Chapter 1 — Part 1

NAVWEPS 00-BOT-BO

BASIC AERODYNAMICS

Chapter 1

BASIC AERODYNAMKS

In order to understand the characteristics of

his aircraft and develop precision flying tech-

niques, the Naval Aviator must be familiar

with the fundamentals of aerodynamics. There

are certain physical laws which describe the

behavior of airflow and define the various

aerodynamic forces and moments acting on a

surface. These principles of aerodynamics pro-

vide the foundations for good, precise flying

techniques.

WING AND AIRFOIL FORCES

PROPERTIES OF THE ATMOSPHERE

The aerodynamic forces and moments acting

on a surface are due in great part to the prop-

erties of the air mass in which the surface is

operating.~ The composition, of the earth’s

atmosphere by volume is approximately 78

percent. nitrogen, 21 percent oxygen, and 1

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BASIC AERODYNAMICS

percent water vapor, argon, carbon dioxide,

etc. For the majority of all aerodynamic con-

siderations air is considered as a uniform

mixture of these gases. The usual quantities

used to define the properties of an air mass are

as follows:

STATIC PRESSURE. The absolute static

pressure of the air is a property of primary

importance. The static pressure of the air

at any altitude results from the mass of air

supported above that level. At standard sea

level conditions the static pressure of the air

is 2,116 psf (or 14.7 psi, 29.92 in. Hg, etc.)

and at 40,000 feet altitude this static pressure

decreases to approximately 19 percent of the

sea level value. The shorthand notation for

the ambient static pressure is “p” and the

standard sea level static pressure is given the

subscript “a” for zero altitude, pa. A more

usual reference in aerodynamics and perform-

ance is the proportion of the ambient sta~tic

pressure and the standard sea level static

pressure. This static pressure ratio is assigned

the shorthand notation of 8 (delta).

Altitude pressure ratio

Ambient static pressure

=Standard sea level static pressure

6 = PIP0

Many items of gas turbine engine perform-

ance are directly related to some parameter

involving the altitude pressure ratio.

TEMPERATURE. The absolute tempera-

cure of the air is another important property.

The ordinary temperature measurement by the

Centigrade scale has a/datum at the freezing

point of water but absolute zero temperature

is obtained at a temperature of -273“ Centi-

grade. Thus, the standard sea level tcmpera-

ture of 15” C. is an absolute temperature of

288”. This scale of absolute temperature using

the Centigrade increments is the Kelvin scale,

e.g., o K. The shorthand notation for the

ambient air temperature is “T” and the stand-

ard sea level air temperature of 288’ K. is

signified by Ta. The more usual reference is,

the proportion of the ambient air temperature

and the standard sea level air temperature.

This temperature ratio is assigned the short-

hand notation of 0 (theta).

Temperature ratio

Ambient air temperature

=Standard sea level air temperature

@=TITtl

,+273

Many items of compressibility effects and jet

engine performance involve consideration of

the temperature ratio.

DENSITY. The density of the air is a prop-

erty of greatest importance in the study of

aerodynamics. The density of air is simply

the mass of air per~cubic foot of volume and

is a direct measure of the quantity of matter

in each cubic foot of air. Air at standard sea

lcvcl conditions weighs 0.0765 pounds per cubic

foot and has a density of 0.002378 slugs per

cubic foot. At an altitude of 40,000 feet the

air density is approximately 25 percent of the

sea level value.

The shorthand notation used for air density

is p (rho) and the standard sea level air density

is then pO. In many parts of aerodynamics it

is very convenient to consider the proportion

of the ambient air density and standard sea

level air density. This density ratio is assigned

the shorthand notation of c (sigma).

density ratio= ambient air density

standard sea level air density

a = PIP0

A general gas law defines the relationship of

pressure temperature, and density when there

is no change of state or heat transfer. Simply

stated this would be “density varies directly

with pressure, inversely with temperature.”

Using the properties previously defined,

density ratio= Pressure rat’o.

temperature rat10

,. n

,:,j

,-g # I

PlAVWEPS 00-8OT-80

BASIC AERODYNAMICS

This relationship has great application in

aerodynamics and is quite fundamental and

necessary in certain parts of airplane perform-

ance.

VISCOSITY. The viscosity of the air is

important in scale and friction effects. The

coefficient of absolute viscosity is the propor-

tion between the shearing stress and velocity

gradient for a fluid flow. The viscosity of

gases is unusual in that the viscosity is gen-

erally a function of temperature alone and an

increase in temperature increases the viscosity.

The coefficient of absolute viscosity is assigned

the shorthand notation I, (mu). Since many

parts of aerodynamics involve consideration of

viscosity and density, a more usual form of

viscosity measure is the proportion of the co-

efficient of absolute viscosity and density.

This combination is termed the “kinematic

viscosity” and is noted by Y (nu).

kinematic viscosity

cc coefficient of absolute viscosity

density

v=PlP

The kinematic viscosity of air at standard sea

level conditions is 0.0001576 square feet per

second. At an altitude of 40,000 feet the

kinematic viscosity is increased to 0.0005059

square foot per second.

In order to provide a common denominator

for comparison of various aircraft, a standard

atmosphere has been adopted. The standard

atmosphere actually represents the mean or

average properties of the atmosphere. Figure

1.1 illustrates the variation of the most im-

portant properties of the air throughout the

standard atmosphere. Notice that the lapse

rate is constant in the troposphere and the

stratosphere begins with the isothermal region.

Since all aircraft performance is compared

and,evaluated in the environment of the stand-

ard atmosphere, all of the aircraft instrumenta-

tion is calibrated for the standard atmosphere.

Thus, certain corrections must apply to the

instrumentation as well as the aircraft per-

formance if the operating conditions do not

fit the standard atmosphere. In order to prop-

erly account for the nonstandard atmosphere

certain terms must be defined. Pressure .&itudc

is the altitude in the standard atmosphere

corresponditrg to a particular pressure. The

aircraft altimeter is essentially a sensitive

barometer calibrated to indicate altitude in

the staotlard atmosphere. If the altimeter is

set for 29.92 in. Hg the altitude indicated is

the pressure altitude-the altitude in the stand-

ard atmosphere corresponding to the sensed

pressure. Of course, this indicated pressure

altitude may not be the actual height above

sea level due to variations in remperature,

lapse rate; atniospheric pressure, and possible

errors in the sensed pressure.

The more appropriate term for correlating

aerodynamic performance in the nonstandard

atmosphere is density &it&-the altitude in

the standard atmosphere corresponding to a

particular value of air density. The computa-

tion of density altitude must certainly involve

consideration of pressure (pressure altitude)

and temperature. Figure 1.6 illustrates the

manner in which pressure altitude and tem-

perature combine to produce a certain density

altitude. This chart is quite standard in use

and is usually included in the performance

section of the flight handbook. Many subject

areas of aerodynamics and aircraft performance

will emphasize density altitude and temperature

as the most important factors requiring con-

sideration.

BERNOULLI’S PRINCIPLE AND SUBSONIC

AIRFLOW

All of the external aerodynamic forces on a

surface are the result of air pressure or air fric-

tion. Friction effects are generally confined to

a thin layer of air in the immediate vicinity of

the surface and friction forces are not the pre-

dominating aerodynamic forces. Therefore,

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BASIC AERODYNAMICS

ICAO STANDARD ATMOSPHERE

*GEOPOTENTIAL OF THE TROPOPAUSE

Figure 1.7. Standard Altitude Table

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BASIC AERODYNAMICS

the pressure forces created on an aerodynamic

surface can be studied in a simple form which

at first neglects the effect of friction and vis-

cosity of the airflow. The most appropriate

means of visualizing the effect of airflow and

the resulting aerodynamic pressures is to study

the fluid flow within a closed tube.

Suppose a stream of air is flowing through

the tube shown in figure 1.2. The airflow at

station 1 in the tube has a certain velocity,

static pressure, and density. As the airstream

approaches the constriction at station 2 certain

changes must take place. Since the airflow

is enclosed within the tube, the mass flow at

any point along the tube must be the same and

the velocity, pressure, or density must change

to accommodate this continuity of flow.

BERNOULLI’S EQUATION. A distin-

guishing feature of submnic airflow is that

changes in pressure and velocity take place

with sniall and negligible changes in density.

For this reason the study of subsonic airflow

can be simplified by neglecting the variation

of density in the flow and assuming the flow

to be incomprmiblc. Of course, at high flow

speeds whjch approach the speed of sound, the

flow must be considered as compressible and

“compressibility effects” taken into account.

However, if the flow through the tube of

figure 1.2 is considered subsonic, the density of

the airstream is essentially constant at all sta-

tions along the length.

If the density of the flow remains constant,

static pressure and velocity are the variable

quantities. As the flow approaches the con-

striction of station 2 the velocity must increase

to maintain the same mass flow. As the

velocity increases the static pressure will de-

crease and the decrease in static pressure which

accompanies the increase in velocity can be

verified in two ways:

(I) Newton’s laws of motion state the

requirement of an unbalanced force to pro-

duce an acceleration (velocity change). If

the airstream experiences an increase in veloc-

ity approaching the constriction, there must

be an unbalance of force to provide the ac-

celeration. Since there is only air within the

tube, the unbalance of force is provided by

the static pressure at station 1 being greater

than the static pressure at the constriction,

station 2.

(2) The total energy of the air stream in

the tube is unchanged. However, the air-

.’ stream energy may be in two forms. The

airstream may have a potential energy which

is related by the static pressure and a kimtic

energy by virtue of mass and motion. As

the total energy is unchanged, an increase in

velocity (kinetic energy) will be accompa-

nied by a decrease in static pressure (poten-

tial energy). This situation is analagous to

a ball rolling along-a smooth surface. As

the ball rolls downhill, the potential energy

due to position is exchanged for kinetic

energy of motion. If .friction- were negli-

gibie, the change of potential energy would

equal the change in ki,netic energy. This- is

also the case for the airflow within the tube.

The relationship of static pressure and veloc-

ity is maintained throughout the length of the

tube. As the flow moves past the constriction

toward station 3, the velocity decreases and

the static pressure increases.

The Bernoulli equation for incompressible

flow is most readily explained ,by accounting

for the energy of the~airflow within the tube.

As the airstream has no energy added or sub-

tracted at any point, the sum of the potential

+id kinetic energy must be constant. The

kinetic energy of an object is found by:

“KE. =%MV=

where K;E. = kinetic energy, ft.-lbs.

M = mass, slugs

V’=velocity, ft./set.

The kinetic energy of a cubic foot of air is:

K&x,,

where g= kinetic energy per cu. ft., psf

p=air density, slugs per cu. ft.

V=ait velocity, ft./set.

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BASIC AERODYNAMICS

INCREASEOVELOC

DECREASE0 HEIG

PE + KE = CONSTANT

Ftaure 1.2. Airflow Within a Tube

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BASIC AERODYNAMICS

H=P+q

I 1500 I

ci P

500 I

70K

P=21 16 PSF P = 2014 PSF P = 2133 PSF

q= 34 PSF 9 = 136 PSF q= I7 PSF

H- 2150 PSF H = 2150 PSF H = 2150 PSF

Figure 1.3. Variation o\ Pressure in Tube

If the potential energy is represented by the

static pressure, p, the sum of the potential and

kinetic energy is the total pressure of the air-

stream.

