Chapter 1 — Part 6

NAVWEPS 00-BOT-80

STABILITY ,AND CONTROL

slipstream creates a normal force at the plane

of the propeller similar to a wing creating lift

by deflecting an airstream. As this normal

force will increase with an increase in airplane

angle of attack, the effect will be destabilizing

when the propeller is ahead of the cg. The

magnitude of the unstable contribution de-

pends on the distance from the c.g. to the

propeller and is largest at high power and low

dynamic pressure. The normal force created

thrust line is below the c.g., thrust produces a

positive or noseup moment and the effect is de-

stabilizing. On the other hand, if the thrust

line is ,located above the c.g., a negative

moment is created and the effect is stabilizing.

A propeller or inlet duct located ahead of

the c.g. contributes a destabilizing effect. As

shown in figure 4.11, a rotating propeller in-

clined to the windstream causes a deflection

of the airflow. The momentum change of the

NAVWEPS OD-BOT-80

S-lABlLlTY AND CONTROL

EFFECT OF VERTICAL LOCATION OF THRUST LINE

d DESTABILIZING

STABILIZING

DESTABILIZING INCRE

IN NORMAL FORCE

DESTABILIZING INCREASE

IN DUCT INLET NORMAL

FORCE

Figure 4.11. Direct Power Effects

NAVWEPS GO-BOT-BO

STABILITY AND CONTROL

n f WING.NACELLE,AND FUSELAGE

MOMENTS AFFECTED BY

SLIPSTREAM

-DYNAMIC PRESSURE

AT TAIL AFFECTED

BY SLIPSTREAM

WING LIFT AFFECTED

BY SLIPSTREAM

FLOW INDUCED BY

JET EXHAUST

DOWNWASH AT TAIL

Figure 4.12. Indirect Power Effects.

NAVWEPS 00-8OT-90

STABHITY AND CONTROL

at the inlet of a jet engine contributes a similar

destabilizing effect when the inlet is ahead

of the c,g. As with the propeller, the magni-

tude of the stability contribution is largest at

high thrust and low flight speed.

The indirect effects of power are of greatest

concern in the propeller powered airplane

rather than the jet powered airplane. As

shown in figure 4.12, the propeller powered

airplane creates slipstream velocities on the

various surfaces which are different from the

flow field typical of power-off flight. Since

the various wing, nacelle, and fuselage surfaces

are partly or wholly immersed in this slip-

stream, the contribution of these components

to stability can be quite different from the

power-off flight condition. Ordinarily, the

change of fuselage and nacelle contribution

with power is relatively small. The added

lift on the portion of the wing immersed in

the slipstream requires that the airplane oper-

ate at a lower angle of attack to produce the

same effective lift coefficienr. Generally, this

reduction in angle of attack to effect the same

CL reduces the tail contribution to stability.

However, the increase in dynamic pressure at

the tail tends to increase the effectiveness of

the tail and may be a stabilizing effect. The

magnitude of this contribution due to the

slipstream velocity on the tail will depend on

the c.g. position and trim lift coefficient.

The deflection of the slipstream by the nor-

mal force at the propeller tends to increase the

downwash at the horizontal tail and reduce

the contribution to stability. Essentially the

same destabilizing effect is produced by the

flow induced at the exhaust of the jet power-

plant. Ordinarily, the induced flow at the

horizontal tail of a jet airplane is slight and is

destabilizing when the jet passes underneath

the horizontal tail. The magnitude of the

indirect power effects on stability tends to be

greatest at high Cr, high power, and low flight

speeds.

The combined direct and indirect power

effects contribute to a general reduction of

static stability at high power, high CL, and

low 4. It is generally true that any airplane

will experience the lowest level of static longi-

tudinal stability under these conditions. Be-

cause of the greater magnitude of both direct

and indirect power effects, the propeller pow-

ered airplane usually experiences a greater

effect than the jet powered airplane.

An additional effect on stability can be from

the extension of high lift devices. The high

lift devices tend to increase downwash at the

tail and reduce the dynamic pressure at the tail,

both of which are destabilizing. However,

the high lift devices may prevent an unstable

contribution of the wing at high CL. While

the effect of high lift devices depends on the

airplane configuration, the usual effect is de-

stabilizing. Hence, the airplane may experi-

ence the most critical forward neutral point

during the power approach or waveoff. Dur-

ing these conditions of flight the static stability

is usually the weakest and particular attention

must be given to precise control of the air-

plane. The power-on neutral point may set

the most aft limit of c.g. position.

CONTROL FORCE STABILITY. The static

longitudinal stability of an airplane is defined

by the tendency to return to equilibrium upon

displacement. In otherwords, the stable air-

plane will resist displacement from the trim or

equilibrium. The control forces of the air-

plane should reflect the stability of the air-

plane and provide suitable reference for precise

control of the airplane.

The effect of elevator deflection on pitching

moments is illustrated by the first graph of

figure 4.13. If the elevators of the airplane are

fixed at zero deflection, the resulting line of

CM versus C’s for 0’ depicts the static stability

and trim lift coefficient. If the elevators are

fixed at a deflection of 10” up, the airplane

static stability is unchanged but the trim lift

coefficient is increased. A change in elevator

or stabilizer position does not alter the tail

contribution to stability but the change in

pitching moment will alter the lift coeflicient

NAVWEPS 00-SOT-80

STABILITY AND CONTROL

EFFECT OF ELEVATOR DEFLECTION

CM -L ELEVATOR nre, CCTl,-..,

TRIM FOR

CG@20% MAC

TRIM C, VERSUS ELEVATOR DEFLECTION

A TRIM AIRSPEED VS ELEVATOR DEFLECTION

ii UP ’ X~SLE

:

oz EQUIVALENT

/ ~RSPEED

a /

2 DOWN /

ii /

Figure 4.13. Longitudinal Control

NAVWEPS 00-BOT-80

STABILITY AND CONTROL

at which equilibrium will occur. As the ele-

vator is fixed in various positions, equilibrium

(or trim) will occur at various lift coefficients

and the trim CL can be correlated with elevator

deflection as in the second graph of figure 4.13.

When the c,g. position of the airplane is

fixed, each elevator position corresponds to a

particular trim lift coefficient. AS the c.g. is

moved aft the slope of this line decreases and

the decrease in stability is evident by a given

control displacement causing a greater change

in trim lift coefficient. This is evidence that

decreasing stability causes increased controlla-

bility and, of course, increasing stability de-

creases controllability. If the c.g. is moved

aft until the line of trim CL versus elevator de-

flection has zero slope, neutral static stability

is obtained and the “stick-fixed” neutral point

is determined.

Since each value of lift coefhcient corresponds

to a particular value of dynamic pressure re-

quired to support an airplane in level flight,

uim airspeed can be correlated with elevator

deflection as in the third graph of figure 4.13.

If the c.g. location is ahead of the stick-fixed

neutral point and control position is directly

related to surface deflection, the airplane will

give evidence of stick podion mbility. In

other words, the airplane will require the

stick to be moved aft to increase the angle

of attack and trim at a lower airspeed and to

be moved forward to decrease the angle of

attack and trim at a higher airspeed. To be

sure, it is desirable to have an airplane demon-

strate this feature. If the airplane were to

have stick position instability, the airplane

would require the stick to be moved aft to trim

at a higher airspeed or to be moved forward to

trim at a lower airspeed.

There may be slight differences in the static

longitudinal stability if the elevators are

allowed to float free. If the elevators are

allowed to float free as in “hands-off” flight,

the elevators may have a tendency to “float”

or streamline when the horizontal tail is given

a change in angle of attack. If the hot&ma1

tail is subject to an increase in angle of attack

and the elevators tend to float up, the change

in lift on the tail is less than if the elevators

remain fixed and the tail contribution to

stability is reduced. Thus, the “stick-free”

stability of an airplane is usually less than the

stick-fixed stability. A typical reduction of

stability by free elevators is shown in figure

4.14(A) where the airplane. stick-free demon-

strates a reduction of the slope of CM versus Cs.

While aerodynamic balance may be provided

tu reduce control forces, proper balance of the

surfaces will reduce floating and prevent great

differences between stick-fixed and stick-free

stability. The greatest floating tendency oc-

curs when the surface is at a high angle of

attack hence the greatest difference between

stick-fixed and stick-free stability occurs when

the airplane is at high angle of attack.

If the controls are fully powered and actu-

ated by an irreversible mechanism, the sur-

faces are not free to float and there is no differ-

ace between the stick-fixed and stick-free

static stability.

The control forces in a conventional air-

plane are made up of two components. First,

the basic stick-free stability of the airplane

contributes an incremem of force which is

independent of airspeed.. Next, there. is an

increment of force dependent on the trim tab

setting which varies with-the dynamic pres-

sure or the square of ‘equivalent airspeed.

Figure 4.14(B) indicates the variation of

stick force with airspeed and illustrates the

effect of tab setting on stick force. In order

te trim the airplane at point (1) a certain

amount of up elevator is required and zero

stick force is obtained~ with’the nse of the tab.

To trim the airplane for higher speeds corre-

sponding to points (2) and (3) less and less

nose-up tab is required. Note that when the

airplane is properly trimmed, a push force is

required to increase airspeed and a pull force

is required to decrease airspeed. In this man-

ner, the airplane would indicate positive stick

force stability with a stable “feel” for air-

)

a,,, I,

-- F

TAB FORCE INCREMENT

NAVWEPS 00-BOT-80

STABILITY AND CONTROL

STICK -FIXED

PULL

PUSH

INCREMENT EQUIVALENT

CG AT 20% MAC I

CG POSITION

10% MAC

p-z; ,/’ EQUlVALENT

PULL

,o T

D -

FRICTION FORC

BAND

Figure 4.74. Control Force Stability

NAVWEPS 00-801-80

STABILITY AND CONlRO’L

speed, If the airplane were given a large nose

down tab setting the pull force would in-

crease with airspeed. This fact points out the

possibility of “feel” as not being a true indi-

cation of airplane static stability.

If the c.g. of the airplane were varied while

maintaining trim at a constant airspeed, the

effect of c.g. position on stick force stability

could be appreciated. As illustrated in figure

4,14(C), moving the c,g. aft decreases the

slope of the line of stick force through the

trim speed. Thus, decreasing stick force

stability is evident in that smaller stick forces

are necessary to displace the airplane from

the trim speed. When the stick force gradient

(or slope) becomes zero, the c.g. is at the

stick-free neutral point and neutral stability

exists. If the c.g. is aft of the stick-free

neutral point, stick force instability will

exist, e.g. the airplane will require a push

force at a lower speed or a pull force at a higher

speed. It should be noted that the stick force

gradient is low at low airspeeds and when

the airplane is at low speeds, high power,

and a c.g. position near the aft limit, the

“feel” for airspeed will be weak.

