
more
stiff
wind.
to the
airflow
air,
the aerodynamic
attitude
the
body
a body,
of the
and the
body,
fluid
the
(air).
been
places
his
for
is higher
by
compared.
A
in the
is one
the factors
hand
factor
that
of subsonic
along
determines
(high
depends
the aerodynamic
to a
speeds
flight
example,
that
broadside
but if one
directly
although
the
resistance
is
greater
To illustrate,
than
in the
a much
resistance
larger,
A considerable
is another
resistance
of the
fluid,
consider
up against
resistance
is felt.
that,
is dependent
the
relative
lift force
Density
a stiff
shaped
by stating
if
by a body.
similarly
factor
so.
difficult,
of air.
felt
determining
and the
to doing
more
the density
of cardboard
the discussion
properties
resistance
It is considerably
piece
Now hold
to generalize
about
than
speed
be explained
the resistance
factor
hold a small
exposed
drag
consider
aerodynamic
speed.
is much
It is now possible
and
52
length)
wake
is demonstrated
In the preceding
is little
same
determining
same
smaller
velocity.
of water
is experienced.
the
2.
of 20 km/hr,
there
at the
another
up against
times
a beach,
density
viscosities),
that
a much
is felt,
flow problems
small
higher
experiment:
resistance
cardboard
fluid,
The
represents
One
length
at the
If one
Velocity
(velocity)
times
in the water
not impossible.
fluid
or
is five
as great
If one walks
Little
relatively
separa-
have
measure
resistance
is considerable.
(velocity)
of 100 km/hr
little
the
The
may
experience,
on a body.
considering
under
times
25 times
of the
felt
higher
coefficient.
everyday
at 20 km/hr,
In fact,
number
From
resistance
window
the
on (velocity)
drag
facts
reduced
bracing.
the flow
flow speeds,
This
wire
pressure
However,
contradictory
different
of the
velocity).
and
a smaller
size.
is needed.
coefficients.-
the resistance.
velocity
under
this
of
the introduction
flow at a much
cylinder
to expect
These
of the performance
at 100 km/hr,
But try
larger.
the aerodynamic
Reynolds
one
of the same
for
free-stream
of the
speeds
A considerably
the need
the
slow
same
because
However,
in the
the
is large
for the
streamlined.
operating
lead
values,
reason
eliminated
to be the nondimensional
determine
about
would
drag
Aerodynamic
were
shoulders
cylinder
is much
actual
wire
it has
drag
is considered.
by increasing
of the
result
drag
used
is a cylinder
(accomplished
are
that
bracing
pressure
the
approximately
Surprisingly,
The
to imagine
structures
of 104 is a cylinder
thickness.
shape.
if the
better
is evidenced.
realizing
wire
realized
body
number
streamlined
all the
been
Reynolds
tion
when
number
shape
It is not hard
have
The
streamline
larger
wake.
biplanes
drag
of the
much
the turbulent
37 at a Reynolds
wind.
sheet
of
Area
of resistance.
in the flow of the
on the
size,
velocity
defined
(or
shape,
between
as the
aero-
real
dynamic
vious
reaction
perpendicular
discussion,
For
lift
an ideal
fluid,
For
a real
force.
important.
an effect
on
to the
depends
on
fluid
properties
the
fluid,
(size,
however,
to the
shape
the
Based
on
demonstrated
shape,
attitude,
for
attitude
direction.
fluid
density)
elastic,
and
the
velocity
(except
viscous,
In addition
force.
free-stream
and
of the
introductory
From
properties,
did
not
of this
also
roughness
section,
has
it may
be
that
\
/
Lift
lift
are
surface
pre-
velocity).
the
properties
the
discussion
and
influence
turbulent
body,
the
= p_,
x V
2 × S × Factor
'is,
\
-
p_V_C
p
V_ , surface
' a_
roughness,
air
turbulence)
(12)
/
where
PoC,
free-stream
fluid
Vo_
free-
velocity
stream
characteristic
body
frontal
characteristic
body
length
ot
attitude
P
coefficient
a
(S
is
times
(chord
check
body
the
its
Also,
the
dimensionless
associated
influenced
the
the
of the
wing
definition
a..__
V_
with
frontal
For
times
previously
R.
degree
length.
particular
or
of sound
a wing,
span
shown
is defined
for
S
that
associated
the
compressibility.
transition
wake
from
formed
for
the
the
it is
the
be
the
consistent
diameter
with
a
of the
usually
taken
to be
wing).
Thus,
it is
P,oV_
is
Reynolds
number
or
fluid
viscosity
Surface
M.
points.
flow.
the
The
the
planform
necessary
to
was
Air
number
Reynolds
whereas
roughness
to a turbulent
separation
to be
a body.)
quantity
Mach
chosen
it would
a rectangular
with
a laminar
past
usually
a cylinder
used
quantity
is
however,
to be the
fluid
that
For
of
been
of fluid
area
experiments.
length
It has
is
speed
of comparison
cylinder
area
of viscosity
a characteristic
series
area
of body
free-stream
¢_3_.
density
the
number
Mach
shown
number
to have
turbulence
Furthermore,
is
represents
the
effects
of
53
attitude
and shape
called
K, then,
of a body
Lift
The dynamic
1.
- is included
2
same,
2K
=p_xV_
lumped
together
into
the factor.
Letting
the
factor
be
2 xSxK
pressure
of a fluid
in equation
may
are
(13)
flow was
(13) and
be replaced
previously
the value
by
C L.
of
K
defined
1 _V 2
_p
as
is doubled
to keep
so if a value
the equation
of
the
Finally,
1
Lift
Equation
= C L ×_
of lift.
acteristic
body
upon
tude,
and body
having
equation
of lift
important
the Reynolds
wind-tunnel
lift formula
states
times
for
usual
simply
that
the free-stream
aircraft
flight.
CL
the aerodynamic
dynamic
is known
lift
pressure
to realize
number,
shape.
that
Mach
the lift
number,
experiments
of the
body
CL
is deter-
times
the
lift
is a number
roughness,
a constant.
by measuring
dimensions.
coefficient
surface
It is not by any means
or flight
a knowledge
char-
CL
and the
air
depend-
turbulence,
is generally
free-stream
found
attiby
conditions
direction.
1
p_V_
aerodynamic
Drag
(15)
2, × S
drag
One obtains
and
Thus,
Lift
CL-
The
as
area.
It is very
ent
The
by a coefficient
(14)
2 x S
(14) is the fundamental
the coefficient
mined
p_V_
is the
analogous
1
= C D x_p_V_
aerodynamic
equations
resistance
to equations
parallel
(14) and
to the
(15),
free-stream
namely,
(16)
2 xS
or
CD =
Drag
1 p_V
2
where
CD
parameters.
54
is the
drag
(17)
2 × S
coefficient,
dependent
on the previously
enumerated
Separati
on
point
Flat
plate
(B roa(
length
Separati
point
R
on
"
----_
_
s ide)
d
CD
2.0
....
_ 10 5
Cylinder
diameter
R
=
S ep;/rat
point
= 10 5
:
d
CD =
1.2
CD
=
0.12
CD
=
1.2
CD
=
0.6
i on
Streamline
bed y
thickness
:d
Separation
Cvlinder
=- 1
10
diameter
R
= 10 7
Cylinder
diameter
Figure
The
its
center
a moment
moment
d
moment
acting
of gravity.
distance.
equation
38.-
Drag
on a body
This
moment
Let it be stated
as used
Moment
for
the lift
coefficients
of various
is a measure
represents
that
of the body's
the
a similar
and drag
1
2
× S x _
= Cm × _ p<V_,
resultant
derivation
equations
=d
bodies.
tendency
to turn
aerodynamic
may
(14) and
force
be applied
(16) such
about
times
to the
that,
(18)
or
Cm =
Moment
1
5 P_V_2S
(19)
_
55
Cm
is the
sary
for
coefficient
of moment
dependent
attitude,
on the
Reynolds
and body
shape.
It is now possible
pare
the
first
three
had
five
the
Mach
The
bodies
bodies
same
CD
same
37 except
ficients
C D.
der,
streamline
and
the combined
The
reduced
From
the
cylinder,
cylinder
The
that
last
The
boundary
layer
further
along
before
stalling.
results.
of smaller
size
nullifies
shape
have
equivalent
at the
higher
cylinders
V_
drag
drag
becomes
turbulent
against
Separation
Compare
this
the
viscous
occurs
condition
upstream
flow close
with
of the
separation
coef-
plate,
cylin-
include
its diameter
has
effect
a
of 1.2.
CD
and
drags.
of 107, has
a
CD
Its aerodynamic
the higher
of the
the
CD
of larger
wake
surface
and
The
shoulders
and
and wake
at the
and,
the
turbulence
the fluid
unfavorable
drag
numbers,
cylinder.
of
Reynolds
smaller
At high Reynolds
and the
drag
values
of 104 with
to obtain
along
forces
the
These
number
to the
downstream
the flat
previously.
component.
further
for
(17),
the results
by the
aerodynamic
the effect
CD
the frontal
drag.
the
increased
indicates
coefficient
reenergizes
cylinder
been
coefficient
pressure
the
has
discussed
coefficient
38 repeats
examples,
Reynolds
same
with the flow.
replaced
values
number
effect
as the
Figure
pressure
of the previous
because
layer
and
dimension
as large
in the boundary
drag
All
By equation
1.2, and 0.12.
at a Reynolds
operating
smaller
smaller
skin-friction
2.0,
basic
cylinder,
37 is large
number.
CD
respectively,
and streamline
is, half
in figure
hence,
(16), the
of 105, the
The
R = 105, the
for the bodies,
been
com-
resistance.
pressure.
drag.
has
37 and
and the drag
length
force
turbulence,
symmetrically
drag
a unit
drag
number
operating
the
entirely
measured
relative
are,
of the
to one-tenth
small
0.6,
shape
alined
are
streamlining.
number
as is the dynamic
to the
now the
Reynolds
effects
equation
bodies
proportional
that
At the
small
therefore,
By assuming
for all the
directly
of figure
was,
resistance.
of the
more
Reynolds
and
air
with figure
as a measure
to be smooth
Cm
roughness,
associated
same
_ is neces-
CD, and
of progressively
d, the
assumed
surface
coefficient
effects
dimension
resistance
of this
is then
the
number,
length
CL,
discussion
force
demonstrated
aerodynamic
is the
to the
the
characteristic
To reiterate,
Mach
to return
and were
is a measure
S
number,
body
an additional
correct.
by using
basic
number,
area
and
it to be dimensionally
drives
pressure
gradient
a smaller
wake
lower
Reynolds
number.
Figure
Reynolds
number.
experimentally
subcritical
separates
56
39 is a plot of drag
The
values
determined
Reynolds
upstream
CD
for each
body
of the
CD
curve
numbers
of the
coefficient
up to about
shoulders
of the
are
105,
(based
shown.
of cylinders
the laminar
cylinder
and
on frontal
Also,
tested
the
against
solid
line
in wind
boundary
produces
area)
layer
a very
is an
tunnels.
stalls
broad
At
and
wake
I
3.(_--
Curve
Flat
pIate
O
Lart_e
O
Streamline
cylinder
[]
/N
Hiah
Small
shape
t_evnolds
cylinder
number
c,,'[indcr
for
2.(
g
c_
1.0
O
I
10
I
I
102
103
I
I
104
Royllo[ds
Figure
and
high
CD
laminar
of
values.
boundary
smaller
CD
105
and
It is
a turbulent
tant
ideas
erences
or
unsteady
dimensional
since
craft
as
operating
far
principles.
and
direction
are
thus
well
the
has
thus
been
other
parallel
to it.
in a subsonic
flow.
from
separation
between
and
larger,
hence,
the
the
Reynolds
very
smooth
decrease
106
numbers
numbers.
behavior
than
number.
is delayed;
occurs
exhibit
rather
behavior
turbulent
and
I
109
of Reynolds
Reynolds
rather
shapes
in the
I
108
their
similar
as
they
drag
once
to that
of cyl-
were,
to
coefficient.