H=p+% P V’

where H=total pressure, psf (sometimes re-

ferred to as “head ’ pressure)

p=static pressure, psf.

p=density, siugs per cu. ft.

V= velocity, ft./set.

This equation is the Bernoulli equation for

‘incompressible flow. It is important to ap-

preciate that the term >$pV2 has the units of

pressure, psf. This term is one of the most

important in all aerodynamics and appears so

frequently t&it is given the name “dynamic

pressure” and the shorthand notation “4”.

q= dynamic pressure, psf

= jgpv2

With this definition it could be said that the

sum of static and dynamic pressure in the flow

tube remains constant.

Figure 1.3 illustrates the variation of static,

dynamic, and total pressure of air flowing

through a closed tube. Note that the total

pressure is con,stant throughout the length

and any change in dynamic pressure produces

the same magnitude change in static pressure.

The dynamic pressure of a free airstream is

the one ‘common denominator of all aero-

dynamic forces and moments. Dynamic pres-

sure represents the kinetic energy of the free

airstream and is a factor relating the capability

for producing changes in static pressure on a

surface. As defined, the dynamic, pressure

varies directly as the density and the square of

the velocity. Typical values of dynamic pres-

sure, 4, are shown in table l-1 for various true

airspeeds in the standard atmosphere. Notice

that the dynamic pressure at some fixed veloc-

ity varies directly with the density ratio at any

altitude. Also, appreciate the fact that at an

altitude of 40,oM) feet (where the density ratio,

b, is 0.2462) it is necessary to have a true air

velocity twice that at sea level in order to

product the same dynamic pressure.

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BASIC AERODYNAMICS

TABLE l-l. Effect of Speed and Altitvde on Dwzmnic Prerrure

True air

speed

(fr./scc.)

m=

I, 013

-

,I I

_-

AIRSPEED MEASUREMENT. If a sym-

metrically shaped object were placed in a

moving airstream, the flow pattern typical of

figure 1.4 would result. The airstream at the

very nose of the object would stagnate and the

relative flow velocity at this point would be

zero. The airflow ahead of the object pos-

sesses some certain dynamic pressure and

ambient static pressure. At the very nose of

the object the local velocity will drop to zero

and the airstream dynamic pressure will be

converted into an increase in static pressure at

the stagnation point. In other words, there

will exist a static pressure at the stagnation

point which is equal to the airstream total

pressure-ambient static pressure plus dynamic

pressure.

Around the surface of the object the airflow

will divide and the local velocity will increase

from zero at the stagnation point to some

maximum on the sides of the object. If fric-

tion and viscosity effects are neglected, the

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BASIC AERODYNAMICS

FORWARD STAGNATION AFT STAGNATION

POINT POINT

AIRSTREAM AHEAD STAGNATION PRESSURE

HAS AMBIENT STATIC IS AIRSTREAM TOTAL

PRESSURE AND DYNAMIC PRESSURE

PRESSURE P+q

Ftgure 1.4. Flow Pattern on a Symmetrical Object

surface anflow continues to the aft stagnation

point where the local velocity is again zero.

The important point of this example of aero-

dynamic flow is existence of the stagnation

point. The change in airflow static pressure

which takes place at the stagnation point IS

equal to the free stream dynamic pressure, q.

The measurement of free stream dynamic

pressure is fundamental to the indication of

airspeed. In fact, airspeed indicators are sim-

ply pressure gauges which measure dynamic

pressure related to various airspeeds. Typical

airspeed measuring systems are illustrated in

figure 1.5. The pitot head has no internal

flow velocity and the pressure in the pitot tube

is equal to the total pressure of the airstream.

The purpose of the static-ports is to sense the

true static pressure of the free airstream. The

total pressure and static pressure lines are

attached to a differential pressure gauge and

the net pressure indicated is the dynamic

pressure, q. The pressure gauge is then cali-

brated to indicate flight speed in the standard

sea level air mass. For example, a dynamic

pressure of 305 psf would be realized at a sea

level flight ,speed of 300 knots.

Actually there can be many conditions of

flight where the airspeed indicator does not

truly reflect the actual velocity through the

air mass. The corrections that must be applied

are many and lisred in sequence below:

(1) The indicated airspeed (IAS) is the

actual instrument indication for some given

flight condition. Factors such as an altitude

other than standard sea level, errors of the

instrument and errors due to the installation,

compressibility, etc. may create great vari-

ance between this instrument indication and

the actual flight speed.

(2) The calibrated airspeed (CM) is the

result of correcting IAS for errors of the

NAVWEPS 00-807-80

BASIC AERODYNAMICS

PITOT-STATIC SYSTEM

w / :% . I. q

PITOT WITH SEPARATE

STATIC SOURCE

PRESSURE INDICATED BY GAUGE IS

DIFFERENCE BETWEEN TOTAL AND

STATIC PRESSURE, H-p= q

Figure. 1.5. Airspeed Measurement

instrument and errors due to position or lo-

cation of the installation. The instrument

error must be small by design of the equip-

ment and is usually negligible in equjpment

which is properly maintained and cared for.

The position error of the installation must

be small in the range of airspeeds involving

critical performance conditions. Position

errors are most usually confine,d to the static

source in that the actual static pressure

sensed at the static port may be different

from the free airstream static pressure.

When the .,aircraft is operated through a

large range’ of angles of attack, the static

pressure distribution varies ‘quite greatly

and it becomes quite difficult to’minimize

the static source error. In most instances a

compensating group of static sources may

be combined to reduce the position error.

In order to appreciate the magnitude of this

problem, at flight speed near 100 knots a

0.05 psi position error is an airspeed error

of 10 knots. A typical variation of air-

speed system position error is illustrated in

figure 1.6.

(3) The equivalent airspeed (PAS) is the

result of correcting the (CAS) for compressi-

bility effects. At high flight speeds the

stagnation pressure recovered in the pitot

tube is not representative of the airstream

dynamic pressure due to a magnification

by compressibility. Compressibility of the

airflow produces a stagnation pressure in

the pitot which is greater than if the flow

were incompressible. As a result, the air-

speed indication is given an erroneous mag-

nihcation. The standard airspeed indicator

is calibrated to read correct when at standard

sea level conditions and thus has a com-

pressibility correction appropriate for these

conditions. However, when the aircraft is

operating above standard sea level altitude,

Revised January 1965

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BASIC AERODYNAMICS

TYPICAL POSITION ERROR CORRECTION

INDICATED AIRSPEED, KNOTS

COMPRESSIBILITY CORREt

CALIBRATED AIRSPEED, KNOTS

Figure 1.6. Airspeed Corrections (sheet 1 of 2)

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BASIC AERODYNAMICS

DENSITY ALTITUDE CHART

+g&

‘Id -30fl1111v AlISNxl

Figure 1.6. Airspeed Corrections (sheet 2 of 2)

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BASIC AERODYNAMICS

the inherent compensation is inadequate and

additional correction must be applied. The

subtractive corrections that must be applied

to CA$ depend on pressure altitude and CAS

and are shown on figure 1.6 for the subsonic

flight range. The equivalent airspeed (EAS)

is the flight speed in the standard sea level

air mass which would produce the same free

stream dynamic pressure as the actual flight

condition.

(4) The true airspeed (TAS) results when

the &4X is corrected for density altitude.

Since the airspeed indicator is calibrated

for the dynamic pressures corresponding to

airspeeds at standard sea level conditions,

variations in air density must be accounted

for. To relate EAS and TAX requires con-

sideration that the EAS coupled with stand-

.ard sea level density produces the same dy-

namic pressure as the TAX Soupled with the

^^_._^ 1 .:.. 2---:... ,.f *L., bl:A.* rnrJ;r;m.. dCLUd, ‘all UcIIJIcy “I L11L “‘6°C C”IIUACI”L‘.

From this reasoning, it can be shown that:

(TAS)2p=(EAS)2 po

-

or, TAS=EAS 62 P

TAS= EAS 2

where TAX= true airspeed

EAS=equivalent airspeed

p=actual air density

PO= standard sea level air density

n=altitude density ratio, p/pa

The result shows that the TAX is a function

of EAS and density altitude. Figure 1.6 shows

a chart of density altitude as a function of

pressure altitude and temperature. Each par-

ticular density altitude fixes the proportion

between TAX and EAS. The use of a naviga-

tion computer requires setting appropriate

values of pressure altitude and temperature on

the scales which then fixes rhe proportion be-

tween the scales of TAS and EAS (or TAS and

CAS when compressibiliry corrections are

applicable).

Revlted Jmuoy 1965

Thus, the airspeed indicator system measures

dynamic pressure and will relate true flight

velocity when instrument, position, compress-

ibility, and density corrections are applied.

These corrections are quite necessary for ac-

curate determination of true airspeed and

accurate navigation.

Bernoulli’s principle and the concepts of

static, dynamic, and total pressure are the basis

of aerodynamic fundamentals. The pressure

distribution caused by the variation of local

stack and dynamic pressures on a surface is

the source of the major aerodynamic forces

and moment.

DEVELOPMENT OF AERODYNAMIC

FORCES

The typical airflow patterns exemplify the

relationship of static pressure and velocity

defined by Bernoulli. Any object placed in an

airstream will have the a& to impact or stag-

nate at some point near the leading edge. The

pressure at this point of stagnation will be an

absolute static pressure equal to the total pres-

sure of the airstream. In other words, the

static pressure at the stagnation point will be

greater than the atmospheric pressure by the

amount of the dynamic pressure of the air-

stream. As the flow divides and proceeds

around. the object, the increases in local ve-

locity produce decreases in static pressure.

This procedure of flow is best illustrated by the

flow patterns and pressure distributions of

figure 1.7.

STREAMLINE PATTERN AND PRES-

SURE DISTRIBUTION. The flow pattern of

the cylinder of figure 1.7 is characterized by

the streamlines which denote the local flow

direction. Velocity distribution is noted by

the streamline pattern since the streamlines

effect a boundary of flow, and the airflow

between the streamlines is similar to flow in a

closed tube. When the streamlines contract

and are close together, high local velocities

exist; when the streamlines expand and are

far apart, low local velocities exist. At the

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BASIC AERODYNAMICS

PEAK SUCTION

PRESSURE

PRESSURE DISTRIBUTION ON A 5v’ )ER

STAGNATION

NEGLECTING FRICTION

(PERFECT FLUID)

CONSIDERING FRICTION EFFECTS

(VISCOUS FLOW)

PRESSURE DISTRIBUTION ON A SYMMETRICAL AIRFOIL AT ZERO LIFT

-PEAK SUCTION

AFT STAGNATION POINT

NEGLECTING FRICTION

VISCOUS FLOW

Figure 1.7. Streamline Pattern and Pressure Distribution

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BASIC AERODYNAMICS

forward stagnation point the local velocity

is zero and the maximum positive pressure re-

sults. As the flow proceeds from the forward

stagnation point the velocity increases as

shown by the change in streamlines. The

local velocities reach a maximum at the upper

and lower extremities and a peak suction pres-

sure is produced at these points on the cylinder.

(NOTE: Positive pressures are pressures above

atmospheric and negative or .ruction pressures

are less than atmospheric.) As the flow

continues aft from the peak suction pressure,

the diverging streamlines indicate decreasing

local velocities and increasing local pressures.

