Chapter 1 — Part 5

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HIGH SPEED AERODYNAMICS

CONE IN SUPERSONIC FLOW

CONICAL WAVE

REF:LECTED OBLIOUE WAVES

MODEL IN WIND

TUNNEL WITH wows

REFL\Cmg FROM

Figure 3.5. Three Dimensional and Reflected Shock Waves

209 Revised Januaty I%5

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HIGH SPEED AERODYNAMICS

OBLlOuE SHOCK

WAVES

NORMAL

/

,SHOCK WAVE

Figure 3.6. Normal ShockWave Formation

wave also occurs when a wedge or cone angle

exceeds some critical value. Whenever the

shock wave forms perpendicular to the up-

stream flow, the shock wave is termed a

“normal” shock wave and the flow immediately

behind the wave is subsonic. Any relatively

blunt object in a supersonic airstream will form

a normal shock wave immediately ahead of the

leading edge slowing the airstream to subsonic

SO the airstream may feel the presence of the

blunt nose and flow around it. Once past the

blunt nose the airstream may remain subsonic

or accelerate back to supersonic depending on

the shape of the nose and the Mach number of

the free stream.

In addition to the formation of normal

shock waves described above, this same type

of wave may be formed in an entirely different

manner when there is no object in the super-

sonic airstream. It is particular that whenever

a supersonic airscream is slowed to subsonic

without a change in direction a normal shock

wave will form as a boundary between the

supersonic and subsonic regions. This is an

important fact since aircraft usually encounter

some “compressibility effects” before the flight

speed is sonic. Figure 3.6 illustrates the man-

ner in which an airfoil at high subsonic speeds

has local flow velocities which are supersonic.

As the local supersonic flow moves aft, a

normal shock wave forms slowing the flow

to subsonic. The transition of flow from

subsonic to supersonic is smooth and is not

accompanied by shock waves if the transition

is made gradually with a smooth surface. The

transition of flow from supersonic to subsonic

without direction change always forms a

normal shock wave.

A supersonic airstream passing through a

normal shock wave will experience these

changes:

(1) The airstream is slowed to subsonic;

the local Mach number behind the wave is

approximately equal to the reciprocal of the

Mach number ahead of the wave-e.g., if

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HIGH SPEED AERODYNAMICS

Mach number ahead of the wave is 1.25,

the Mach number of the flow behind the

wave is approximately 0.80.

(2) The airflow direction immediately

behind the wave is unchanged.

(3) The static pressure of the airstream

behind the wave is increased greatly.

(4) The density of the airstream behind

the wave is increased greatly.

(5) The energy of the airstream (indi-

cated by total pressure-dynamic plus static)

is greatly reduced. The normal shock wave

is very wasteful of energy.

EXPANSION WAVE. If a supersonic air-

stream were turned away from the preceding

flow an expansion wave would form. The

flow “around a corner” shown in figure 3.7

will not cause sharp, sudden changes in the

airflow except at the corner itself and thus is

not actually a “shock” wave. A supersonic

airstream passing through an expansion wave

will experience these changes:

(1) The airstream is accelerated; the ve-

locity and Mach number behind the wave

are greater.

(2) The flow direction is changed to

flow along the surface-provided separa-

tion does not occur.

(3) The static pressure of the airstream

behind the wave is decreased.

(4) The density of -the airstream behind

the wave is decreased.

(5) Since the flow changes in a rather

gradual manner there is no “shock” and

no loss of energy in the airstream. The

expansion wave does not dissipate air-

stream energy.

The expansion wave in three dimensions is

a slightly different case and the principal

difference is the tendency for the static pres-

sure to continue to increase past the wave.

The following table is provided to summa-

rize the characteristics of the three principal

wave forms encountered with supersonic flow.

21’1

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EXPANSION WAVE,

SUPERSONIC FLOW

AROUND A CORNER

SERIES OF EXPANSION WAVES7

SUPERSONIC FLOW

AROUND A SMOOTti CORNER

Figure 3.7. Expansion Wove Formation

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TABLE 3-P. Suprnonk Wave Charactwiltks

Type of wave formation

Flow direction change.

Efkct cm velociry and Mach

number.

Effect on static pressure and

density.

_-

Oblique shock wave

“Flow into a corner,”

turned into preceding

flow.

Decreased but still supcr-

sonic.

Increase. :.

DKICaSe

_-

__

__

__

-

Normal shock wave.

No change.

Great increase,

Great decrease

-

__

-.

-.

-.

-

Expansion wwc.

‘/ //

<

- ,/$y

“Flow around a corner,”

turned away from pre-

ceding flow.

Increased to higher super-

sonic.

DeCrWSe.

No change (no shock).

SECTIONS IN SUPERSONIC FLOW

In order to appreciate the effect of these

various wave forms on the aerodynamic char-

acteristics in supersonic flow, inspect figure 3.8.

Parts (a) and (b) show the wave pattern and

resulting pressure distribution for a thin flat

plate at a positive angle of attack. The air-

stream moving over the upper surface passes

through an expansion wave at the leading edge

and then an oblique shock wave at the trailing

edge. Thus, a uniform suction pressure exists

over the upper surface. The airstream moving

underneath the flat plate passes through an

oblique shock wave at the leading edge then an

expansion wave at the trailing edge. This pro-

duces a uniform positive pressure on the under-

side of the section. This distribution of pres-

sure on the surface will produce a net lift and

incur a subsequent drag due co lift from the in-

clination of the resultant lift from a perpen-

dicular co the free stream.

Parts (c) and (d) of figure 3.8 show the

wave pattern and resulting pressure distribu-

tion for a double wedge airfoil at zero lift.

The airstream moving over the surface passes

through an oblique shock, an expansion wave,

and another oblique shock. The resulting

pressure distribution on the surfaces produces

no net lift, but the increased pressure on the

forward half of the chord along with the de-

creased pressure on the aft half of the chord

produces a “wave” drag. This wave drag is

caused by the components of pressure forces

which are parallel to the free scream direction.

The wave drag is in addition to the drag due

to friction, separatien, lift, etc., and can be

a very considerable part of the total drag at

high supersonic speeds.

Parts (e) and (f) of figure 3.8 illustrate the

wave pattern and resulting pressure distribu-

tion for the double wedge airfoil at a small

positive angle of attack. The net pressure

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HIGH SPEED. AERODYNAMlCS

0 a FLAT PLATE WAVE PATTERN

0 c DOUBLE WEDGE WAVE PATTERN

AT ZERO LIFT

ANGLE

ATTAC

O e DOUBLE WEDGE WAVE PATTERN

AT POSITIVE ANGLE OF ATTACK

NOTE: CENTER OF PRESSURE

IS AT 50% CHORD

v b FLAT PLATE PRESSURE DISTRIBUTION

NO NET LIFT BUT

HAVE “WAVE DRAG”

0 d REDOUBLE WEDGE PRESSURE

DISTRIBUTION AT ZERO LIFT

DRAG DUE TO LIFT

‘CLEFT

L-WAVE DRAG

0 f DOUBLEWEDGEPRESSURE

DISTRIBUTION AT POSITIVE LIFT

0 9 CIRCULAR ARC TYPE AIRFOIL 0 b CONVENTIONAL BLUNT NOSE

AIRFOIL

Figure 3.8. Typical Supersonic Flow Patterns and Distribution of Pressure

distribution produces an inclined lift with

drag due to lift which is in addition to the

wave drag at zero lift. Part (g) of figure 3.8

shows the wave pattern for a circular arc air-

foil. After the airflow traverses the oblique

shock wave at the leading edge, the airflow

undergoes a gradual but continual expansion

until the trailing edge shock wave is en-

countered. Part (h) of figure 3.8 illustrates

the wave pattern on a conventional blunt nose

airfoil in supersonic flow. When the nose is

blunt the wave must detach and become a

normal shock wave immediately ahead of the

leading edge. Of course, this wave form

produces an area of subsonic airflow at the

leading edge with very high pressure and

density behind the detached wave.

The drawings of figure 3.8 illustrate the

typical patterns of supersonic flow and point

out these facts concerning aerodynamic surfaces

in two dimensional supersonic flow:

(1) All changes in velocity, pressure,

density and flow direction will take place

quite suddenly through the various. wave

forms. The shape of the object and the

required flow ,direction change dictate the

type and strength of the wave formed.

(2) As always, lift results from the distri-

bution of pressure on a surface and is the net

force perpendicular to the free stream direc-

tion. Any component of the lift in a direc-

tion parallel to the windstream will be

drag due to lift.

(3) In supersonic flight, the zero lift drag

of an airfoil of some finite thickness will

include a “wave drag.” The thickness of

the airfoil will have an extremely powerful

effect on this wave drag since the wave drag

varies as the square of the thickness ratio-

if the thickness is reduced 50 percent, the

wave drag is reduced 73 percent. The lead-

ing edges of supersonic shapes must be sharp

or the wave formed at the leading edge will

be a strong detached shock wave.

(4) Once the flow on the airfoil is super-

sonic, the aerodynamic center of the surface

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HIGH SPEED AERODYNAMICS

will be located approximately at the SO per-

cent chord position. As this contrasts with

the subsonic location for the aerodynamic

center of the 23 percent chord position, sig-

nificant changes in aerodynamic trim and

stability may be encountered in transonic

flight.

CONFIGURATION EFFECTS

TRANSONIC AND SUPERSONIC PLIGHT

Any object in subsonic flight which has some

finite thickness or is producing lift will have

local velocities on the surface which are

greater than the free stream velocity. Hence,

compressibility effects can be expected to

occur at flight speeds less than the speed of

sound. The transonic regime of flight pro-

vides the opportunity for mixed subsonic and

supersonic flow and. accounts for the first 1

significant effects of compressibility.

Consider a conventional airfoil shape as

shown in figure 3.9. If this airfoil is at a

flight Mach number of 0.50 and a slight posi-

tive angle of attack, the maximum local

velocity on the surface will be greater than

the flight speed but most likely less than

sonic speed. Assume that an increase in

flight Mach number to 0.72 would produce

lfrst cvidmc of local son@ flow. This condition

of flight would be the highest flight speed

possible without supersonic flow and would

be termed the “critical Mach number.” Thus,

critical Mach number is the bouodary between

subsonic and transonic flight and is an im-

portant ~point of reference for all compressi- 1

bility effects encountered in transonic flight.

By delinition, critical Mach number is the

“free stream Mach number which produces

6rst evidence of local sonic flow.” Therefore,

shock waves, buffet, airflow separation, etc.,

take place above critical Mach number.