Control system friction can create very un-

desirable effects on control forces. Figure

4.14(D) illustrates that the control force

versus airspeed is a band rather than a line.

A wide friction force band can completely

mask the stick force stability when the stick

force stability is low. Modern flight control

systems require precise maintenance to mini-

mize the friction force band and preserve

proper feel to the airplane.

MANEUVERING STABILITY. When an

airplane is subject to a normal acceleration,

the flight path is curved and the airplane is

subject to a pitching velocity. Because of

the pitching velocity in maneuvering flight,

the longitudinal stability of the airplane is

slightly greater than in steady flight condi-

tions. When an airplane is subject to a pitch-

1 ing velocity at a given lift coefficient, the air-

plane develops a pitching moment resisting

the pitch motion which adds to the restoring

moment from the basic static stability. The

principal source of this additional pitching

moment is illustrated in figure 4.15.

During a pull-up the airplane is subject to

an angular rotation about the lateral axis and

the horizontal tail will experience a component

of wind due to the pitching velocity. The

vector addition of this component velocity to

the flight velocity provides a change in angle

of attack for the tail and the change in lift on

the tail creates a pitching moment resisting

the pitching motion. Since the pitching mo-

ment opposes the pitching motion but is due

to the pitching motion, the effect is a damping

in pitch. Of course, the other components of

the airplane may develop resisting moments

and contribute to pitch damping but the

horizontal tail is usually the largest contri-

bution. The added pitching moment from

pitch damping will effect a higher stability

in maneuvers than is apparent in steady flight.

From this consideration, the neutral point for

maneuvering flight will be aft of the neutral

point for unaccelerated flight and in most cases

will not be a critical item. If the airplane

demonstrates static stability in unaccelerated

flight, it will most surely demonstrate stability

in maneuvering flight.

The most direct appreciation of the ma-

neuvering stability of an airplane is obtained

from a plot of stick force versus load factor

such as shown in figure 4.15. The airplane

with positive maneuvering stability should

demonstrate a steady increase in stick force

with increase in load factor or “G”. The

maneuvering stick force gradient-or stick

force per G-must be positive but should be

of the proper magnitude. The stick force

gradient must not be excessively high or the

airplane will be difficult and tiring to maneuver.

Also, the stick force gradient must not be too

low or the airplane may be overstressed in-

advertently when light control forces exist.

A maneuvering stick force gradient of 3 to 8

lbs. per G is satisfactory for most fighter and

NAVWEPS 00-801-80

STABILITY AND CONTROL

CHANGE IN TAIL LIFT

RELATIVE WIND

FROM ANGULAR ROTATION

CHANGE IN TAIL ANGLE OF

ATTACK DUE TO PITCHING

VELOCITY

co

!!I 30

; 20 MANEUVERING STICK

:: FORCE GRADIENT

g IO

I 2 3 4 5 6 7 8

LOAD FACTOR, n

(OR G)

CG POSITION

% MAC /

LOAD FACTOR

Figure 4.15. Maneuvering Stability

NAVWEPS 00-8’X-60

STABILITY AND CONTROL

attack airplanes. A large patrol or transport

type airplane would ordinarily show a much

higher maneuvering stick force gradient be-

cause of the lower limit load factor.

When the airplane has high static stability,

the maneuvering stability will be high and

a high stick force gradient will result. A

possibility exists that the forward c.g. limit

could be set to prevent an excessively high

maneuvering stick force gradient. As the

c.g. is moved aft, the stick force gradient de-

creases with decreasing maneuvering stability

and the lower limit of stick force gradient

may be reached.

The pitch damping of the airplane is obvi-

ously related to air density. At high altitudes,

the high true airspeed reduces the change in

tail angle of attack for a given pitching velocity

and reduces the pitch damping. Thus, a de-

crease in maneuvering stick force stability can

be expected with increased altitude.

TAILORING CONTROL FORCES. The

control forces should reflect the stability of

the airplane but, at the same time, should be

of a tolerable magnitude. The design of the

surfaces and control system may employ an

infinite variety of techniques to provide satis-

factory control forces.

Aerodynamic balance must be thought of in

two different senses. First, the control surface

must be balanced to reduce hinge moments due

to changes in angle of attack. This is necessary

to reduce the floating tendency of the surface

which reduces the stick-free stability. Next,

aerodynamic balance can reduce the hinge

moments due to deflection of the control sur-

face. Generally, it is difficult to obtain a high

degree of deflection balance without incurring

a large overbalance of the surface for changes

in angle of attack.

Some of the types of aerodynamic balance

are illustrated in figure 4.16. Thesimple horn

type balance employs a concentrated balance

area located ahead of the hinge line. The

balance area may extend completely to the

leading edge (unshielded) or partway to the

leading edge (shielded). Aerodynamic balance

can be achieved by the provision of- a hinge

line aft of the control surface leading edge.

The resulting overhang of surface area ahead

of the hinge line will provide a degree of

balance depending on the amount of overhang.

Another variation of aerodynamic balance is

an internal balance surface ahead of the hinge

line which is contained within ,the surface.

A flexible seal is usually incorporated to in-

crease the effectiveness of the balance area.

Even the bevelling of the trailing edge..of the

control surface is effective also as a balancing

technique. The choice of the type of aerody-

namic balance will depend on many factors

such as required degree of balance, simplicity,

drag, etc.

Many devices can be added to a control

system to modify or tailor the stick force

stability to desired levels. If a spring is added

to the control system as shown in figure 4.16,

it will tend to center the stick and provide a

force increment depending on stick displace-

ment. When the control system has a fixed

gearing between stick position and surface

deflection, the centering spring will provide a

contribution to stick force stability according

to stick position. The contribution to stick

force stability will be largest at low flight

speeds where relatively large control deflec-

tions are required. The contribution will be

smallest at high airspeed because of the smaller

control deflections required. Thus, .the stick

centering bungee will increase the airspeed

and maneuvering stick force stability but the

contribution decreases at high airspeeds. A

variation of this device would be a spring

stiffness which would be controlled to vary

with dynamic pressure, 4. In this case, the

contribution of the spring to stick force

stability would, not diminish with. speed.

A “downspring” added to a control system

is~ a means ~of increasing airspeed stick force

stability without a change in airplane static

2,70

NAVWEPS 00-8OT-80

STABILITY AND CONTROL

TYPES OF AERODYNAMIC BALANCE

OVERHANGORLEADINGEDGE

BALANCE BY OFFSET HINGE 7

INTERNAL BALANCE

WITH FL’XlBLESE& <I

HORN TYPE BALANCE

---‘I “1G EDGE BEVEL -,

EFFECT LaF STICK CENTERING SPRING

TICK CENTERING

RING OR BUNGEE

A PULL FORCE INCREMENTADDED

8 y

BY SPRING

E EQUIVALENT e

i5 \ AIRSPEED

I=

m PUSH

LOAD FACTOR

figure 4.16. loiloring Control forces

NAVWEPS 00-801-80

STABILITY AND CONTROL

EFFECT OF DOWNSPRING

u P*RELO+DED SPRING

PULL

EQUIVALENT

lRSPEED

EFFECT OF BOBWEIGHT

PULL

EQUIVALENT

PUSH

RETRIMMED

FORCE INCREMENT

PROVIDED

BY BOBWEIGHT

LOAD FACTOR c

Figure 4.77. Tailoring Control Forces

stability. As shown in figure 4.17, a down-

spring consists of a long preloaded spring at-

tached to the control system which tends to

rotate the elevators down. The effect of the

downspring is to contribute an increment of

pull force independent of control deflection or

airspeed. When rhe downspring is added to

the control system of an airplane and the air-

plane is retrimmed for the original speed, the

airspeed stick force gradient is increased and

there is a stronger feel for airspeed. The down-

spring would provide an “ersatz” improve-

ment to an airplane deficient in airspeed stick

force stability, Since the force increment from

the downspring is unaffected by stick position

or normal acceleration, the maneuvering stick

force stability would be unchanged.

The bobweight is an effective device for im-

proving stick force stability. As shown in

figure 4.17, the bobweight consists of an eccen-

tric mass attached to the control system

which-in unaccelerated flight--contributes

an increment of pull force identical to the

downspring. In fact, a bobweight added to

the control system of an airplane produces an

effect identical to the downspring. The bob-

weight will increase the airspeed stick force

gradient and increase the feel for airspeed.

A bobweighr will have an effect on the

maneuvering stick force gradient since the bob-

weight mass is subjected to the same accelera-

tion as the airplane. Thus, the bobweight will

provide an increment of stick force in direct

proportion to the maneuvering acceleration of

the airplane. Because of the linear contribu-

tion of the bobweight, the bobweight can be

applted to Increase the maneuvering stick force

stability if the basic airplane has too low a

value or develops a decreasing gradient at high

lift coefficients.

The example of the bobweight is useful to

point out the effect of the control system dis-

tributed masses. All carrier aircraft must have

the control system mass balanced to prevent

undesirable control forces from the longi-

tudinal accelerations during catapult launching.

NAVWEPS 00-EOT-80

STABILITY AND CONTROL

Various control surface tab devices can be

utilized to modify control forces. Since the de-

flection of a tab is so powerful in creating hinge

moments on a control surface, the possible

application of tab devices is almost without

limit, The basic trim tab arrangement is

shown in figure 4.18 where a variable linkage

connects the tab and the control surface. Ex-

tension or contraction of this linkage will de-

flect the tab relative to the control surface and

create a certain change in hinge mon~ent coef-

ficient. The use of the trim tab will allow the

pilot to reduce the hinge moment to zero and

trim the control forces to zero for a given flight

condition. Of course, the trim tab should have

adequate effectiveness so that control forces

can be trimmed out throughout the flight speed

range.

The lagging tab arrangement shown in figure

4.18 employs a linkage between the fixed sur-

face and the tab surface. The geometry is

such that upward deflection of the control

surface displaces the tab down relative to the

control surface. Such relative displacement

of the tab will aid in deflection of the control

surface and thus reduce the hinge moments due

to deflection. An obvious advantage of this

device is the reduction of deflection hinge

moments without a change in aerodynamic

balance.