If friction and compressibility effects are not

considered, the velocity would decrease to zero

at the aft stagnation point and the full stagna-

tion pressure would be recovered. The pressure

distribution for the cylinder in perfect fluid

flow would be symmetrical and no net force

(lift or dragj wvuid rcsuit. Of course, thr

relationship between static pressure and ~eloc-

ity along the surface is defined by Bernoulli’s

equation.

The flow pattern for the cylinder in an actual

fluid demonstrates the effect of friction or

viscosity. The viscosity of air produces a thin

layer of retarded flow immediately adjacent

to the surface. The energy expended in this

“boundary layer” can alter the pressure dis-

tribution and destroy the symmetry of the

pattern. The force unbalance caused by the

change in pressure distribution creates a drag

force which is in addition to the drag due to

skin friction.

The streamline pattern for the symmetrical

airfoil of figure 1.7 again provides the basis

for the velocity and pressure distribution.

At the leading edge the streamlines are widely

diverged in the vicinity of the positive pres-

sures. The maximum local velocities and

suction (or negative) pressures exist where the

streamlines are the closest together, One

notable difference between the flow on the

cylinder and the airfoil is that the maximum

velocity and minimum pressure points on the

airfoil do not ,necessarily occtir at the point of

maximum thickness. However, a similarity

does exist in that the minimum pressure points

correspond to the points where the streamlines

are closest together and this condition exists

when the streamlines are forced to the great-

est curvature.

GENERATION OF LIFT. An important

phenomenon associated with the production

of lift by an airfoil is the “circulation” im-

parted to the airstream. The best practical

illustration of this phenomenon is shown in

figure 1.8 by the streamlines and pressure dis-

tributions existing on cylinders in an airstream.

The cylinder without circulation has a sym-

metrical streamline pattern and a pressure dis-

tribution which creates n-0 n_et lift. If the

cylinder is given a clockwise rotation and

induces a rotational or circulatory flow, a dis-

tinct change takes place in the streamline pat-

tern and p’ess.~re &str~‘“u~~oii, The vriocitirs

due to the vortex of circulatory flow cause

increased 104 velocity on the upper surface

of the cylinder and decreased local velocity on

the lower surface of the cylinder. Also, the

circulatory flow produces an upwash immedi-

ately ahead and downwash immediately be-

hind the cylinder and both fore and aft stagna-

tion points are lowered.

The effect of the addition of circulatory flow

is appreciated by the change in the pressure

distribution on the cylinder. The increased

local velocity on the upper surface causes an

increase in upper surface suction while the

decreased local velocity on the lower surface

causes a decrease in lower surface suction. As

a result, the cylinder with circulation will

produce a net lift. This mechanically induced

circulation-called Magnus effect-illustrates

the relationship between circulation and lift

and is important to golfers, baseball and tennis

players as well as pilots and aerodynamicists.

The curvature of the flight path of a golf ball

or baseball rcluites an unbalance df force

which is created by rotation of the ball. The

pitcher that can accurately control a .powerful

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BASIC AERODYNAMICS

CYLINDER WITHOUT CIRCULATION

INCREASED LOCAL

VELOCITY

UPWASH mSWNWASH

----

\

LDECREASED LOCAL

VELOCITY

CYLINDER WITH CIRCULATION

MAGNUS EFFECT BY

ROTATING CYLINDER

AIRFOIL LIFT

-ZERO LIFT

UPWASH

7 INCREASED LOCAL

I ,-VELOCITY

POSITIVE LIFT

DECREASED LOCAL

VELOCITY

Figure 1.8. Generation of Lift (sheet 1 of 2)

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Figure 7.8. Generation of Lift (sheet 2 of 2)

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BASIC AIRFOIL SHAPE

AND ANGLE OF ATTACK

ORIGINAL ANGLE OF ATTACK

AND DYNAMIC/PRESSURE, 9

ORIGINAL ANGLE OF ATTACK

BUT INCREASED DYNAMIC PRESSURE

ORIGINAL ANGLE OF ATTACK AND DYNAMIC

PRESSURE BUT ONE-HALF ORIGINAL SIZE

AIRFOIL SHAPE AND ANGLE OF ATTACK DEFINE

RELATIVE PRESSURE DISTRIBUTION

Figure 1.9. Airfoil Pressure Distribution

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BASIC AERODYNAMICS

rotation will be quite a “curve ball artist”

the golfer that cannot control the lateral mo-

tion of the club face striking the golf ball will

impart an uncontrollable spin and have trouble

with a “hook” or “slice.”

While a rotating cylinder can produce a net

lift from the circulatory flow, the method is

relatively inefficient and only serves to point

out the relationship between lift and circula-,

tion. An airfoil is capable of producing lift

with relatively high efficiency and the process

is illustrated in figure 1.8. If a symmetrical

airfoil is placed at zero angle of attack to the

airstream, the streamline pattern and pressure

distribution give evidence of zero lift. HOW-

ever, if the airfoil is given a positive angle of

attack, changes occur in the streamline pattern

and pressure distribution similar to changes

caused by the addition of circulation to the

cylinder. The positive angle of attack causes

increased velocity on the upper surface with

an increase in upper surface suction while the

decreased velocity on the lower surface causes

a decrease in lower surface suction. Also,

upwash is generated ahead of the airfoil, the

forward stagnation point moves under the

leading edge, and a downwash is evident aft

of the airfoil. The pressure distribution 0”

the airfoil now provides a net force perpendicu-

lar to the airstream-lift.

The generation of lift by an airfoil is depend-

ent upon the airfoil being able to create circu-

lation in the airstream and develop the lifting,

pressure distribution on the surface. In all

cases, the generated lift will be the net force

caused by the distribution of pressure over the

upper and lower surfaces of the airfoil. At

low angles of attack, suction pressures usually

will exist on both upper and lower surfaces.

but the upper surface suction must be greater

for positive lift. At high angles of attack

near that for maximum lift, a positive pressure

will exist on the lower surface but this will

account for approximately one-third the net

lift.

The effect of free stream density and velocity

is a necessary consideration when studying the

development of the various aerodynamic forces.

Suppose that a particular shape of airfoil is

fixed at a particular angle to the airstream.

The relative velocity and pressure distribution

will be determined by the shape of the airfoil

and the angle to the airstream. The effect of

varying the airfoil size, air density and air-

speed is shown in figure 1.9. If the same air-

foil shape is placed at the same angle to an

airstream with twice as great a dynamic pres-

sure the magnitude of the pressure distribution

will be twice as great but the r&rive shape of

the pressure distribution will be the same.

With twice as great a pressure existing over

the surface, all aerodynamic forces and mo-

ments will ~double. If a half-size airfoil ib

placed at the same angle to the original air-

stream, the magnitude of the pressure distri-

bution is the same as the origina! airfoi! and

again the relative shape of the pressure dis-

tribution is identical. The same pressure act-

ing on the half-size surface would reduce all

aerodynamic forces to one-half that of the

original. This similarity of flow patterns

means that the stagnation point occurs at the

same place, the peak suction pressure occurs

at the same place, and the actual magnitude of

the aerodynamic forces and moments depends

upon the airstream dynamic pressure and the

surface area. This concept is extremely im-

portant when attempting to separate and ana-

lyze the most important factors affecting the

development of aerodynamic forces.

AIRFOIL TERMINOLOGY. Since the

shape of an airfoil and the inclination to the

airstream are so important in determining the

pressure distribution, it is necessary to properly

define the airfoil terminology. Figure 1.10

shows a typical airfoil and illustrates the

various items of airfoil terminology

(1) The chord line is a straight line connect-

ing the leading and trailing edges of the

airfoil.

NAVWEPS 00-8DT-80

BASIC AERODYN,AMlCS

LOCAT,ON DF THICKNESS

MAX. THICKNESS UPPER SURFACE

MEAN CAMBER

t CA

CH6RD

-I

LOCATION OF

MAXIMUM CAMBER

RE;L:r;

0 7 LIFT

&

0 G

DRAG

Figure 1.10. Airfoil ~erminoh

\

NAVWEPS oOgOT-8O

BASIC AERODYNAMICS

(2) The chord is the characteristic dimen-

sion of the airfoil.

(3) The mean-camber line is a line drawn

halfway between the upper and lower sur-

faces. Actually, the chord line connects the

ends of the mean-camber line.

(4) The shape of the mean-camber line is

very important in determining the aerody-

namic characteristics of an airfoil section.

The maximum camber (displacement of the

mean line from the chord line) and the Ioca-

tion of the maximum camber help to define

the shape of the mean-camber line. These

quantities are expressed as fractions or per-

cent of the basic chord dimension. A typi-

cal iow speed airfoil may have a maximum

camber of 4 percent located 40 percent aft of

the leading edge.

(5) The thickness and thickness distribu-

tion of the profile are important properties

of a section. The maximum tbicknus and

location of maximum thickness define thick-

ness and distribution of thickness and are

expressed as fractions or percent of the chord.

A typical low speed airfoil may have a.

maximum thickness of 12 percent located

30 percent aft of the leading edge.

(6) The leading edge radius of the airfoil is

the radius of curvature given the leading edge

shape. It is the radius of the circle centered

on a line tangent to the leading edge camber

and connecting tangency pcints of upper and

lower surfaces with the leading edge. Typi-

cal leading edge radii are zero (knife edge)

to 1 or 2 percent.

(7) The Iift produced by an airfoil is the

net force produced perpendicular to the n&a-

tive wind.

(8) The drag incurred by an airfoil is the

net force produced parallel to the relative wind.

(9) The angle of attack is the angle between

the chord line and the relative wind. Angle

of attack is given the shorthand notation

a (alpha). Of course, it is important to dif-

i ferentiate between pitch attitude angle and

angle of attack. Regardless of the condi-

tion of flight, the instantaneous flight path

of the surface determines the direction of the

oncoming relative wind and the angle of

attack is the angle between the instantaneous

relative wind and the chord line. To respect

the definition of angle of attack, visualize

the flight path of the aircraft during a loop

and appreciate that the relative wind is

defined by the flight path at any point dur-

ing the maneuver.

Notice that the description of an airfoil

profile is by dimensions which are fractions or

percent of the basic chord dimension. Thus,

when an airfoil. profile is specified a relative

shape is described. (NOTB: A numerical sys-

tem of designating airfoil profiles originated

by the National ~Advisory Committee for Aero-

nautics [NACA] is used to describe the main

geometric features and certain aerodynamic

properties. NACA Report Nol 824 wi!! pro-

vide the detail of this system.)

AERODYNAMIC FORCE COEFFICIENT.

The aerodynamic forces of lift and drag depend

on the combined effect of many different vari-

ables. The important single variables could

IX:

(1) Airstream velocity

(2) Air density

(3) Shape or profile of the surface

(4) Angle of attack

(5) Surface area

(6) Compressibility effects

(7) Viscosity effects

If the effects of viscosity and compressibility

are not of immediate importance, the remain-

ing items can be combined for consideration.

Since the major aerodynamic forces are the

result of various pressures distributed on a

surface, the surface area will be a major factor.