Much
result.
flow
streamline
velocity
as
and
Fluid
flow
critical
spheres
layer
distances
and
dimpled
t
107
numbers
transition
the
that
are
boundary
to airfoil
layer
of today
discussion
and
are
to note
bails
driving
abrupt
values
function
Reynolds
turbulent
A rather
These
as
supercritical
106
nu l/ib¢_ F
coefficients
becomes
interesting
induce
The
At
values.
Golf
Drag
layer
106 .
inders.
improved
39.-
I
105
flow
With
general
has
and
demonstrated.
Viscous
been
made.
wake
have
been
these
ideas
introduced
been
have
parameters
has
examined.
vary
in mind,
normal
one
many
impor-
Numerous
flow
of the
The
flow
to the
may
now
ref-
boundary
is
two-
free-stream
study
air-
57
58
IV. SUBSONIC
FLOW
Airfoils
The
wing
airfoil
section.-
and viewing
it from
cross
section
shape
is determined.
The
or more
ultimate
Figure
the
objective
plane
in the
air.
A flat
create
the
1800's
demonstrated
Figure
has
the
by taking
of the
The
question
the
the airfoil
produced
called
arises
used
and wood
wings,
the airfoil
as to how this
lift necessary
Cayley
more
section
out of an airplane
airfoil
for example,
Sir George
surfaces
a slice
shape
of attack,
is excessive.
13 shows
that
is to obtain
at an angle
curved
Wings
section.
of an airfoil
lift but the drag
surfaces.
one
airfoil
plate
that
13 showed
side,
simply
and
EFFECTS
to keep
could
be used
and Otto
lift
to
Lilienthal
and less
by the Wright
an air-
drag
in the
than
Brothers
flat
in their
1903 airplane.
In those
theory.
The
ments
came
early
days
usual
from
of canvas
procedure
at that
adopted.
Early
tests
showed,
rounded
leading
edge
and
The
hit and
systematic
Advisory
determine
World
miss
methods
National
the design
siderably
of most
The
"cut
shapes
and try"
helped
evolved
method.
Improve-
performance,
surface,
from
it was
the desirability
of a
edge.
early
days
by the Royal
for Aeronautics
as possible
investigations
NACA
following
trailing
at G/Jttingen,
of today's
the
to a curved
of these
information
II, NACA
on these
in addition
a sharp
Committee
was
If the modification
methods
used
as much
War
time
experimentation.
few airfoil
Air
(NACA).
about
produced
airplanes.
were
Force,
The
"families"
results
The
replaced
that
by much
and
finally
purpose
here
of airfoil
are
discussions
that
still
by the
was
shapes.
in use
follow
better,
are
to
During
or influence
based
con-
results.
six terms
are
essential
in determining
the
shape
of a typical
airfoil:
(1) The
leading
edge
(2) The
trailing
edge
(3) The
chord
(4) The
camber
(5) The
upper
surface
(6) The
lower
surface
line
line
(or mean
Figure
40 illustrates
the step-by-step
(1) the
desired
of the airfoil
length
line)
geometric
section
construction
is determined
of an airfoil
by placing
the
section:
leading
and
59
Chord
Set up leading edge
and trailing edge and
construct chord line
between
them.
2.
Add curvature
camber
line.
\
Leading
with
thickness
line
to
surface.
;Trailing
edge
edge
Camber
Upper
Wrap
camber
upper
line
line
surface
Chord
Wrap
about
form
same
camber
lower
trailing
edges
points
together,
curvature
their
and below
about
the
last
shape.
Figure
40.-
desired
aids
Geometric
an airfoil
camber
line;
this
the
final
shows
apart.
section's
line,
characteristics
construction
The
of curvature
camber
surface
added
(__
distance
the
step
aerodynamic
airfoil
(2) the amount
greatly
"wrapped"
(4) the
Final
line
thickness
line
to
surface.
Lower
4.
added
about
form
that
thickness
result
all its
chord
one
adds
a typical
own which
is drawn
by the
abilities,
the
determines
-
line
is determined
lifting
is,
of an airfoil.
may
connecting
camber
line.
(3) a thickness
same
amount
the upper
airfoil
the two
This
function
is
of thickness
and lower
shape.
It has
be determined
from
above
surfaces,
a specific
set
of
wind-tunnel
testing.
Figure
41 illustrates
airfoil
sections.
line).
If the
foil
When
line,
6O
Figure
camber
(the upper
surface
the free-stream
no lift
all the aforementioned
is produced.
42 illustrates
line
is the
velocity
The
an important
same
is a mirror
as the
image
of the
angle
terms
chord
aspect
line,
of the lower
oncoming
of attack
for
surface
is the
differently
of the camber
one
airstream
a
several
has
is alined
angle
line
a symmetric
about
chord
along
the
the
(or
mean
air-
the
between
shaped
line).
chord
chord
line
surface
G/Jttingen
airfoil
387
Upper
Leading
edge
surface
Chord
Camber_
line
line
_
Trailing
edge
NACA
f
Upper
surface
Leading
edge
symmetric
Chord
line
equal to camber
surface
0012
airfoil
Trailing
edge
line
Whitcomb
er
Leading
surface
//---Chord
line
/
edge
airfoil
/
----'
A
Lower
surface
c,_._.
, _='"_"
Figure
41.-
Symmetric
lift
i.e.
airfoil
at
eL
a
- 0 °.
--
Trailing
"'"_ --
terminology.
camber
Camber
Angle
line
of zero
lift
Chord
line,
is also
O,
_ 0 °.
= 0
_z
ift
v_
ve
Asymmetric
Positive
airfoil
lift
edge
/
|'.n
Airfoil
Zero
no
supercritical
at
--
Camber
a = 0 °.
line
above
chord
camber
line:
a L = 0 <0°
v_
ve
camber
"lift"
Asymmetric
Negative
Figure
airfoil
"lift"
at
42.-
--
Camber
a = 0 °.
Airfoil
aL
line
below
chord
line:
= 0 > O°
camber
line
variations.
61
and
the
free-stream
the
angle
of attack
If the
results.
camber
velocity
chord
line
(that
must
is,
The
namic
causing
case
two
(c_ = 0o),
span
as
fluid
lation,
the
the
where
(to
air
is
no
that
fig.
44(a))
the
airfoil
(see
fig.
44(b)).
F
the
if the
be of any
pointed
infinite.
As
this
value
Kutta-Joukowsky
is
and
of
F
of the
the
is
the
wing
tips
limitand
to separate
effects.
be
obtained
tunnel
fig.
for
43(b).)
the
airfoil
iMluence
at
wing
for),
by
meaIn this
wing
behaves
section
that
}__'illg
_. - The
fluid
patterns
-
one
other
is
a circulatory
two
flows
coexist
and
the
These
free-stream
value?
not
flow
A physical
trailing
tangentially
required
supcrimposed
(see
is,
show
section
the
wind
(See
be corrected
variation
will
of aerody-
may
in the
other.
is
aerody-
limiting
the
characteristics.
airfoil
question
can
OtL= 0
is trying
simulation
zero
nega-
three-dimensional
placed
to the
spanwise
discussion
aerodynamic
of two
when
and
around
One
wing's
The
manner
airfoil
span,
free-
to obtain
lift
the
flowing
the
no variation
43(a)
the
a close
wall
stream
has
section
results.
of zero
later).
but
one
effects
there
from
the
section,
tunnel-wall
the
angle
along
from
from
Thus,
When
In a similar
wing
be discussed
airfoil
tunnel
is,
0°'!.
the
anywhere
in length
= 0 °.
airfoil
lift
free
In fig_are
to prevent
the
by
The
is
A later
l = p_V_r
62
wind
than
direction.
B or
a
surface.)
a positive
A two-dimensional
infinite
of the
the
lower
to the
less
airfoil
station
is
minor
about
edge
is
ab_o_ut _a _tw_oz_diln?j}s_ional
The
trailing
aL=
respect
characteristics
model
on
around
flow
0
of this
that
about
becoming
edge.
at
no wing
for
represented
lift
effects
consisting
pattern.
sets
as
point
Circulation
viewed
with
wing.-
same
has
inclined
asymmetrical
characteristics.
wing
The
of zero
an
dimensionally,
namic
the
negatively
chord
is,
an asymmetrical
line
spans
(except
then
the
The
that
line,
along
in a spanwise
the
chord
that
0 = 0 °.
is alined
course,
surements,
the
aL=
of the
aerodynamic
insuring
above
or
case,
image
three-dimensional
Of
zero,
in this
a mirror
two-dimensional
airfoil's
is
zero
is not
angle
in span.
It is
surface
yields
0 °.
A is
less
lift
lies
characteristics
station
vector.
zero
line
be
the
tive camber
greater
than
the
for
(Upper
stream
lift
velocity
edgc
smoothly
such
theorem
with
(fig.
that
turn
the
relates
a real
44(c)).
rear
th.
about
is the
to give
stagnation
circ_daliop,
is
flow
the
Kutta
to the
or
the
be
circutotal
flow
circulation,
answer.
without
the
point
the
the
corner
fluid,
This
call
may
motionof
flow,
provides
a sharp
an airfoil
free-stream
prescribed,
condition
caImOt
possible
is
flow
the
instead
leaves
condition
moves
section
velocity
to the
lift
and
the
it
trailing
by
(20)
Infinite
length
infinite__
length
(a) Two-dimensional
(2D) wing.
This
Free
this
stream
direction
to show
wine
in
tunr_el
(b) Testing
from
_
_'
j_'V_
_
by using
Figure
43.-
section's
mounted
/
_
\
L..
for airfoil
side
....
_ms
on
}
de mounted
slae
mo
near
wall
aerodynamic
a two-dimensional
Two-dimensional
Wing
spans
_
characteristics
(2D) wing.
wing
testing.
63
elocity
about
sharp
trailing
(a) Flow
with
no circulation.
(b) Circulatory
(c) Flow
Figure
44.-
flow only.
with
span
Circulation
of two-dimensional
Poo
free-stream
air
Voo
free-stream
velocity
F
circulation
64
density
strength
Flow
leaves
edge
smoothly
circulation.
about
where
lift/unit
edge
wing
a 2D wing.
trailing
Thus, the circulation strenglh I' is set by a necessary physical condition, and the
lift l is uniquely determined.
For a perfect
fluid
the drag per unit length is zero.
However,
in a viscous
drag
along
wing
is considered
may
drag,
and center
has
the airfoil
The
attack.
the
angle
namic
about
point
There
or the
45(c)
for
changes
drag
that
of attack.
This
45(a)
components
occur
and
a pressure
when
a finite
the
along
a system
of angle
45(d)
shows
system
of r,,porting
and the
resultant
in figure
to vary
center
through
chord,
for
center
45(b).
of
The
lift,
as the angle
of
of pressure
this
point.
example,
unless
If one
a quarter
the
of a
resultant
aero-
of pressure.
is generally
a lift,
line
aerodynamic
at the
passes
aerodynamic
a function
drag,
of angle
and moment
of
about
the
of attack.
center,
Figure
line
shown
to the
of reporting
the aerodynamic
The
is not zero
point
functions
chord
airfoil
the
moment
resultant
present
force
point
the
as shown
are
corresponds
point
of the
the cambered
fixed
shows
of pressure.
moments
edge,
all are
is a point,
center.
center
the quart(,r-chord
shows
-
Figure
of the aerodynamic
the leading
moment
quarter-chord
Latex" the
and drag
at seine
is zero
Figure
lift
are
of action
behind
force
a skin-friction
of intersection
No aerodynamic
mounted
length
dynamic
into
is the
of pressure
the line
chord
:force
be resolved
is changed.
because
q'h,., point
resultant
force
of lift.
include
coefficiel:ts.-
on an airfoil,
of this
attack
loss
must
wi]l be shown.
two-dimensional
acting
action
ilow one
with a resulting
The
force
fluid
where
the lift,
the
drag,
moment
is independent
and moment
is convenient
for
about
a number
of
the aerody-
of aerodynamic
calculations.