The leading tab arrangement shown in figure

4.18 also employs a linkage between the fixed

surface and the tab surface. However, the

geometry of the linkage is such that upward

deflection of the control surface displaces the

tab up relative to the control surface. This

relationship serves to increase the control sur-

face hinge moments due to deflection of the

surface.

The servo tad shown in figure 4.18 utilizes a

horn which has no direct connection to the

control surface and is free to pivot about the

hinge axis. However, a linkage connects this

free horn to the tab surface. Thus, the control

system simply deflects the tab and the resulting

hinge moments deflect the control surface.

NAVWEPS 00-EOT-80

STABILITY AND CONTROL

TRIM TAB

VARIABLE LINKAGE

LAGGING TAB

LEAOING TAB

SERVO TAB

HORN FREE TO

PIVOT ON HINGE 13X6

SPRING TAB

ON HINGE AXIS

FIXED TO SURFACE

SPRING LLADED TAB

ROTATES TAB UP

Figure 4.18. Various Tab Devices

Since the only control forces are those of the

tab, this device makes possible the deflection

of large surfaces with relatively small control

forces.

A variation of the basic servo tab layout is

the sprirzg tab arrangement of figure 4.18.

When the control horn is connected to the

control surface by springs, the function of the

tab is to provide a given portion of the required

control forces. The spring tab arrangement

can then function as a boost to reduce control

forces. The servo tab and spring tab are

usually applied to large or high speed subsonic

airplanes to provide tolerable stick forces.

The spring Zoadcd tab of figure 4.18 cotisists

of a free tab preloaded with a spring which

furnishes a constant moment about the tab

hinge line. When the airplane is at zero air-

speed, the tab is rotated up to the limit of

deflection. As airspeed is increased, the aero-

dynamic hinge moment on the tab will finally

equal the spring torque and the tab will begin

to streamline. The effect of this arrangement

is to provide a constant hinge moment to the

control system and contribute a constant push

force requirement at speeds above the preload

speed. Thus, the spring loaded tab can im-

prove the stick force gradient in a manner

similar to the downspring. Generally, the

spring loaded tab may be more desirable

because of greater effectiveness and the lack of

undesirable control forces during ground

operation.

The various tab devices have almost un-

limited possibilities for tailoring control forces.

However, these devices must receive proper

care and maintenance in order to function

properly. In addition, much care must be

taken to ensure that no slop or play exists in

the joints and fittings, otherwise destructive

flutter may occur.

LONGITUDINAL CONTROL

To be satisfactory, an airplane must have

adequate controllability as well as adequate

NAVWEPS OtWOT-80

STABILITY AND CONTROL

stability. Ati airplane with high static longi-

tudinal stability will exhibit great resistance

to displacement from equilibrium. Hence,

the most critical conditions of controllability

will occur when the airplane has high sta-

bility, i.e., the lower limits of controllability

will set the upper limits of stability.

There are three principal conditions of

fli~ght which provide the critical requirements

of longitudinal control power. Any one

or combination of these conditions can de-

termine the longitudinal control power and

set a limit to forward c.g. position.

MANEUVERING CONTROL REQUIRE-

MENT. The airplane should have sufficient

longitudinal control power to attain the maxi-

mum usable lift coefficient or limit load factor

during maneuvers. As shown in figure 4.19,

forward movement of the c.g. increases the

longiturjinal stability of an airplane and

requires larger control deflections to produce

changes in trim lift coefficient. For the

example shown, the maximum effective de-

flection of the elevator is not capable of trim-

ing the airplane ‘at C,,,, for c.g. positions

ahead of 18 percent MAC.

This particular control requirement can be

most critical for an airplane in supersonic

flight. Supersonic flight is usually accom- . panied by large increases in static longltu-

dinal stability and a reduction in the effective-

ness of control surfaces. In order to cope with

these trends, powerful all-movable surfaces

must be used to attain limit load factor or

maximum usable C, in supersonic flight. This

requirement is so important that once satis-

fied, the supersonic configuration usually has

sufficient longitudinal control power for all

other conditions of flight.

TAKEOFF CONTROL REQUIREMENT.

At takeoff, the airplane must have sufficient

control power to assume the takeoff attitude

prior to reaching takeoff speed. Generally,

for airplanes with tricycle landing gears, it

is desirable to have at least sufficient control

power to attain the takeoff attitude at 80

NAVWEPS 00-80’1-80

SlABILITY AND CONTROL

MAXIMUM MOST FORWARD

DEFLECTION CG FOR MANEUVERING

CONTROLLABILITY

DOWN POSITION

TAIL

LOAD

!'.',i:'.

WEIGHT

TAKE OFF CONTROL

REDUCED DOWNWASH

DUE TO GROUND EFFECT

. .:,.,. ‘,:::.;,y ,;,,.,,>: ::..‘~~,‘i;,:,‘,,:.~,,‘: y: :, ,: ,/. :“‘J.:;:‘j:~!,.: : :., :, .‘. ;. ~.. i... .,-: -, :,.: ~, :,., :.:, :~’

LANDING CONTROL

Figure 4.19. Longitudinal Control Requirements

percent of the stall speed for propeller air-

planes or 90 percent of the stall speed for jet

airplanes. This feat must be accomplished on

a smooth runway at all normal service takeoff

loading conditions.

Figure 4.19 illustrates the principal forces

acting on an airplane during takeoff toll.

When the airplane is in the three point attitude

at some speed less than the stall speed, the

wing lift will be less than the weight of the

airplane. As the elevators must be capable

of rotating to the takeoff attitude, the critical

condition will be with zero load on the nose

wheel and the net of lift and weight supported

on the main gear. Rolling friction resulting

from the normal force on the main gear creates

an adverse nose down moment. Also, the

center of gravity ahead of the main gear

contributes a nose down moment and this

consideration could decide the most aft loca-

tion of the main landing gear during design.

The wing may contribute a large nose down

moment when flaps are deflected but this

effect may be countered by a slight increase

in downwash at the tail. To balance these

nose down moments, the horizontal tail

should be capable of producing sufficient nose

up moment to attam the takeoff attitude. at

the specified speeds.

The propeller airplane at takeoff power may

induce considerable slipstream velocity at the

horizontal tail which can provide an increase

in the e&iency of the surface. The jet

airplane does not experience a similar magni-

tude of this effect since the induced velocities

from the jet are relatively small compared

to the slipstream velocities from a propeller.

LANDING CONTROL REQUIREMENT

At landing, the airplane must have suthcient

control power to ensure adequate control at

specified landing speeds. Adequate landing

control is usually assured if the elevators are

capable of holding the airplane just off the

runway at 105 percent of the stall speed. Of

course, the most critical requirement will exist

when the c.g. is in the most forward position,

NAVWEPS 00-BOT-80

STABILITY AND CONTROL

flaps are fully extended, and power is set at

idle. This configuration will provide the

most stable condition which is most demand-

ing of controllability. The full deflection of

flaps usually provides the greatest wing diving

moment and idle power will produce the most

critical (least) dynamic pressure at the hoti-

zontal tail.

The landing control requirement has one

particular difference from the maneuvering

control requirement of free flight. As the

airplane approaches the ground surface, there

will be a change in the three-dimensional flow

of the airplane due to ground effect. A wing in

proximity to the ground plane will experience

a decrease in tip vortices and downwash at

a given lift coefficient. The decrease in down-

wash at the tail tends to increase the static

stability and produce a nosedown moment from

the reduction in download on the tail. Thus,

the airplane just off the runway surface will

requite additional control deflection to trim

at a given lift coefficient and the landing con-

trol requirement may be critical in the design

of longitudinal control power.

As an example of ground effect, a typical

propeller powered airplane may requite as

much as 15” more up elevator to trim at CL-

in ground effect than in free flight away from

the ground plane. Because of this effect, many

aitplaneshavesufIicientcontrolpowertoachieve

full stall out of ground effect but do not have

the ability to achieve full stall when in close

proximity to the ground.

In some cases the effectiveness of the control

surface is adversely affected by the use of trim

tabs. If trim tabs are used to excess in ttim-

ming stick forces, the effectiveness of the

elevator.may be reduced to hinder landing or

takeoff control.

Each of the three principal conditions re-

quiting adequate longitudinal control are ctit-

ical for high static stability. If the forward

c.g. limit is exceeded, the airplane may en-

counter a deficiency of controllability in any

of these conditions. Thus, the forward c.g.

limit is set by the minimum permissible con-

trollability while the aft c.g. limit is set by

the minimum permissible stability.

LONGITUDINAL DYNAMIC STABILITY.

All previous considerations of longitudinal

stability have been concerned with the initial

tendency of the airplane to return to equilib-

rium when subjected to a disturbance. The

considerations of longitudinal dynamic sta-

bility ate concerned with time history response

of the airplane to these disturbances, i.e., the

variation of displacement amplitude with time

following a disturbance. From previous deli-

nition, dynamic stability will exist when the

amplitude of motion decreases with time and

dynamic instability will exist if the amplitude

increases with time.

Of course, the airplane must demonstrate

positive dynamic stability for the major longi-

tudinal motions. In addition, the airplane

must demonstrate a certain degree of longitu-

dinal stability by reducing the amplitude of

motion at a certain rate. The requited degree

of dynamic stability is usually specified by

the time necessary for the amplitude to reduce

to one-half the original value-the time to

damp to half-amplitude.

The airplane in free flight has six degrees of

freedom: rotation in roll, pitch, and yaw and

translation in the horizontal, vertical, and

lateral directions. In the case of longitudinal

dynamic stability, the degrees of freedom can

be limited to pitch rotation, vertical and

horizontal translation. Since the airplane is

usually symmetrical from port to starboard,

there will be no necessity for consideration of

coupling between longitudinal and lateral-

directional motions. Thus, the principal vari-

ables in the longitudinal motion of an airplane

will be:

(1) The pitch attitude of the airplane.

(2) The angle of attack (which will differ

from the pitch attitude by the inclination of

the flight- path).

(3) The flight velocity.

NAVWEPS DD-801-80

STABILITY AND CONTROL

(4) The displacement or deflection of the

elevator when the stick-free condition is

considered.

The longitudinal dynamic stability of an

airplane generally consists of three basic modes

(or manners) of oscillation. While the longi-

tudinal motion of the airplane may consist of a

combination of these modes, the characteristics

of each mode are sufficiently distinct that each

oscillatory tendency may be studied separately.