As critical Mach number is exceeded an

area of ~uprrronic airflow is created and a normal

Revised January 1965

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HIGH SPEED AERODYNAMICS

MAXIMUM LOCALVELOCITY

M=.50 IS LESS THAN SONIC

MAXIMUM LOCAL VELOCITY

EOUALTO SONIC

M =.72

(CRITICAL MACH NUMB

NORMAL SHOCK WAVE

POSSIBLE SEPARATION

su NORMAL SHOCK

\\I NORMAL SHOCK

NORMAL SHOCK

Figure 3.9. Transonic Flow Patterns (sheet 1 of 2)

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WING IN TRANSONIC FLOW

I M = .700 a= +2O CL= ,370

NO SHOCK WAVES

I M-.800 a=+2O CL=.442

SHOCK FORMATION IS APPARENT AT

25 TO 30 % CHORD POSITION

I M=.075 a=+20 CL=.450

SHOCK INDUCED SEPARATION ALONG

AFT PORTION OF WING PLAPJFORM

Figure 3.9. Transonic Flow Patterns (sheet 2 of 2)

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shock wave forms as the boundary between

the supersonic flow and the subsonic flow on

the aft portion of the airfoil surface. The

acceleration of the airflow from subsonic to

supersonic is smooth and unaccompanied by

shock waves if the surface is smooth and the

transition gradual. However, the transition

of airflow from supersonic to subsonic is

always accompanied by a shock wave and,

when there is no change in direction of the

airflow, the wave form is a normal shock

wave.

Recall that one of the principal effects of

th,e normal shock wave is to produce a large

increase in the static pressure of the airstream

behind the wave. If the shock wave is

strong, the boundary layer may not have

sufficient kinetic energy to withstand the

large, adverse pressure gradient and separation

will occur. At speeds only slightly beyond

critical Mach number the shock wave formed

is not strong enough to cause spearation or

any noticeable change in the aerodynamic

force coefficients. However, an increase in

speed above critical Mach number sufhcient

to form a strong shock wave can cause sepa-

ration of the boundary layer and produce

sudden changes in the aerodynamic force

coefficients. Such a flow condition is shown

in figure 3.9 by the flow pattern for M=O.n.

Notice that a further increase in Mach number

to 0.82 can enlarge the supersonic area on the

upper surface and form an additional area of

supersonic flow and normal shock wave on the

lower surface.

As the flight speed approaches the speed of

sound the areas of supersonic flow enlarge and

the shock waves move nearer the trailing

edge. The boundary layer may remain sepa-

rated or may reattach depending much upon

the airfoil shape and angle of attack. When

the flight speed exceeds the speed of sound

the “bow” wave forms at the leading edge and

this typical flow pattern is illustrated in

figure 3.9 by the drawing for M= 1.05. If the

speed is increased to some higher supersonic

value all oblique portions of the waves incline

more greatly and the detached normal shock

portion of the bow wave moves closer to the

leading edge.

Of course, all components of the aircraft

are affected by compressibility in a manner

somewhat similar to that of basic airfoil.

The tail, fuselage, nacelles, canopy, etc. and

the efkct of the interference between the

various surfaces of the aircraft must be

considered.

FORCE DIVERGENCE. The airflow sepa-

ration induced by shock wave formation can

create significant variations in the aerody-

namic force coefficients. When the free stream

speed is greater than critical Mach number some

typical effects on an airfoil section are as

follows :

(1) An increase in the section drag coeffi-

cient for a given section lift coe5cient.

(2) A decrease in section lift coefficient

for a given section angle of attack.

(3) A change in section pitching moment

coe5cient.

A reference point is usually taken by a plot

of drag coe5cient versus Mach number for

a constant lift coefficient. Such a graph is

shown in figure 3.10. The Mach number

which produces a sharp change in the drag

coe5cient is termed the “force divergence”

Mach number and, for most airfoils, usually

exceeds the critical Mach number at least 5

to 10 percent. This condition is also referred

to as the “drag divergence” or “drag rise.”

PHENOMENA OF TRANSONIC FLIGHT.

Associated with the “drag rise” are buffet,

trim and stability changes, and a decrease

in control surface effectiveness. Conventional

aileron, rudder, and elevator surfaces sub

jetted to this high frequency buffet may

“buzz,” and changes in hinge moments may

produce undesirable control forces. Of course,

if the buffet is quite severe and prolonged,

structural damage may occur if this operation

is in violation of operating limitations. When

airflow separation occurs on the wing due to

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HIGH SPEED AERODYNAMICS

DRAG

COEFFICIENT

FORCE DIVERGENCE

MACH NUMBER

CRITICAL

MACH NUMBER.

I I c

0.5 1.0

ht,MACH NUMBER

Figure 3ilO. Compressibility Drag Rise

shock wave formation, there will be a loss of

lift and subsequent loss of downwash aft of

the affected area. If the wings shock unevenly

due to physical shape differences or sideslip,

a rolling moment will be created in the

direction of the initial loss of lift and con-

tribute to control difficulty (“wing drop”).

If the shock induced separation occurs sym-

metrically near the wing root, a decrease in

downwash behind this area is a corollary of

the loss of lift. A decrease in downwash on

the horizontal tail will create a diving moment

and the aircraft will “tuck under.” If these

conditions occur on a swept wing. planform,

the wing center of pressure shift contributes

to the trim change-root shock first moves

the wing center of pressure aft and adds to the

diving moment; shock formation at the wing

tips first moves the center of pressure forward

and the resulting climbing moment and tail

downwash change can contribute to “pitch

up.”

Since most of the dificulties of transonic

flight are associated with shock wave induced

flow separation, any means of delaying or

alleviating the shock induced separation will

improve the aerodynamic characteristics. An

aircraft conhguration may utilize thin surfaces

of low aspect ratio with sweepback to delay

and reduce the magnitude of transonic force

divergence. In addition, various methods of

boundary layer control, high lift devices,

vortex generators, etc., may be applied to

improve transonic characteristics. For exam-

ple, the application of vortex generators to a

surface can produce higher local surface veloci-

ties and increase the kinetic energy of the

boundary layer. Thus, a more severe pressure

gradient (stronger shock wave) will be neces-

sary to produce airflow separation.

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HIGH SPEEO AERODYNAMICS

Once the configuration of a transonic air-

craft is fixed, the pilot must respect the effect

of angle of attack and altitude. The local flow

1 velocities on any upper surface increase with an

increase in angle of attack. Hence, local sonic

flow and subsequent shock wave formation

can occur at lower free stream Mach numbers.

A pilot must appreciate this reduction of force

divergence Mach number with lift coefficient

since maneuvers at high speed may produce

compressibility effects which may not be en-

countered in unaccelerated flight. The effect

of altitude is important since the magnitude

of any force or moment change due to com-

pressibility will depend upon the dynamic

pressure of the airstream. Compressibility

effects encountered at high altitude and low

dynamic pressure may be of little consequence

in the operation of a transonic aircraft. How-

ever, the same compressibility effects en-

countered at low altitudes and high dynamic

pressures will create greater trim changes,

heavier buffet, etc., and perhaps transonic

flight restrictions which are of principal inter-

est only to low altitude.

can be quite weak, the pressure waves can be

of sufficient magnitude to create an audible

disturbance. Thus, “sonic booms” will be a

simple consequence of supersonic flight.

The aircraft powerplant: for supersonic flight

must be of relatively high thrust output.

Also, in many cases it may be necessary to

provide the air breathing powerplant with

special inlet configurations which will slow

the airflow to subsonic prior to reaching the

compressor face or combustion chamber. Aero-

dynamic heating of supersonic flight can pro-

vide critical inlet temperatures for the gas

turbine engine as well as critical structural

temperatures.

The density variations in airflow may be

shown by certain optical techniques. Schlieren

photographs and shadowgraphs can define the

various wave patterns and their effect on the

airflow. The Schlieren photographs presented

in figure 3.11 define the flow conditions on an

aircraft in supersonic flight. I

TRANSONIC AND SUPERSONIC CONFIGU-

RATIONS

PHENOMENA OF SUPERSONIC FLIGHT.

While many of the particular effects of super-

sonic flight will be presented in the detail of

later discussion, many general effects may be

anticipated. The airplane configuration must

have aerodynamic shapes which will have low

drag in compressible flow. Generally, this will

require airfoil sections of low thickness ratio

and sharp leading edges and body shapes of

high fineness ratio to minimize the supersonic

wave drag. Because of the aft movement of the

aerodynamic center with supersonic flow, the

increase in static longitudinal stability will

demand effective, powerful control surfaces to

achieve adequate controllability for super-

sonic maneuvering.

Aircraft configurations developed for high

speed flight will have significant differences in

shape and planform when compared with air-

craft designed for low speed flight. One of

the outstanding differences will be in the

selection of airfoil profiles for transonic or

supersonic flight.

As a corollary of supersonic flight the shock

wave formation on the airplane may create

special problems outside the immediate vicinity

of the airplane surfaces. While the shock

waves a great distance away from the airplane

no

AIRFOIL SECTIONS. It should be ob-

vious that airfoils for high speed subsonic

flight should have high critical Mach num-

bers since critical Mach number defines the

lower limit for shock wave formation and

subsequent force divergence. An additional

complication to airfoil selection in this

speed range is that the airfoil should have

a high maximum lift coefficient and sufficient

thickness to allow application of high lift

devices. Otherwise an excessive wing area

would be required to provide maneuverability

and reasonable takeoff and landing speeds.

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FE!4 MODEL AT VARIOUS

MACH NUMBERS

a-O0 pee

M* 1.2 W 1.6

Figure 3.11. Schliemn Photographs of Supersonic Flight (sheet 1 of 2)

Figure 3.7 1. Schlieren Photographs of Supersonic Flight (sheet 2 of 2)

However, if high speed flight is the primary

consideration, the airfoil must be chosen to

have. the highest practical critical Mach

number.

Critical Mach number has been defined as

the flight Mach number which produces first

evidence of local sonic flow. Thus, the air-

foil shape and lift coe&ient-which determine

the pressure and velocity distribution-will

have a profound effect on critical Mach number.

Conventional, low speed airfoil shapes have

relatively poor compressibility characteristics

because of the high local velocities near the

leading edge. These high local velocities are

inevitable if both the maximum thickness and

camber are well forward on the chord. An

improvement of the compressibility character-

istics can be obtained by moving the points of

maximum camber and thickness aft on the

chord. This would distribute the pressure and

velocity more evenly along the chord and

produce a lower peak velocity for the same

lift coefficient. Fortunately, the airfoil shape

to provide extensive lamiaar flow and low

profile drag in low speed, subsonic flight will

provide a pressure distribution which is favor-

able for high speed flight. Figure 3.12

illustrates the pressure distributions and

variation of critical Mach number with lift

coefficient for a conventional low speed airfoil

and a high speed section.