Dynamic prcssurc of the airstream is another

common denominator of aerodynamic forces

and is a major factor since the magnitude of a

pressure distribution depends on the source

energy of the free stream. The remaining

major factor is the relative peJJ#re dittribution

existing on the surface. Of course, the ve-

locity distribution, and resulting pressure dis-

tribution, is determmed by the.shape or pro-

file of the surface and the angle of a’track.

Thus, any aerodynamic force can be repre-

sented as the product df three major factors:

the surface area of the objects

the dynamic pressure of the airstream

the coefficient or index of force determined

by the relative pressure distribution

This relationship is expressed by the following

equation :

F= C,qS

where

F = aerodynamic force, lbs.

C,=coeflicient of aerodynamic force

,iay;mic pressure, psf

S=surface area, sq. ft.

In order to fully appreciate the importance

of the aerodynamic force coe&cient, C,, the ,

above equation is rearranged to alternate

forms :

In this form, the aerodynamic force coefficient

Js appreciared as the aerodynamic force per

surface area and dynamic pressure. In other

words, the force coefficient is a dimensionless

ratio between the average aerodynamic pres-

sure (aerodynamic force.per ‘area) and the air-

stream dynamic pressure. All the aerodynamic

forces of lift and drag are studied on this basis-

the common denominator in each case being

surface area and dynamic pressure. By such a

definition, a “lift coefficient” would .be the

ratio between lift pressure and dynamic pres-

sure; a “drag coefficient” would be the ratio

between drag pressure and.:d.ynamic pressure.

The use of the coefficient form of an aero-

dynamic force is necessary since the force

coellicient is:

(1) An index 04 the aerodynamic force

independent of area, density, and velocity.

NAVWEPS m-60T-30

BASIC AERODYNAMICS

It is derived from the relative pressure and

velocity distribution.

(2) Influenced only by the shape of the

surface and angle of attack since these factors

determine the pressure distribution.

(3) An index which allows evaluation of

the effects of compressibility and viscosity.

Since the effects of area, density, and velocity

are obviated by the coefficient form, com-

pressibility and viscosity effects can be

separated for study.

THE BASIC LIFT EQUATION. Lift has

been dehned as the net force developed per-

pendicular to the relative wind. The aero-

dynamic force of lift on an airplane results

from the generation of a pressure distribution

on the wing. This lift force is described by

the following equation:

L=C&

where

L=lift, lbs.

C, = lift coefficient.

q= dy;:mic pressure, psf

+p

S= wing surface area, sq. ft.

The lift coefhcient used in this equation is the

ratio of the lift pressure and dynamic pressure

and is a function of the shape of the wing and

angle of attack. If the lift coefficient of a

conventional airplane wing planfoi-m were

plotted versus angle of attack, the result would

be typical of the graph of figure 1.11. Since

the effects of speed, density, area, weight, alti-

tude, etc., are eliminated by the coefficient form,

an indication of the true lift capability is ob-

tained. Each angle of attack produces a par-

ticular lift coefficient since the angle of attack

is the controlling factor in the pressure dis-

tribution. Lift coeflicient increases with angle

of attack up to the maximum lift coefficient,

c L,,,~., and, as angle of attack is increased be-

yond the maximum lift angle, the airflow is

unable to adhere to the upper surface. The

airflow then separates from the upper surface

and stall occurs.

JNTERPRETATION OF THE LIFT EQUA-

TION. Several important relationships are

H P

LIFT

COEFFICIENT

LIFT PRESSURE

DYNAMIC PRESSURE

qs

ANGLE OF ATTACK, DEGREES

Figure 7.7 1. Typical lib Characteristics

NAVWEPS 00.401-80

BASIC AERODYNAMICS

Thus, a sea level airspeed (or EAS) of 100

knots would provide the dynamic pressure

necessary at maximum lift to produce 14,250

Ibs. of lift. If the airplane were operated at a

higher weight, a higher dynamic pressure

would be required to furnish the greater lift

and a higher stall speed would result. If the

airplane were placed in a steep turn, the greater

lift required in the turn would increase the

stall speed. If the airplane were flown at a

higher density altitude the TAX at stall would

increase. However, one factor common to

each of these conditions is that the angle of

attack at C,,,, is the same. It is important to

realize that stall warning devices must sense

angle of attack (a) or pressure distribution

(related to CL).

Another important fact related by the basic

lift equation and lift curve is variation of angle

of attack and lift coefficient with airspeed.

Suppose that the example airplane is flown in

steady, wing 1eveJ flight at various airspeeds

with lift equal to the weight. It is obvious

that an increase in airspeed above the stall

speed will require a corresponding decrease in

lift coeflicient and angle of attack to maintain

steady, lift-equal-weight flight. The exact

relationship of lift coefficient and airspeed is

evolved from the basic lift equation assuming

constant lift (equal to weight) and equivaIent

airspeeds.

derived from study of the basic lift equation

and the typical wing lift curve. One impor-

tant fact to be appreciated is that the airplane

shown in figure 1.11 stalls at the same angle

of attack regardless of weight, dynamic pres-

sure, bank angle, etc. Of course, the stall

speed of the aircraft will be affected by weight,

bank angle, and other factors since the product

of dynamic pressure, wing area, and lift co-

efficient must produce the required lift. A

rearrangement of the basic lift equation de-

fines this relationship.

L = c&Y

using q =$ (I’ in knots, TAX)

solving for V, -

V=17.2 & J L,J

Since the stall speed is the minimum flying

speed necessary to sustain flight, the lift co-

efficient must be the maximum (CL,,,,).

Suppose that the airplane shown in’ figure

1.11 has the following properties:

Weight = 14,250 lbs

Wing area=280 sq. ft.

C &=1.5

If the airplane is flown in steady, level flight at

sea level with lift equal to weight the stall

speed would be:

,-

V.= 17.24&$

where

V.= stall speed, knots TAS

W= weight, lbs. (lift = weight)

va= 17.2 J (I.&4E;280)

= 100 knots

C‘ v, p -= - C %n.* 0 V

The example airplane was specified to have:

Weight = 14,250 lbs.

C L,,,=lS

V,= 100 knots EAS

The following table depicts the lift coefficients

and angles of attack at various airspeeds in

steady flight.

NAWWEPS 00-8OT-80

BASIC AERODYNAMICS

loo. ................. l.lm 1.30 20.00

110 .................. ,826 1.24 15.P

17.0 .................. ,694 1.04 12.7’

lY) .................. .444 .61 8.20

200 .................. 230 .38 4.6’

MO. ................. ,111 .I7 2.10

4&l. ................. .c453 .o!J 1.10

30.7. ................. ,040 .06 .T=

600 .................. .028 .04 .5O

Note that for the conditions of steady flight,

each airspeed requites a specific angle of attack

and lift coefficient. This fact provides a fun-

damental concept of flying technique: Angle

of attack is tbs primary Control of airspeed in steady

flight. Of course, the control stick or wheel

allows the pilot to control the angle of attack

and, thus, control the airspeed in steady flight.

In the same sense, the throttle controls the

output of the powerplant and allows the pilot

to control rate of climb and descent at various

airspeeds.

The teal believers of these concepts ate pro-

fessional instrument pilots, LSO’s, and glider

pilots.. The glider pilot (or flameout enthusi-

ast) has no recourse but to control airspeed by

angle of attack and accept whatever rate of

descent is incurred at the various airspeeds.

The LSO must become quite proficient at judg-

ing the flight path and angle of attack of the

airplane in the pattern. The more complete

visual reference field available to the LSO

allows him to judge the angle of attack of

the airplane mote accurately than the pilot.

When the airplane approaches the LSO, the

precise judgment of airspeed is by the angle

of attack rather than the rate of closure. If

the LSO sees the airplane on the desired flight

path but with too low an angle of attack, the

airspeed is too high; if the angle of attack is

too high, the airspeed is too low and the ait-

plane is approaching the stall. The mirror

landing system coupled with an angle of attack

indicator is an obvious refinement. The mit-

tot indicates the desired flight path and the

NAVWEPS WOT-BO

BASIC AERODYNAMICS

angle of attack indicator allows precision con-

trol of the airspeed. The accomplished insttu-

ment pilot is the devotee of “attitude” flying

technique-his creed being “attitude plus

power equals performance.” During a GCA

approach, the professional instrument pilot

controls airspeed with stick (angle of attack)

and rate of descent with power adjustment.

Maneuvering flight and certain transient

conditions of flight tend to complicate the

relationship of angle of attack and airspeed.

However, the majority of flight and, certainly,

the most critical regime of flight (takeoff, ap-

proach, and landing), is conducted in essen-

tially steady flight condition.

AIRFOIL LIFT CHARACTERISTICS. Air-

foil section properties differ from wing or

airplane properties because of the effect of the

planform. Actually, the wing may have vati-

ous airfoil sections from root to tip with taper,

twist, sweepback and local flow components

in a spanwise direction. The resulting aeto-

dynamic properties of the wing are determined

by the action of each section along the span

and the three-dimensional flow. Airfoil sec-

tion properties are derived from the basic shape

or profile in two-dimensional flow and the force

coefficients are given a notation of lower case

letters. For example, a wing or airplane lift

coefficient is C, while an airfoil section lift

coefficient is termed cr. Also, wing angle of

attack is Q while section angle of attack is

differentiated by the use of 01~. The study of

section properties allows an objective consider-

ation of the effects of camber, thickness, etc.

The lift characteristics of five illustrative

airfoil sections are shown in figure 1.12. The

section lift coe&icient, c,, is plotted versus

section angle of attack, olO, for five standard

NACA airfoil profiles. One characteristic fea-

ture of all airfoil sections is that the slope of

the various lift curves is essentially the same.

At low lift coefhcients, the section lift coeffi-

cient increases approximately 0.1 for each

degree increase in angle of attack. For each

of the airfoils shown, a S’ change in angle of

NAVWEPS OD-8OT-80

BASIC AERODYNAMICS

(DATA FROM NACA REPORT NO. 824)

SECTION ANGLE OF ATTACK

mo, DEGREES

Figure 1.12. Lift Characteristics of lypicol Airfoil Sections

attack would produce an approximate 0.5

change in lift coefficient. Evidently, lift,~curve

slope is not a factor important in the selection

of an airfoil.

An important lift property affected by the

airfoil shape is the section maximum lift co-

efficient, ci-. The effect of airfoil shape on

ci- can be appreciated by comparison of the

lift curves for the five airfoils of figure 1.12.

The NACA airfoils 63X06,63-009, and 63i-012

ate symmetrical sections of a basic thickness

distribution but maximum thicknesses of 6,

9, and 12 percent respectively. The effect of

thickness on ~1% is obvious from an inspec-

tion of these curves :

NACA 63-005 .~. :. Cl.82 9.0°

NACA 6Mo9. 1.10 10.5~

NACA 63‘-01?,. 1.40 13.80

The 12-percent section has a cr- approxi-

mately 70 percent greater than the 6-percent

thick section. In addition, the thicker airfoils

have greater benefit from the use of various

high lift devices.

The effect of camber is illustrated by the lift

curves of the NACA 4412 and 631-412 sections.

The NACA 4412 section is a 12 percent thick

airfoil which has 4 percent maximum camber

located at 40 percent of the chord. The

NACA 63i-412 airfoil has the same thickness

and thickness distribution as the 631-012 but

camber added to give a “design”’ lift coefficient

(c, for minimum section drag) of 0.4. The

lift curves for these two airfoils show that

camber has a beneficial e&t on cl-.