The first mode of dynamic longitudinal sta-

bility consists of a very long period oscillation

referred to as the phagoid. The phugoid or long

period oscillation involves noticeable vatia-

tions in pitch attitude, altitude, and airspeed

but nearly constant angle of attack. Such an

oscillation of the airplane could be considered

as a gradual interchange of potential and

kinetic energy about some equilibrium airspeed

and altitude. Figure 4.20 illustrates the char-

acteristic motion of the phugoid.

The period of oscillation in the phugoid is

quite large, typical values being from 20 to 100

seconds. Since the pitching rate is quite low

and only negligible changes in angle of attack

take place, damping of the phugoid is weak and

possibly negative. However, such weak or

negative damping does not necessarily have any

great consequence. Since the period of oscilla-

tion is so great, the pilot is easily able to

counteract the oscillatory tendency by very

slight and unnoticed control movements. In

most cases, the necessary corrections ate so

slight that the pilot may be completely un-

aware of the oscillatory tendency.

Due to the nature of the phugoid, it is not

necessary to make any specific aerodynamic

provisions to contend with the oscillation.

The inherent long period of the oscillation al-

lows study to be directed to more important

oscillatory tendencies. Similarly, the diffet-

ences between the stick-fixed and stick-free

phugoid are not of great importance.

The second mode of longitudinal dynamic sta-

bility is a relatively short period motion that

NAVWEPS OO-BOT-80

STABILITY AND CONTROL

IST MODE OR PHUGOID

ANGLE OF ATTACK AT EACH

INS%; ,,“L&blSG$~,lGH~ &

5 LoNG PERIOD ------I kw a0 f 2 -

g: *a

2 0

2ND MODE OR SHORT PERIOD OSCILLATION

MOTION OCCURS AT ESSENTIALLY CONSTANT SPEED

L TIME TO DAMP TO

HALF AMPLITUDE

Lb-- TIME

/

/

-6.HORT PERIOD -

UNSTABLE OSCILLATION

Figure 4.20. Longiitudinal Dynamic Sttxbility

can be assumed to take place with negligible

changes in velocity. The second mode consists

of a pitching oscillation during which the air-

plane is being restored to equilibrium by the

static stability and the amplitude of oscillation

decreased by pitch damping. The typical mo-

tion is of relatively high frequency with a

period of oscillation on the order of 6.5 to 5

seconds.

For the conventional subsonic airplane, the

second mode stick-fixed is characterized by

heavy damping with a time to damp to half

amplitude of approximately 0.5 seconds. IJsu-

ally, if the airplane has static stability stick-

fixed, the pitch damping contributed by the

horizontal tail will assume sufficient dynamic

stability for the short period oscillation. How-

ever, the second mode stick-free has the possi-

bility of weak damping or unstable oscilla-

tions. This is the case where static stability

does not automatically imply adequate dy-

namic stability. The second mode stick-free is

essentially a coupling of motion between the

airplane short period pitching motion and ele-

vator in rotation about the hinge line. Ex-

treme care must be taken in the design of the

control surfaces to ensure dynamic stability for

this mode. The elevators must be statically

balanced about the hinge line and aerodynamic

balance must be within certain limits. Control

system friction must be minimized as it con-

tributes to the oscillatory tendency. If insta-

bility were to exist in the second mode, “por-

poising” of the airplane would result with

possibility of structural damage. An oscilla-

tion at high dynamic pressures with large

changes in angle of attack could produce severe

flight loads.

The second mode has relatively short periods

that correspond closely with the normal pilot

response lag time, e.g., 1 or 2 seconds or less.

There is the possibility that an attempt to

forceably damp an oscillation may actually re-

inforce the oscillation and produce instability.

This is particularly true in the case of powered

controls where a small input energy into the

NAVWEPS 00-BOT-80

STABILITY AND CONTROL

control system is greatly magnified. In addi-

tion, response lag of the controls may add to

the problem of attempting to forceably damp

the oscillation. In this case, should an oscilla-

tion appear, the best rule is to release the con-

trols as the airplane stick-free will demonstrate

the necessary damping, Even an attempt to

fix the controls when the airplane is oscillating

may result in a small unstable input into the

control system which can reinforce the oscilla-

tion to produce failing flight loads. Because

of the very short period of the oscillation, the

amplitude of an unstable oscillation can reach

dangerous proportions in an extremely short

period of time.

The third mode occurs in the elevator free case

and is usually a very short period oscillation.

The motion is essentially one of the elevator

flapping about the hinge line and, in most

cases, the oscillation has very heavy damping.

A typical flapping mode may have a period of

0.3 to 1.5 seconds and a time to damp to half-

amplitude of approximately 0.1 second.

Of all the modes of longitudinal dynamic

stability, the second mode or porpoising oscil-

lation is of greatest importance. The por-

poising oscillation has the possibility of

damaging flight loads and can be adversely

affected by pilot response lag. It should be

remembered that when stick-free the airplane

will demonstrate the necessary damping.

The problems of dynamic stability are acute

under certain conditions of flight. Low static

stability generally increases the period (de-

creases frequency) of the short period oscil-

lations and increases the time to damp to half-

amplitude. High altitude-and consequently

low density-reduces the aerodynamic damp-

ing. Also, high Mach numbers of supersonic

flight produce a decay of aerodynamic damping.

MODERN CONTROL SYSTEMS

In order to accomplish the stability and

control objectives, various configurations of

control systems are necessary. Generally, the

?Bl

NAVWEPS 00-BOT-BO

STABILITY AND CONTROL

type of flight control system is decided by the

size and flight speed range of the airplane.

The conventional control system consists of

direct mechanical linkages from the controls

to the control surfaces. For the subsonic

airplane, the principal means of producing

proper control forces utilize aerodynamic bal-

ance and various tab, spring, and bobweight

devices. Balance and tab devices are capable

of reducing control forces and will allow the

use of the conventional control system on large

airplanes to relatively high subsonic speeds.

When the airplane with a conventional

control system is operated at transonic speeds,

the great changes in the character of flow

can produce great aberrations in control sur-

face hinge moments and the contribution of

tab devices. Shock wave formation and

separation of flow at transonic speeds will

limit the use of the conventional control

system to subsonic speeds.

The power-boosted control system employs a

‘mechanical actuator in parallel with the

mechanical linkages of a conventional control

system. The principle of operation is to pro-

vide a fixed, percentage of the required control

forces thus reducing control forces at high

speeds. The power-boosted control system

requires a hydraulic actuator with a control

valve which supplies boost force in fixed

proportion to control force. Thus, the pilot

is given an advantage by the boost ratio to

assist in deflecting the control surface, e.g.,

with a boost ratio of 14, the actuator provides

14 lbs. of force for each 1 lb. of stick force.

The power-boosted control system has the

obvious advantage of reducing control forces

at high speeds. However, at transonic speeds,

the changes in control forces due to shock

waves and separation still take place but to a

lesser degree. The “feedback” of hinge

moments is reduced but the aberrations in

stick forces may still exist.

The power-opsrdted, irreversible control system

consists of mechanical actuators controlled

by the pilot. The control surface is deflected

by the actuator and none of the hinge moments

are fed back through the controls. In such

a control system, the control position decides

the deflection of the control surfaces regardless

of the airloads and hinge moments. Since the

power-operated control system has zero feed-

back, control feel must be synthesized other-

wise an infinite boost would exist.

The advantages of the power-operated COR-

trol system are most apparent in transonic and

supersonic flight. In transonic flight, none of

the erratic hinge moments are fed back to the

pilot. Thus, no unusual or erratic control

forces,will be encountered in transonic flight.

Supersonic flight generally requires the use of

an all-movable horizontal surface to achieve

the necessary control effectiveness. Such con-

trol surfaces must then be actuated and posi-

tively positioned by an irreversible device.

The most important item of an artificial feel

system is the stick-centering spring or bungee.

The bungee develops a stick force in proportion

to stick displacement and thus provides feel

for airspeed and maneuvers. A bobweight

may be included in the feel system to develop

a steady positive maneuvering stick force

gradient which is independent of airspeed for

ordinary maneuvers.

The gearing between the stick position and

control surface deflection is not necessarily a

linear relationship. The majority of powered

control systems will employ a nonlinear gear-

ing such that relatively greater stick deflection

per surface deflection will occur at the neutral

stick position. This sort of gearing is to

advantage for airplanes which operate at flight

conditions of high dynamic pressure. Since

the airplane at high 4 is very sensitive to small

deflections of the control surface, the nonlinear

gearing provides higher stick force stability

with less sensitive control movements than

the ‘system with a linear gearing. Figure 4.21

illustrates a typical linear and nonlinear control

system gearing.

The second chart of figure 4.21 illustrates

the typical control system stick force variation

NAVWEPS 00-ROT-80

STABILITY AND CONTROL

CONTROL SYSTEM GEARING

CONTROL SYSTEM STICK FORCE

-40

STICK FORCE LBS.

-30

PULL

-20

-10

STABILIZER DEFLECTION

LEADING EDGE DOWN LEADING EDGE UP

25O 200 I50 100 50 50 I00

Figure 4.27. Longitudinal Control System

NAVWEPS OO-ROT-80

STABILITY AND CONTROL

with control surface deflection. While it is

desirable to have a strong centering of the

stick near the neutral position, the amount of

force required to create an initial displacement

must be reasonable. If the control system

“break-out” forces are too high, precise control

of’the airplane at high speeds is diflicult. As

the solid friction of the control system con-

tributes to the break-out forces, proper mainte-

nance of the control system is essential. Any

increase in control system friction can create

unusual and undesirable control forces.

The trim of the powered control system is

essentially any device to produce zero control

force for a given control surface deflection.

One system may trim off bungee force at a

given stick position while another system may

trim by returning the stick to neutral position.

Flight at high supersonic Mach numbers

might require a great variety of devices in the

longitudinal control system. The deteriora-

tion of pitch damping with Mach-number may

require that dynamic stability be obtained

synthetically by pitch dampers in the control

system. The response of the airplane to

longitudinal control may be adversely affected

by flight at high dynamic pressures. In such

conditions of flight stick forces must be ade-

quate to prevent an induced oscillation. Stick

forces must relate the transients of flight as

well as the steady state conditions. Such a

contribution to control system forces may be

provided by a pitching acceleration bobweight

and a control system viscous damper.

DIRECTIONAL STABILITY AND CONTiOL

DIRECTIONAL STABILITY

The directional stability of an airplane is

essentially the “weathercock” stability and

involves moments about the vertical axis and

their relationship with yaw or sideslip angle.