The
data
obtained
two-dimensional
data.
cient
el,
point
(Cm)0.25c,
These
coefficients
moments
the drag
per
l
dynamic
Similarly,
and the
are
is the
pressure
testing
Aerodynamic
coefficient
unit
c/
where
by wind-tunnel
obtained
length
characteristics
Cd, the
moment
of the
of NACA
moment
coefficient
wing
of airfoil
recorded
coefficient
about
by measuring,
airfoil
families
include
about
tests,
and nondimensionalizing
d
lift coeffi-
center
the
(em)ac.
forces
and
as follows:
z
(21)
qc
measured
lift per unit length of the airfoil
wing,
q is the testing
1
section.
or
_pV 2, and
c is the chord length of the airfoil
d
c d -=_-_
where
the
are
the quarter-chord
the aerodynamic
in wind-tunnel
sections
is the measured
(22)
drag
per
unit
length
of the airfoil
wing
65
Resultant
aerodynamic
force
of
V_
Chord
line
pressure
--]
Line
of
resultant
action
force
of
(a)
Lift
Lift
_
=
00_
v_
Chordwise
on shape
position
camber
of
/_enter
of pressure
moves
forward
as
of attack
increases
angle
depends
line
(b)
Lift
Quarter
chord
point
.__
Moment
one-quarter
(depends
Aerodynamic__.._
center
about
on
chord
o)
Moment
about
aerodynamic
center
(independent
of a)
point
(d)
(c)
Figure
45.-
Airfoil
aerodynamic
characteristics.
and,
Cm = m
qc 2
where
m
is the
quarter-chord
body
number
number,
data
reported
point
of this
angle
of attack,
shown
negligible
and
Reynolds
or any
(angle
on the airfoil
other
of attack
turbulence.
For
not be indicated
as a separate
airfoil
shape,
dependence
and surface
namely,
of the
roughness.
(whether
at the
desired).
are
dependent
or), Reynolds
number,
low subsonic
is dependent
the
point
coefficients
turbulence
is to show
number,
acting
aerodynamic
attitude
and air
need
the
and air
for a particular
figure
unit length
center
that
chosen),
roughness,
roughness
main
66
section
are
per
aerodynamic
been
surface
effects
and surface
shows
(airfoil
moment
or the
previously
shape
Mach
measured
point
It has
(23)
on the
flow,
Reynolds
dependency.
an NACA 2415
aerodynamic
on
Mach
number
Figure
airfoil.
coefficients
46
The
on
This
indicates
of
cl,
Cd,
shape,
the
and
an_le
number,
Air
dependence
c m
of
and
on
Reynolds
surface
turbulence
is
.2
airfoil
attack,
_=g<
rout_hness.
included
in
o
tile
-.2
Reyl]olds
number
and
dependency.
Math
effects
2.0
not
roughlless
0
.2
,4
.C,
.8
1 .C_
_.0_l
number
includ(!d.
-o
-
.020
--
--
.016
1.6
g
1.2
.01_
.008
.8
•_
.4
.004
g
0
0
o
0
ca
-.l
-.4
_,|
Aerl)d;llat!lic
8
-,2
-.2
s-
-1.2
_
K2"
z2_--
I_"
-.4
3.0
.241
.014
[]
6.0
.246
.013
4"_
9.0
.246
•013
Standard
roughness
-.5
-1.6
-2.o
-32
l
,
-24
Section
x
-8
angle
2415
Specific
46.-
,
-[6
NACA
Figure
of
Wirlg
body
y
variation
t
_
t
0
8
16
attack,
o0,
T
-.5
24
32
Figure
----L_A
J
-l.2
deg
-.8
shapu
NACA
(see
upper
distances
dependencies,
along
X
and
in a general
some
c
Y
of the airfoil section.
One
cambered
manner,
airfoils and was
Above
discussed
next that from
There
denotes
cl
:tio
chord
length,
respectively.
the variation of the coef-
against the angle of attack
earlier.
positive lift. This
One
must
lift. A symmetric
move
is the
to a nega-
airfoil was
shown
be expected.
0 ° up to about 10 ° or 12 ° the "liftcurve"
is a linear increase
this angle, however,
angle at which
nt,
se
J
1.6
liftcoefficient (hence zero lift). It will be remem-
an angle of zero liftequal to 0 ° as might
straight line.
wine
1.2
typical features often found in the
of coefficient of lift cI
that this angle is called the angle of zero
Notice
coefficit,
.8
of the first things noticed is the fact that at an angle of
tive angle of attack to obtain zero
to have
lift
2415
axes,
attack of 0 °, there is a positive coefficient of lift,and, hence,
bered
J
.4
of these results.
47 is a typical graph
case of most
0
right)
coefficient
denote
-.4
Section
ficients with angle of attack and to discuss
graphs
____1
-1.6
Section
Aerodynamic
and
attack
It is best at this point to examine,
informative
,_X 6.0
-.4
of
10 6
-•3
;;at|at|on
Sur face
roughness
variation
Angle
x
p_)sltD_ll
y/i.
O
lber
-.3
ct,ll[/,l
x/,,
-•8
is almost
a
in the coefficient of liftwith angle of attack.
the liftcoefficient reaches
the liftcoefficient (or lift)reaches
a peak and then declines.
a maximum
The
is called the stall angle.
67
0
o
Negative
stall
]
....
-16
Angle
Figure
The coefficient
the stall angle,
the flow
being
has
from
the separation
the trailing
the pressure
increased
occurred.
0 ° to past
points
edge.
drag
aircraft
flight.
68
attack,
,_ ,de_
of lift as a funcliun
the
airfoil
Near
the
abruptly.
separated
of attack
on the
Figure
rises
It is interesting
angles
Coefficient
of
g
of lift at the stall angle is the ma.xinmm
one may state that the airfoil
is stalled
pattern
raised
47.-
L
0
-8
and
stall
stall
48 shows
angle
move
angle
Past
flow is to decrease
to note
that
will be operating
(fig.
a negative
the
lift.
at a positive
the
angle
angle
slowly
of attack
that
below
but remain
the
move
rapidly
of the
also.
the lift
is
angle,
close
forward
to
and
greatly
through
In general,
to obtain
stall
relatively
effects
continues
Beyond
in
of attack
the
curve"
occurs
angle
el,ma x.
change
points
angle,
"lift
whose
Note
separation
stall
47) that
stall
of attack.
the
of attack.
lift coefficient
and a remarkable
an airfoil
forward
the
uf angle
negative
however,
necessary
an
for
points
Separation
c_ =
00
Turbulent
__:,_
=
.....
/--Separation
point
wake
moves
5°
Maximum
lift
16°.
Separation
point
jumps
(Stall
_ = angle_
..._._
___'__
----_
Separated
expands
_
flow region
and reduces
lift
5
Large
(Reduced
lift
turbulent
and
Figure
small
positive
only gradually
increase
in
occurring.
cd
The
angle
of attack
at the
lower
is rapid
drag
pressure
drag)
48.-
Stall
formation.
angles.
because
coefficient
of the
curve
in figure
near-linear
before
and
function
the same
of angle of attack,
comments
apply.
of an aircraft
and will
46.
of moment
be discussed
to a positive
As one
as shown
coefficient
coefficient
of drag
the minimum
drag
corresponding
coefficient
The
_
large
Figure
49 is a typical
graph of the
of attack
of the airfoil
section.
Usually,
"-3
nears
greater
may
Since
also
the lift
the
cd
is an important
when
that
lift
the stall
amount
coefficient
angle,
however,
and
as a function
up to the
appears
parameter
subject
coefficient
of turbulent
be plotted
curve
c d as a function
coefficient
occurs
much
in the
stall
the
stability
of angle
at a
and builds
the
separated
flow
of the lift
angle
same
and
is a
as
control
is introduced.
Two-dimensional
wing compared
with three-dimensional
in figure
50 is a finite-span
three-dimensional
(3D) version
wing.The wing
of the infinite-span
shown
two-
69
.O2O
Rapid increases/
incd towards .I
u
.01C
u
¢9
_--_Minimum
drag
at small cr
i
i
-12
-8
I
I
I
I
-4
4
8
12
Angle of attack,
Figure
49.-
Coefficient
of drag
as
of airfoil
dimensional
the
(2D)
chord
wing
length
c
tested
times
a function
of angle
of attack
section.
in the
wind
tunnel
wing
span
b.
the
_, deg
(fig.
43).
The
wing
area
is
S
and
Thus
S = bc
This
on
is
this
also
wing;
and
CL,
(24)
known
3D wing
pressure,
as
and
the
planform
area.
nondimensionalizes
chord
CD,
length,
and
Cm
one
obtains
If one
by
using
the
3D
measures
the
the
wing
lift,
area,
aerodynamic
M
qSc
and
moment
free-stream
dynamic
of the
where
(D = Total
C m =_
drag,
characteristics
(L = Total
7O
is
(M = Total
moment
lift
on wing)
(25)
drag
on
wing)
(26)
acting
on
wing)
(27)
/
/
Particularly
sinlp]c
,
W:
_
//_---
;"
./"
//{¢_>"
same
'd ct
u_lL
x_in_
hi
il(__qiL(
VES_
I)ifferenl
IIIGY_IStlFt_d
C'tJ¢'i'P't_
<'{, c(p
Figure
Notice
flow
that
are
50.the
coefficients
case
important
airfoil
characteristics
wing?
Or
C m.
wing
tips
are
c d = CD,
answer
the
not
allow
for
But
the
3D wing
The
the
is freely
two-dimensional
dimensional
5all/O
are
how
lift,
C D,
three-dimensional
whereas
used
been
At first
glance
this
C m
conditions.
the
coefficients
to distinguish
of airflow
exposed
nmst
about
in the
be
wind
Cd,
one
the
use
for
2D
finite-span
experimental
moments
and
cm
out
in the
might
on
related
to
lree
conclude
that
Where
does
the
spanned
the
tunnel
stream
modified
tips,
and
that
is,
spanwise
to account
2D
finite
CL,
stream
Why?
wing
NACA
a real,
tunneI
the
free
one
and
moved
is wrong!
in the
can
drag,
Cl,
simply
tested
results
coeffici_mts
CL,
3D
CD,
so that
and
the
c l = CL,
problem
lie?
walls
The
and
did
spanwise
fIow
flow
occur.
may
for
the
effects
of three-
As
was
shown
earlier
of air.
flow.
Circulation
discussion
way,
But
possibility
notation
How
the
has
2D wing
with
c:_pitallzed
arises:
to obtain
exposed.
c m = C m.
that
_}1("
coefficients.
now
wing
are
is the
infinite-span
it another
freely
and
is
3I) flow
quvstion
50 the
t'('lli+tiI1
compared
This
data
to put
In figure
for
letters.
the
I)!P!
_
Two-dimensic)md
from
The
I)t)
cm
coefficients
lower
it'ltl._
and
the
vortex
of a two-dimen_sion:d
sy,'ste m or'_ _}f![Utc,
',vina.
the
airfoil
_ing.could
be
represented
in the
by a free-stream
71
flow and
For
a circulation
an infinite,
wing
exactly
a finite
of air
for
For
a finite
from
outside
the wing
These
that
shown
static
on the lower
in figure
faces.
The
of air
surface
tendency
(from
the
exists
these
two movements
wing
on the oncoming
wing
surface
wise
flow is strongest
(fig.
the
and
by the
the
names
same
oncoming
free
operating
must
become
gradient
flow direction
equal
between
surface
has
flow
tips
region
of air
view
the
wing.
the
spanwise
lower
to zero
to the
Equal
pressures--
.
/_-_"
free-stream
_
of
wing
at the
free-stream
"
f
_-1-1-_'_
/ / 1 / / / /1
pressure
..
1",.
_'Equal
l]_.._fpre==.re=
\
Higher
static
_-
than free-stream
|
pressure
b
(a)
Figure
51.-
Finite-wing
flow
tendencies.
pressure
and lower
sur-
parti-
tip to the upper
In addition,
(See fig.