ScCdO” %.I a0 for “&*

NACA 6h-312 (symmctricd) :. 1.40 13.e

NACA 631-412 Whmd). 1.73 IS. z”

An additional effect of camber is the change

in zero lift angle. While the symmetrical

NAVWEPS OO-BOT-BO

BASIC AE,RODYMAMlCS

sections have zero lift at zero angle of attack,

the sections with positive camber have nega-

tive angles for zero lift.

The importance of maximum lift coefficient

is obvious. If the maximum lift coefficient is

high, the stall speed will be low. However,

the high thickness and camber necessary for

high section maximum lift coefficients may

produce low critical Mach numbers and large

twisting moments at high speed. In other

words, a high maximum lift coefficient is just

one of the many features desired of an airfoil

section.

DRAG CHARACTERISTICS. Drag is the

net aerodynamic force parallel to the relative

wind and its source is the pressure distribution

and skin friction on the surface. Large, thick

bluff bodies in an airstream show a predomi-

nance of form drag due to the unbalanced pres-

sure distribution. However, streamlined

bodies with smooth contours show a ptedomi-

nance of drag due to skin friction. In a

fashion similar to other aerodynamic forces,

drag forces may be considered in the form of a

coefficient which is independent of dynamic

pressure and surface area. The basic drag

equation is as follows:

D=GqS

where

D=drag, lbs.

C,= drag coefficient

q= dynamic pressure, psf

UP =z (V in knots, TAS)

S= wing surface area, sq. ft.

The force of drag is shown as the product of

dynamic pressure, surface area, and drag co-

efficient, C,. The drag coefficient in this

equation is similar to any other aerodynamic

force coefficient-it is the ratio of drag pres-

sure to dynamic pressure. If the drag co-

efficient of a conventional airplane were plotted

versus angle of attack, the result would be

typical of the graph shown in figure 1.13. At

low angles of attack the drag coefficient is

low and small changes in angle of attack create

only slight changes in drag coefficient. At

NAVWEPS 00-BOT-80

BASIC AERODYNAMICS

I ANGLEOFATTACK,DEGREES

Figure 7.73. Drag Characteristics (sheet 1 of 21

ANGLE OF ATTACK, DEGREES

Figure 7.13. Brag Characferistics (sheet 2 of 2)

NAVWEPS Oe8OT-80

BASIC AERODYNAMICS

higher angles of attack the drag coefficient is

much greater and small changes in angle of

attack cause significant changes in drag. As

stall occurs, a large increase in drag takes

place.

A factor more important in airplane per-

formance considerations is the lift-drag ratio,

L/D. With the lift and drag data available for

the airplane, the proportions of CL and CD can

be calculated for each specific angle of attack.

The resulting plot of lift-drag ratio with angle

of attack shows that L/D increases to some

maximum then decreases at the higher lift

coefficients and angles of attack. Note that

the maximum lift-drag ratio, (L/D),,,, occurs

at one specific angle of attack and lift coefIi-

cient. If the airplane is operated in steady

flight at (L/D),,,, the total drag is at a mini:

mum. Any angle of attack lower or higher

than that for (L/D),,, reduces the lift-drag

ratio and consequently increases -the total

drag for a given airpiane iift.

The airplane depicted by the curves of Figure

1.13 has a maximum lift-drag ratio of 12.5 at

an angle of attack of 6”. Suppose this airplane

is operated in steady flight at a gross weight

of 12,500 lbs. If flown at the airspeed and

angle of attack corresponding to (L/D),..,

the drag would be 1,000 lbs. Any higher or

lower airspeed would produce a drag greater

than 1,000 lbs. Of course, this same airplane

could be operated at higher or lower gross

weights and the same maximum lift-drag ratio

of 12.5 could be obtained at the same angle of

attack of 6”. However, a change’ in gross

weight would require a change in airspeed to

support the new weight at the same lift co-

efficient and angle of attack.

Type airplane: (L/D) emz

High performance sailplane. 25-40

Typical patrol or transport.. 12-20

High Performance bomber. 2~25

Propeller powered trainer.. 1~15

J et trainer.. 14-16

Transonic fighter or attack.. lo-13

Supersonic fighter or attack. 4-9 (subsonic)

Revised Januay 1965

The configuration of an airplane has a great

effect on the lift-drag ratio. Typical values

of (L/D),.. are listed for various types of

airplanes. While the high performance sail-

plane may have. extremely high lift-drag

ratios, such an aircraft has no real economic

or tactical purpose. The supersonic fighter

may have seemingly low lift-drag ratios in

subsonic flight but the airplane configurations

required for supersonic flight (and high [L/D]‘*

at high Mach numbers) precipitate this situa-

tion.

Many important items of airplane perform-

ance are obtained in flight at (L/D),... Typi-

cal performance conditions which occur at

(L/D),., are:

maximum endurance of jet powered air-

planes

maximum range of propeller driven air-

planes

maximum climb angle for jet powered air-

planes

maximum power-off glide range, jet or

Prop

The most immediately interesting of these

items is the power-off glide range of an air-

plane. By examining the forces acting on an

airplane during a glide, it can be shown that

the glide ratio is numerically equal to the

lift-drag ratio. For example, if the airplane

in a glide has an (L/D) of 15, each mile of alti-

tude is traded for 15 miles of horizontal dis-

tance. Such a fact implies that the airplane

should be flown at (L/D)- to obtain the

greatest glide distance.

An unbelievable feature of gliding perform-

ance is the effect of airplane gross weight.

Since the maximum lift-drag ratio of a given

airplane is an intrinsic property of the aero-

dynamic configuration, gross weight will not

affect the gliding performance. If a typical

jet trainer has an (L/@- of 15, the aircraft 1

can obtain a maximum of 15 miles horizontal

distance for each mile of altitude. This would

be true of this particular airplane at any gross

weight if the airplane is flown at the angle

of attack for (L/D),. Of course, the gross

weight would affect the glide airspeed neces-

sary for this particular angle of attack but the

glide ratio would be unaffected.

AIRFOIL DRAG CHARACTERISTICS.

The total drag of an airplane is composed of

the drags of the individual components and

the forces caused by interference between these

components. The drag of an airplane con-

figuration must include the various drags due

to lift, form, friction, interference, leakage,

etc. To appreciate the factors which affect

the drag of an airplane configuration, it is

most logical to consider the factors which

affect the drag of airfoil sections. In order to

allow an objective consideration of the effects

of thickness, camber, etc., the properties of

two-dimensional sections must be studied.

Airfoil section properties are derived from the

basic profile in two-dimensional. flow and are

provided the lower case shorthand notation

to distinguish them from wing or airplane

properties, e.g., wing or airplane drag coe5-

cient is C, while airfoil section drag coefficient

is c,.

The drag characteristics of three illustrative

airfoil sections are shown in figure 1.14. The

section drag coe&cient, c,, is plotted versus

the section lift coefficient, cr. The drag on

the airfoil section is composed of pressure drag

and skin friction. When the airfoil is at low

lift coe&cients, the drag due to skin friction

predominates. The drag curve for a conven-

tional airfoil tends to be quite shallow in this

region since there is very little variation of

skin friction with angle of attack. When the

airfoil is at high lift coefficients, form or

pressure drag predominates and the drag co-

efficient varies rapidly with lift coefficient.

The NACA 0006 is a thin symmetrical profile

which has a maximum thickness of 6 percent

located at 30 percent of the chord. This

section shows a typical variation of cd and cr.

The NACA 4412 section is a 12 percent thick

airfoil with 4 percent maximum camber at

NAVWEPS OO-EOT-RO

BASIC AERODYNAMICS

40 percent chord. When this section is com-

pared with the NACA 0006 section the effect

of camber can be appreciated. At low lift

coefficients the thtn, symmetrical section has

much lower drag. However, at lift coeffi-

cients above 03 the thicker, cambered section

has the lower drag. Thus, proper camber and

thickness can improve the lift-drag ratio of

the section.

The NACA 63,412 is a cambered 12 percent

thick airfoil of the ‘“laminar flow” type.

This airfoil is shaped to produce a design lift

coe5cient of 0.4. Notice that the drag curve

of this airfoil has distinct aberrations with

very low drag coefficients near the lift coeffi-

cient of 0.4. This airfoil profile has its camber

and thickness distributed to produce very low

uniform velocity on the forward surface (mini-

mum pressure point well aft) at this lift coeffi-

cient. The resulting pressure and velocity

distribution enhance extensive laminar flow

in the boundary layer and greatly reduce the

skin friction drag. The benefit of the laminar

flow is appreciated by comparing the minimum

drag of this airfoil with an airfoil which has

one-half the maximum thickness-the NACA

ooo6.

The choice of an airfoil section will depend

on the consideration oftmany different factors.

While the cI, of the section is an important

quality, a more appropriate factor for con-

sideration is the maximum lift coefficient of

the section when various high lift devices are

applied. Trailing edge flaps and leading edge

high lift devices are applied to increase the

cr,, for low speed performance. Thus, an

appropriate factor for comparison is the ratio

of section drag coe5cient to section maximum

lift coefficient with flaps-cd/crm,. When this

quantity is corrected for compressibility, a

preliminary selection of an airfoil section is

possible. The airfoil having the lowest value

of c&~, at the design flight condition (en-

durance, range, high speed, etc.) will create

the least section drag for a given .design stall

speed.

NAVWEPS DD-BOT-BD

BASK AERODYNAMICS

(DATA FROM NACA REPORT ~0.824)

SMOOTH SURFAC

e-L--

-.2 Cl .2 .4 .6 .8 LO’---I.2 1.4 1.6 1.8

SECTION LIFT COEFFICIENT

Figure 1.14. Drag Characteristics of Typical Airfoil Sections

PLIGHT AT HIGH LIFT CONDITIONS

It is frequently stated that the career Naval

Aviator spends more than half his life “below

a thousand feet and a hundred knots.” Re-

gardless of the implications of such a state-

ment, the thought does cunnute the relation-

ship of minimum flying speeds and carrier

aviation. Only in Naval Aviation is there

such importance assigned to precision control

of the aircraft at high lift conditions. Safe

operation in carrier aviation demands precision

control of the airplane at high lift conditions.

The aerodynamic lift characteristics of an

airplane are portrayed by the curve of lift

coefficient versus angle of attack. Such a

curve is illustrated in figure 1.15 for a specific

airplane in the clean and flap down configura-

tions. A given aerodynamic configuration ex-

periences increases in lift coefficient with in-

creases in angle of attack until the maximum

lift coefficient is obtained. A further increase

in angIe of attack produces stall and the lift

coefficient then decreases. Since the maximum

lift coefficient corresponds to the minimum

speed available in flight, it is an important

point of reference. The stall speed of the air-

craft in level flight is related by the equation:

V7.=17.2 J-- c w

.ln2s

where

V.-stall speed, knots TAS

W=gross weight, lbs.

c Lnoz= airplane maximum lift coefficient

csaltitude density ratio

S= wing area, sq. ft.