In order to obtain a high critical Mach

number from an airfoil at some low lift

coefficient the section must have:

(u) Low thickness ratio. The point of

maximum thickness should be aft to smooth

the pressure distribution.

(6) Low camber. The mean camber line

should be shaped to help minimize the

local velocity peaks.

In addition, the higher the required lift

coefficient the lower the critical Mach number

and more camber is required of the airfoil.

If supersonic flight is a possibility the thick-

ness ratio and leading edge radius must be

small to decrease wave drag.

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HIGH SPEED AERODYNAMICS

Figure 3.13 shows the flow patterns for

two basic supersonic airfoil sections and pro-

vides the approximate equations for lift,drag,

and lift curve slope. Since the wave drag is

the only factor of difference between -the two

airfoil sections, notice the configuration fac-

tors which affect the wave drag. For the

same thickness ratio, the circular arc airfoil

would have a larger wedge angle formed

between the upper and lower surfaces at the

leading edge. At the same flight Mach num-

ber the larger angle at the leading edge would

form the stronger shock wave at the nose and

cause a greater pressure change on the circular

arc airfoil. This same principle applies when

investigating the effect of airfoil thickness.

Notice that the wave drag coefficients for

both airfoils vary as the SQUARE of the

thickness ratio, e.g., if the thickness ratio

were doubled, the wave drag coefhcient would

he four times as great. If the thickness were

increased, the airflow at the leading edge will

experience a greater change in direction and

a stronger shock wave will be formed. This

powerful variation of wave drag with thick-

ness ratio necessitates the use of very thin air-

foils with sharp leading edges for supersonic

flight. An additional consideration is that

thin airfoil sections favor the use of low aspect

ratios and high taper to obtain lightweight

structures and preserve stiffness and rigidity.

The parameter JMz-l appears in the

denominator of each of the equations for the

aerodynamic coefficients and indicates a de-

crease in each of these coefficients with an

increase in Mach number. Essentially, this

means that any aerodynamic surface becomes

less sensitive to changes in angle of attack at

higher Mach numbers. The decrease in lift

curve slope with Mach number has tremendous

implications in the stability and control of

high speed aircraft. The vertical tail becomes

less sensitive to angles of sideslip and the

directional stability of the aircraft will deteri-

orate with Mach number. The horizontal

tail of the airplane experiences the same

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HIGH SPEED AERODYNAMICS

-1.0

PRESSURE

COEFFICIENT 0

PP, 4

1.0

SAME Cl LOW PEAK FOR

HIGH SPEED SECTION

(LAMINAR FLOW)

SECTION LIFT COEFFICIENT

Figure 3.72. High speed Section Characteristics

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HIGH SPEED AERODYNAMICS

DOUBLE WEDGE SECTION

WAVE DRAG COEFFICIENT:

LIFT COEFFICIENT:

DRAG DUE .TO LIFT:

LIFT CURVE SLOPE:

CIRCULAR ARC SECTION

WHERE

( +/c ) = AIRFOIL THICKNESS RATIO

a 2 ANGLE OF ATTACK (IN RADIANS)

M = MACH NUMBER

Figure 3.73. Approximate Equations for Supersonic Section Characteristics

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HIGH SPEEO AERODYNAMICS

general effect and contributes less damping to

longitudinal pitching oscillations. These ef-

fects can become so significant at high Mach

numbers that the aircraft might require com-

plete synthetic stabilization.

PLANFORM EFFECTS. The development

of surfaces for high speed involves considera-

tion of many items in addition to the airfoil

sections. Taper, aspect ratio, and sweepback

can produce major effects on the aerodynamic

characteristics of a surface in high speed flight.

Sweepback produces an unusual effect on the

high speed characteristics of a surface and has

basis in a very fundamental concept of aero-

dynamics. A grossly simplified method of

visualizing the effect of sweepback is shown in

figure 3.14. The swept wing shown has the

streamwise velocity broken down to a com-

ponent of velocity perpendicular to the leading

edge and a component parallel to the leading

edge. The component of speed perpendicular

to the leading edge is less than the free.stream

speed (by the cosine of the sweep angle) and

it is this velocity component which determines

the magnitude of the pressure distribution.

The component of speed parallel to the lead-

ing edge could be visualized as moving across

constant sections and; in doing so, does not

contribute to the pressure distribution on the

swept wing. Hence, sweep of a surface pro-

duces a beneficial e&ct ‘in high speed flight

since higher flight speeds may be obtained be-

fore components of speed perpendicular to the

leading edge produce critical conditions on the

wing. This is one of the most important ad-

vantage of sweep since there is an increase in

critical Mach number, force divergence Mach

number, and the Mach number at which the

drag rise will peak. In other words, sweep will

delay the onset of compressibility effects.

Generally, the effect of wing sweep will

apply to either sweep back or sweep forward.

While the swept forward wing has been used

1 in rare instances, the aeroelastic instability of

such a wing creates such a problem that sweep

back is more practical for ordinary applica-

tions.

In addition to the delay of the onset of com-

pressibility effects, sweepback will reduce the

magnitude of the changes in force coefficients

due to compressibility. Since’ the component

of velocity perpendicular to the leading edge is

less than the free stream velocity, the magni-

tude of all pressure forces on the wing will be

reduced (approximately by the square of the

cosine of the sweep angle). Since compressi-

bility force divergence occurs due to changes in

pressure distribution, the use of sweepback will

“soften” the force divergence. This effect is

illustrated by the graph of figure 3.14 which

shows the typical variation of drag coeiIicient

with Mach number for various sweepback

angles. The straight wing shown begins drag

rise at M=O.lO, reaches a peak near M=l.O,

and begins a continual drop past M= 1.0. Note

that the use of sweepback then deh+y~ the drag

rise to some~ higher Mach number and wdms

the magnitude of the drag rise.

In view of the preceding discussion, sweep-

back will have the following principal ad-

vantages :

(1) Sweepback will delay the onset of all

compressibility effects. Critical Mach num-

ber and force divergence Mach number will

increase since the velocity component affect-

ing the pressure distribution is less than the

free stream velocity. Also, the peak of drag

rise is delayed to some higher supersonic

speed-approximately the speed which pro-

duces sonic flow perpendicular to the leading

edge. Various sweeps applied to wings of

.moderate aspect ratio will produce these

approximate effects in transonic flight:

Sweep angle(k)

Revised Jaanuar~ 1965

NAVWEPS 00-80T-80

HIGH SPEED AERODYNAMICS

FREE STREAM

/

VELOCITY

VELOCITY COhlPONENT

PARALLEL TO LEADING

EDGE

\

SWEEP ANGLE, 11

VELOCITY COMPONENT

PERPENDICULAR TO

LEADING EDGE

DFf AG

COEFFICIENT

0 I.0 2.0 3.0

MACH NUMBER, M

UM

t IlC.IT ,STRAIGHT

MAXIM’

MACH NUMBER, M MACH NUMBER, M

Figure 3.14. General Effects of Sweepbock

NAVWEPS DD-ROT-80

HIGH SPEE’D AERODYN,AMlCS

EFFECT OF SWEEPBACK ON LOW SPEED LIFT CURVE

LIFT

COEFFICIENT

SWEPT

ANGLE OF ATTACK,O

EFFECT OF SWEEPBACK ON YAW AND ROLL MOMENTS /

YAW MOMENT

SWEPT WING AT SWEPT WING IN A

ZERO SIDESLIP SIDESLIP TO THE RIGHT

SWEPT WING

IN LEVEL FLIGHT

SWEPT WING IN A

S IDESLIP TOWARD

THE DOWN WING

Figure 3.15. Aerodynamic Effects Due to Sweepbach

NAVWEPS 00-801-80

HIGH SPEED AERODYNAMICS

(1) The wing lift curve slope is reduced

for a given aspect ratio. This is illustrated

by the lift curve comparison of figure 3.15

for the straight and swept wing. Any

reduction of lift curve slope implies the

wing is less sensitive to changes in angle of

attack. This is a beneficial effect only when

the effect of gusts and turbulence is con-

sidered. Since the swept wing has the

lower lift curve slope it will be less sensitive

to gusts and experience less “bump” due

to gust for a given aspect ratio and wing

loading. This is a consideration particular

to the aircraft whose structural design shows

a predominating effect of the gust load

spectrum, e.g., transport, cargo, and patrol

types.

(2) “Divergence” of a surface is an aero-

elastic problem which can occur at high

dynamic pressures. Combined bending and

twisting deflections interact with aerody-

namic forces to produce sudden failure of

the surface at high speeds. Sweep forward

will aggravate this situation by “leading”

the wing into the windstream and tends to

lower the divergence speed. On the other

hand, sweepback tends to stabilize the

surface by “trailing” and tends to raise the

divergence speed. By this tendency, sweep-

back may be beneficial in preventing di-

vergence within the anticipated speed range.

(3) Sweepback contributes slightly to the

static directional-or weathercock-stability

of an aircraft. This effect may be appre-

ciated by inspection of hgure 3.13 which

shows the swept wing in a yaw or sideslip.

The wing into the wind has less sweep and

a slight increase in drag; the wing away

from the wind has more sweep and less

drag. The net effect of these force changes is

to produce a yawing moment tending to

retarn the nose into the relative wind.

This directional stability contribution is

usually small and of importance in tailless

aircraft only.

(2) Sweepback will reduce the magnitude

of change in the aerodynamic force coeffi-

cients due to compressibility. Any change

in drag, lift, or moment coefbcients will be

reduced by the use of sweepback. Various

sweep angles applied to wings of moderate

aspect ratio will produce these approximate

effects in transonic flight.

00 ............................... 0

150. ............. ................ 5

M” .............................. 15

45’.............................. 35

600 .............................. 60

-

-_

-

These advantages of drag reduction and preser-

vation of the transonic maximum lift coefficient

are illustrated in figure 3.14.

Thus, the use of sweepback on a transonic

aircraft will reduce and delay the drag rise and

preserve the maneuverability of the aircraft

in transonic flight. It should be noted that a

small amount of sweepback produces very

little benefit. If sweepback is to be used at all,

at least 30’ to 33’ must be used to produce any

significant benefit. Also note from figure 3.14

that the amount of sweepback required to

d&y drag rise in supersonic flight is very large,

e.g., more than 60° necessary at M=2.0. By

comparison of the drag curves at high Mach

numbers it will be appreciated that extremely

high (and possibly impractical) sweepback is

necessary to delay drag rise and that the lowest

drag is abtained with zero sweepback. There-

fore, the planform of a wing designed to operate

continuously at high Mach numbers will tend

to be very thin, low aspect ratio, and unswept.

An immediate conclusion is that sweepback is

a device of greatest application in the regime of

transonic flight.