An airplane which has static directional sta-

bility would tend to return to an equilibrium

when subjected to some disturbance from equi-

librium. Evidence of static directional sta-

bility would be the development of yawing

moments which tend to restore the airplane

to equilibrium.

DEFINITIONS. The axis system of an air-

plane will define a positive yawing moment,

N, as a moment about the vertical axis which

tends to rotate the nose to the right. As in

other aerodynamic considerations, it is con-

venient to consider yawing moments in the

coefficient form so that static stability can be

evaluated independent of weight, altitude,

speed, etc. The yawing moment, N, is de-

fined in the coefficient form by the following

equation:

or

N = C,qSb

C,=N 0 where

N=yawing moment, ft.-lbs;

positive to the right

q= dynamic pressure, psf

S=wing area, sq. ft.

b=wing span, ft.

C,=yawing moment coefficient, positive

to the right

The yawing moment coefficient, C,, is based on

the wing dimensions $ and 6 as the wing is the

characteristic surface of the airplane.

The yaw angle of an airplane relates the dis-

placement of the airplane centerline from some

reference azimuth. and is assigned the short-

,hand notation I& (psi). A positive yaw angle

occurs when the nose of the airplane is dis-

placed to the right of the azimuth direction.

The definition of sideslip angle involves a sig-

nificant difference. Sides&p angle relates the

displacement of the airplane centerline from

the relative wind rather than some reference

azimuth., Sideslip angle is’provided the short-

hand notation p (beta) and is positive when

ihe rela&e wind is displaced to the right of

the,airplane centerline. Figure 4.22 illustrates

the definitions of sideslip and yaw angles.

The sideslip angle, 8, is essentially the di-

rectional angle of attack of the airplane and

is the primary reference in lateral stability as

well as directional stability considerations.

The yaw angle, #, is a primary reference for

wind tunnel tests and time history motion of

an airplane. From the definitions there is no

direct relationship between @ and # for an

airplane in free flight, e.g., an airplane flown

through a 360° turn has yawed 360” but side-

slip may have been zero throughout the entire

turn. Since the airplane has no directional

sense, static directional stability of the air-

plane is appreciated by response to sideslip.

The static directional stability of an airplane

can be illustrated by a graph of yawing moment

coe&cient, C., versus sideslip angle, 8, such as

shown in figure 4.22. When the airplane is

subject to a positive sideslip angle, static direc-

tional stability will be evident if a positive

yawing moment coefficient results. Thus,

when the relative wind comes from the right

(+p), a yawing moment to the right (+C.)

should be created which tends to weathercock

the airplane and return the nose into the wind.

Static directional stability will exist when the

curve of C,, versus fi has a positive slope and the

degree of stability will be a function of.the

slope of this curve. If the curve has zero slope,

there is no tendency to return to equilibrium

and neutral static directional stability exists.

When the curve of C. versus /3 has a negative

slope, the yawing moments developed by side-

slip tend to diverge rather than restore and

static directional instability exists.

The final chart of figure 4.22 illustrates the

fact that the instantaneous slope of the curve of

C,, versus @ will describe the static directional

stability of the airplane. At small angles of

sideslip a strong positive slope depicts strong

directional stability. Large angles of sideslip

produce zero slope and neutral stability. At

very high sideslip the negative slope of the

curve indicates directional instability. This

decay of directional stability with increased

sideslip is not an unusual condition. However,

directional instability should not occur at the

angles of sideslip of ordinary flight conditions.

NAVWEPS 00-ROT-80

STABILITY AND CONTROL

Static directional stability must be in evi-

dence for all the critical conditions of flight.

Generally, good directional stability is a ftm-

damental quality directly affecting the pilots’

impression of an airplane.

CONTRIBUTION OF THE AIRPLANE

COMPONENTS. The static directional sta-

bility of the airplane is a result of contribution

of each of the various airplane components.

While the contribution of each component is

somewhat dependent upon and related to other

components, it is necessary to study each

component separately.

The vertical tail is the primary source of

directional stability for the airplane. As

shown in figure 4.23, when the airplane is in

a sideslip the vertical tail will experience a

change in angle of attack. The change in

lift-or side force-on the vertical tail creates

a yawing moment about the center of gravity

which tends to yaw the airplane into the

relative wind. The magnitude of the vertical

tail contribution to static directional stability

then depends on the change in tail lift and the

tail moment arm. Obviously, the tail moment

arm is a powerful factor but essentially dic-

tated by the major configuration properties of

the airplane.

When the location of the vertical tail is set,,

the contribution of the surface to directional

stability depends on its ability to produce

changes in lift-or side force-with changes in

sideslip. The surface area of the vertical tail

is a powerful factor with the contribution of

the vertical tail being a direct function of the

area. When all other possibilities are ex-

hausted, the required directional stability may

be obtained by increases in tail area. How-

ever, increased surface area has the obvious

disadvantage of increased drag.

The lift curve slope of the vertical tail

relates how sensitive the surface is to changes

in angle of attack. While it is desirable to

have a high lift curve slope for the vertical

surface, a high aspect ratio surface is not

necessarily practical or desirable. The stall

NAVWEPS 00-ROT-80

STABILITY AND CONTROL

+N,YAWlNG MOMENT

YAWING MOMENT

COEFFICIENT,Cn

+Cn

p SIDESLLANGLE,

Figure 4.22. Static Directional Stability

angle of the surface must be sufficiently great

to prevent stall and subsequent loss of effec-

tiveness at ordinary sideslip angles. The high

Mach numbers of supersonic flight produces a

decrease in lift curve slope with the consequent

reduction in tail contribution to stability. In

order to have sufficient directional stability at

high Mach numbers, the typical supersonic

configuration will exhibit relatively large

vertical tail surfaces.

The flow field in which the vertical tail

operates is affected by the othei components

of the airplane as well as powe; effects. The

dynamic pressure at the vertical tail could

depend on the slipstream of a propeller or the

boundary layer of the fuselage. Also, the

local flow direction at the vertical tail is in-

fluenced by the wing wake, fuselage crossflow,

induced flow of the horizontal tail, or the

direction of slipstream from a propeller. Each

of these factors must be considered as possibly

affecting the contribution of the vertical tail

to directional stability.

The contribution of the wing tb %tatic direc-

tional stability is tisually small: The swept

wing provides a stable contribution’depending

on the amount of sweepback but the contribu-

tion is relatively weak when compared with

other components. :. The contribution of the fuselage and nacelles

is of primary importance since these compo-

nents furnish rhe greatest destabilizing in-

fluence. The contribution of the fuselage and

nacelles is similar to the longitudinal case

with the exception that there is no large in-

fluence of the induced flow field of the wing.

The subsonic center of pressure of the fuselage

will be located at or forward of the quarter-

length point and, since the airplane c.g. is

usually considerably aft of this point, the

fuselage contribution will be destabilizing.

However, at large angles of sideslip the large

destabilizing contribution of the fuselage di-

minishes which is some relief to the problem

of maintaining directional stability at large

displacements. The supersonic pressure,. dis-

tribution on the body provides a relatively

NAVWEPS OO-ROLRO

STARIUTY AND CONTROL

greater aerodynamic force and, generally, a

continued destabilizing influence.

Figure 4.23 illustrates a typical buildup of

the directional stability of an airplane by

separating the contribution of the fuselage

and tail. As shown by the graph of C. versus

6, the contribution of the fuselage is de-

stabilizing but the instability decreases at

large sideslip angles. Tbe contribution of the

vertical tail alone is highly stabilizing up to

the point where the surface begins to stall.

The contribution of the vertical tail must be

large enough so that the complete airplane

(wing-fuselage-tail combination) exhibits the

required degree of stability.

The dorsal fin has a powerful effect on pre-

serving the directional stability at large angles

of sideslip wliich would produce stall of the

vertical tail. The addition of a dorsal fin to

the airplane will allay the decay of directional

stability at high sideslip in two ways. The

least obvious but most important effect is a

large increase in the fuselage stability at large

sideslip angles. In addition, the effective

aspect rario of the vertical tail is reduced

which increases the stall angle for the surface.

By this twofold effect, the addition of the

dorsal fin is a v useful’ device.

Poluer effects on static directional stability

are similar to the power effects on static

longitudinal stability. The direct effects are

confined to the normal force at the propeller

plane or the jet inlet and, of course, are de-

stabilizing when the propeller or inlet is

located ahead of the c.g. The indirect effects

of power induced velocities and flow dirkccion

changes at the vertical tail are quite significant

for the propeller driven airplane and can pro-

duce large directional trim changes. As in

the lontitudinal case, the indirect effects are

negligible for the jet powered airplane.

The contribution of the direct and indirect

power effects to static directional stability is

greatest for the propeller powered airplane

and usually slight for the jet powered airplane.

In either case, the general effect of power is

NAVWEPS oO-801-80

STABILITY AND CONTROL

CONTRIBUTION OF VERTICALTAIL

CHANGE IN

TAIL LIFT

TYPICAL DIRECTIONAL STABILITY

BUILD-UP

AIRPLANE WITH

DORSAL FIN

STALL ,-ADDED

Figure 4.23. Contribution of Components to Directional Stability

NAVWEPS Oe8OT-80

STABILITY AND CONTROL

EFFECT OF RUDDER FLOAT ON STATIC

DIRECTIONAL STABILITY

\ RUDDER-FIXED

RUDDER-FREE

RUDDER FLOAT

-e ANGLE

SIDESLIP ANGLE, p

EFFECT OF ANGLE OF ATTACK

HIGH ANGLE

OF ATTACK

SIDESLIP ANGLE, fla

EFFECT OF MACH NUMBER

SIDESLIP ANGLE, p

Figure 4.24. Factors Affecting Direcfional Stability

NAVWRPS DD-807-80

STABILITY AND CONTROL

destabilizing and the greatest contribution

will occur at high power and low dynamic

pressure as during a waveoff.

As in the case of longitudinal static stability,

freeing the controls will reduce the effective-

ness of the tail and alter the stability. While

the rudder must be balanced to reduce control

pedal forces, the rudder will tend to float or

streamline and reduce the contribution of the

vertical tail to static directional stability. The

floating tendency is greatest at large angles of

sideslip where large angles of attack for the

vertical tail tend to decrease aerodynamic bal-

ante. Figure 4.24 illustrates the difference be-

tween rudder-fixed and rudder-free static di-

rectional stability.