This equation illustrates the effect on stall

speed of weight and wing area (or wing load-

ing, W/S), maximum lift coefficient, and alti-

tude. If the stall speed is desired in EAS, the

density ratio will be that for sea level (u=

1.000).

EFFECT OF WEIGHT. Modern configu-

rations of airplanes are characterized by a large

percent. of the maximum gross weight being

NAVWEPS 00-BOT-RO

BASIC AERODYNAMICS

fuel. Hence, the gross weight and stall speed

of the airplane can vary considerably through-

out the flight. The effect of only weight on

stall speed can be expressed by a modified form

of the stall speed equation where density ratio,

c r,,,.,, and wing area are held constant.

V _i_z- K

J v.,- K

where

V*,=stall speed corresponding to some

gross weight, WI

V@a= stall speed corresponding to a dif-

ferent gross weight, WP

As an illustration of this equation, assume

that a particular airplane has a stall speed of

100 knots at a gross weight of 10,000 lbs.

The stall speeds of this Sam: airplane at other

gross weights would be:

ll,W 100x 4, ‘&~=lO,

12,ooO 110

14,4al 120

9mJ 95

8,100 90

Figure 1.15 illustrates the effect of weight on

stall speed on a percentage basis and will be

valid for any airplane. Many specific condi-

tions of flight are accomplished at certain fixed

angles of attack and lift coefficients. The

effect of weight on a percentage basis on the

speeds for any specific lift coefficient and angle

of attack is identical. Note that at small

variations of weight, a rule of thumb may

express the effect of weight on stall speed-

“a 2 percent change in weight causes a I per-

cent change in stall speed.”

EFFECT OF MANEUVERING FLIGHT.

Turning flight and maneuvers produce an

effect on stall speed which is similar to the

effect of weight. Inspection of the chart on

figure 1.16 shows the forces acting on an airplane

in a steady turn. Any steady turn requires

that the vertical component of Iift be equal to

NAVWEPS OD-SOT-80

BASIC AERODYNAMICS

EFFECT OF FLAPS

LIFT

COEFFICIENT

5 IO I5 20 25

ANGLE OtATTACK

EFFECT OF WEIGHT ON STALL SPEED

Figure 1.15. Flight at High Lift Conditions

NAVWEPS 00-8OT-80

BASIC AERODYNAMICS

EFFECT OF HIGH LIET DEVICES. The

primary purpose of high lift devices (flaps,

slots, slats, etc.) is to increase the CLn, of the

airplane and reduce the stall speed. The take-

off and landing speeds are consequently re-

duced. The effect of a typical high lift device

is shown by the airplane lift curves of figure

1.15 and is summarized here:

weight of the airplane and the horizontal com-

ponent of lift be equal to the centrifugal force.

Thus, the aircraft in a steady turn develops a

lift greater than weight and experiences in-

creased stall speeds.

Trigonometric ‘relationships allow deter-

mination of the effect of bank angle on stall

speed and load factor. The load factor, B, is

the proportion between lift and weight and is

determined by:

L fizz-- W

1 n=- cos I$

where

n=load factor (or “G”)

cos 6 = cosine of the bank angle, + (phi)

Typical values of load factor determined by

this relationship are:

.+.- 00 130 300 450 600 759

n-l.00 1.035 1.154 1.414 z.ooo 4.ooo

The stall speed in a turn can be determined by:

where

v,+= stall speed at some bank angle +

V,= stall speed for wing level, lift-equal-

weight flight

n=load factor corresponding to the

bank angle

The percent increase in stall speed in a turn is

shown on figure l.i6. Since this chart is predi-

cated on a steady turn and constant CL,, the

figures a!e valid for any airplane. The chart

shows that no appreciable change in load fac-

tor or stall speed occurs at bank angles less than

30“. Above 4S” of bank the increase in load

factor and stall speed is quite rapid. This fact

emphasizes the need for avoiding steep turns at

low airspeeds-a flight condition common to

stall-spin accidents.

c.mip~tion L. (II far C‘,

clun(tla~Up) . . . . . . . . . . . . . 1.5 200

Php down. 2.0 IS.9

The principal effect of the extension of flaps is

to increase the C,, and reduce the angle of

attack for any given lift coefficient. The in-

crease in CL,, afforded by flap deflection re-

duces the stall speed in a certain proportion,

the effect described by the equation:

-

v,=v, z% J Ch,

where

V,,= stall speed with flaps down

v,=stall speed without flaps

C,= maximum lift coefficient of

the clean configuration

C&,= maximum lift coefficient

with flaps down

For example, assume the airplane described by

the lift curves of figure 1.15 has a stall speed of

100 knots at the landing weight in the clean

configuration. If the flaps are lowered the

reduced stall speed is reduced to:

=86.5 knots

NAVWWS 00-8OT-80

BASIC AERODYNAMICS

.#a, GANK~ANGLE, DEGREES

EFFECT OF c LMAX

ONSTALL SPEED

ANT

150 %

IO 20 30 40 50

PERCENTDECREASE

IN STALL SPEED

Figure 7.76. Flight at High Liff Conditions

Revised Jarwary 1965

Thus, wirh rhe higher lift coefficienr available,

less dynamic pressure is required to provide

the necessary lift.

Because of the stated variation of stall speed

with C-, large changes in CL- are necessary

to produce significant changes in stall speed.

This effect is illustrated by the graph in figure

1.16 and certain typical values are shown

below:

Percent increase in CL. .~. 2 10 so loo 300

Percent reduction in stall speed 1 5 18 29 50

The contribution of the high lift devices must

be considerable to cause large reduction in

stall speed. The most elaborate combination

of flaps, slots, slats, and boundary layer con-

trol throughout the span of the wing would

be required to increase C,- by 300 percent.

A common case is that of a typical propeller

driven transport which experiences a 70 per-

cent increase in CzIM1 by full flap deflection.

A typical single engine jet fighter with a thin

swept wing obtains a 20 percent increase in

CL- by full flap deflection. Thin airfoil sec-

tions with sweepback impose distinct limita-

tions on the effectiveness of flaps and the 20

percent increase in CL- by flaps is a typical-

if not high-value for such a configuration.

One factor common to maximum lift condi-

tion is the angle of attack and pressure distri-

bution. The maximum lift coefficient of a

particular wing configuration is obtained at

one angle of attack and one pressure distribu-

tion. Weight, bank angle, load factor, density

altitude, and airspeed have no direct effect on

the stall angle of attack. This fact is sufficient

justification for the use of angle of attack indi-

cators and stall warning devices which sense

pressure distribution on the wing. During

flight maneuvers, landing approach, takeoff,

turns, etc. the airplani will stall if the critical

angle of attack is cxcccdcd. The airspeed ar

which stall occurs will be determined by

weight, load factor, and altitude but the stall

NAVWEPS OO-EOT-RO

BASIC AERODYNAMICS

angle of attack is unaffected. At any parricu-

lar altitude, the indicated stall speed is a func-

tion of weight and load factor. An increase

in altitude will produce a decrease in density

and increase the true airspeed at stall. Also,

an increase in altitude will alter compressibility

and viscosity effects and, generally speaking,

cause the in,&ztcd stall speed to increase.

This parti&lar consideration is usually sig-

nificant only above altitudes of 20,000 ft.

Recovery from stall involves a very simple

concept. Since stall is precipitated by an

excessive angle of attack, the angle of attack

must be dccmmd. This is a fundamental princi-

ple which is common to any airplane.

An airplane may be designed to be “stall-

proof” simply by reducing the effectiveness of

the elevators. If the elevators are not power-

ful enough to hold the airplane to high angles

of attack, the airplane cannot be stalled in any

condition of flight. Such a requirement for a

tactical military airplane would seriously re-

duce performance. High lift coefficients near

the maximum are required for high maneuver-

ability and low landing and takeoff speeds.

Hence, the Naval Aviator must appreciate the

effect of the many variables affecting the stall

speed and regard “attitude flying,” angle of

attack indicators, and stall warning devices

as techniques which allow more precise control

of the airplane at high lift conditions.

HIGH LIFT DEVICES

There are many different types of high lift

devices used to increase the maximum lift co-

efficient for low speed flight. The high lift

devices applied to the trailing edge of a section

consist of a flap which is usually 15 to 25 per-

cent of the chord. The deflection of a flap

produces the effect of a large amount of camber

added well aft on the chord. The principal

types of flaps are shown applied to a basic sec-

tion of airfoil. The effect of a 30’ deflection of

a 25 percent chord flap is shown on the lift

and drag curves of figure 1.17.

NAVWEPS 00-BOT-80

BASIC AERODYNAMICS

BASIC SECTION

PLAIN FLAP SPLIT FLAP

SLOTTED FLAP FOWLER FLAP

EFFECT ON SECTION-LIFT AND DRAG

CHARACTERISTICS OF A 25% CHORD

FLAP DEFLECTED 30°

I SLOTTED

3.0 -

2.5 -

2.0 -

1.5 -

I.O-

.5 -

0 -I-

FOW&ER

SECTION ANGLE OF ATTACK SECTION DRAG COEFFICIENT

o,,, DEGREES cd

Figure 1.17. Flap Configurations

Revised January 1965

The plainjap shown in figure 1.17 is a simple

hinged portion of the trailing edge. The effect

of the camber added well aft on the chord

causes a significant increase in cbr. In addi-

tion, the zero lift angle changes to a more

negative value and the drag increases greatly.

The split flap shown in figure 1.17 consist of

plate deflected from the lower surface of the

section and produces a slightly greater change

in c ImoT than the plain flap. However, a much

larger change in drag results from the great

turbulent wake produced by this type flap.

The greater drag’may not be such a disadvan-

rage when ir is realized that it may be advan-

tageous to accomplish steeper landing ap-

proaches over obstacles or require higher power

from the engine during approach (to minimize

engine acceleration time for waveoR).

The slottedPap is similar to the plain flap but

the gap between the main section and flap

leading edge is given specific contours. High

energy air from the lower surface is ducted to

the flap upper surface. The high energy air

from the slot accelerates the upper surface

boundary layer and delays airflow separation

to some higher lift coefficient. The slotted

flap can cause much greater increases in c,,,

than the plain or split flap and section drags

are much lower.

The Fowkr&zp arrangement is similar to the

slotted flap. The difference is that the de-

flected flap segment is moved aft along a set of

tracks which increases the chord and effects

an increase in wing area. The Fowler flap is

characterized by large increases in c,,, with

minimum changes in drag. ,.

One additional factor requiring consider-

ation in a comparison of flap types is the aero-

dynamic twisting moments caused by the

flap. Positive camber produces a nose down

twisting moment-especially great when large

camber is used well aft on the chord (an

obvious implication is that flaps are not prac-

tical on a flying wing or tailless airplane).

The deflection of a flap causes large nose down

moments which create important twisting

NAVWEPS OO-BOT-BO

BASIC AERODYNAMICS

loads on the structure and pitching moments

that must be controlled with the horizontal

tail. Unfortunately, the flap types producing

the greatest increases in c,,- usually cause the

greatest twisting moments. The Fowler flap

causes the greatest change in twisting moment

while the split flap causes the least. This

factor-along with mechanical complexity of

the installation-may complicate the choice

of a flap configuration.

The effectiveness of flaps on a wing con-

figuration depend on many different factors.