51(b).)
flow about
flow of air
wing
static
since
As
so that
the wing
inward
on the
parallel
tips
differences
lower
lift.
of low pressure).
an inclined
being
than
back
formation
part
positive
52(a)).
Lower
the vortex
the
the upper
around
and decreases
there
but
vortices."
at the wing
(superimpose
one
at the wing
end in
to trail
most
at a normally
to the
combined
outward
them
is for the
flow approaching
stream),
cannot
Physically,
any pressure
Head-on
72
no net
is not the
Instead,
forces
F.
exists
wing
pressure
are
an inclined
exists
This
is permissible
or "wing-tip
of a wing
wing
free-stream
of air
of the
as follows.
is to equalize
of high
flow
strength
surface
the lower
line
which
wingtips.
vortices"
circulation
pressures
from
end at the
"trailing
of the
of the air
region
there
F.
or vortex
the free-stream
A pressure
to move
there
evidenced
the
so that
in front
circulation
to infinity
simply
on the upper
function.
tend
cannot
where
surface
51(a),
by the
extends
can be explained
pressure
the upflow
of the wing,
of circulation
vortex
tips
the
vortices
is a continuous
cles
hence,
have
trailing
The
than
tips,
rear
caused
a line
the
line
the wing
tip vortices
of these
at the
speeds,
condition.
wing.
wing,
the vortex
by the Kutta-Joukowsky
at subsonic
the wing
of Helmholtz,
an infinite
wing,
continues
past
three-dimensionai
By a theorem
midair.
determined
wing,
the downflow
movement
for
F
two-dimensional
balances
downward
case
of strength
surface.
midspan
If
the
on the upper
The
point
direction
spanas
Tip
flow
(b)
Figure 51.-
Flow
over
top
Concluded.
Flow
surface
over
bottom
surface
lll//j ""
i
l
I
;i
I I
I i
I
I' I
t
I
l
(a)
Figure
When
the air
leaves
is inclined
to that
whole
of vortices
line
at the tips
tance
ces
picture
constitute
trail
lower
back
of the tip vortex
from
so-called
system
of the
the wing,
the vortex
combine
"tip vortices."
replacing
the air
paths
at midspan.
up and
vortices.
wing,
and helical
to zero
roll
of wing-tip
edge
surface
rapidly
the vortices
the
Formation
the trailing
the
and decreasing
downstream
which
from
52.-
from
or vortices
(See
fig.
the vortex
52(c)
distribution
upper
result.
"strength"
being
52(b).)
into two distinct
Figure
the
A
strongest
A short
cylindrical
shows
just
the
surface
disvorti-
simplified
discussed.
I
(b)
Figure
52.-
Continued.
73
Tip
vortex
vortex
(c)
Figure
An account
aerodynamic
The
called
of the
tip-vortex
coefficients
vortex
into
in the
the bound
wing
vortex.
(sometimes
known
system
must
be closed
in some
vortex
which
starting
because
rapidly
is left
behind
(fig.
53(c)).
vorticity
vortices
of the
are
air's
the further
they
shows
manner
If the
and
when
modifications
of the
to the lift of the wing
Also,
vortex
vortex
system).
the wing
the
starts
their
from
rest
are
vortex
(at
____/.,4-----
1/4 c line)
1/4c
(a)
F
._
..(....
,-
F
Tip
(b)
74
53.-
Complete-wing
vortex
system.
for
vortex
changed,
on the flow behind
__
is
starting
of connew
soon dissipated
left.
/_
the
in the case
continually
vortices
influence
53(a))
by the so-called
is being
starting
(fig.
Also,
f
Figure
2D airfoil
and the tip vortices
is accomplished
lift of the wing
Generally,
are
the
the bound
as the horseshoe
viscosity.
back
constitutes
is equivalent
53(b)
the wing
shed.
Concluded.
3D counterparts.
(which
Figure
wing
stant
effects
their
a finite
52.-
vortex
a wing
decays
F
F
_-_(_.
_-
'rip
vortex
r
CYC_
-
(Lef 2- tairport
Tip
vortex
when
off
-
(c)
Figure
The
tip vortices
and roll
toward
dissipate,
their
this
the
The
important
the bound
The
dimensional
some
vortex
rotates
case.
rotates
For
a finite
Again,
the
or
are
eventually
shown
system.
viewed
to the
the
from
to other
in figure
to sink
tip vortices
later,
aircraft.
54.
Indicated
The
left-tip
vortex
(when
viewed
from
the left
lift on the wing
relation
a tendency
As will be discussed
counterclockwise
(when
have
to be dangerous
system
related
wing
they
by viscosity.
clockwise
is directly
and
wing.
due to the vortex
vortex
vortex
tips
prove
of the vortex
lift
Concluded.
of the
and may
movement
influence
drag)
the wing
transformed
time
effects
right-tip
bound
from
downstream
being
take
of air
the
back
other
energy
may
clockwise,
and
each
change
directions
trail
53.-
plmm
takes
it does
not
are
rotates
behind),
side).
as in the
two-
becomes
L = p_V_bF
(28)
where
L
lift on three-dimensional
Poo
free-stream
air
Voo
free-stream
velocity
b
wing
F
circulation
In both the
the
downflow
finite-wing
influence
of the
density
span
(spin
2D and
one must
starting
strength)
3D cases
(or downwash)
case
wing
in back
also
vortex
take
the
upflow
of the
(or upwash)
wing
into account
is negligible).
caused
in front
by the
the tip vortices
The
tip vortices
of the
bound
wing
vortex.
(assuming
cause
balanced
But,
that
additional
in the
the
down-
75
¢_'et'"
q
t
tf_\
\
_.._
_
Upwash
"-h'
/
Rear
.....
view
_'\.
.11,..
Downwash
ahead
of
airplane
_
_.JqBound
v/
Figure
54.-
Vortex
due
wash
behind
the air
the
(fig.
downwash)
called
plane
The
tip vortices
is an airplane
to roll
the
vortex
over.
into
structural
problems
the airplane
Federal
Aviation
tendency,
in the airplane
that
are
is a large
of the airplane
may
through
are
lose
is
of the air-
upwash
in that
very
large
at the
it.
Also
tendency
not effective
control
in
is called
(this
path
and
can become
fixed
(this
upwards
downwash,
flying
there
downwards
to the flight
upwash,
the pilot
downwash
is moving
to upwash,
surfaces
airplane
for an observer
is moving
perpendicular
Note
the
and
that,
system
will encounter
motions
shown
for the
air-
enough
to
or in a violent
case
failure.
of severe
new generation
low and
roll
system
flying
upwash
can see
the vortex
of downwash
control
that
behind
and the tip vortices.
One
the vortex
a tip vortex.
If the
experience
76
pattern
extreme
Note
"_--,
vortex
Downwash
vortex
span.
an aircraft
and cause
flying
wing
outside
or change
the airplane
of the
within
gradient,
counteract
The
air
that
effects.
the bound
the
all the air
Note
creating
flow
to both
within
55) all the
whereas
upwash).
order.
plane
wing
" _,
tip vortices
of jumbo
jets.
is operating
Agency
has
During
at high
shown
are
that
compounded
these
times
lift
coefficients
for
a 0.27
MN
by the
the
take-off
speed
to maintain
(600 000 lb)
and landings
of the airplane
flight.
plane,
The
the tip
is
I I
I
//
[
"',.
,
J,
•
i
_
I
_
[
_
_
n
..........
k
Downwash
]
I
"
_
.L[
/
f
/sL_._.-------"_
_
/_
_--
vortices
may
approach
craft
traced
160 meters
per
into
a vortex
1969 at least
vortex
in tip vortex
The
Aircraft rolls
over in
tip vortex
It may
way
be noted
associated
not possess
drag)
wing
contribution
power
required
point
ratio
the
FAA
that
and
downwash
a small
may
light
air-
90°/sec.
Between
incidents
could
is requesting
jets
may
=
at and
requires
to induce
force
that
induced
known
drag
A finite
drag
an induced
drag
be defined
as
Wing
field
be
much
small
aircraft
this
To
of energy
component
as induced
of downwash
drag.
Addition-
effects.
operating
together
if generating
the wing.
expenditure
is an ideal
wing
(taken
behind
the
by the tip vortex
viscosity.
(Wing
Aspect
drag
or pressure
possess
ratio
show
other
the large
to the downwash
is decreased
at this
a skin-friction
aspect
between
also
and the
exceeding
countless
this,
an airplane.
and landings.
with a fluid's
but will still
The
and distances
The
on the
at rates
and
around
the airplane
Tests
over
Realizing
with an additional
the net lift
from
accidents
due to finite-wing
may be associated
ally,
fields
(500 ft/min).
contribute
or power.
5 miles
be rolled
100 airplane
tip vortices
unit time
for
minute
take-offs
downwash
and downwash
strongly
could
times
during
Upwash
phenomenom.
separation
especially
per
back
to this
greater
create
extend
flying
1964 and
55.-
inturbulent
flying
across vortices
in tip
vortex
t,
_
/
Figure
Very
ride
-_-
fluid
effect
in an ideal
often
lift and
called
thus
not in any
fluid
will
parasitic
a circulation
r.
span) 2
area
(29a)
or
S
for
(_.9b)
any wing.
77
For the
special
case
of a rectangular
wing
S=b×c
so that
AR = b = Wing
c
Chord
for
a rectangular
thin wing
has
wing.
span
length
Aspect
a high aspect
(30)
ratio
ratio
is a measure
compared
with
of the
a short
slenderness
stubby
of a wing;
wing
a long
of low aspect
ratio.
With
The
this
2D wing
an infinite
mined
in mind,
is the
ratio.
by equation
(30).
obtained
for both wings
ces
in creating
have
wing.
at the
This
ure
the
by the
56, this
amount
over
that
increase
ces on the
The
3D wing
Figure
case
additional
in angle
downwash
wing
the
downwash
less
3D wings
and,
aspect
evident
w
at the
is obtained
to get
the same
whose
value
curves
is the
effect
the
for the
in figure
one can
of lift
wing;
lift
shown
as such,
ratio
coefficient
Readily
of attack
say
it has
is deter-
('2ift
that
50.
curves")
the
lift curve
smaller
tip vortiis flattened
aspect
ratio
effect.
where
one wants
characteristics,
by raising
= a2D
span
2D and
a finite
56 shows
2D aerodynamic
of the
of the
has
by experiment.
angle
is achieved
a3D
This
the
same
case
of an infinite
is not a beneficial
Consider
predicted
to the
equivalent
aspect
out so that
return
2D wing,
the angle
that
lift
or namely,
of attack
from
the finite
C L = c l.
of the finite
wing
wing
From
fig-
by a small
is,
+ ,xa
(C L = c/)
of attack
to obtain
in changing
the
as
the same
relative
flow
(31)
lift is due to the
seen
by the wing
effect
where
of tip vortifor
small
angles
w
Vo_
It may
wing
2D drag
be stated
coefficient
(32)
that
the
plus
drag
the induced
CD = c d + (CD)induce
78
coefficient
d
drag
for the
coefficient
finite
3D wing
is the
infinite-
or
(33)
Infiaite
aspect
ratio
Finite
I
of
lift
ratio
I
I
,
Angle
zero
aspect
I
I
_a2D
Angle
iO3D
of
attack,
0
Figure
where
cd
here
drag
coefficient)
sary
to get
(CD)induce
factor"
e
This
is greater
than
K
shown
by theory
is proportional
is related
To summarize
lift
coefficient
angle
yields
one
to
at the higher
the
original
to the
comes
to give
at
a2D.
and
an "efficiency
elliptic
spanwise
(e = 1).
lift
Also,
(34)
to the aspect
ratio
to this
a finite-span
point,
and the
parasitic
an increase
coefficient.