CRITICAL CONDITIONS. The most criti-

cal conditions of,staric directional stability are

usually the combination of several separate

effects. The combination which produces the

most critical condition is much dependent upon

the type and mission of the airplane. In addi-

tion, there exists a coupling of lateral and di-

rectional effects such that the required degree

of static directional stability may be deter-

mined by some of these coupled conditions.

Center of gravity position has a relatively

negligible effect on static directional stability.

The usual range of c.g. position on any air-

plane is set by the Jinits of long&d&a/ stability

and control. Within this limiting range of

c.g. position, no significant changes take place

in the contribution of the vertical tail, fuselage,

nacelles, etc. Hence, the static directional

stability is essentially unaffected by the varia-

tion of c.g. position within the longitudinal

limits.

When the airplane is at a high angle of a$tack

a decrease in static directional stability can be

anticipated. As shown by the second chart of

figure 4.24, a high angle of attack reduces the

stable slope of the curve of C,, versus 8, The

decrease in static directional stability is due in

great part to the reduction in the contribution

of the vertica1 tail. At high angles of attack,

the effectiveness of the vertical tail is reduced

because of increase in the fuselage boundary

layer at the vertical tail location. The decay of

dir&ctional stability with angle of attack is

most significant for the low aspect ratjo air-

plane with sweepback since this configuration

requires such high angles of attack to achieve

high lifr coefficients. Such decay in directional

stability can have a profound effect on the re-

sponse of the airplane to adverse yaw and spin

characteristics.

High Mach ntrmbers of supersonic flight reduce

the contribution of the vertical tail to direc-

tional stability because of the reduction of lift

cnrve slope with Mach number. The third

chart of figure 4.24 illustrates the typical decay

of directional stability with Mach number. To

produce the required directional stability at

high Mach numbers, a viziy large vertical tail

area may be necessary. Ventral fins may be

added as an additional contribution to direc-

tional stability but landing clearance require-

ments may limir their size or require the fins to

be retractable.

Hence, the most critical demands of static

directional stability will occur from some

combination of the following effects:

(1) high angle of sideslip

(2) high power at low airspeed

(3) high angle of attack

(4) high Mach number

The propeller powered airplane may have such

considerable power effects that the critical

conditions may occur at low speed while the

effect of high Mach numbers may produce the

critical conditions for the typical supersonic

airplane. In addition, the coupling of lateral

and directional effects may require prescribed

degrees of directional stability.

DIRECTIONAL CONTROL

In addition to directional stability, the air-

plane must have adequate directional control

to coordinate turns, balance power effects,

create sideslip, balance unsymmetrical power,

etc. The principal source of directional con-

trol is the rudder and the rudder must be

capable of producing sufhcient yawing moment

for the critical conditions of flight.

The effect of rudder deflection is to produce

a yawing moment coefficient according to

control deflection and produce equilibrium at

some angle of sideslip. For small deflections

of the rudder, there is no change in stability

but a change in equilibrium. Figure 4.25

shows the effect of rudder deflection on yawing

moment coefficient curves with the change in

equilibrium sideslip angle.

If the airplane exhibits static directional

stability with rudder lixed, each angle of side-

slip requires a particular deflection of the

rudder to achieve equilibrium. Rudder-free

directional stability will exist when the float

angle of the rudder is less than the rudder

deflection required for equilibrium. However

at high angles of sideslip, the floating tend-

ency of the rudder increases. This is illus-

trated by the second chart of figure 4.25 where

the line of rudder float angle shows a sharp

increase at large values of sideslip. If the

floating angle of the rudder catches up with

the required rudder angle, the, rudder pedal

force will decrease to zero and rudder lock will

occur. Sideslip angles beyond this point pro-

duce a floating angle greater than the required

rudder deflection and the rudder tends to float

to the limit of deflection.

Rudder lock is accompanied by a reversal of

pedal force and rudder-free instability will

exist. The dorsal fin is a useful addition in

this case since it will improve the directional

stability at high angles of sideslip. The re-

sulting increase in stability requires larger

deflections of the rudder to achieve equilibrium

at high sideslip and the tendency for rudder

lock is reduced.

Rudder-free directional stability is appre-

ciated by the pilot as the rudder pedal force to

maintain a given sideslip. If the rudder pedal

force gradient is too low near zero sideslip, it

will be difficult to maintain zero sideslip dur-

ing various maneuvers. The airplane should

NAVWEPS 00-SOT-80

STABIUTY AND CONTROL

have a stable rudder pedal feel through the

available range of sideslip.

DIRECTIONAL CONTROL REQUIRE-

MENTS. The control power of the rudder

must be adequate to contend with the many

unsymmetrical conditions of flight. Gener-

ally, there are five conditions of flight which

provide the most criticalrequirements of di-

‘rectional control power. The type and mission

of the airplane will decide which of these

conditions is most important.

ADVERSE YAW. When an airplane is

rolled into a turn yawing moments are pro-

duced which require rudder deflection to main-

tain zero sideslip, i.e., coordinate the turn.

The usual source of adverse yawing moment is

illustrated in figure 4.26. When the airplane

shown is subject to a roll to the left, the down-

going port wing will experience a new relative

wind and an increase in angle of attack. The

inclination of the lift vector produces a com-

ponent force forward on the downgoing wing.

The upgoing starboard wing has its lift in-

clined with a component force aft. The re-

sulting yawing moment due to rolling motion

is in a direction opposite to the roll and is

hence “adverse yaw.” The yaw due to roll is

primarily a function of the wing lift coefficient

and is greatest at high C,.

In addition to the yaw due to rolling motion

there will be a yawing moment contribution

due to control surface deflection. Conventional

ailerons usually contribute an adverse yaw

while spoilers may contribute a favorable or

“proverse” yaw. The high wing airplane

with a large vertical tail may encounter an

influence from inboard ailerons. Such a con-

figuration may induce flow directions at the

vertical tail to cause proverse yaw.

Since adverse yaw will be greatest at high

C, and full deflection of the ailerons, coordi-

nating steep turns at low speed may produce

a critical requirement for rudder control power.

SPIN RECOVERY. In the majority of air-

planes, the rudder is the principal control for

spin recovery. Powerful control of sideslip at

NAVWEPS 00-807-80

STABILITY AND CONTROL

EFFECT OF RUDDER DEFLECTION ON

EOlJlLlSRlUM SIDESLIP ANGLE

RUDDER DEFLECTION

RUDDER LOCK.

RUDDER DEFLECTION

FLOAT ANGLE

/ SIDESLIP ANGLE, p +

EFFECT DF RUDDER LOCK ON PEDAL FORCE

RUDDER LOCK

+P

---

DORSAL FIN ADDED

Figure 4.25. Directional Control

ADVERSE YAW DUE TO ROLL

FORCE FORWARD

DOWNGOING

PORT WING

,IRPLANE.IN ROLL TO LEFT

NAVWEPS 00-8OT-30

STABILITY AND CONTROL

\FOR SAKE OF CLARITY. /

SLIPSTREAM SWIRL ON THE PROPFLLER POWERED AIRPLANE

YAWING MOMENT COEFFICIENT

FROM ASYMMETRICAL /

THRUST

YAWING MOMENT DUE TO ASYMMETRICAL THRUST

EQUIVALENT AIRSPEED, KNOTS

Figure 4.26. Requirements for Directional Control

NAVWEPS 00-8OT-80

STABILITY AND CONTROL

high angles of attack is required to effect re-

covery during a spin. Since the effectiveness

of the vertical tail is reduced at large angles of

attack, the directional control power neces-

sary for spin recovery may produce a critical

requirement of rudder power.

SLIPSTREAM ROTATION. A critical di-

rectional control requirement may exist when

the propeller powered airplane is at high

power and low airspeed. As shown in figure

4.26, the single rotation propeller induces

a slipstream swirl which causes a change in

flow direction at the vertical tail. The rudder

must furnish sufficient control power to balance

this condition and achieve zero sideslip.

CROSSWIND TAKEOFF AND LANDING.

Since the airplane must make a true path down

the runway, a crosswind during takeoff or

landing will require that the airplane be.con-

trolled in a sideslip. The rudder must have

sufficient control power to create the required

sideslip for the expected crosswinds.

ASYMMETRICAL POWER. The design

of a multiengine airplane must account for the

possibility of an engine failure at low airspeed.

The unbalance of thrust from a condition of

unsymmetrical power produces a yawing mo-

ment dependent upon the thrust unbalance

and the lever arm of the force. The deflection

of the rudder will create a side force on the tail

and contribute a yawing moment to balance

the yawing moment due to the unbalance of

thrust. Since the yawing moment coefficient

from the unbalance of thrust will be greatest

at low speed, the critical requirement will be

at a low speed with the one critical engine

out and the remaining engines at maximum

power. Figure 4.26 compares the yawing

moment coeflicient for maximum rudder deflec-

tion with the yawing moment coefficient for

the unbalance of thrust. The intersection of

the two lines,determines the minimum speed

for directional control, i.e., the lowest speed

at which the rudder control moment can equal

the moment of unbalanced thrust, It is usually

specified that the minimum directional control

speed be no greater than 1.2 times the stall

Revised January 1965

speed of the airplane in the lightest practical

takeoff configuration. This will provide ade-

quate directional control for the remaining

conditions of flight.

Once defined, the minimum directional con-

trol speed is not a function of weight, altitude,

etc., but is simply the equivalent airspeed (or

dynamic pressure). to produce a required yaw-

ing moment with the maximum rudder deflec-

tion. If the airplane is operated in the critical

unbalance of power below the minimum con

trol speed, the airplane will yaw uncontrolla-

bly into the inoperative engine. In order to

regain directional control below the minimum

speed certain alternatives exist: reduce power

on the operating engines or sacrifice altitude

for airspeed. Neither alternative is satisfac-

tory if the airplane is in a marginal condition

of powered flight so due respect must be given

to the minimum control speed.

Due to the side force on the vertical tail, a

slight bank is necessary to prevent turning

flight at zero sideslip. The inoperative engine

will be raised and the inclined wing lift will

provide a component of force to balance the 1

side force on the tail.

In each of the critical conditions of required

directional control, high directional stability

is desirable as it will reduce the displacement

of the aircraft from any disturbing influence.

Of course, directional control must he sufficient

to attain zero sideslip. The critical control

requirement for the multiengine airplane is

the condition of asymmetrical power since

spinning is not common to this type of airplane.

The single engine propeller airplane may have

either the spin recovery or the slipstream rota-

tion as a critical design condition. The single

engine jet airplane may have a variety of

critical items but the spin recovery require-

ment usually predominates.