A few of the less significant advantages of

sweepback are as follows:

Revised January l%S

(4) Sweepback contributes to lateral sta-

bility in rhe same sense as dihedral. When

the swept wing aircraft is placed in a side-

slip, the wing into the wind experiences an

increase in lift since the sweep is less and

the wing away from the wind produces less

lift since rhe sweep is greater. As shown in

figure 3.15, the swept wing aircraft in a

sideslip experiences lift changes and a sub-

sequent rolling moment which tends to

right the aircraft. This lateral stability

conrribution depends on the sweepback and

the lift coefficient of the wing. A highly

swept wing operating at high lift coeflicient

usually experiences such an excess of this

lateral stability contribution that adequate

controllability may be a significant problem.

As shown, the swept wing has certain im-

portant advantages. However, the use of

sweepback produces certain inevitable disad-

vantages which are important from the stand-

point of both airplane design and flight oper-

ations. The most important of these disad-

vantages are as follows:

(1) When sweepback is combined with

taper there is an extremely powerful tendency

for the wing to stall tip first. This pattern

of stall is very undesirable since there would

be little stall warning, a serious reduction

in lateral control effectiveness, and the for-

ward shift of the center of pressure would

contribute to a nose up moment (“pitch up”

or “stick force lightening”). Taper has its

own effect of producing higher local lift

coefhcients toward the tip and one of the

effects of sweepback is very similar. All

outboard wing sections are affected by the

upwash of the preceding inboard sections

and the lift distribution resulting from sweep-

back alone is similar to that of high taper.

An additional effect is the tendency to

develop a strong spanwise flow of the bound-

ary layer toward the tip when the wing is at

high lift coefficients. This spanwise flow

produces a relatively low energy boundary

layer near the tip which can be easily sep-

NAVWEPS 00-801-80

HIGH SPEED AERODYNAMICS

arated. The combined effect of taper and

sweep present a considerable problem of tip

stall and this is illustrated by the flow pat-

terns of figure 3.16. Design for high speed

performance may dictate high sweepback,

while structural efficiency may demand a

highly tapered planform. When such is the

case, the wing may require extensive aero-

dynamic tailoring to provide a suitable stall

pattern and a lift distribution at cruise condi-

tion which reduces drag due to lift. Wash-

out of the tip, variation of section camber

throughout span, flow fences, slats, leading

edge extension, etc., are typical devices used

to modify the stall pattern and minimize

drag due to lift at cruise condition.

(2) As shown by the lift curve of figure

3.15 the use of sweepback will reduce the lift

curve slope and the subsonic maximum lift

coefficient. It is important to note this

case is definitely subsonic since sweepback

may be used to improve the transonic ma-

neuvering capability. Various sweep angles

applied to wings of moderate aspect ratio

produce these approximate effects on the

subsonic lift characteristics:

sweep Angle (A):

O”................................. 0

w................................ 4

300. 14

450.......... 30

M)Q................................ yl

The reduction of the low speed maximum

lift coefficient (which is in addition to that

lost due to tip stall) has very important

implications in design. If wing loading is

not reduced, stall speeds increase and sub-

sonic maneuverability decreases. On the

other hand, if wing loading is reduced, the

increase in wing surface area may reduce

the anticipated benefit of sweepback in the

transonic flight regime. Since the require-

ments of performance predominate, certain

increases of stall speeds, takeoff speeds,

NAVWEPS OO-EOT-80 NAVWEPS OO-EOT-80

HIGH SPEED AERODYNAMICS HIGH SPEED AERODYNAMICS

SPANWISE LIFT O~STR~BUT~ON SPANWISE LIFT DISTRIBUTION

WC

TIP STALL TENDENCY TIP STALL TENDENCY

OF UNMOOIFIEO WING OF UNMOOIFIEO WING

::G

g:: - - - - - - - - 1.0 1.0

Ot+ ,s

- I.0 - I.0

t ” 3

it

zi WING MODIFIED BY WING MODIFIED BY

OCJ WASHOUT, CAMBER, WASHOUT, CAMBER,

;$

SECTION VARIATION, ETC. SECTION VARIATION, ETC.

v) 0 0 0 f ! 0

ROOT TIP

TYPICAL STALLSEQUENCE

SPANWISE FLOW OF

BOUNDARY LAYER

DEVELOPS AT HIGH CL

STALL AREA

Figure 3.16. Stall Characteristics of Tapered Swept Wing

NAVWEPS 00-8OT-80

HIGH SPEED AERODYNAMICS

STRIJ;U;RAL

STRAIGHT WING OF SAME

AREA, ASPEC&ATIO, AN0

AEROD&AMIC

WING BENDING PRODUCES

-/TIP ROTATION

---

TIP VIEW TRAILING EDGE VIEW

figure 3.17. Structurd Complications Due to Sweephk

NAVWEPS 00-ROT-80

HIGH SPEED AERODYNAMICS

and landing speeds usually will be accepted.

While the reduction of lift curve slope may

be an advantage for gust considerations,

the reduced sensitivity to changes in angle

of attack has certain undesirable effects in

subsonic flight. The reduced wing lift

curve slope tends to increase maximum lift

angles of attack and complicate the problem

of landing gear design and cockpit visi-

bility. Also, the lower lift curve slope

would reduce the contribution to stability

of a given tail surface area.

(3) The use of sweepback will reduce

the effectiveness of trailing edge control

surfaces and high lift devices. A typical

example of this effect is the application of

a single slotted flap over the inboard 60

percent span to both a straight wing and a

wing with 35” sweepback. The flap applied

to the straight wing produces an increase

in maximum lift coefficient of approxi-

mately 50 percent. The same type flap

applied to the swept wing produces an

increase in maximum lift coefficient of

approximately 20 percent. To produce some

reasonable maximum lift coefficient one a

swept wing may require unsweeping the

flap hinge line, application of leading edge

high lift devices such as slots or slats, and

possibly boundary layer control.

(4) As described previously, sweepback

contributes to lateral stability by producing

stable rolling moments with sideslip. The

lateral stability contribution of sweepback

varies with the amount of wing sweepback

and wing lift coefficient-large sweepback

and high lift coefficients producing large

contribution to lateral stability. While sta-

bility is desirable, any excess of stability will

reduce controllability. For the majority of

airplane configurations, high lateral sta-

bility is neither necessary nor desirable, but

adequate control in roll is absolutely neces-

sary for good flying qualities. An excess of

lateral stability from sweepback can aggra-

vate “Dutch roll” problems and produce

marginal control during crosswind takeoff

and landing where the aircraft must move in

a controlled sideslip. Therefore, it is not

unusual to find swept wing aircraft with

negative dihedral and lateral control de-

vices designed principally to meet cross wind

takeoff and landing requirements.

(5) The structural complexity and aero-

elastic problems created by sweepback are of

great importance. First, there is the effect

shown in figure 3.17 that swept wing has a

greater structural span than a straight wing

of the same area and aspect ratio. This effect

increases wing structural weight since

greater bending and shear material must be

distributed in the wing to produce the same

design strength. An additional problem is

created near the wing root and “carry-

through” structure due to the large twisting

loads and the tendency of the bending stress

distribution to concentrate toward the trail-

ing edge. Also shown in figure 3.17 is the

influence of wing deflection on the spanwise

lift distribution. Wing bending produces

tip rotation which tends to unload the tip

and move the center of pressure forward.

Thus, the same effect which tends to allay

divergence can make an undesirable contri-

bution to longitudinal stability.

EFFECT OF ASPECT RATIO AND TIP

SHAPE. In addition to wing sweep, plan-

form properties such as aspect ratio, and tip

shape, can produce significant effects on the

aerodynamic characteristics at high speeds.

There is no particular effect of aspect ratio on

critical Mach number at high or medium

aspect ratios. The aspect ratio must be less

than four or five to produce any apparent

change in critical Mach number. This effect

is shown for a typical 9 percent thick sym-

metrical airfoil in the graph of figure 3.18.

Note that very low aspect ratios are required

to cause a significant increase in critical Mach

number. Very low aspect ratios create the

extremes of three dimensional flow and sub-

sequent increase in free stream speed to create

NAVWEPS 00-801-80

HIGH SPEED AERODYNAMICS

APPROXIMATE VARIATION OF CRITICAL

i.oo- MACH NUMBER WITH ASPECT RATIO FOR

A 9% THICK AIRFOIL SECTION

.95-

CRITICAL .90-

MACH .85-

NUMBER

MCR .80-

.75 -

.7od I 1 1 I 1 9 I

01 2 3 4 5 6 7 8 9 IO II I2

ASPECT RATIO, AR

MACH CONES FORMED AT

TIPS OF RECTANGULAR

\-

WING IN SUPERSONIC FLOW

PRESSURE DISTRIBUTION

AT THE TIP OF THE

RECTANGULAR WING

Y- MACH CONE

VORTEX CREATED WITHIN

THE MACH CONE AT THE TIP

OF THE RECTANGULAR WING

WING WITH TIPS

“RAKED” OUTSIDE

THE TIP CONES

Figure 3.18. Generd Pknform Effects

NAVWEPS 00-ROT-80

HIGH SPEED AERODYNAMICS

local sonic flow. Actually, the extremely

low aspect ratios required to produce high

critical Mach number are not too practical.

Generally, the advantage of low aspect ratio

must be combined with sweepback and high

speed airfoil sections.

The thin rectangular wing in supersonic

flow illustrates several important facts. AS

shown in figure 3.18, Mach cones form at the

tips of the rectangular wing and affect t~he

pressure distribution on the area within the

cone. The vortex develops within the tip

cone due to the pressure differenti,al and the

resulting average pressure on the area within

thecone is approximately one-half the pressure

between the cones. Three-dimensional flow

on the wing is then confined to the area within

the tip cones, while the area between the

cones experiences pure two-dimensional flow.

It is important to realize that the three-

dimensional flow on the rectangular wing in

supersonic flight differs greatly from that of

subsonic flight. A wing of finite aspect ratio

in subsonic flight experiences a three-dimen-

sional flow which includes the tip vortices,

downwash behind the wing, upwash ahead of

the wing, and local induced velocities along

the span. Recall that the local induced veloc-

ities along the span of the wing would incline

the section lift aft relative to the free stream

and result in “induced drag.” Such a flow

condition cannot be directly correlated with

the wing in supersonic flow, ~ The flow pattern

for the rectangular wing of figure 3.18 dem-

onstrates that the three-dimensional flow is

confined to the tip, and pure two-dimensional

flow exists on the wing area between the tip

cones. If the wing tips were to be “raked”

outside the tip cones, the entire wing flow

would correspond to the two-dimensional (or

section) conditions.