In this
not to confuse
converts
the
the
drag
coefficient
efficiency
version
in the
If one
neces-
d = KCL2
causes
It is important
a3D
operating
AR
drag
pressure
Thus
of attack
drag
cd
an ideal
induced
plus
of attack
of
ratio
to achieving
minimum
CL 2.
of lift.
drag
angle
value
aspect
angle
an induced
on coefficient
(skin-friction
(C L = c/) only if its
of attack
represents.
proportional
how close
ratio
coefficient
operating
(CD)induce
where
drag
2D wing
is inversely
(CD)induced
of aspect
of the
relating
distribution
Effect
is the parasitic
C L.
d
56.-
way,
factor.
of a 2D wing
is raised
drag
will give
slightly.
This
the
same
increase
in
coefficient
and,
in addition,
the 2D wind-tunnel
data
are
coefficient
to actual
with
induced
the actual
drag,
drag
one finds
modified.
force
it
that
it is
79
inversely
b 2, and
proportional
(3) the free-stream
Methods
NACA
if proper
corrections
the
the
b
to be as small
drag
span efficiency
(or aspect
fact
points
and
relatively
drag
induced
speeds.
since
by proper
Both
wings
are
only
difference
is that
Ideally,
both wings
(higher
aspect
ciency.
nearly
a wing
idealized
to
lift
the wing
that
span of the
the
second
same
less
the tip vortex
effects
span
being
the
is twice
that
small.
57.-
Wing-span
same
80
effect
lift
on induced
coefficient,
and
drag
same
for
airplanes
dynamic
The
wing.
span wing
a greater
wing
This
having
effi-
spans,
would
In fact,
pressure.
area.
longer
longer
AR).
be con-
of the first
of first
Figure
flight)
wings.
wing
But the
with
(high
very
last
com-
may
rectangular
and therefore,
drag
span
of the total
that
same
drag.
drag,
induced
long wing
have
lift and
This
(cruising
factors
with
wing
wing
drag.
physical
they
the induced
with
an extremely
flow,
and
these
How
it is a considerable
two airplanes
coefficient
one-fourth
arises
span are
the
5 to 15 percent
or landing)
like
(1) increase
Vow.
speeds
entire
drag.
(2) increase
at high
about
would
one may
velocity
of the total
57 shows
has
with
only
(take-off
and wing
Figure
as possible,
that
on the
the least
discussion
component
it constitutes
it can be seen
acting
One
lift with
the free-stream
is a small
produce
ratio)
e = 1
results
and drag
included.
the previous
(3) increase
should
The thought
not make
most
e
same
stated
the lift
to get the
for up to 70 percent
design.
the
as possible
drag
factor
at the
From
to obtain
From
span squared
V_ 2.
are
since
it accounts
e, (2) the wing
tip vortices
At low speeds
The efficiency
trolled
drag.-
be used
to as close
unimportant
factor
for the
/k_), and
up that
efficiency
squared
be reduced?
factor
ratio
at those
ponent
induced
data may
corrections
induced
span
velocity
of reducing
2D wind-tunnel
3D wing
may
to (1) the
why
give
as figure
58
pl_e
same
wing
area,
illustrates,
sailplanes
wings.
wing
that
But structural
requires
essary
comes
to smaller
vortex
formance.
This
weight
the
wing
effects.
show
also
sailplanes
ratio
Another
tanks
ing
as shown
span
valuable
define
three
other
give
from
airfoil
of reducing
59.
This
ratio).
reduction
Normally,
looking
taper
and twist
for a wing.
distinct
ways
the
further
along
of the airfoil
the wing
and twist
taper
is the
the root
section
(near
also
remain
For
wing.
may
airfoil
Planform
sections
at methods
section
of the
taper
tends
are
weight
nec-
drag
the
optimum
as fuel
capacity,
due
percontrol
of airplane
single-engine
airplanes
light
with
air-
an aspect
(1958)
AR = 24.
is by the
use
to promote
or tip
a 2D flow by inhibit-
physical
not used
of tip plates
effect
since
as an increase
there
are
other
in
more
methods.
Before
of attack
drag
the same
these
thin long
A survey
fighter
wing.
arrangement
have
give
of 15 or more,
induced
They
slender
of decreased
factors.
supersonic
High-aspect-ratio
of tip vortices.
(or aspect
drag
shape
angles
way
in figure
the formation
wing
the
interesting
58.-
long
structural
such
HP-8
Figure
A very
would
on factors
ratio
6, and
factor.
the advantage
aspect
an aspect
of about
very
it.
counteracts
dependent
do have
of increasing
and numerous
with
ratio
a dominant
disadvantage
span
allowances,
an aspect
efficiencies,
to support
A compromise
is necessarily
size
planes with
ratio of _.
on high
become
where
increased
characteristics,
categories
structural
a point
to support
rely
considerations
a large
There
must
of reducing
a general
wing,
First,
the size
change
as one moves
sections
may
change
-
that
are
terms
reduction
the
induced
fuselage)
geometrically
the airfoil
or chord
along
it is necessary
sections
length
along
the
may
vary
change;
the wing,
wing.
may
to
and
These
in
second,
lastly,
the
variations
now considered.
of the chord
to the
drag,
length
tip section
similar.
(See
and
thickness
(at the
fig.
wing
as one proceeds
tip)
so that
the
60(a).)
81
Tip
plates
inhibit
tips
_
_
v
Loe
Figure
_iPw ta_kuSt
k_
inhibit
wing
59.-
Tip plates
and
tip
tip tanks.
ileduction
in thickness
airfoil
thickness
;lnd sections
charltte
Thickness
Ch,)rd = Constant
Reduction
in chord
length - airfoil
sections
sinnlar
(a) Planform
taper.
Figure
Thickness
the
tions
at the wing
shows
a typical
this
ness
fig.
82
root
taper
from
normal
so that
60(d).)
section
taper
the
tip.
wing
was
wing
is the
to the
(See
with
the
tips
(b) Thickness
60.-
Planform
reduction
tip section
fig.
60(b).)
and thickness
of only
-
this
The
chord
and thickness
XF-91
which
were
thicker
has
and wider
thickness
results
remains
both planform
fighter
taper.
the airfoil's
reduction
taper.
inverse
than
taper.
as one proceeds
in thinner
constant.
One
taper
the inboard
Figure
notable
in planform
stations.
airfoil
sec-
60(c)
exception
to
and thick(See
__.
Redtlctbnl
and ('hl)rd
_.
(c) Planform
m thickness
length
-
iirf,nl
secti(ms
and thickness
taper.
(d) Inverse
Figure
Wings
decrease
in angle
given
minimum
toward
of changing
should
be as close
bution.
A number
the
drag
the
airfoil
sections
lift distribution
it was
of methods
Same
used
Root
s e c ti o n _<
\ Neg.ative
are
NACA
available
"-I../
and thickness.
the
span
that
is the
twist
A
an increase
(fig.
61(a))
aerodynamic
an aerodynamic
(fig.
the spanwise
span.
whereas
represents
manner
the
whereas
Geometric
61(b)).
efficiency
case
of an elliptic
to modify
the spanwise
To give
factor
spanwise
distribution
e
lift
distriof lift.
sections
_
throughout
along
washout
washin.
in a spanwise
This
varies
the lift distribution,
along
demonstrated
to 1 as possible.
of attack
tip is called
tip is called
of changing
in planform
Concluded.
angle
the wing
method
different
induced
so that
toward
the wing
a geometric
by using
method
twist
of attack
of attack
represents
twist,
are
in angle
60.-
taper
...."_tk\
_o_x\\\\
S,'une NACA
/
_'/positi"
ve
_
used
sections
throughout
Washout
sR2:tlon
(a) Geometric
/
Washin-_
twist.
Root
section
NACA
4 -221
X-Tip
section
NACA
0024
(b) Aerodynamic
Figure
61.-
Geometric
and
twist.
aerodynamic
twist.
83
These methodsinclude
figure
62(a)
and/or
all
for the
point
of view
twist
to obtain
are
that
as the
cant.
This
fall
result
is remarkably
Taper
is discussed
plane
so that
One
the
tips
being
62(c)
favorable
one.
and twist
later.
are
most
fact
and
at the
presents
perhaps
With
the
is a piece
that
wing
point
of
seams"
these
devices
and
It is in the
may
the
safety
interest
as possible.
But also,
Consider
equal
to the lift
would
be operating
solving
one
a near-level
(L = W).
formation
devices"
as slats,
art.
of air
to perform
minimizing
62(d)
problem
indi-
of stalling
is the
flaps,
sound
spoilers,
of flaps
the
condition
in which
flying
speed
at maximum
lift or
CL,ma
x.
(take-off
From
velocity,
might
slats
exists
opening
"coming
for
all of
at as low
characteristics
airplane
to
weight
or landing)
equation
Vmi n
traveler
maneuvers
flying
the
dive
on them.
landing
normal
to achieve
of the wing
is dependent
and
number
and
and
But a purpose
take-off
vast
wing
air
inspection
travel
not want
flight
the
unsuspecting
The
minimum
minimum
appears
figure
to a simple
slots,
the
For
for the
distribution.
of flight
affixed
with a visual
flight
be insignifi-
lift distribution
whereas
when
as
Devices
on a wing,
does
nearly
may
and thus
shape,
the unknowledgeable.
of safety
the
the
Surprisingly,
of the tip vortices,
importance
such
and economy
wing.
drag
wing
of aerodynamics
combined
untwisted
is very
an elliptical
wing-tip
of modern
unnerve
induced
for a real
tip vortex
drag
from
fig. 62(b).)
wing
of production
a good
hanging
for a landing
at the
manipulation,
in lift and
(See
in reduced
that
"aerodynamic
devices
apart
be affected.
twist
Of course,
is the untapered,
approximates
subjects
all these
as one approaches
a speed
term,
or decreases
think
in
(3) a combination
is costly.
rectangular
of greater
fascinating
of a better
and
of wing
gains
in minimizing
Figure
of the
of, for want
well
as shown
(2) a geometric
or
manufacturers.
to the
at the wing
shape,
type
Aerodynamic
brakes.
planform
elliptic;
lift distribution;
a square-tipped
be traced
importance
drag.
a less
that
wing
may
wing-tip
increases
an elliptic
to manufacture
by light
elliptic
to be of more
cates
to obtain
elliptic
the best
indicate
off to zero
The
induced
which
is hard
considerably
data
efficient
planform
of construction,
is used
there
does
wing,
taper
methods.
An elliptical
This
Spitfire
aerodynamic
of these
(1) planform
(25) after
the
is
wing
some
yields
(35)
Vmin
84
= t p_
2c_,WmaxS
High
cost
Minimum
complex
induced
(a) Elliptic
drag
wing
-
Supermarine
Spitfire
Mk. I.
q/
Low
induced
drag
Aero
(b) Untapered,
untwisted
(c) Good
Rounded
corner
tip shape.
The
density
Po_ is considered
characteristic
CL,ma
x
Reduction
of induced
to be constant
of the airplane,
to increase
62.-
then
and/or
tip shape.
drag.
and if the weight
it is obvious
the wing
tip shape
drag)
corner
(d) Poor
Figure
that
area
S.
of lift
may
100
wing.
Less
favorable
(Higher
induced
Good
tip shape
for
low induced
drag
Sharp
Commander
is considered
the only way
Slots
and
flaps
a fixed
to reduce
are
used
Vmi n
is
for this
purpose.
Slots.slot
formed
the
operating
the
airfoil.
energizes
can then
The
maximum
coefficient
by a leading-edge
principle.
The
When
the
slot
airfoil
layer
at a higher
called
is open,
slot is a boundary-layer
the boundary
be flown
auxiliary
the
wing
angle
of attack
and
device
retards
before
through
a slat.
the air
control
about
be increased
stall
Figure
flows
through
and
the
the
separation.
occurs
air
the use
63(a)
the
thus
and thus
of a
illustrates
slot
and over
channeled
The
get
airfoil
a higher
85
Slat
Slot
(a)Slat.
airfoil
Normal
Unslotted
|/
I
Angle
(b) Slat
Figure
CL,ma
slotted
less
than
the
stall
are
explanatory;
main
German
angle,
the airfoil
effects.