LATERAL STABILITY AND CONTROL

LATERAL STABILITY

The static lateral stability of an airplane

involves consideration of rolling moments due

to sideslip. If an airplane has favorable rolling

moment due to sideslip, a lateral displacement

from wing level flight produces sideslip and

the sideslip creates rolling moments tending

to return the airplane to wing level flight.

By this action, static lateral stability will be

evident. Of course, a sideslip will produce

yawing moments depending on the nature of

the static directional stability but the consid-

rations of static lateral stability will involve

only the ‘relationship of rolling moments and

sideslip.

DEFINITIONS. The axis system of an

airplane defines a positive rolling, L, as a

moment about the longitudinal axis which

tends to rotate the right wing down. As in

other aerodynamic considerations, it is con-

venient to consider rolling moments in the

coefficient form so that lateral stability can

be evaluated independent of weight, altitude,

speeds, etc. The rolling moment, L, is defined

in the coeflicient form by the following equa-

tion :

or

L=C,qSb

*

+I

where

L=rolling moment, ft.-lbs., positive to

the right

4 = dynamic pressure, psf.

S=wing area, sq. ft.

b = wingspan, ft.

C,=rolling moment coeflicient, positive

to the right

The angle of sideslip, 8, has been defined

previously as the angle between the airplane

centerline and the relative wind and is positive

when the relative wind is to the right of the

centerline.

The static lateral stability of an airplane can

be illustrated by a graph of rolling moment

coefficient, Cl, versus sideslip angle, 8, such

as shown in figure 4.27. When the airplane

is subject to a positive sideslip angle, lateral

stability will be evident if a negative rolling

NAVWEPS 00-8OT-80

STABILITY AND COI’ITROL

moment coefficient results. Thus, when the

relative wind comes from the right (+-a>,

a rolling moment to the left (-Cl> should be

created which tends to roll the airplane to

the left. Lateral stability will exist when

the curve of C1 versus p has a negative slope

and the degree of stability will be a function

of the slope of this curve. If the slope of the

curve is zero, neutral lateral stability exists;

if the slope is positive lateral instability is

present.

It is desirable to have lateral stability or

favorable roll due to sideslip. However, the

required magnitude of lateral stability is deter-

mined by many factors. Excessive roll due to

sideslip complicates crosswind takeoff and

landing and may lead to undesirable oscil-

latory coupling with the directional motion of

the airplane. In addition, a high lateral sta-

bility may combine with adverse yaw to hinder

rolling performance. Generally, favorable han-

dling qualities are obtained with a relatively

light-or weak positive-lateral stability.

CONTRIBUTION OF THE AIRPLANE

COMPONENTS. In order to appreciate the

development of lateral stability in an airplane,

each of the contribution components must be

inspected. Of course, there will be interference

between the components which will alter the

contribution to stability of each component on

the airplane.

The principal surface contributing to the

lateral stability of an airplane is the wing. The

effect of the geometric dihedral of a wing is a

powerful contribution to lateral stability. As

shown in figure 4.28, a wing with dihedral will

develop stable rolling moments with sideslip.

If the relative wind comes from the side, the

wing into the wind is subject to an increase in

angle of attack and develops an increase in lift.

The wing away from the wind. is subject to a

decrease in angle of attack and develops a de-

crease in lift. The changes in lift effect a rolling

moment tending to raise the windward wing

hence dihedral contributes a stable roll due to

sideslip.

NAVWEPS DD-8OT-80

STABILITY AND CONTROL

RELATIVE WIND

+L, ROLLING MOMENT

ROLLING MOMENT COEFFICIENT

UNSTABLE 7,

-I

TABLE ROLL DUE

TO SIDESLIP

SIDESLIP ANGLE, /3

NEUTRAL

Figure 4.27. Static Lateral Stability

NAVWEPS CID-8OT-80

STABILITY AND CONTROL

EFFECT OF DlilEDRAL

EFFECTIVE INCREASE IN

--SE IN

LIFT DUE TO SIDESLIP

EFFECT OF SWEEPBACK

R~~;~~~p

CONTRIBUTION OF VERTICAL TAIL

SIDESLIP CONTRIBUTES

ROLLING MOMENT

Figure 4.28. Contribution of Components to Lateral Stability

NAVWEPS OO-BOT-80

STABILITY AND CONTROL

Since wing dihedral is so powerful in pro-

ducing lateral stability it is taken as a common

denominator of the lateral stability contribu-

tion of all other components. Generally, the

contribution of wing position, flaps, power,

etc., is expressed as an equivalent amount of

“effective dihedral” or “dihedral effect.”

The contribution of the fadage alone is

usually quite small depending on the location

of the resultant aerodynamic side force on the

fuselage. However, the effect of the wing-

fuselage-tail combination is significant since

the vertical placement of the wing on the fuse-

lage can greatly affect the stability of the com-

bination. A wing located at the mid wing

position will generally exhibit a dihedral effect

no different from that of the wing alone. A

low wing location on the fuselage may con-

tribute an effect equivalent to 3’ or 4’ of nega-

tive dihedral while a high wing location may

contribute a positive dihedral of 2’ or 3’. The

magnitude of dihedral effect contributed by

vertical position of the wing is large and may

necessitate a noticeable dihedral angle for the

low wing configuration.

The contribution of wccpback to dihedral ef-

fect is important because of the nature of the

contribution. As shown in figure 4.28, the

swept wing in a sideslip has the wing into

wind operating with an effective decrease in

sweepback while the wing out of the wind

is operating with an effective increase in

sweepback. If the wing is at a positive lift

coefficient, the wing into the wind has less

sweep and an increase in lift and the wing out

of the wind has more sweep and a decrease in

lift. In this manner the swept back wing

would contribute a positive dihedral effect and

the swept forward wing would contribute a

negative dihedral effect.

The unusual nature of the contribution of

sweepback to dihedral effect is that the con-

tribution is proportional to the wing lift

coefficient as well as the angle of sweepback.

It should be clear that the swept wing at zero

lift will provide no roll due to sideslip since

there is no wing lift to change. Thus, the

dihedral effect due to sweepback is zero at zero

lift and increases directly with wing lift

coefficient. When the demands of high speed

flight require a large amount of sweepback, the

resulting configuration may have an excessive-

ly high dihedral effect at low speeds (high CL)

while the dihedral effect may be satisfactory

in normal flight (low or medium C,).

The vertical tail of modern configurations

can provide a sign&ant-and, at times, un-

desirable-contribution to the effective dihe-

dral. If the vertical tail is large, the side force

produced by sideslip may produce a noticeable

rolling moment as well as the important yaw-

ing moment contribution. Such an effect is

usually small for the conventional airplane

configuration but the modern high speed

airplane configuration induces this effect to a

great magnitude. It is difficult then to obtain

a large vertical tail contribution to directional

stability without incurring an additional con-

tribution to dihedral effect.

The amount of effective dihedral necessary

to produce satisfactory flying qualities varies

greatly with the type and purpose of the air-

plane. Generally, the effective dihedral should

not be too great since high roll due to side-

slip can create certain problems. Excessive

dihedral effect can lead to “Dutch roll,”

difficult rudder coordination in rolling maneu-

vers, or place extreme demands for lateral

control power during crosswind takeoff and

landing. Of course, the effective dihedral

should not be negative during the predominat-

ing conditions of flight, e.g., cruise, high

speed, etc. If the airplane demonstrates satis-

factory dihedral effect for these conditions of

flight, certain exceptions can be considered

when the airplane is in the takeoff and landing

configuration. Since the effects of flaps and

power are destablizing and reduce the dihedral

effect, a certain amount of negative dihedral

effect may be possible due to these sources.

The deflection of flaps causes the inboard

sections of the wing to become relatively more

effective and these sections have a small

spanwise moment arm. Therefore, the changes

in wing lift due to sideslip occur closer in-

board and the dihedral effect is reduced. The

effect of power on dihedral effect is negligible

for the jet airplane but considerable for the

propeller driven airplane. The propeller slip-

stream at high power and low airspeed makes

the inboard wing sections much more effective

and reduces the dihedral effect. The reduction

in dihedral effect is most critical when the

flap and power effects are combined, e.g., the

propeller driven airplane in the power approach

or waveoff.

With certain exceptions during the condi-

tions of landing and takeoff, the dihedral

effect or lateral stability should be positive

but light. The problems created by excessive

dihedral effect are considerable and difficult

to contend with. Lateral stability will be

evident to a pilot by stick forces and displace-

ments required to maintain sideslip. Positive

stick force stability will be evident by stick

forces required in the direction of the controlled

sideslip.

LATERAL DYNAMIC EFFECTS

Previous discussion has separated the lateral

and directional response of the airplane to

sideslip. This separation is convenient for

detailed study of each the airplane static

lateral stability and the airplane static direc-

tional stability. However, when the airplane

in free flight is placed in a sideslip, the lateral

and directional response will be coupled, i.e.,

simultaneously the airplane produces rolling

moment due to sideslip and yawing moment

due to sideslip. Thus, the lateral dynamic

motion of the airplane in free flight must

consider the coupling or interaction of the

lateral and directional effects.

The principal effects which determine the

lateral dynamic characteristics of an airplane

are :

(1) Rolling moment due to sideslip or

dihedral effect (lateral stability).

NAVWEPS, OO-ROT-80

STABILITY AND CONTROL

(2) Yawing moment due to sideslip or

static directional stability.

(3) Yawing moment due to rolling veloc-

ity or the adverse (or proverse) yaw.

(4) Rolling moment due to yawing ve-

locity-a cross effect similar to (3). If the

aircraft has a yawing motion to the right,

the left wing will move forward faster and

momentarily develop more lift than the

right and cause a rolling moment to the

right.

(3) Aerodynamic side force due to side-

slip.

(6) Rolling moment due to rolling ve-

locity or damping in roll.

(7) Yawing moment due yawing velocity

or damping in yaw.

(8) The moments of inertia of the air-

plane about the roll and yaw axes.

The complex interaction of these effects pro-

duces three possible types of motion of the

airplane: (a) a directional divergence, (b)

a spiral divergence, and (c) an oscillatory

mode termed Dutch roll.

Directional divergence is a condition which

cannot be tolerated. If the reaction to a small

initial sideslip is such as to create moments

which tend to increase the sideslip, directional

divergence will exist. The sideslip would in-

crease until the airplane is broadside to the

wind or structural failure occurs. Of course,

increasing the static directional stability re-

duces the tendency for directional divergence.