Therefore, for the wing in supersonic flow,

no upwash exists ahead of the wing, three-

dimensional effects are confined to the tip

cones, and no local induced velocities occur

along the span between the tip cones. The

supersonic drag due to lift is a function of the

section and angle of attack while the subsonic

induced drag is a function of lift coefficient

and aspect ratio. This comparison makes it

obvious that supersonic flight does not demand

the use of high aspect ratio planforms typical

of low speed aircraft. In fact, low aspect

ratios and high taper are favorable from the

standpoint of structural considerations if very

thin sections are used to minimize wave drag.

If sweepback is applied to the supersonic

wing, the pressure distribution will be affected

by the location of the Mach cone with respect

to the leading edge. Figure 3.19 illustrates the

pressure distribution for the delta wing plan-

form in supersonic flight with the leading edge

behind or ahead of the Mach cone. When the

leading edge is behind the Mach cone the com-

ponents of velocity perpendicular to the leading

edge are still subsonic even though the free

stream flow is supersonic and the resulting

pressure distribution will greatly resemble the

subsonic pressure distribution for such a plan-

form. Tailoring the leading edge shape and

camber can minimize the components of the

high leading edge suction pressure which are

inclined in the drag direction and the drag due

to lift can be reduced. If the leading edge

is ahead of the h4ach cone, the flow over this

area will correspond to the two-dimensional

supersonic flow and produce constant pressure

for that portion of the surface between the

leading edge and the Mach cone.

CONTROL SURFACES. The design of con-

trol surfaces for transonic and supersonic flight

involves many important considerations. This

fact is illustrated by the typical transonic and

supersonic flow patterns of figure 3.19. Trail-

ing edge control surfaces can be affected ad-

versely by the shock waves formed in flight

above critical Mach number. If the airflow

is separated by the shock wave the resulting

buffet of the control surface can be very objec-

tionable. In addition to the buffet of the sur-

face, the change in the pressure distribution due

to separation and the shock wave location can

NAVWEPS 00-801-60

HIGH SPEED AERODYNAMICS

DELTA WING PLANFORM

-PRESSURE

DISTRIBUTION

MACH CONE MACH CONE

AHEAD OF LEADING

EDGE

CONTFOL SURFACE

FLOW PATTERNS

SONIC FLOW ON

G EDGE CONTROLS

M=.85

SUPERSONIC FLOW CONDITIONS

TRAILING ED

CONTROLSURFACE

Figure 3.19. Planform Effects and Control Surfaces

NAVWEPS 00-ROT-80

HIGH SPEED AERODYNAMICS

create very large changes in control surface

hinge moments. Such large changes in hinge

moments create very undesirable control forces

and present the need for an “irreversible” con-

trol system. An irreversible control. system

would employ powerful hydraulic or electric

actuators to move the surfaces upon control by

the pilot and the airloads developed on the

surface could not feed back to the pilot. Of

course, suitable control forces would be syn-

thesized by bungees, “4” springs, bobweights,

etc.

Transonic and supersonic flight can cause a

noticeable reduction in the effectiveness of

trailing edge control surfaces. The deflection

of a trailing edge control surface at low sub-

sonic speeds alters the pressure distribution on

the fixed portion as well as the movable portion

of the surface. This is true to the extent that a

l-degree deflection of a 40 percent chord eleva-

tor produces a lift change very nearly the

equivalent of a l-degree change in stabilizer

setting. However, if supersonic flow exists on

the surface, a deflection of the trailing edge

control surface cannot influence the pressure

distribution in the supersonic area ahead of the

movable control surface. This is especially

true in high supersonic flight where supersonic

flow exists over the entire chord and the change

in pressure distribution is limited to the area of

the control surface. The reduction in effective-

ness of the trailing edge control surface at tran-

sonic and supersonic speeds necessitates the use

of an all movable surface. Application of the

all movable control surface to the horizontal

tail is most usual since the increase in longi-

tudinal stability in supersonic flight requires a

high degree of control effectiveness to achieve

required controllability for supersonic maneu-

vering.

SUPERSONIC ENGINE INLETS. Air

which enters the compressor section of a jet

engine or the combustion chamber of a ramlet

usually must be slowed to subsonic velocity.

This process must be accomplished with the

least possible waste of energy. At flight speeds

just above the speed of sound only slight modi-

fications to ordinary subsonic inlet design pro-

duce satisfactory performance. However, at

supersonic flight speeds, the inlet design must

slow the air with the weakest possible series-or

combination of shock waves to minimize en-

ergy losses and temperature rise. Figure 3.20

illustrates some of the various forms of super-

sonic inlets or “diffusers.”

One of the least complicated types of inlet

is the simple normal shock type diffuser. This

type of inlet employs a single normal shock

wave at the inlet with a subsequent internal

subsonic compression. At low supersonic Mach J

numbers the strength of the normal shock wave

is not too great and this type of inlet is quite

practical. At higher supersonic Mach num-

bers, the single normal shock wave is very

strong and causes a great reduction in the total

pressure recovered by the inlet. In addition,

it is necessary to consider that the wasted 1

energy of the airstream will appear as an addi-

tional undesirable rise in temperature of the

captured inlet airflow.

If the supersonic’airstream can be captured,

the shock wave formations tiill be swallowed

and a gradual contraction will reduce the speed

to just above sonic. Subsequent diverging flow 1

section can then produce the normal shock

wave which slows the airstream to subsonic.

Further expansion continues to slow the air to

lower subsonic speeds. This is the convergent-

divergent type inlet shown in figure 3.20. If

the initial contraction is too extreme for the

inlet Mach number, the shock wave formation

will not be swallowed and will move out in

front of the inlet. The external location of the

normal shock wave will produce subsonic flow

immediately at the inlet. Since the airstream

is suddenly slowed to subsonic through the

strong normal shock a greater loss of airstream

energy wiIl occur.

Another form of diffuser employs an external

oblique shock wave which slows the super-

sonic airstream before the normal shock occurs.

Ideally, the supersonic airstream could be

Revised January 1965

NAVWEPS 00-8OT-80

HIGH SPEED AERODYNAMICS

NORMALSHOCKINLET CONVERGENT-DIVERGENT INLET

SINGLEOBLIOUE SHOCK IPLE OBLIOUE SHOCK

NORMAL SHOCK WAVE

NEAR DESIGN RANGE BELOW DESIGN RANGE

EFFECT OF DIFFUSER DESIGN AND

MACH NUMBER ON DIFFUSER PERFORMANCE

1.00

.90 -

.BO -

.70 -

.60 -

.50 - -

.40 -

.30 -

.20 -

.I0 7 0 I

I 1.5 2.5 3.5

1.0 2.0 3.0 4.0

MACH NUhl6ER

Figure 3.20. Various Types of Supersonic Mets

NAVWEPS 00-8OT-80

HIGH SPEED AERODYNAMICS

slowed gradually through a series of very

weak oblique shock waves to a speed just

above sonic velocity. Then the subsequent

normal shock to subsonic could be quite weak.

Such a combination of the weakest possible

waves would result in the least waste of energy

and the highest pressure recovery. The ef-

ficiency of various types of diffusers is shown

in figure 3.20 and illustrates this principle.

An obvious complication of the supersonic

inlet is that the optimum shape is variable with

inlet flow direction and Mach number. In

other words, to derive highest efficiency and

stability of operation, the geometry of the

inlet would be different at each Mach number

and angle of attack of flight. A typical super-

sonic military aircraft may experience large

variations in angle of attack, sideslip angle,

and flight Mach number during normal oper-

ation. These large variations in inlet flow

conditions create certain important design

considerations.

(1) The inlet should provide the highest

practical efficiency. The ratio of recovered

total pressure to airstream total pressure is

an appropriate measure of this efficiency.

(2) The inlet should match the demands

of the powerplant for airflow. The airflow

captured by the inlet should match that

necessary for engine operation.

(3) Operation of the inlet at flight condi-

tions other than the design condition should

not cause a noticeable loss of efficiency or

excess drag. The operation of the inlet

should be stable and not allow “buzz”

conditions (an oscillation of shock location

possible during off-design operation).

In order to develop a good, stable inlet design,

the performance at the design condition may

be compromised. A large variation of inlet

flow conditions may require special geometric

features for the inlet surfaces or a completely

variable geometry inlet design,

SUPERSONIC CONFIGURATIONS. When

all the various components of the supersonic

airplane are developed, the most likely general

configuration properties will beas follows:

(1) The wing will be of low aspect ratio,

have noticeable taper, and have sweepback

depending on the design speed range. The

wing sections will be of low thickness ratio

and require sharp leading edges.

(2) The fmelagc and naceller will be of

high fineness ratio (long and slender). The

supersonic pressure distribution may create

significant lift and drag and require con-

sideration of the stability contribution of

these surfaces.

(3) The t&Z surfaces will be similar to

the wing-low aspect ratio, tapered, swept

and of thin section with sharp leading edge.

The controls will be fully powered and ir-

reversible with all movable surfaces the

most likely configuration.

(4) In order to reduce interference drag

in transonic and supersonic flight, the gross

cross section of the aircraft may be “area

ruled” to approach that of some optimum

high speed shape.

One of the most important qualities of high

speed configurations will be the low speed

flight characteristics. The low aspect ratio

swept wing planform has the characteristic

of high induced drag at low flight speeds.

Steep turns, excessively low airspeeds, and

steep, power-off approaches can then produce

extremely high rates of descent during landing.

Sweepback and low aspect ratio can cause

severe deterioration ‘of handling qualities at

speeds below those recommended for takeoff

and landing. On the other hand, thin, swept

wings at high wing loading will have rela-

tively high landing speeds. Any excess of

this basically high airspeed can create an im-

possible requirement of brakes, tires, and arrest

ing gear. These characteristics require that

the pilot account for the variation of optimum

speeds with weight changes and adhere to the

procedures and techniques outlined in the

flight handbook.

NAVWEPS Do-Sd-eD

“,G” SPEED AERODYNAMICS

EFFECT OF SPEED AND ALTITUDE

ON AERODYNAMIC HEATING

STAGNATION

TEMPERATURE

AT

SEA LEVEL

RAM TEMPERATURE

;;I

Z STAGNATION

w TEMPERATURE I- IN THE

STRATOSPHERE

0, --I 0 500 1000 1500 2000 2500 3000

TRUE AIRSPEED, KNOTS

APPROXIMATE EFFECT OF TEMPERATURE

ON TENSILE ULTIMATE STRENGTH, l/2 HR, EXPOSURE

IOO-

go-

30- ,-ALUMINUM

20- ALLOY

IO- L Or I

0 100 200 300 400 500 600 700 SO0 900 ~000

TEMPERATURE, “F

Figure 3.21. Aerodynamic Heating

NAVWEPS 00-BOT-80

H,lGH SPEED AERODYNAMICS

AERODYNAMIC HEATING

When air flows over any aerodynamic surface

certain reductions in velocity occur with cor-

responding increases in temperature. The

greatest reduction in velocity and increase in

temperature will occur at the various stagna-

tion points on the aircraft. Of course, similar

changes occur at other points on the aircraft

but these temperatures can be related to the

ram temperature rise at the stagnation point.