Slat-slot
lift curve
_'_stall
operation.
a
is relatively
for the normal
and the
that for angles of attack
unaffected
whether
The
slot
the
slot
or closed.
There
86
63.-
with
a
x value.
A curve showing
C L as a function
of
airfoil
is given in figure
63(b).
Notice particularly
is opened
wing.
of attack,
aerodynamic
angle
, rIncreased slat
_/
two types
the leading-edge
disadvantage
World
The
of slots
is that
War
automatic
fixed
and
slat
is mounted
it creates
excessive
II designed
slot
-
rocket
depends
fighter
on air
automatic.
a fixed
drag
-
pressure
the
distance
fixed
from
at high speeds.
Me-163
lifting
the
the airfoil.
Figure
with fixed
slat
is self-
away
slots
from
Its
64 shows
in the
the wing
a
at high angles of
attack
against
leading
the
slot.
Its
wing
main
One
to open the
edge
disadvantages
main
disadvantage
airplane
must
approach
reduced
visibility.
slot.
At low angles
and
reduces
are
its added
drag
of both types
for
a landing
at high
of attack
speeds
complexity,
of slots
is the high
nose-up
slat
is flush
compared
weight,
in an extreme
the
and
with
the fixed
cost.
stall
angle
attitude
created.
which
The
promotes
slot
Me-163
Figure
F_.llaps.- Flaps
wing
area,
change
flap
same
may
or both.
in the
is one
shape
method
shaped
be used
A change
of the
to increase
airfoil
section
with a simple
flap
lift coefficient
for
the airfoil
unflapped
airfoil.
the
coefficients
tially
range.
Also,
This
unchanged
is shown
from
tion where
a higher
disadvantage
that
that
stall
the
slot
in figure
of the
angle
has
the
maximum
lift
Figure
lift coefficient,
coefficient
65(a)
in the down
with the
obtained.
in high landing
Note
airfoil.
The
may
shows
flapped
a normal
over
that
airfoil
is opposed
airfoil
and the
camber.
than
the
the stall
the
by a
trailing-edge
is greater
increased
This
The
for increased
flap
also
increase
be realized
camber.
position
simple
of lift are
65(b).
unflapped
was
slots.
or by increased
this.
maximum
attack
Fixed
in the maximum
of accomplishing
airfoil
64.-
that
entire
angle
to the
reduces
The
for
the
angle-ofis essenslot
opera-
the
angles.
87
Inc reased
r
Normal
airfoil
flapped
airfoil
(a) Flap.
CL
CL,ma.x
flapped
CL, max
normal
airfoil
Simple
flapped
_- Normal
airfoil-_
airfoil
////
Angle
(b) Flap
Figure
of attack,
a
aerodynamic
65.-
Simple
effects.
flap operation.
Increases
Closed
1)
2)
camber
wing
area
position
(a) Fowler
flap.
Slot-----_
X_Flap
Closed
(b) Complex
Figure
88
system
position
slotted
66.-
flap
Types
Open
position
of Boeing
737.
of flaps.
•
Figure 66(a)shows a Fowler flap which is hinged such that it can move back and
increase the airplane wing area. Also, it may be rotated downto increase the camber.
A very large increase in maximum lift coefficient is realized.
There are many combinations of slots andflaps available for use on airplanes.
Figure 66(b)showsthe arrangement on a Boeing 737airplane which utilizes a leadingedgeslat and a triple-slotted trailing-edge flap. This combination is a highly efficient
lift-increasing arrangement. The slots in the flaps help retard separation over the
flap segmentsand thus enhancelift.
It may also be notedthat flaps in an extreme downposition (50° to 90o) act as a
high-drag device andcan retard the speedof an airplane before and after landing.
Boundary-layer
control.boundary-layer
control.
The
boundary
layer
kinetic
nar
energy
flow for
larger
shown
and let it be replaced
to the
a longer
boundary
layer
distance
over
by high-energy
as shown
low-energy
in figure
backward
boundary
67(a)
facing
Both
the airfoil,
delay
layer
may
or high-energy
holes
flow from
directly.
angle of attack
before
stall occurs,
and
to be one means of passing
high-energy
The
through
Another
method of increasing
CL,ma
idea is to either
remove
the low-energy
or slots
of these
air
separation,
be blown
into the
as shown
in figure
67(b).
layer
of boundary
/_--Add
Figure
6'/.-
Forms
slots
may
by
(b) Reenergizing
and
is by
segment
of the
or by adding
maintain
allow
CL,ma x.
top surface
through
Boundary
(a) Suction
above
methods
thus a higher
flow over the
be sucked
x
a lami-
one to get
a
The slot was
of a wing.
or holes
boundary
in the
wing
layer
controlled
suction
layer.
energy
to boundary
by blowing
high pressure
through
holes
or slots
the boundary
of boundary-layer
layer
air
layer.
control.
89
Spoilers.- Spoilers are devices used to reduce the lift on the airplane wing.
They may serve the purpose as on gliders to vary the total lift and control the glide
angle. Or on large commercial jets they may be usedto help the aileron control by
"dumping" lift on one wing and thus help to roll the airplane. Also, on landing, with
spoilers up, the lift is quickly destroyed and the airplane may quickly settle on its
landing gear without bouncing. Figure 68 showsthe spoiler arrangement on a Boeing
707wing.
f
/
Figure
Dive
speed.
brakes.-
Whether
in a dive,
operating
order.
adequate
increase
after
root
section
The
tions
should
in a turbulent
first
This
and
be the
"dead
when
last
air"
to stall
wake).
Use
Figure
dive
discussion
has
stall
is gradual,
and
by "forcing"
the
the
the wing
ailerons
of twist,
tips.
remain
namely
to control
a landing,
Essentially,
aircraft
toward
so that
for
they
69 shows
brake
descent
after
landing,
promote
or
a large
a civilian
aircraft
arrangements.
concentrated
CL,ma x. A further
stall characteristics
may be achieved
let it progress
in airplanes
approaching
drag.
present
(2) the
used
helpful.
condition
favorable
stall,
ol spoilers.
are
and two military
of the
a stall.
brakes
are
?- Spoi, rsop;
Use
the pressure
near or at the stall
A wing should possess
warning
68.-
quickly
brakes
characteristics.-
spin
9O
and
arrangement
Stall
down
aerodynamic
wake
speed-brake
(or speed)
slowing
these
separation
Dive
//
considerably
on
word about stalling
is in
so that (1) the pilot has
(3) there
stall
The
to occur
outboard,
effective
washout,
is little
(are
is often
tendency
to
at the wingwing-tip
sta-
not immersed
employed
so
Fokker
Speed
F-28
brakes
Speed
brakes
F-105D
open
x.
_-..___
_
_
Speed
bra.ke
F-IOOD
Figure
that
the
wing-root
sections
stall
section
with gradual
reaches
the
inboard
root
and buffets
the
device.
With
a gradual
few spin
tendencies.
(speed)
stall
fig.
stall,
controls.
stall
Up to now the
that
three
and
(3) induced
and
each
drag
on both wings,
acting
components
drag.
will introduce
Drag
on a finite
are
present:
Of course,
a total
first.
more
turbulent
This
Total
shown
are
arrangements.
(See
fig.
favorable
70(a).)
than
ones
Also,
airfoil
with quick
70(b).)
stations
pilot's
brake
angle
characteristics
(See
plane
with
Dive
stall
characteristics.
As the
69.-
the wing
condition
is an adequate
the
should
plane
strikes
stall
maintain
the
tail-
warning
a level
attitude
of Airplane
wing
has
been
(1) skin-friction
an airplane
drag
flow from
of its own.
is composed
Possible
considered.
drag,
of many
airplane
It has
(2) pressure
other
been
drag,
components
component
drags
91
V_
•
--_
o
..
J/iHtEIA.oo<
Negative
Washout
(a) Twist
and
toward
stall.
wing
Note
that
tip as wing
stalled
angle
_ACA
region
of attack
moves
increases.
651-212
/__
spread
out"
-\NACA64,-,18
i
Wing
(b) Gradual
Figure
include
(4) drag
stores,
aircraft
are
(1) drag
of wing,
of nacelles,
(7) drag
combined
of engines,
into
the drag
change
in the
(Drag)l+
92
the
of the
Stall
and
sum
of the
of the
one
These
effects
component
drags
2 = (Drag)l
+ (Drag)
(6) drag
(3) drag
of wing
of miscellaneous
drag
aircraft,
stall.
of fuselage,
gear,
(8) drag
of attack
characteristics.
(2) drag
of landing
a complete
of another.
sum
flaps,
(5) drag
is not simply
hence,
wing
70.-
angle
tanks
parts.
components.
component
are
called
is called
can affect
interference
interference
2 + (Drag)interference
of tail
surfaces,
and external
The
When
net
the
drag
components
the flow field,
effects,
drag.
of an
and
Thus,
and
the
Generally, interference drag will addto the componentdrags but in a few cases, for
example, addingtip tanks to a wing, total drag will be less than the sum of the two
componentdrags becauseof reduced induceddrag.
Interference drag can be minimized by proper fairing andfilleting which induces
smooth mixing of air past the components. Figure 71 showsa Grumman F9F Panther
Jet with a large degree of filleting. No adequatetheoretical methodwill predict interference drag; thus, wind-tunnel or flight-test measurementsare required. For rough
computational purposesa figure of 5 percent to 10 percent can be attributed to interference drag on a total aircraft.
(
F9F
Figure
Small
they
items
can greatly
craft
from
changes
components
Figure
73 shows
breakdown
decreased
all aided
in the
what
has
prediction
results,
final
nique,
and
use
reduction
been
of drag
accuracy
are
drag
of the
subsequent
Jet
71.-
Wing
aircraft
German
of the drag
(includes
fighter
bracing
with
trivial,
a TBF
coefficient
It is beyond
total
Avenger
as these
the
be obtained
scope
drag
of test
by flight
II.
of the
drag
wires,
measurements
is dependent
War
drag)
air-
small
coefficient
tests.
on flight-test
behind
surfaces
discussion
at subsonic
of models
has
engines
of polished
of this
Shown is the
components.
shielding
and use
airplane
evaluation
evaluation
World
airplane
techniques,
drag
proper
seemingly
72 shows
interference
and wind-tunnel
measurements
from
away
about
must
in drag
total
of flush-riveting
introduced
Figure
of how the
of drag.
and although
for.
a Me-109G
Doing
drag
the increase
accounted
a graph
fillets.
top speed.
II and shows
the years.
cowls,
total
the aircraft's
74 presents
over
streamline
upon
War
and
Figure
add to the
reduce
World
percentage
the
also
Panther
to expand
speeds.
does
Even
Although
yield
here,
equipment,
have
good
however,
pilot
tech-
data.
93
(National
Advisory
Committee
for
Aeronautics.)
C D at C L
Condition
Airplane
configuration
= 0.245
1
Airplane
2
Flat
3
Seals
removed
from
flapped-cowling
4
Seals
gaps
removed
from
cowling-flap
completely
plate
Exhaust
Canopy
sealed
replaced
fairing
removed,
and
Aerial, mast,
installed
Canopy
from
stacks
Tail
wheel
uncovered
9
sealed
removed
and
and
10
Leak seals removed
cover
plate, and
11
Leak seals removed
and miscellaneous
12
Fairings
13
Wheel-well
14
Seals
15
Plates over
removed.
exits
from
0.0189
1
0.0006
0.0199
2
0.0010
0.0203
3
0.0004
0.0211
4
0.0008
0.0222
5
0.0011
0.0223
6
0.0001
0.0227
7
0.0004
0.0230
8
0.0003
0.0234
9
0.0004
leaks
tube
removed
from shock strut,
wing-fold axis
bomb-bay
doors
seals removed
hooks
plates
removed
removed
tail-surface
gaps
wing-tip slot openings
Airplane
in service condition
Total-drag
change
0.0236
I0
0.0002
0.0237
11
0.0001
0.0251
12
0.0014
0.0260
13
0.0009
0.0264
14
0.0004
..........