One important factor is the amount of the

wing area affected by the flaps. Since a

certain amount of the span is reserved for

ailerons, the actual wing maximum lift prop-

erties will be less than that of the flapped

two-dimensional section. If the basic wing

has a low thickness, any type of flap will be

less effective than on a wing of greater thick-

ness. Sweepback of the wing can cause an

additional significant reduction in the effec-

tiveness of flaps.

High lift devices applied to the leading edge

of a section consist of slots, slats, and small

amounts of local camber. The fixed slot in a

wing conducts flow of high energy air into the

boundary layer on the upper surface and delays

airflow separation to some higher angle of

attack and lift coefficient. Since the slot

alone effects no change in camber, the higher

maximum lift coefficient will be obtained at a

higher angle of attack, i.e., the slot simply

delays stall to a higher angle of attack. An

automatic slot arrangement consists of a

leading edge segment (slat) which is free to

move on tracks. At low angles of attack the

slat is held flush against the leading edge by

the high positive local pressures. When the

section is at high angles of attack, the high

local suction pressures at the leading edge

create a chordwise force forward to actuate

the slat. The slot formed then allows the

section to continue to a higher angle of attack

and produce a clno. greater than that of the

NAVWEPS CO-BOT-BO

BASIC AERODYNAMICS

AUTOMATIC SLOT

BOUNDARYLAYERCONTROL

BY UPPER SURFACE SUCTION

BOUNDARY LAYER CONTROL

BY FLAP AUGMENTATION

0 2.4

FIXED SLOT\ I

LOW SUCTION

,BASIC SECTION

NO SUCTION

0-l 0~ :

-5 0 5 IO I5 20 0 5 IO I5 20 25

SECTION ANGLE OF ATTACK SECTION ANGLE OF ATTACK

00, DEGREES 00, DEGREES

Figure 7.18. Ekt of Slots and Boundary Layer Control

basic section. The effect of a fixed slot on

the lift characteristics is shown in figure 1.18.

.UO~J ana’ &Z~J can produce significant in-

creases in cl, but the increased angle of

attack for maximum lift can be a disadvantage.

If slots were the only high lift device on the

wing, the high take off and landing angles of

attack may complicate the design of the

landing gear. For this reason slots or slats

are usually used in conjunction with flaps

since the flaps provide reduction in the maxi-

mum lift angle of attack. The use of a slot

has two important advantages: there is only a

negligible change in the pitching moment

due to the slot and no significant change in

section drag at low angles of attack. In fact,

the slotted section will have less drag than

the basic section near the maximum lift angle

for the basic section.

The slot-slat device finds great application

in modern airplane configurations. The tail-

less airplane configuration can utilize only the

high lift devices which have negligible effect

on the pitching moments. The slot and slat

are often used to increase the cl- in high speed

flight when compressibility effects are con-

siderable. The small change in twisting mo-

ment is a favorable feature for any high lift

device to be used at high speed. Leading edge

high lift devices are more effective on the

highiy swept wing than trailing edge flaps

since slats are quite powerful in controlling the

flow pattern. Small amounts of local camber

added to the leading edge as a high lift device

is most effective on wings of very low thick-

ness and sharp leading edges. Most usually

the slope of the leading edge high lift device

is used to control the spanwise lift distribution

on the wing.

‘Boundary larcr control devices are additional

means of increasing the maximum lift coe&-

cient of a section. The thin layer of airflow

adjacent to the surface of an airfoil shows re-

duced local velocities from the effect of skin

friction. When at high angles of attack this

boundary layer on the upper surface tends to

NAVWEPS OO-BOT-RO

BASIC AERODYNAMICS

stagnate and come to a stop. If this happens

the airflow will separate from the surface and

stall occurs. Boundary layer control for high

lift applications features various devices to

maintain high velocity in the boundary layer

to allay separation of the airflow. This con-

trol of the boundary layer kinetic energy can

be accomplished in two ways. One method is

the application of a suction through ports to

draw off low energy boundary layer and replace

it with high velocity air from outside the

boundary layer. The effect of surface suction

boundary layer control on lift characteristics

is typified by figure 1.18. Increasing surface

suction produces greater maximum lift coe5-

cients which occur at higher angles of attack.

The effect is similar to that of a slot because

the slot is essentially a boundary layer control

device ducting high energy air to the upper

surface.

Another method of boundary layer control

is accomplished by injecting a high speed jet

of air into the boundary layer. This method

produces essentially the same results as the

suction method and is the more practical in-

stallation. The suction type BLC requires the

installation of a separate pump while the

“blown” BLC system can utilize the high pres-

sure source of a jet engine compressor. The

typical installation of a high pressure BU

system would be the augmentation of a de-

flected flap. Since any boundary layer control

tends to increase the angle of attack for maxi-

mum lift, it is important to combine the bound-

ary layer control with flaps since the flap de-

flection tends to reduce the angIe of attack for

maximum lift

OPERATION OF HIGH LIFT DEVICES.

The management of the high lift devices on an

airplane is an important factor in flying opera-

tions. The devices which are actuated auto-

matically-such as automatic slats and slots-

are usually of little concern and cause little

complication since relatively small changes in

drag and pitching moments take place. How-

ever, the flaps must be properly managed by

the pilot to take advantage of the capability

S3lWvNAaOtl3v~ mva

08-108-00 Sd3MAQN

of such a device. To illustrate a few principles

of flap management, figure 1.19 presents the

lift and drag curves of a typical airplane in the

clean and flap down configurations.

In order to appreciate some of the factors

involved in flap management, assume that the

airpIane has just taken off and the flaps are

extended. The pilot should not completely

retract the flaps until the airplane has sufficient

speed. If the flaps are retracted prematurely

at insufhcient airspeed, maximum lift coefi-

cient of the clean configuration may not be

able to support the airplane and the airplane

will sink or stall. Of course, this same factor

must be considered for intermediate flap posi-

tions between fully retracted and fully ex-

tended. Assume that the airplane is allowed

to gain speed and reduce the flight lift coefii-

cient to the point of flap retraction indicated

on figure 1.19. As the configuration is altered

from the “cluttered” to the clean configura-

tion, three important changes take place:

(1) The reduction in camber by flap re-

traction changes the wing pitching moment

and-for the majority of airplanes-requires

retrimming to balance the nose up moment

change. Some airplanes feature an automat-

ic retrimming which is programmed with

flap deflection.

(2) The retraction of flaps shown on

figure 1.19 causes a reduction of drag coeffi-

cient at that lift coefficient. This drag

reduction improves the acceleration of the

airplane.

(3) The retraction of flaps requires an

increase in angle of attack to maintain the

same lift coefficient. Thus, if airplane accel-

eration is low through the flap retraction

speed range, angle of attack must be in-

creased to prevent the airplane from sinking.

This situation is typical after takeoff when

gross weight, density altitude, and tempera-

ture are high. However, some aircraft have

such high acceleration through the flap re-

traction speed that the rapid gain in air-

speed requtres much less noticeable attitude

change.

NAVWEPS OO-EOT-SO

BASIC AERODYNAMICS

When the flaps are lowered for landing essen-

tially the same items must be considered. Ex-

tending the flaps will cause these. changes to

take place:

(1) Lowering the flaps requires retrim-

ming to balance the nose down moment

change.

(2) The increase in drag requires a higher

power setting to maintain airspeed and

altitude.

(3) The angle of attack required to pro-

duce the same lift coefficient is less, e.g.,

flap extension tends to cause the airplane to

“balloon.”

An additional factor which must be consid-

ered when rapidly accelerating after takeoff,

or when lowering the flaps for landing, is the

limit airspeed for flap extension. Excessive

airspeeds in the flap down configuration may

cause structural damage.

In many aircraft the effect of intermediate

flap deflection is of primary importance in

certain critical operating conditions. Small

initial deflections of the flap cause noticeable

changes in C’s,, without large changes in drag

coefficient. This feature is especially true of

the airplane equipped with slotted or Fowler

flaps (refer to fig. 1.17). Large flap deflections

past 30’ to 33’ do not create the same rate of

change of Cs- but do cause greater changes in

CD. A fact true of most airplanes is that the

first 50 percent of flap deflection causes mwc

than half of the total change in Cr.- and the

last 50 percent of flap deflection causes mo~c

than half of the total change in Cs.

The effect of power on the stall speed of an

airplane is determined by many factors. The

most important factors affecting this relation-

ship are powerplant type (prop or jet), thrust-

to-weight ratio, and inclination of the thrust

vector at maximum lift. The effect of the

propeller is illustrated in figure 1.20. The

slisstream velocity behind the propeller is

different from the free stream velocity depend-

ing on the thrust developed. Thus, when the

propeller driven airplane is at low air+ceds

NAVWEPS OO-BOT-80

BASIC AERODYNAMICS

n INDUCED FLOW

r SLIPSTREAM

FROM PROPELLER

n c;

figure 1.20. Power Effects

and high power, the dynamic pressure in the

shaded area can be much greater than the free

stream and this causes considerably greater

lift than at zero thrust. At high power con-

ditions the induced flow also causes an effect

similar to boundary layer control and increases

the maximum lift angle of attack. The typical

four-engine propeller driven airplane may have

60 to 80 percent of the wing area affected by

the induced flow and power effects on stall

speeds may be considerable. Also, the lift of

the airplane at a given angle of attack and air-

speed will be greatly affected. Suppose the

airplane shown is in the process of landing

flare from a power-on approach. If there is

a sharp, sudden reduction of power, the air-

plane may drop suddenly because of the reduced

lift.

The typical jet aircraft does not experience

the induced flow velocities encountered in

propeller driven airplanes, thus the only sig-

nificant factor is the vertical component of

thrust. Since this vertical component con-

tributes to supporting the airplane, less aero-

dynamic lift is required to hold the airplane

in flight. If the thrust is small and the thrust

inclination is slight at maximum lift angle,

only negligible changes in stall speed will re-

sult. On the other hand, if the thrust is very

great and is given a large inclination at maxi-

mum lift angle, the effect on stall speed can

be very large. One important relationship

remains-since there is very little induced flow

from the jet, the angle of attack at stall is

essentially the same power-on or power-off.

DEVELOPMENT OF AERODYNAMIC

PITCHING MOMENTS

The distribution of pressure over a surface

is the ,source of the aerodynamic moments as

well as the aerodynamic forces. A typical

example of this fact is the pressure distribution

acting on the cambered airfoil of figure 1.21.

The upper surface has pressures distributed

which produce the upper surface lift; the lower

surface has pressures distributed which pro-

duce the lower surface lift. Of course, the

NAVWEPS 00-801~0

BASIC AERODYNAMICS

net lift produced by the airfoil is difference

between the lifts on the upper and lower sur-

faces. The point along the chord where the

distributed lift is effectively concentrated is

termed the “center of pressure, c.p.“ The

center of pressure is essentially the “center of

gravity” of the distributed lift pressure and

the location of the c.p. is a function of camber

and section lift coe&cient

Another aerodynamic reference point is the

“aerodynamic center, d.e.” The aerodynamic

center is defmed as the point along the chord

where all changes in lift effectively take place.