While subsonic flight does not produce temper-

atures of any real concern, supersonic flight

can produce temperatures high enough to be

of major importance to the airframe and power-

plant structure. The graph of figure 3.21 il-

1 lustrates the variation of ram temperature rise

with airspeed in the standard atmosphere.

The ram temperature rise is independent of

altitude and is a function of true .airspeed.

Actual temperatures would be the sum of the

temperature rife and the ambient air temper-

ature. ~Thus, low altitude flight at high Mach

numbers will produce the highest temperatures.

In addition to the effect on the crew member

environment, aerodynamic heating creates

special problems for the airplane structure

and the powerplant. The effect of tempera-

ture on the short time strength of three typical

structural materials is shown in figure 3.21.

Higher temperatures produce definite reduc-

tions in the strength of aluminum alloy and

require the use of titanium alloys, stainless

steels, etc., at very high temperatures. Con-

tinued exposure at elevated temperatures effects

further reductions of strength and magnifies the

problems of “creep” failure and structural

stiffness.

The turbojet engine is adversely affected by

high compressor inlet air temperatures. Since

the thrust output of the turbojet is some func-

tion of the fuel flow, high compressor inlet air

temperatures reduce the fuel flow that can be

used within turbine operating temperature

limits. The reduction in performance of the

turbojet engines with high compressor inlet

air temperatures requires that the inlet design

produce the highest practical efficiency and

minimize the temperature rise of the air

delivered to the compressor face.

High flight speeds and compressible flow

dictate airplane configurations which are much

different from the ordinary subsonic airplane.

To achieve safe and efficient operation, the pilot

of the modern, high speed aircraft must under-

stand and appreciate the advantages and dis-

advantages of the configuration. A knowledge

of high speed aerodynamics will contribute

greatly to this understanding.

Revised January 1965

NAVWEPS 00-80T-80

STABILITY AND CONTROL

Chapter 4

STABILITY AND CONTROL

An aircraft must have satisfactory handling

qualities in addition to adequate performance.

‘lYhe aircraft must have adequate stability to

maintain a uniform flight condition and recover

from the various disturbing influences. It is

necessary to provide sufficient stability to

minimize the workload of the pilot. Also, the

aircraft must have proper response to the

controls so that it may achieve the inherent

performance. There are certain conditions of

flight which provide the most critical require-

ments of stability and control and these condi-

tions must be understood and respected to

accomplish safe and efficient operation of the

aircraft.

DEFINITIONS

STATIC STABILITY

An aircraft is in a state of equilibrium when

the sum of all forces and all moments is equal

NAVWEPS 00-8OT-80

STABILITY AND CONTROL

POSITIVE STATIC STABILITY

TENDENCY TO RETURN

TO EOUILIBRIUM

L EOUILIBRIUM

TENDENCY TO CONTINUE

IN/DISPLACEMENT DIRECTION

\

NEGATIVE STATIC STABILITY

EOulLlBRlUM ENCOUNTERED

AT ANY POINT OF DISPLACEMENT

(-1

Figure 4.1. Static Stability

to zero. When an aircraft is in equilibrium,

there are no accelerations and the aircraft

continues in a steady condition of flight. If

the equilibrium is disturbed by a gust or deflec-

tion of the controls, the aircraft will experi-

ence acceleration due to unbalance of moment

or force.

The static stability of a system is defined by

the initial tendency to return to equilibrium

conditions following some disturbance from

equilibrium. If an object is disturbed from

equilibrium and has the tendency to return

to equilibrium, positive .rtatic Jtability exists.

If the object has a tendency to continue in the

direction of disturbance, negative static stability

or static instability exists. An intermediate

condition could occur where an object dis-

placed from equilibrium remains in equilibrium

in the displaced position. If the object subject

to a disturbance has neither the tendency to

return nor the tendency to continue in the dis-

placement direction, ncutrnl Jtatic stability ex-

ists. These three categories of static stability

are illustrated in figure 4.1. The ball in a

trough illustrates the condition of positive

static stability. If the ball is displaced from

equilibrium at the bottom of the trough, the

initial tendency of the ball is to return to the

equilibrium condition. The ball may roll

back and forth through the point of equilib-

rium but displacement to either side creates

the initial tendency to return. The ball on a

hill illustrates the condition of static insta-

bility. Displacement from equilibrium at the

hilltop brings about the tendency for greater

displacement. The ball on a flat, level surface

illustrates the condition of neutral static sta-

bility. The ball encounters a new equilibrium

at any point of displacement and has neither

stable nor unstable tendencies.

The term “static” is applied to this form of

stability since the resulting motion is not

considered. Only the tendency to return to 1. eqmlibrtum conditions is considered in static

stability. The static longitudinal stability of

an aircraft is appreciated by displacing the

NAVWEPS 00-802-80

STABILITY ,AND CONTROL

aircraft from some trimmed angle of attack.

If the aerodynamic pitching moments created

by this displacement tend to return the air-

craft to the equilibrium angle of attack the

aircraft has positive static longitudinal

stability.

DYNAMIC STABILITY

While static stability is concerned with the

tendency of a displaced body to return to

equilibrium, dynamic stability is defined by

the resulting motion with time. If an object is

disturbed from equilibrium, the time history

of the resulting motion indicates the dynamic

stability of the system. In general, the system

will demonstrate positive dynamic stability

if the amplitude of motion decreases with

time. The various condirions of possible

dynamic behavior are illustrated by the time

history diagrams of figure 4.2.

The nonoscillatory modes shown in figure

4.2 depict the time histories possible without

cyclic motion. If the system is given an initial

disturbance and the motion simply subsides

without oscillation, the mode is termed “sub-

sidence” or “deadbeat return.” Such a motion

indicates positive static stability by the tend-

ency to return to equilibrium and positive dy-

namic stability since the amplitude decreases

with time. Chart B illustrates the mode of

“divergence” by a noncyclic increase of ampli-

tude with time. The initial tendency to con-

tinue in the displacement direction is evidence

of static instability and the increasing ampli-

tude is proof of dynamic instability. Chart C

illustrates the mode of pure neutral stability.

If the original disturbance creates a displace-

ment which remains constant thereafter, the

lack of tendency for motion and the constant

amplitude indicate neutral static and neutral

dynamic stability.

The oscillatory modes of figure 4.2 depict the

time histories possible with cyclic motion.

One feature common to each of these modes is

that positive static stability is demonstrated in

the cyclic motion by tendency to return to

NAVWEPS 00-EOT-80

STABILITY AND CONTROL

NON-OSCILLATORY MODES

(OR DEAD BEAT RETURN)

5 (POSITIVE STATIC) (NEGATIVE STATIC)

0 (POSITIVE DYNAMIC) (NEGATIVE DYNAMIC)

(NEUTRAL STATIC)

(NEUTRAL DYNAMlc)

OSCILLATORY h

5 g E 1: 0. (POSITIVE STATIC) ;

(POSITIVE DYNAMIC)

0 E

UNDAMPED OSCILLATION

(POSITIVE STATIC)

(NEUTRAL DYNAMIC)

(P0slTl~E

(NEGATIVE

STATIC)

DYNAMIC)

Figure 4.2. Dynamic Sfabihty

quilibrium conditions. However, the dy-

namic behavior may be stable, neutral, or un-

stable. Chart D illustrates the mode of a

damped oscillation where the amplitude de-

creases with time. The reduction of amplitude

with time indicates there is resistance to mo-

tion and that energy is being dissipated. The

dissipation of energy-or “damping’‘-is nec-

essary to provide positive dynamic stability.

If there is no damping in the system, the mode

of chart E is the result, an undamped oscilla-

tion. Without damping, the oscillation con-

tinues with no reduction of amplitude with

time. While such an oscillation indicates posi-

tive static stability, neutral dynamic stability

exists. Positive damping is necessary to elimi-

nate the continued oscillation. As an example,

an automobile with worn shock absorbers (or

“dampers”) lacks sufficient dynamic stability

and the continued oscillatory motion is neither

pleasant nor conducive to safe operation. In

the same sense, the aircraft must have sufficient

damping to, rapidly dissipate any oscillatory

motion which would affect the operation of

the aircraft. When natural aerodynamic damp-

ing cannot be obtained, a synthetic damping

must be furnished to provide the necessary

positive dynamic stability.

Chart F of figure 4.2 illustrates the mode of

a divergent oscillation. This motion is stat-

ically stable since it tends to return to the

equilibrium position. However, each subse-

quent return to equilibrium is with increasing.

velocity such that amplitude continues to

increase with time. Thus, dynamic insta-

bility exists. The divergent oscillation occurs

when energy is supplied to the motion rather

than dissipated by positive damping. The

most outstanding illustration of the divergent

oscillation occurs with the short period pitch-

ing oscillation of an aircraft. If a pilot un-

knowingly supplies control functions which

are near the natural frequency of the airplane

in pitch, energy is added to the system, nega-

tive damping exists, and the “pilot induced

oscillation” results.

NAVWEPS OO-ROT-80

STABILITY AND CONTROL

In any system, the existence of static sta-

bility does not necessarily guarantee the

existence of dynamic stability. However,

the existence of dynamic stability implies

the existence of static stability.

Any aircraft must demonstrate the required

degrees of static and dynamic stability. If

the aircraft were allowed to have static in-

stability with a rapid rate of divergence, the

aircraft would be very difficult-if not impos-

sible-to fly. The degree of difficulty would

compare closely with learning to ride a uni-

cycle. In addition, positive dynamic stability

is mandatory in certain areas to preclude

objectionable continued oscillations of the

aircraft.

TRIM AND CONTROLLABILITY

An aircraft is said to be trimmed if all

moments in pitch, roll, and yaw are equal to

zero. The establishment of equilibrium at

various conditions of flight is the function of

the controls and may be accomplished by

pilot effort, trim tabs, or bias of a surface

actuator.

The term “controllability” refers to the

ability of the aircraft to respond to control

surface displacement and achieve the desired

condition of flight. Adequate controllability

must be available to perform takeoff and

landing and accomplish the various maneuvers

in flight. An important contradiction exists

between stability and controllability since

adequate controllability does not necessarily

exist with adequate stability. In fact, a high

degree of stability tends to reduce the controlla-

bility of the aircraft. The general relation-

ship between static stability and controlla-

bility is illustrated by figure 4.3.