Figure 72.- Small item influence on total airplane drag.
94
_C D
openings
seals
from
leak
1)
hinge-line
trailing antenna
leak
(see
column
0.0183
air
turret
catapult
cover
removed
faired
nose
arresting-hook
turret
over
and
Reference
condition
0.0081
Component
Percent
Wing
.............................
Fuselage
........................
rail
surfaces
..................
Engine
and radiator
.........
Appendages
....................
Induced
drag
...................
j
of total
drag
37.5
13.7
6.9
23.3
11.4
7.2
S
Figure
73.-
Typical
fighter-drag
breakdown.
.10
.0_
-"
_9
D
.06 _
Wright
_hers
.04
B 17
St,
homs
P-B_1
•
.O2 -
o
1900
I
1910
I
1920
I
Date,
Figure
74.-
Decrease
I
1930
in airplane
1940
• N
P-80
•
Comet
1
1950
I
I
1960
19q0
years
drag
coefficient
with
time.
95
Propellers
Propellers.into
propeller
stood
per
behind
backward
This
second
times
a spinning
force
motion
force
at a constant
the
axis
by acting
determined
(See
as a "drag"
by the
engine
was
is a small
of this
airplane
force).
forced
to this
air.
at rest
configurations
blade
of an engine's
of air
by the
If one
ever
Four-bladed
propeller
Pup
propeller
B-29
Figure
96
75.-
oa
on
Various
has
on the ground,
torque
on military
producing
may
this
The
torque
in the plane
force
In equilibrium,
equal
and
opposes
the propeller
opposite
Three-bladed
Me-109G
Eight-bladed
propeller
propeller
contrarotating
on Antonov
AN-22
configurations.
and
civil-
a resultant
be resolved
and a force
76.)
on it.
wing
discussion,
(thrust),
fig.
used
to the
torque.
Two-bladed
Beagle
crankshaft
backward
noticeable.
of propeller
of the
(the torque
engine
rate
the
the airplane
the purposes
power
mass
imparted
is very
a propeller
turning
to the
velocity
while
slipstream,
for
the
is equal
added
a variety
which
along
blades
of the
the
Basically,
pointing
propeller
air,
converts
thrust
propeller
75 shows
airplanes.
aerodynamic
propeller
force.
moving
Figure
jan
The
the thrust
and Rotors
on
propellers
into
a
of the
the
rotary
rotates
propeller
Direction
of
rotation
_'rhrust
T
Figure
As
figure
77 shows,
tions
which
fixed
with
respect
(fig.
78(a)),
the
oncoming
may
and
relative
velocity
root
closer
As
one
plane
the
tip
of the
of the
respect
sum
propeller
rotation
airplane,
of the
airplane
78(b).)
is
helix
are
relative
velocity
vector
aircraft,
that
the
velocity
of the
and
is
of air
it sees
an
free-stream
angle
between
the
helix
angle
angle
propeller
a wing
flow
The
called
this
sec-
Although
free-stream
to the
fig.
velocity
of airfoil-shaped
blade.
relative
(See
root,
free-stream
root
velocity.
of the
the
of a set
the
vector
airplane
sections
approaches
to the
only
the
of a propeller.
consists
with
is
a particular
oncoming
obtain
to the
peller
rotation
angle
of attack
angle.
an
aerodynamic
relative
for
and
the
force,
velocity
to the
chord
that
A propeller
revolving
varies
faster
than
the
or
from
comes
is,
this
the
the
root
inclined
helix
angle
root
vector.
line
section
blade
the
with
blade
shown
appears
sections
Thus,
of the
as
airfoil
the
blade
section
total
section
angle
is the
in figure
to be twisted
large
blade
78(c).
with
angles
is
placed
from
sum
This
the
tip
due
in main
at
an
angle
of
the
plane
of the
pro-
of the
helix
angle
and
is
known
sections
as
with
to the
the
small
increase
blade
blade
in
angle.
The
a propeller
pitch
rotating
which
torque
90 ° .
attack
ground
the
tip
sees
rotational
For
since
to the
To
helix
and
tip
approaches
angles
propeller
of advance.
sections.
of air
the
and
also
and
blade
from
airplane
is
flow
Thrust
propeller
in shape
propeller
the
to the
the
to the
relative
velocity
angle
vary
76.-
blade
blade,
(adjustable
propeller).
angle
is
also
called
hence
a fixed-pitch
pitch
propeller)
The
efficiency
the
or
pitch
angle.
This
propeller,
or
controlled
automatically
of a propeller
is
may
pitch
power
be
angle
adjustable
output
in
the
divided
may
be
by hand
air
fixed
for
on the
(controllable
by
power
input
97
blade
__ller
_
_
Figure
77.-
Propeller
blade
sections.
Airfoil
_ections
a,
denotes
Wing
7
v--" Propeller
fixed
angle
to
of attack
of airfoil
airplane
3
Free-stream
velocity
(a)
Plane
of
rotation
Velocity
and
of airplane
q
motion
fT'U
Blade
Rotational
velocity
of
this
blade
section
relative
to
airplane
.o¢,
Helix
angle
(b)
5
/9
Angle
of attack----_
of blade
_x
.z_
/_#-
angle
--
Tntai
a.ng[e
blade
(c)
Figure
98
78.-
Propeller
terminology.
angle
or
pitch
angle
sections.
and
would
desirably
efficiency
is
requires
pitch
be
proportional
a different
(flat
blade
A coarse
effect
or
is
as
close
to a value
to the
free-stream
pitch-angle
angle
high
or
pitch
illustrated
used
for
in figure
I
%
For
angle
(or
100
velocity
setting.
small
is
of one
cruising
and
take-off,
of attack)
percent)
for
gives
high
low
possible.
maximum
an airplane
to provide
and
as
The
efficiency
uses
a fine
revolutions
per
revolutions
per
or
low
minute.
minute.
This
79(a).
l
_
r
_
I
I I
I]
I
I
I I
!
I
I
II
I
4-
fl
I_I
%
I
I
I
I
I
%
l
t
I
I
o
I
I
I
•
f
I
I
...//
2/
Coarse
pitch
- Cruise
'rake- off
(a) Pitch
\
/
/
_'X
Fin('
(low)
pitch
/
I
_
_
_
I
l
I
% I
\I
I
I
I
I
/
/
1\
\
(high)
flight
control.
(brake)
- propeller
stopped
fi_"
(b) Feathered
.qq_'°_'_'_''_:'_ _
propeller.
(c)
Figure
Some
turned
so that
velocity.
the
use
as
by turning
The
of which
mise
propellor
shaped
the
may
leading
Feathering
decrease
for
propellers
propeller
edges
of the
(See
the
to a large
design
is
blade
blades
(See
contradictions
used
on the
slender
or
fig.
more
mission
with
propeller
brake.
that
alined
to avoid
Some
blades
to the
an engine
have
negative
are
free-stream
damaging
propellers
case,
the
reversible
thrust
is
and
to
pitch
obtained
of attack.
airplane,
The
means
are
In this
angle
an
This
propeller
79(c).)
Landing
thrust
control.
sections
79(b).)
in design.
dependent
is usually
are
airfoil
fig.
like
of pitch
in flight.
negative
of a propeller,
largely
Use
on a stopped
drag.
brake.
cause
and
feathered
a landing
blade
79.-
be
is used
Negative
is
influenced
overall
to be
rounded
blades
shape
by
is
performed.
tips.
are
For
many
factors,
determined
by
For
high
speeds
low
speeds
larger
some
comprothe
paddle-
used.
99
The
wards.
slipstream
It is a cylindrical
tailplane.
mental
this
is produced
The
and
some
means
that
larger.
The
effective
control
surfaces
are
may
be low.
plane
the
opposite
producing
since
square
and other
of taxiing
or take-off
of the
slipstream,
however,
in a later
be counteracted
Figure
80 shows
have
air
Figure
80.-
-
an effect
The
aircraft
used
Contrarotating
VTO
propellers.
and
detriflow;
to it is
in providing
produced
moving
on the
XB-42
XFV-I
some
exposed
over
of the
this
for
by these
them.
velocities
to strike
stability
propellers
that
back-
the free-stream
the air
effects
air
fuselage
the free-stream
device.
Lockheed
effects
parts
causes
contrarotating
three
the
forces
of the
when
discussion).
by using
over
and is beneficial
velocity
may
by forcing
than
the aerodynamic
of the
This
back
important
tailplane,
the tailplane
surfaces
flows
thrust
flow is faster
Douglas
100
has
cases
(considered
directions).
that
tailplane
slipstream
over
and not headon.
may
producing
air
fuselage,
on the
motion
at an angle
of the airplane
of the
moves
in the
the
The
by the tail
rotary
the propeller
drag
of spiraling
it strikes
beneficial.
dependent
is important
core
that
slipstream
This
The
fact
by a propeller
the
and
rotary
(spinning
form
tail-
control
motion
in
of a thrust-
of
Lifting
blades
The
rotors.-
of the
number
For
rotor
are
of blades
employing
a different
blades
used
are
a helicopter,
airfoil
vary
with
number
to reduce
the
shaped
the design.
of blades.
the load
rotor
and are
that
is the
long and
Figure
81 shows
Generally,
each
must
lift-producing
slender
for
device.
(large
aspect
The
ratio).
three
helicopters,
each
the heavier
helicopter,
more
carry.
Bell AH-16
Heuy-Cobra
Two-bladed
Hughes
OH-6A
Four-bladed
Sikorsky
CH-3C
Six-bladed
Figure
As for
defined
blades.
controlled
the
airplane
as the angle
The
81.-
pitch
propeller,
between
of the
individually
Helicopters
the
blades
(cyclic
with varying
the helicopter
plane
may
of rotation
be controlled
rotor
blade
blades
of the blades
collectively
numbers.
have
and
a pitch
the
(collective
angle
chord
line
pitch)
of the
or
pitch).
101
Collective pitch changes the pitch of allblades together and with changes in
engine power settings,produces the liftnecessary for the helicopter to take-off,hover,
climb, and descend.
Cyclic pitch is controlled by the swashplate of the rotor head which allows the
pitch of individual blades to vary as they rotate about the hub.
fly forward, the swashplate is tiltedforward.
ward position
lift
(toward
is reduced,
is increased,
to tilt
(see
and
the
the whole
fig.
plished
its flight
blade
rotor
the
rotation
disk
by a tail
ency.
Additionally,
copter
may
path
main
body
rotor.
forward
blades
in the opposite
produces
It provides
direction.
sufficient
by controlling
the thrust
thrust
pitch decreases,
rotates
path
angle,
is given
its
blade
and the flight
to the desired
rotor
cycle,
As the
component
the total
to the
/i
rotation
o[
rotor,
Thrust
component
yielding
forward
m orion
I
1
Main
Main
rotors
rotors
V_
Figure
102
82.-
Helicopter
forward
the pitch
net
lift vector
effect
is
is rotated
motion.
which
control
to counteract
of
blades
is
forwardJ
rear,
The
torque
Directional
Thrust
Axis
the blade
helicopter.
a reactive
of the tail
to the
ascends.
be controlled.
._
a pilotwishes to
As each rotor blade approaches the forof its
descends.
thrust
of the
helicopter
of flight)
lift is increased,
82) and a forward
The
rotate
the direction
When
this
tends
to
is accomrotational
the heading
tend-
of the heli-
V. TRANSONICFLOW
Up to this point the airplane was considered to be in motion at subsonic speeds.
The air was treated as thoughit were incompressible and a study of the aerodynamics
involved using this simplifying assumption was made. As the airplane speedincreases,
however, the air loses its assumedincompressibility andthe error in estimating, for
example, drag, becomesgreater andgreater.
The question arises as to howfast an airplane nmst be moving before one must
take into accountcompressibility. Oneimportant quantity which is an indicator is the
speedof soundof the air through which the airplane is flying.
A disturbance in the air will sendpressure pulses or wavesout into the air at the
speedof sound. Consider the instance of a cannon fired at sea level.