To visualize the existence of such a point,

notice the change in pressure distribution with

angle of attack for the symmetrical airfoil

of figure 1.21. When at zero lift, the upper

and lower surface lifts are equal and located

at the same point. With an increase in angle

of attack, the upper surface lift increases while

the lower surface lift decreases. The change

,of lift has taken place with no change in the

center of pressure-a characteristic of sym-

metrical airfoils.

Next, consider the cambered airfoil of

figure 1.21 at zero lift. To produce zero lift,

the upper and lower surface lifts must be equal.

One difference noted from the symmetrical air-

foil is that the upper and lower surface lifts are

not opposite one another. While no net lift

exists on the airfoil, the couple produced by

the upper and lower surface lifts creates a nose

down moment. As the angle of attack is in-

creased, the upper surface lift increases while

the lower surface lift decreases. While a

change in lift has taken place, no change in

moment takes place about the point where

the lift change occurs. Since the moment

about the aerodynamic center is the product

of a force (lift at the c.P.) and a lever arm

(distance from c.9. to a.~.), an increase in lift

moves the center of pressure toward the aero-

dynamic center.

It should be noted that the symmetrical air-

foil at zero lift has no pitching moment about

the aerodynamic center because the upper and

NAVWEPS DD-BOT-80

BASIC AERODYNAMICS

CAMBERED AIRFOIL

UPPER DEVELOPING POSITIVE

LIFT

NET

LIFT

LOWER SURFACE LIFT

SYMMETRICAL AIRFOIL

AT ZERO LIFT CAMBERED AIRFOIL

AT ZERO LIFT

UPPER SURFACE

LOWER SURFACE

LIFT

SYMMETRICAL AIRFOIL

AT POSITIVE LIFT

UPPER SURFACE LIFT

LOWER SURFACE LIFT

CHANGE IN LIFT

+

O.C.

A- UPPER SURFACE

FLOWER SURFACE LIFT

CAMBERED AIRFOIL

AT POSITIVE LIFT

A- UPPER SURFACE LIFT

LOWER SURFACE LIFT

CHANGE IN LIFT

+

PITCHING MOMENT

0.e.

Figure 1.27. Development of Pitching Moments

lower surface lifts act along the same vertical

line. An increase in.lift on the symmetrical

airfoil produces no change in this situation and

the center of pressure remains fixed at the aero-

dynamic center.

The location of the aerodynamic center of an

airfoil is not affected by camber, thickness, and

angle of attack. In fact, two-dimensional in-

compressible airfoil theory will predict the

aerodynamic center at the 25 percent chord point

for any airfoil regardless of camber, thickness,

and angle of attack. Actual airfoils, which

are subject to real fluid flow, may not have the

lift due to angle of .attack concentrated at the

exact 25 percent chord point. However, the

actual location of the aerodynamic center for

various sections is rarely forward of 23 percent

or aft of 27 percent chord point.

The moment about the aerodynamic center

has its source in the relative pressure distribu-

tion and requires application of the coefficient

form of expression for proper evaluation. The

moment about the aerodynamic center is ex-

pressed by the following equation :

where

A&, = moment about the aerodynamic center,

a.c., ft.-lbs.

CMa.c,=coefbcient of moment about the a.c.

q= dynamic pressure, psf

S=wing area, sq ft.

c=chord, ft.

The moment coefficient used in this equation is

the dimensionless ratio of the moment pressure

to dynamic pressure moment and is a function

c ML3.C.

%.c. = p-

of. the shape of the airfoil mean camber line.

Figure 1.22 shows the moment coefficient,

NAVWEPS O&601-80

BASIC AERODYNAMICS

C%C. versus lift coefficient for several repre-.

sentative sections. The sign convention ap-

plied to moment coefficients is that the nose-up

moment is positive.

The NACA Ooog airfoil is a symmettical sec-

tion of 9 percent maximum thickness. Since

the mean line of this airfoil has no camber,

the coefhcient of moment about the aerody-

namic center is zero, i.e., the c.p. is at the ac.

The departure from zero cno.+ occurs only as the

airfoil approaches maximum lift and the stall

produces a moment change in the negative

(nose-down) direction. The NACA 4412 and

63,-412 sections have noticeable positive cam-

ber which cause relatively large moments about

the aerodynamic center. Notice that for each

sectionshowninfrgure 1.22, the c,,,.... isconstant

for all lift coefficients less than cl,-.

The NACA 23012 airfoil is a very efficient

conventional section which has been used on

many airplanes. One of the features of the

~section is a relatively high c& with only a

small c,,,,,,; The pitching moment coefficients 1

for this section are shown on figure 1.22 along

with the effect of various type flaps added to

the basic section. Large amounts of camber

applied well aft on the chord cause large nega-

tive moment coefficients. This fact is illus-

trated by the large negative moment coefli-

cients produced by the 30” deflection of a 25

percent chord flap.

me kc. is a quantity determined by the

shape of the mean-camber line. Symmetrical

airfoils have zero c,,,,. and the c.p. remains at

the a.~. in unstalled flight. The airfoil with

positive camber will have a negative c,,,~,~,

which means the c.p. is behind the a.~. Since

the c5.c. is constant in unstalled flight a certain

relationship between lift coefficient and center

of pressure can be evolved. An example of

this relationship is shown in figure 1.22 for the

NACA 63i-412 airfoil by a plot of c.p. versus

c,. Note that at low lift coefficients the center

of pressure is well aft-even past the trailing

edge-and an increase in C~ moves the c.p, for-

ward toward the a.~. The c.9. approaches the

Revised Jmuoy 1965

NAVWEPS 00-801-80

BASIC AERODYNAMICS

5 1 I 25k I I g -0.2

NACA 23012 WITH SPLIT FLAP AT 3D”

I \

z I ” I I 1 1 I

I 25%

-0.3 - NACA 23012 WITH PLAIN FLAP AT 30’

1 I --T--rT~, I I I

. \

NACA 23012 WITH SLOTTED FLAP &T 30”

-0.4

Revised January 1965

CP POSITION PERCENT CHORD

AFT OF LEADING EDGE

Figure 1.22. Section Moment Characteristics

CHANGE IN LIFT

DUE TO UPGUST

NAVWEPS D&801-80

BASIC AERODYNAMICS

CHANGE IN LIFT

DUE TO UPGUST

C:G. 1

O.C.

t (UNSTABLE)

C:G.

t LIFT

1 WEIGHT

Figure 1.23. Application to Stability

AC. as a limit but as stall occurs, the drop in

suction near the leading’ edge cause the c.p. to

move aft.

Of course, if the airfoil has negative camber,

or a strongly reflexed trailing edge, the moment

about the aerodynamic center will be positive.

In this case, the location of the aerodynamic

center will be unchanged and will remain at

the quarter-chord position.

The aerodynamic center is the point on the

chord where the coefficients of moment are

constant-the point where all changes in lift

take place. The aerodynamic center is an cx-

tremely important aerodynamic reference point

and the most direct application is to the longi-

tudinal stability of an airplane. To simplify

the problem assume that the airplane is a

tailless or flying wing type. In order for this

type airplane to have longitudinal stability,

the center of gravity must be ahead of the

aerodynamic center. This very necessary fea-

ture can be visualized from the illustrations of

figure 1.23.

If the two symmetrical airfoils are subject

to an upgust, an increase in lift will take place

at the 4.c. If the c.g. is ahead of the ax., the

change in lift creates a nose down moment

about the c.g. which tends to return the air-

foil to the. equilibrium angle of attack. This

stable, “weathercocking” tendency to return

to equilibrium is a very necessary feature in

any airplane. If the c.g. is aft of the a.~., the

change in lift due to the upgust takes place at

the AC. and creates a nose up moment about

the c.g. This nose up moment tends to displace

the airplane farther from the equilibrium and

is unstable-the airplane is similar to a ball

balanced on a peak. Hence, to have a stable

airplane, the c.g. must be located ahead of the

airplane rl.c.

NAVWEPS OO-SOT-SO

BASIC AERODYNAMICS

An additional requirement of stability is

that the airplane must stabilize and be trimmed

for flight at positive lift. When the c.g. is

located ahead of d.c., the weight acting at the

c.g. is supported by the lift developed by the

section. Negative camber is required to pro-

duce the positive moment about the aerody-

namic center which brings about equilibrium

ot balance at positive lift.

Supersonic flow produces important changes

in the aerodynamic characteristics of sections.

The aerodynamic center of airfoils in subsonic

flow is located at the 25 percent chord point.

As the airfoil is subject to supersonic flow, the

aerodynamic center changes to the 50 percent

chord point. Thus, the airplane in transonic

flight can experience large changes in longitu-

dinal stability because of the large changes in

the position of the aerodynamic center.

FRICTION EFFXTS

&--v~se the +ir hAas .~~.v-~c~~v air -7ill --- , .“I”., L, , I. 11 -11

counter resistance to flow over a surface. The

viscous nature of airflow reduces the local

velocities on a surface and accounts for the

drag of skin friction. The retardation of air

particles due to viscosity is greatest immedi-

ately adjacent to the surface. At the very sur-

face of an object, the air particles are slowed to

a relative velocity of near zero. Above this

area other particles experience successively

smaller retardation until finally, at some dis-

tance above surface, the local velocity reaches

the full value of the airstream above the sur-

face. This layer of air over the surface which

shows local retardation of airflow from vis-

cosity is termed the “boundary layer.” The

characteristics of this boundary layer are illus-

trated in figure 1.24 with the flow of air over

a smooth flat plate.

The beginning flow on a smooth surface gives

evidence of a very thin boundary layer with

the flow occurring in smooth laminations,

The boundary layer flow near the leading edge

is similar to layers or laminations of air slid-

ing smoothly over one another and the obvi-

ous term for this type of flow is the “laminar”

boundary layer. This smooth laminar flow

exists without the air particles moving from

a given elevation.

As the flow continues back from the leading

edge, friction forces in the boundary layer

continue to dissipate energy of the airstream

and the laminar boundary layer increases in

thickness with distance from the leading edge.

After some distance back from the leading

edge, the laminar boundary layer begins an

oscillatory disturbance which is unstable. A

waviness occurs in the laminar boundary layer

which ultimately grows larger and more

severe and destroys the smooth laminar flow.

Thus, a transition takes place in which the

laminar boundary layer decays into a “turbu-

lent” boundary layer. The same sort of

transition can be noticed inthe smoke from a

cigarette in still air. At, first, the smoke

ribbon is smooth and laminar, then develops

a definite waviness, and decays into a random

turbulent smoke pattern.

As soon as the transition to. the turbulent

boundary layer takes place, the boundary

layer thickens and grows at a more rapid rate.

(The small scale, turbulent flow within the

boundary layer should not be confused with

the large scale turbulence associated with

airflow separation.) The flow in the turbu-

lent boundary layer allows the air particles to

travel from one layer to another producing an

energy exchange. However, some small lami-

nar flow continues to exist in the very lower

levels of the turbulent boundary layer and is

referred to as the “laminar sub-layer.” The

turbulence which exists in the turbulent bound-

ary layer allows determination of the point of

transition by several means. Since the turbu-

lent boundary layer transfers heat more easily

than the laminar layer, frost, water, and oil

films will be removed more rapidly from the

area aft of the transition point. Also, a-small

probe may be attached to a stethoscope and

positioned at various points along a surface.

When the probe is in the laminar area, a low

“hiss” will be heard; when the probe is in