Figure 4.3 illustrates various degrees of

static stability by a ball placed on various

surfaces. Positive static stability is shown by

the ball in a trough; if the ball is displaced

from equilibrium at the bottom of the trough,

there is an initial tendency to return to equilib-

rium. If it is desired to “control” the ball

NAVWEPS 00-ROT-80

STABILITY AND CONTROL

POSITIVE STATIC

STABILITY

CREASED POSIT,VE

TIC STABILITY

NEUTRAL STATIC STABILITY

NEGATIVE

STATIC STABILITY

Figure 4.3. Stability and Control/ability

and maintain it in the displaced position, a

force must be supplied in rhe direction of

displacement co balance the inherent tendency

to return to equilibrium. This same stable

tendency in an aircraft resists displacement

from trim by pilot effort on the controls or

atmospheric disturbances.

The effect of increased stability on con-

trollabilicy is illustrated by rhe ball in a

steeper trough. A greater force is required to

“control” the ball to the same lateral dis-

placement when the stability is increased.

In this manner, a large degree of stability tends

to make the aircraft less controllable. It is

necessary to achieve the proper balance be-

tween stability and tontrollability during rhe

design of an aircraft because the ~ppcr limits

of stability arc set by the lower 1imitJ of controlla-

bility.

The effect of reduced stability on .controlla-

bility is illustrated by the ball on a flat surface.

When neutral static stability exists, the ball

may be displaced from equilibrium and there

is no stable tendency to return. A new point

of equilibrium is obtained and no force is

required to maintain the displacement. As

the static stability approaches zero, controlla-

bility increases to infinity and the only resist-

ance to displacement is a resistance to the

motion of displacement-damping. For this

reason, the lower Limits of stability may be Set

by the upper limits of controllability. If the

stability of the aircraft is too low, control

deflections may create exaggerated displace-

ments of the aircraft.

The effect of static instability. on controlla-

bility is illustrated by the ball on a hill. If

the ball is displaced from equilibrium at the

top of the hill, the initial tendency is for the

ball td continue in the displaced direction.

In order to “control”~the ball to some lateral

displacement, a force must be applied oppo&

to the direction of displacement. This effect

would be appreciated during flight of an un-

stable aircraft by an unstable “feel” of the air-

craft. If the controls were deflected co in-

NAVWEPS DD-8OT-80

STABILITY AND CONTROL

&ease the angle of attack, the aircraft would

be trimmed at the higher angle of attack by

a push force to keep the aircraft from con-

tinuing in the displacement direction. Such

control force reversal would evidence the aii-

plane instability; the pilot would be supply-

ing the stability by his attempt to maintain

the equilibrium. An unstable aircraft can be

flown if the instability is slight with a low

rate of divergence. Quick reactions coupled

with effective controls can allow the pilot to

cope with some degree of static instability.

Since such flight would require constant at-

tention by the pilot, slight instability can be

tolerated only in airships, helicopters, and

certain minor motions of the airplane. How-

ever, the airplane in high speed flight will

react rapidly to any disturbances and any in-

stability would create unsafe conditions. Thus,

it is necessary to provide some positive static

stability to the major aircraft degrees of

freedom.

AIRPLANE REFERENCE AXES

In order to visualize the forces and moments

on the aircraft; it is necessary to establish a

set of mutually perpendicular reference axes

originating at the center of gravity. Figure

4.4 illustrates a conventional right hand axis

system. The longitudinal or X axis is located

in a plane of symmetry and is given a positive

direction pointing into the wind. A moment

about this axis is a rolling moment, L, and the

positive direction for a positive rolling moment

utilizes the right hand rule. The vertical or 2

axis also is in a plane of symmetry and is estab-

lished positive downward. A moment about

the vertical axis is a yawing moment, N, and a

positive yawing moment would yaw the air-

craft co the right (right hand rule). The

lateral or Y axis is perpendicular to the plane

of symmetry and is given a positive direction

out the right side of the aircraft. A moment

about the lateral axis is a pitching moment, M,

and a positive pitching moment is in the nose-

up dlrection.

NAVWEPS 00-8OT-80

STABELITY AND CONTROL

CENTER OF ..-.. ,.-.. _

1 VERTICAL AXIS

Figure 4.4. Airplane Rekre&e Axes

LONGITUDINAL STABILITY AND

CONTROL

STATIC LONGITUDINAL STABILITY

GENERAL CONSIDERATIONS. An air-

craft will exhibit positive static Iongitudinal

stability if it tends to return to the trim angle

of attack when displaced by a gust or control

movement. The aircraft which is unstable will

continue to pitch in the disturbed direction

until the displacement is resisted by opposing

control forces. If the aircraft is neutrally

stable, it tends to remain at any displacement

to which it is disturbed. It is most necessary

to provide an airplane with positive staric

longitudinal stability. The stable airplane is

safe and easy to fly since the airplane seeks and

tends to maintain a trimmed condition of

flight. It also follows that control deflec-

tions and control “feel” are logical in direction

and magnitude. Neutral static longitudinal

stability usually defines the lower limit of

airplane stability since it ‘is the boundary

between stability and instability. The air-

plane with neutral static stability’ may be

excessively responsive to controls and the

aircraft has no tendency to return to trim fol-

lowing a disturbance. The airplane with

negative sradc longitudinal stability is in-

herently divergent from any intended trim

condition. If it is at all possible to fly the

aircraft, the aircraft. cannot be trimmed and

illogical control forces and deflections are rc-

quired to provide equilibrium with a change

of attitude and airspeed.

Since static longitudinal stability depends

upon the relationship of angle of attack and

pitching moments, it is necessary to study the

pitching moment contribution of each com-

ponent of the aircraft. In a manner similar

to all other aerodynamic forces, the pitching

moment about the lateral axis is studied in

the coefficient form.

or

M = C,qS(MAC)

&= qS(MAC)

where

M=pitching moment about the c.g., ft.-

lbs., positive if in a nose-up direction

q= dynamic pressure, psf

S= wing area, sq. ft.

MAC=mean aerodynamic chord, ft.

C,= pitching moment coefficient

The pitching moment coefficients contributed

by all the various components of the aircraft

are summed up and plotted versus lift coeffi-

cient. Study of this plot of C, versus C,

will relate the static longitudinal stability

of the airplane.

Graph A of figure 4.5 illustrates the variation

of pitching moment coefficient, C,, with lift

coefficient, C,, for an airplane with positive

static longitudinal stability. Evidence of

static stability is shown by the tendency to re-

,t,urn to equilibrium-or “trim”- upon dis-

.,placement. The airplane described by graph A

is in trim or equilibrium when C,=O and, if the

‘airplane is disturbed to some different C,, the

pitching moment change tends to return the

aircraft to the.point of trim. If the airplane

‘were disturbed to some higher C, (point Y), a

negative or nose-down pitching moment is de-

veloped which tends to decrease angle of attack

back to the trim point. If the airplane were

disturbed to some lower C,, (point X), a posi-

tive, or nose-up pitching moment is developed

which tends to increase the angle of attack

back to the trim point. Thus, positive static

longitudinal stability is indicated by a negative

slope of C, versus C,, i.e., positive stability is

evidenced by a decrease in CM with an increase

in C,.

The degree of static longitudinal stability is

indicated by the slope of the curve of pitching

moment coefficient with lift coefficient. Graph

NAVWE,PS OO-ROT-80

STABILITY AND CONTROL

B of figure 4.5 provides comparison of the

stable and unstable conditions. Positive sta-

bility is indicated by the curve with negative

slope. Neutral static stability would be the

result if the curve had zero slope. If neutral

stability exists, the airplane could be dis-

turbed to some higher or lower lift coefficient

without change in pitching moment coefficient.

Such a condition would indicate that the air-

plane would have no tendency to return to

some original equilibrium and would not hold

trim. An airplane which demonstrates a posi-

tive slope of the C, versus C, curve would be

unstable. If the unstable airplane were subject

to any disturbance from equilibrium at the

trim point, the changes in pitching moment

would only magnify the disturbance. When

the unstable airplane is disturbed to some

higher CL, a positive change in C, occurs which

would illustrate a tendency for continued,

greater displacement. When the unstable air-

plane is disturbed to some lower C,,, a negative

change in C, takes place which tends to create

continued displacement.

Ordinarily, the static longitudinal stability

of a conventional airplane configuration does

not vary with lift coefficient. In other words,

the slope of C, versus CL does not change with

CL. However, if the airplane has sweepback,

large contribution of power effects to stability,

or significant changes in downwash at the

horizontal tail, noticeable changes in static

stability can occur at high lift coefficients.

This condition is illustrated by graph C of

figure 4.5. The curve of C, versus CL of this

illustration shows a good stable slope at low

values of CL. Increasing CL effects a slight

decrease in the negative slope hence a decrease

in stability occurs. With continued increase

in C,, the slope becomes zero and neutral

stability exists. Eventually, the slope be-

comes positive and the airplane becomes un-

stable or “pitch-up” results. Thus, at any

lift coefficient, the static stability of the air-

pl.ane is depicted by the slope of the curve of

CM versus CL.

NAVWEPS 00-8OT-80

STABILITY AND CONTROL

TRIM

CM=0

LIFT COEFFICIENT

-I

0 0

+

CM ---- b CL

-

-

LESS STABLE -NEUTRAL

Figure 4.5. Airphmc Static Longitudinal Stability

CONTRIBUTION OF THE COMPONENT

SURFACES. The net pitching moment about

the lateral axis is due to the contribution of

each of the component surfaces acting in their

appropriate flow fields. By study of the con-

tribution of each component the effect of each

component on the static stability may be ap-

preciated. It is necessary to recall that the

pitching moment coefficient is defined as:

‘“=qS(MAC)

Thus, any pitching moment coefficient-re-

gardless of source-has the common denomi-

nator of dynamic pressure, q, wing area, S, and

wing mean aerodynamic chord, MAC. This

common denominator is applied to the pitch-

ing moments contributed by the fuselage and

nacelles, horizontal tail, and power effects

as well as pitching moments contributed by

the wing.

WING. The contribution of the wing to

stability depends primarily on the location

of the aerodynamic center with respect to the

airplane center of gravity. Generally, the

aerodynamic center-or a.c.-is defined as the

point on the wing mean aerodynamic chord

where the wing pitching moment coefficient

does not vary with lift coefficient. All changes

in lift coefficient effectively take place at the

wing aerodynamic center. Thus, if the wing

experiences some change in lift coefficient, the

pitching moment created will be a direct

function of the relative location of the a.c. and

c.g.

Since stability is evidenced by the develop-

ment of restoring moments, the c.g. must be

forward of the a.c. for the wing to contribute

to positive static longitudinal stability. As

shown in figure 4.6, a change in lift aft of the

c,g. produces a stable restoring moment de-

pendent npon the lever arm between the a.c.

and c.g. In this case, the wing contribution

would be stable and the curve of CM versus CL

for the wing alone would have a negative slope.