An observer
situated
the
some
sound
wave
can easily
cannon
distance
is heard
compute
from
precise,
shown
it depends
under
standard
altitude
upon
sends
separates
plane
and
little
time
pulses
airplane
the
air
pulses
merge
elapses
airplane's
move
at the
into a "shock
temperature,
airplane
below
these
and
and abruptly
to break
there
is a change
sible
flow speeds.
away
from
in the
him.
The
of the
K) the
speed
indicates
the
speed,
speed
and,
of sound
in all directions
"messages"
before
But as the
closer
same
wave"
passes
aerodynamic
gets
At the
is an almost
The
air
through
the airplane
approaches
and
forces
has
the
from
those
altitude
up against
in the
speed
There
about
experienced
flow
of the air-
(fig.
airplane
84(c))
together
line
ahead
of sound,
of the
merge
of the
Air
and the
in front
instantaneous
not flow smoothly
at this
of sound
They
system.
of sound
84(a).
a warning
no warning
shock
the
84(b))
speed
as the airplane.
which
density.
arrives
the air
time.
speed
the airplane
(fig.
but at an
speed
a disturbance
in figure
together
the time
arrival
creates
level
m/sec
comes
as shown
airplane
and closer
between
actual
therefore,
83.
At sea
flying
out
To be more
K the
an airplane
and the
in figure
is 340.3
to 216.7
observer
propagates
temperature.
of sound
that
him
with altitude.
is down
but
The
between
as shown
varies
absolute
later.
disturbance
shell
of sound
instantaneously
time
the distance
the temperature
the airplane.
pulses
pressure
of the
root
almost
some
hemispherical
difference
well
receives
and the
pressure,
This
flash
is felt)
to reach
(T o = 288.15
out pressure
approach
of the
sound
square
the
by dividing
7, the speed
the
flying
around
pressure
the
see
wave
speed of sound at a slower
effects
sooner.
of the airplane
the
pressure
where
m/sec.
An airplane
and
will
of sound
in figure
conditions
encounters
the
compressibility
cannon
in an expanding
of 15 kilometers
is only 295.1
air
speed
it takes
the cannon
As was
the
(or the
the
by the time
away
from
the
ahead
of change
impending
in
approach
is a tendency
for
it; as a result,
at low incompres-
103
Time
Cannon
fires
BOOM
= t
0
Cannon
flash
observed
Distance
D
Time
- t1
time elapses
_Direetion
I
Time
= tB
I BOOM
A
is heard
Speed
Figure
The
sound.
may
words,
it is a number
to an airplane
For
than
is hypersonic
flow
one,
regime.
numbers
flow,
Additionally,
patterns
change
flow
flow nor
from
presents
those
that
Mach
than
transonic
of the airplane
relate
the
number
85 shows
one,
and for
of a disturbance.
ratio
may
Figure
less
D
time
of sound
The
to 1916).
supersonic
flow.
Transonic
ing subsonic
104
Mach
Distance
Elapsed
of the
approach.
(1838
=
Speed
In other
regimes.
the
83.-
is a measure
professor
to 1.2.
sound
number
have
which
of
Mach
Austrian
greater
of
degree
is named
the names
one has
Mach
speed
subsonic
of warning
Ernst
to various
flow,
for
greater
flow pertains
to the
range
than
versa,
to supersonic
or vice
a special
problem
as neither
supersonic
flow may
that
after
subsonic
describing
speed
given
numbers
area
to the
5 the
about
be accurately
an
flight
numbers
name
of speeds
equations
air
Mach,
Mach
of
used
in
Mach
0.8
describapplied
to
/-
Pressure
move
Disturbanee__
pulses
away
f tom
Disturbance
at
(a)
sour
Pressure
ce
i_
putses"
//
begin
to
[
pile
up -J
rest
Zero
and
low-speed
\\
_/_
_"
/
_
•
t-Pressure
left by
_ D_isturbance,
,
begms
movmg
pulses
disturbance
disturbance.
Shock-wave
discontinuity _
pressure
Pressure
pulses
just barely
out racing
the
dmturbance
/
/
M = 0.75 /
)
.... /
_\\_
\\_
Pressure
pulses
cannot outrace
disturbance
- air
in front
has
no
warning
of particle
(or airplane)
approach
1
/
_-_/
(b) Nearing
Mach
1.
/
84.-
Shock-wave
_ , n
_" _. _-"
/
_
]
/
1
j
/
(c) Mach
Figure
f/fil/1Utl//fl
_-_
/_
/ _
/
__
1.
formation.
t
Subsonie/J
._ransonie
..{{_: _i{i::ii:
.8
1.2
3
5
Maeh
Figure
85.-
6
7
number
Flight
regime
terminology.
105
With
flow
these
at high
sonic
speeds.
speeds.
pressure
there
mental
changes
This
drag
and large
wave
and
induced
erable
is due
part
of the
from
shock
formation
lished,
however,
shows
the
drag
lift and
clearly
to exceed
sonic
the
flight,
the
the transonic
required
speeds,
wing
sound
regime,
drag
transonic
barrier
increases
the
drag,
to funda-
drag
drag
and the
However,
The
though
"Sound
drag
(drag
barrier"
barrier
as it proceeds
toward
coefficient
enough
early
days
speeds.
show
/
\\
\
o
"_
]/
.=_
_._.
/ Due
........
l°
coefficient
wave
drag
2_ .......
/-Drag-divergence
/
Mach
106
number
1.0
0
Figure
Mach
86.-
Variation
of wing
number
drag
coefficient
with
Mach
Once
thrust
a decrease).
r\
/ \
/
(or
number.
thrust
of tran-
supersonic
Barr[er"-__
?-
of zero
up rather
and less
may
total
and wave
provide
higher
86
(1) zerodrag
to higher
estab-
The
to lift)
In the
decreases,
drag
been
Figure
shows
must
coef-
erratic
number.
due
drag
the
of the
flow has
Mach
drag
into two categories:
is encountered.
coefficient
(even
with
"sound
a real
because
This
separation
the
is reduced.
the airplane
represented
sharply
a consid-
range,
a supersonic
The
in speed.
(or pressure-related)
infamous
that
rises
and to the induced
coefficient
of induced
drag.
transforms
transonic
can be divided
The
which
coefficient
and wave
wave
increases
range
Once
drag
drag
to fly supersonically.
the drag
heat,
composed
to lift.
waves
into
to fly supersonically
the
at sub-
due
is called
further
Throughout
the drag
speeds
of skin-friction
due
the
and supersonic
of the airplane,
in the supersonic
and
supersonic
part
to obtain
flow instabilities.
of an airplane
maximum
any
energy
than
flow stabilizes
86 since
detail
skin-friction
of the airplane
speeds
of shock
surfaces.
the
drag
in figure
propulsive
general
composed
-
At transonic
drag
high
matter,
formation
and
(2) lift-dependent
more
to be in motion
components
to lift).
at these
necessary
is greater
and
pressure-related)
are
unstable
available
due
considered
in the total
or for that
the airplane
variation
at transonic
(or drag
in a little
distribution.
in thrust
of the airplane
was
main
encountered
to the
now examine
of three
increase
wing,
may
the airplane
drag
pressure
increase
increases
of the flow
ficient
in the
one
composed
is a substantial
airplane
drag
drag
was
drag
of the
in mind,
Up to now,
Drag
drag,
speeds
lift
definitions
past
is
There is a famous little story, untrue of course, of the pilot who flew his plane
beyondthe soundbarrier andthen got trapped there becauseof insufficient reverse
thrust to get back below the speedof sound. Another case of perpetual motion.
It is a large loss in propulsive energy due to the formation of shocks that causes
wavedrag; figure 87 showsthis shock formation about an airfoil. Up to a free-stream
Mach number of about0.7 to 0.8, compressibility effects have only minor effects on the
flow pattern anddrag. The flow is subsoniceverywhere (fig. 87(a)). As the flow must
speedup as it proceeds aboutthe airfoil, the local Mach number at the airfoil surface
will be higher than the free-stream Mach number. There eventually occurs a freestream Machnumber called the critical Machnumber at which a sonic point appears
somewhereon the airfoil surface, usually near the point of maximumthickness and
indicates that the flow at that point has reachedMach 1 (fig. 87(b)). As the freestream Mach number is increased beyondthe critical Mach number andcloser to
Mach 1, larger andlarger regions of supersonic flow appear on the airfoil surface
(fig.
87(c)).
through
In order
a shock
increase
(pressure
anywhere
vature
and thickness,
decelerate
the
boundary
layer
increase
The
increases
thrust
has
shock
wave
would
is known
Mach
number
The
goal.
flight
87(d)
shows
to one where
large
regions
a free-stream
allel
Most
to the
the boundary
layer
shock.
the
further
its
speed
indicated
be explained
that
later
so that
a separation
condition
must
drag
the
shock.
of the
accounts
for
of the
airplane
Large
increases
speed.
by the
originally
If an airplane
designed
was
in
drag-divergence
as a supersonic
of high drag,
how success
a
separation.
number.
in airplane
because
due to cur-
the wave
through
will be limited
was
where,
airflow
flow
shocks
coefficient
Mach
F-102A
etc.)
These
(boundary-layer)
drag
increases
drag.
of energy
This
as shock-induced
an
it would
achieved
for
never
this
airplane
redesigning.
Figure
nose.
a loss
pass
by an
represents
1.0 and the
transonic
from
Convair
tests
It will
For
it must
is accompanied
heat
nacelles,
88(a)).
the
flow,
as wave
engine
exceeds
at which
thrust,
This
number
behind
any
of velocity
be presented
the drag-divergence
prototype
but early
proper
with
which
number.
through
(fig.
immediately
of insufficient
this
fuselage,
occurs
to produce
achieve
(wing,
in drag
required
interceptor
may
Mach
loss
to subsonic
of heat.
be estimated
interacts
is called
This
which
of sound
markedly
an engine
Mach
than
free-stream
are
flow to return
a production
localized
speed
is greater
In fact,
airplane
the
the
is,
energy
on the
below
increase
that
of propulsive
appear
supersonic
discontinuity).
in temperature,
expenditure
large
for this
Mach
of the
body
the
are
number
airfoil
surface
character
of the
in supersonic
greater
than
is in supersonic
and stabilize,
flow at a free-stream
flow and the
1, a bow shock
flow.
and the
The
flow
shock-induced
shocks
appears
begins
Mach
number
close
very
strong.
At
are
around
the airfoil
to realine
separation
itself
par-
is reduced.
107
Shock
(leads
wave
formation
to wave
drag)
point(M=
Sao
=
1.0)
°8
Subsonic
0
Subsonic
Subsonic
flow
(Critical
Mach
number)
everywhere
(a)
(b)
Supersonic
rsonic
= .90
M_
Moo = .85
Subsonic
Subsonic
Subsonic
Subsonic
Supersonic
(c)
flow
Subsonic
A
M_
s
= .95
\
\.Bows.ock
/
Subsonic
Supersomc
,
wraPoSs_°en_///
/
(d)
Figure
This
condition
behaved
than
dynamic
forces
and the
thus
disrupting
and
flow
however,
in the
region
lift(fig.88(b)).
108
first
airplane
the transonic
to the
and
tail
of both
configurations
little
types
Supersonic
jump back
the
wing
and
to probe
gradually
that
tail
or no difficulty
the
and forth
The
the sound
evolved
flow,
result
This
barrier.
to the point
in terms
along
the
sends
is that
aero-
surface,
pulsing
the pilot
condition
With
where
of wing
the
flow is unsteady
This
controls.
well-
can predict
surface.
of the airplane.
wing
flow is more
theories
in transonic
may
flow over
surfaces
airplane
formation.
adequate
Often,
surface
the
vibration
posed
are
present.
separating
Shock
coefficients.
there
on the body
back
a buffeting
drag
flow and
and moments
waves
especially
in lower
transonic
shock
unsteady
feels
results
87.-
occurred
proper
flying
buffeting
design,
through
or loss
of
"_---------M>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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