If the c.g. were located at the a.c., C, would

NAVWEPS OO-BOT-BO

STABILITY AND CONTROL

not vary with C, since all changes in lift would

take place at the c.g. In this case, the wing

contribution to stability would be neutral.

When the c.g. is located behind the a.c. the

wing contribution i,s unstable and the curve

of C, versus CL for the wing alone would have

a positive slope.

Since the wing is the predominating aero-

dynamic surface of an airplane, any change in

the wing contribution may produce a sig-

nificant change in the airplane stability. This

fact would be most apparent in the case of the

flying wing or tailless airplane where the wing

contribution determines the airplane stability.

In order for the wing to achieve stability, the

c.g. must be ahead of the a.c. Also, the wing

must have a positive pitching moment about

the aerodynamic center to achieve trim at

positive lift coefficients. The first chart of

figure 4.7 illustrates that the wing which is

stable will trim at a negative lift coefficient if

the C,,, is negative. If the stable wing has a

positive C,,, it will then trim at a useful posi-

tive CL. The only means available to achieve

trim at a positive CL with a wing which has a

negative C,,, is an unstable c.g. position aft of

the ax. As a result, the tailless aircraft

cannot utilize high lift devices which incur

any significant changes in C,,,.

WhiIe the trim lift coefficient may be altered

by a change in c.g. position, the resulting

change in stability is undesirable and is unsat-

isfactory as a primary means of control. The

variation of trim CL by deflection of control

surfaces is usually more effective and is less

inviting of disaster. The early attempts at

manned flight led to this conclusion.

When the aircraft is operating in subsonic

flight, the a.c. of the wing remains fixed at the

25 percent chord station. When the aircraft

is flown in supersonic flight, the ax. of the

wing will approach the 50 percent chord sta-

tion. Such a large variation in the location

of the a.c. can produce large changes in the

wing contribution and greatly alter the air-

plane longitudinal stability. The second chart

NAVWEPS 00-801-80

STABILITY AND CONTROL

t CHANGE IN LIFT

~AERODYNAMIC CENTER

CENTER OF GRAVITY

-

Figure 4.6. Wing Contribution

NAVWEPS 00-BOT-80

STABILITY AND CONTROL

4 STABLE, POSITIVE CyAC

CM .ICl-2A-rI\,C C~ I IDIIETAIPI e

I ai*

STABLE, NEGATIVE f&AC

) =3=Ez.,.

CM + CL

\

SUBSONIC -

\

SUPERSONIC

Figure 4.7. Effect of CM~~ C. G. Position and Mach Nimber

NAVWEPS DD-807-80

STABILITY AND CONTROL

of figure 4.7 illustrates the change of wing

contribution possible between subsonic and

supersonic flight. The large increase in static

stability in supersonic flight can incur high

trim drag or require great control effectiveness

to prevent reduction in maneuverability.

FUSELAGE AND NACELLES. In most

cases, the contribution of the fuselage and

nacelles is destabilizing. A symmetrical body

of revolution in the flow field of a perfect fluid

develops an unstable pitching moment when

given an angle of attack. In fact, an increase

in angle of attack produces an increase in the

unstable pitching moment without the devel-

opment of lift. Figure 4.8 illustrates the pres-

sure distribution which creates this unstable

moment on the body of revolution. In the

actual case of real subsonic flow essentially

the same effect is produced. An increase in

angle of attack causes an increase in the

unstable pitching moment but a negligible

increase in lift.

An additional factor for consideration is the

influence of the induced flow field of the wing.

As illustrated in figure 4.8, the upwash ahead

of the wing increases the destabilizing influence

from the portions of the fuselage and nacelles

ahead of the wing. The downwash behind

the wing reduces the destabilizing influence

from the portions of the fuselage and nacelles

aft of the wing. Hence, the location of the

fuselage and nacelles relative to the wing is

important in determining the contribution to

stability.

The body of revolution in supersonic flow

can develop lift of a magnitude which cannot

be neglected. When the body of revolution in

supersonic flow is given an angle of attack, a

pressure distribution typical of figure 4.8 is the

result. Since the center of pressure is well

forward, the body contributes a destabilizing

influence. AS is usual with supersonic con-

figurations, the fuselage and nacelles may be

quite large in comparison with the wing area

and the contribution to stability may be large.

Interaction between the wing and fuselage and

nacelles deserves consideration in several in-

stances. Body upwash and variation of local

Mach number can influence the wing lift while

lift carryover and downwash can effect the fu-

selage and nacelles forces and moments.

HORIZONTAL TAIL. The horizontal tail

usually provides the greatest stabilizing influ-

ence of all the components of the airplane. To

appreciate the contribution of the horizontal

tail to stability, inspect figure 4.9. If the air-

plane is given a change in angle of attack, a

change in tail lift will occur at the aerody-

namic center of the tail. An increase in lift

at the horizontal tail produces a negative

moment about the airplane c.g. and tends to

return the airplane to the trim condition.

While the contribution of the horizontal tail

to stability is large, the -magnitude of the

contribution is dependent upon the change in

tail lift and the lever arm of the surface. It is

obvious that the horizontal tail will produce a

stabilizing effect only when the surface is aft

of the c.g. For this reason it would be inap-

propriate to refer to the forward surface of a

canard (tail&St) configuration as a horizontal

“stabilizer.” In a logical sense, the horizontal

“stabilizer” must be aft of the c.g. and-

generally speaking-the farther aft, the greater

the contribution to stability.

Many factors influence the change in tail

lift which occurs with a change in airplane

angle of attack. The area of the horizontal

tail has the obvious effect that a large surface

would generate a large change in lift. In a

similar manner, the change in tail lift would

depend on the slope of the lift curve for the

horizontal tail. Thus, aspect ratio, taper,

sweepback, and Mach number would deter-

mine the sensitivity of the surface to changes

in angle of attack. It should be appreciated

that the flow at the horizontal tail is not of

the same flow direction or dynamic pressure as

the free stream. Due to the wing wake, fuse-

lage boundary layer, and power effects, the q

at the horizontal tail may be greatfy different

from the 4 of the free stream. In most in-

NAVWEPS oo-BDT-BD

STABILITY AND CONTROL

BODY OF REVOLUTION IN PERFECT FLUID

INDUCED FLOW FIELD FROM WING

BODY OF REVOLUTION INSUPERSONIC FLOW

Figure 4.8. Body or Nacelle Contribution

NAVWEPS 00-BOT-BO

STABILITY AND CONTROL

_--- -. CHANGE IN LIFT

ON HORIZONTAL TAlL

OF HORIZONTAL TAIL

DOWNWASH AT

FUSELAGE CROSS FLOW

SEPARATION VORTICES

Figure 4.9. Contribution of Tail and Downwash Effects

stances, the 4 at the tail is usually less and this

reduces the efficiency of the tail.

When the airplane is given a change in angle

of attack, the horizontal tail does not expe-

rience the same change in angle of attack as

the wing. Because of the increase in down-

wash behind, the wing, the horizontal tail will

experience a smaller change in angle of attack,

e.g., if a 10" change in wing angle of attack

causes a 4O increase in downwash at the hori-

zontal tail, the horizontal tail experiences

only a 6’ change in angle of attack. In this

manner, the downwash at the horizontal tail

reduces the contribution to stability. Any

factor which alters the rate of change of down-

wash at the horizontal tail will directly affect

the tail contribution and airplane stability.

Power effects can alter the downwash at the

horizontal tail and affect the tail contribution.

Also, the ~downwash at the tail is affected by

the lift distribution on the wing and the flow

condition ,on the fuselage. The low aspect

ratio airplane requires large angles of attack

to achieve high ,lift coefficients and this posi-

tions the fuselage at high angles of attack.

The change in the wing downwash can be

accompanied by crossflow separation vortices

on the fuselage. It is possible that the net

effect obviates or destabilizes the contribu-

tion of the horizontal tail and produces air-

plane instability.

POWER-OFF STABILITY. When the in-

trinsic stability of a configuration is of interest,

power effects are neglected and the stability

is considered by a buildup of the contributing~

components. Figure 4.10 illustrates a typical

buildup of the components of a conventional

airplane configuration. If the c.g. is arbi-

trarily set at 30 percent MAC, the contribu-

tion of the wing alone is destabilizing as indi-

cated by the positive slope of CM versus C,.

The combination of the wing and fuselage

increases the instability. The contribution

of the tail alone is highly stabilizing from

the large negative slope of the curve. The

contribution of the tail must be sufficiently

NAVWEPS OO-BOT-80

STABILITY AND CONTROL

stabilizing so that the complete configuration

will exhibit positive static stability at the

anticipated c.g. locations. In addition, the tail

and wing incidence must be set to provide a

trim lift coefficient near the design condition.

When the configuration of the airplane is

fixed, a variation of c.g. position can cause

large changes in the static stability. In the

conventional airplane configuration, the large

changes in stability with c.g. variation are

primarily due to the large changes in the wing

contribution. If the incidence of all surfaces

remains fixed, the effect of c.g. position on

static longitudinal stability is typified by the

second chart of figure 4.10. As the cg. is

gradually moved aft, the airplane static sta-

bility’ decreases, then becomes neutral then

unstable., The c.g. position which produces

zero ,slope and neutral static stability is re-

ferred to asp the ~“neutral point.” The neutral

point may be imagined as the effective aerody-

namic center of the entire airplane configura-

ration, i.e., with the c.g. at this position, all

changes in net lift effectively occur at this

point and no change in pitching moment

results. The neutral point defines the most

aft c.g. position without static instability.

POWER EFFECTS. The effects of power may

cause significant changes in trim lift coefficient

and static. longitudinal stability. Since the

contribution to stability is evaluated by the

change in moment coefficients, power effects

will be most significant when the airplane

operates at high power and low airspeeds such

as the power approach or waveoff condition.

The effects of power are considered in two

main categories. First, there are the direct

effects resulting from the forces created by the

propulsion unit. Next, there are the indirect

effects of the slipstream and other associated

flow which alter the forces and moments of the

aerodynamic surfaces. The direct effects of

power are illustrated in figure 4.11. The ver-

tical location of the thrust line defines one of

the direct contributions to stability. If the

NAVWEPS OD-BOT-80

STABILITY AND CONTROL

TYPICAL GUILD-UP 0F tzci~m~ENTs

CM ,-WING+ FUSELAGE

WING ONLY/.

- -

-

C.G. @ 30% MAC .

EFFECT OF C.G. WsITION

CM 50% MAC

40% MAC (NEUTRAL pOlNn ---

Figure 4.10. Stability Build-up and Effect of C.G. Positim