Spiral divergence will exist when the static

directional stability is very large when com-

pared with the dihedral effect. The character

of spiral divergence is by no means violent,

The airplane, when disturbed from the equilib-

rium of level flight, begins a slow spiral which

gradually increases to a spiral dive. When a

small sideslip is introduced, the strong direc-

tional stability tends to restore the nose into

the wind while the relatively weak dihedral

effect lags in restoring the airplane laterally,

In the usual case, the rate of divergence in the

NAVWEPS DGROT-50

STABBITY AND CONTROL

spiral motion is so gradual that the pilot can

control the tendency without difficulty.

Dutch roll is a coupled lateral-directional

oscillation which is usually dynamically stable

but is objectionable because of the oscillatory

nature. The damping of this oscillatory mode

may be weak or strong depending on the prop-

erties of the airplane. The response of the air-

plane to a disturbance from equilibrium is a

combined rolling-yawing oscillation in which

the rolling motion is phased to precede the

yawing motion. Such a motion is quite unde-

sirable because of the great havoc it would

create with a bomb, rocket, or gun platform.

Generally, Dutch roll will occur when the

dihedral effect is large when compared to static

directional stability. Unfortunately, Dutch

roll will exist for relative magnitudes of dihe-

dral effect and static directional stability be-

tween the limiting conditions for directional

divergence and spiral divergence. When the

dihedral effect is large in comparison with

static directional stability, the Dutch roll

motion has weak damping and is objectionable.

When the static directional stability is strong

in comparison with the dihedral effect, the

Dutch roll motion has such heavy damping

that it is not objectionable. However, these

qualities tend toward spiral divergence.

The choice is then the least of three evils.

Directional divergence cannot be tolerated,

Dutch roll is objectionable, and spiral diver-

gence is tolerable if the rate of divergence is

low. For this reason the dihedral effect should

be no more than that required for satisfactory

lateral stability. If the static directional sta-

bility is made adequate to prevent objection-

able Dutch roll, this will automatically be

sufficient to prevent directional divergence,

Since the more important handling qualities

are a result of high static directional stability

and minimum necessary dihedral effect, most

airplanes demonstrate a mild spiral tendency.

As previously mentioned, a weak spiral tend-

ency is of little concern to the pilot and cer-

tainly preferable to Dutch roll.

The contribution of sweepback to the lateral

dynamics of an airplane is significant. Since

the dihedral effect from sweepback is a function

of lift coefficient, the dynamic characteristics

may vary throughout the flight speed range.

When the swept wing airplane is at low C,, the

dihedral effect is small and the spiral tendency

may be apparent. When the swept wing air-

plane is at high C,, the dihedral effect is in-

creased and the Dutch Roll oscillatory tendency

is increased.

An additional oscillatory mode is possible

in the lateral dynamic effects with the rudder

free and the mode is termed a “snaking” oscil-

lation. This yawing oscillation is greatly

affected by the aerodynamic balance of the

rudder and requires careful consideration in

design to prevent light or unstable damping

of the oscillation.

CONTROL IN ROLL

The lateral control of an airplane is ac-

complished by producing differential lift on

the wings. The rolling, moment created by

the differential lift can be used to accelerate

the airplane to some rolling motion or control

the airplane in a sideslip by opposing dihedral

effect. The differential lift for control in

roll is usually obtained by some type of ailerons

or spoilers.

ROLLING MOTION OF AN AIRPLANE.

/ When an airplane is given a rolling motion in

flight, the wing tips move in a helical path

through the air. As shown in figure 4.29, a

rolling velocity to the right gives the right

wing tip a downward velocity component and

the left wing tip an upward velocity com-

ponent. By inspection of the motion of the

left wing tip, the velocity of the tip due to

roll combines with the airplane flight path

velocity to define the resultants motion. The

resulting angle between the flight path vector

and the resultant path of the tip is the helix

angle of roll. From the trigonometry of small

angles, the helix angle of roll can be defined as:

Roll helix angle=&; (radians)

where

p=rate of roll, radians per second

6=wing span, ft.

V=airplane flight velocity, ft. per sec.

and, one radian=S7.3 degrees

pb Generally, the maximum values of rVobtained

by control in roll are approximately 0.1 to 0.07.

The helix angle of roll, $i, is, actually a com-

mon denominator of rolling performance.

The deflection of the lateral control surfaces

creates the differential lift and the rolling

moment to accelerate the airplane in roll. The

roll rate increases until an equal and opposite

moment is created by the resistance to rolling

motion or “damping in roll.” The second

illustration of figure 4.29 defines the source

of the damping in roll. When the airplane

is given a rolling velocity to the right, the

downgoing wing experiences an increase in

angle of attack due to the helix angle of roll.

Of course, the upgoing wing experiences a

decrease in angle of attack. In flight at angles

of attack less than that for maximum lift, the

downgoing wing experiences an increase in

lift and the upgoing wing experiences a de-

crease in lift and a rolling moment is developed

which opposes the rolling motion. Thus, the

steady state rolling motion occurs when the

damping moment equals the control moment.

The response of the airplane to aileron deflec-

tion is shown by the time history diagram of

figure 4.29. When the airplane is restrained

so that pure rolling motion is obtained, the

initial response to an aileron deflection is a

steady increase in roll rate. As the roll rate

increases so does the damping moment and the

roll acceleration decreases. Finally, the

damping moment approaches the control mo-

ment and a steady state roll rate is achieved.

NAVWEPS 00-6OT-60

STABILITY AND CONTROL

If the airplane is unrestrained and sideslip is

allowed, the affect of the directional stability

and dihedral effect can be appreciated. The

conventional airplane will develop adverse

yawing moments due to aileron deflection and

rolling motio6. Adverse yaw tends to produce

yawing displacements and sideslip but this is

resisted by the directional stability of the air-

plane. If adverse yaw produces sideslip, di-

hedral effect creates a rolling moment opposing

the roll and tends to reduce the roll rate. The

typical transient motions (A) and (B) of the

time history diagram of figure 4.29 show that

high directional stability with low dihedral

effect is the preferable combination. Such a

combination provides an airplane which has

no extreme requirement of coordinating aileron

and rudder in order to achieve satisfactory

rolling performance. While the coupled mo-

tion of the airplane in roll is important,

further discussion of lateral control will be

directed to pure uncoupled rolling performance.

ROLLING PERFORMANCE. The required

rolling performance of an airplane is generally

specified as certain necessary values of the roll 1

helix angle, &I$ However, in certain condi-

tions of flight, it may be more appropriate to

specify minimum times for the airplane to

accelerate through a given angle of roll.

Usually, the maximum value of 2% should be

on the order of 0.10. Of course, fighters and

attack airplanes have a more specific require-

ment for high rolling performance and 0.09

Pb may be considered a minimum necessary 2v.

Patrol, transport, and bomberairplaneshaveless

requirement for high rolling performance and a

Pb 2-V of 0.07 may be adequate for these types.

The ailerons or spoilers must be powerful

Pb enough to provide the required rV’ While

the size and effectiveness of the lateral control

devices is important, consideration must be

Revised January 1965

NAVWEPS OO-80T-80

STABILITY AND CONTROL

HELIX ANGLE OF ROLL

IP VELOCITY,$

RCUING VELOCITY, P

TIP VELOCITY WE TO ROLL

RESULTANT PATH

( RADIANS 1

DAMPING IN ROLL

STARBOARD WING

AIRPLANE RESPONSE TO AILERON DEFLECTION

PIRPLANE RESTRAINED

TO ROLLING MOTION ONLY

------(A) HIGH DlRECTlCNAL STABILITY

m DIHEDRAL EFFECT

AIRPLANE UNRESTRAINED

\ AND FREE TO SIDESLIP

\ (RUDDER FIXED) ( B ) LOW DIRECTIONAL STABIUTY

.---A HIGH MHEDRAL EFFECT

w TIME, SECONDS

Figure 4.29. Rolling Performance

given to the airplane size. For geometrically

similar airplanes, a certain deflection of the

I!!. ailerons will produce a fixed value of zlr mde-

pendent of the airplane size. However, the

roll rate of the geometrically similar airplanes

at a given speed will vary inversely with the

span, b.

If

Pb -

~-constant

p=(constant) 7

( )

Thus, the smaller airplane will have an ad-

vantage in roll rate or in time to accelerate

through a prescribed angle of roll. For ex-

ample, a one-half scale airplane will develop

twice the rate of roll of the full scale airplane.

This relationship points to the favor of the

small, short span airplane for achieving high

roll performance.

An important variable affecting the rate of

roll is the true airspeed or flight velocity, V.

If a certain deflection of the ailerons creates a

Pb specific value of -7 the rate of roll varies 2V

directly with the true airspeed. Thus, if the

roll helix angle is held constant, the rate of

roll at a particular true airspeed will not be

affected by altitude. The linear variation of

roll rate with airspeed points out the fact that

high roll rates will require high airspeeds.

The low roll rates at low airspeeds are simply

a consequence of the low flight speed and this

condition may provide a critical lateral con-

trol requirement for satisfactory handling

qualities.

Figure 4.30 illustrates the typical rolling

paformance of a low speed airplane. When

the ailerons are at full deflection, the maximum

roll helix angle is obtained. The rate of roll

increases linearly with speed until the control

forces increase to limit of pilot effort and full

control deflection cannot be maintained. Past

NAVWEPS OO-BOT-BO

STABILIJY AND CONTROL

the critical speed, with some limited amount

of force applied by the pilot (usually the limit

of lateral force is assumed to be 30 lbs.), the

Pb ailerons cannot be held at full deflection, ~~

drops, and rate of roll decreases. In this exam-

ple, the rolling performance at high speeds is

limited by the ability of the pilot to maintain

full deflection of the controls. In an effort to

reduce the aileron hinge moments and control

forces, extensive application is made of aerody-

namic balance and various tab devices. How-

ever, 100 percent aerodynamic balance is not

always feasible or practical but a sufficient

Pb value of - must be maintained at high speeds. ZV

Rather than developing an extensive weight

lifting program mandatory for all Naval

Aviators, mechanical assistance in lateral con-

trol can be provided. If a power boost is

provided for the lateral control system, the

rolling performance of the airplane may be

extended to higher speeds since pilot effort

will not be a limiting factor. The effect of a

power boost is denoted by the dashed line

extensions of figure 4.30. A full powered,

irreversible lateral control system is common

for high speed airplanes. In the power oper-

ated system there is no immediate limit to the

deflection of the control surfaces and none of

the aberrations in hinge moments due to com-

pressibility are fed back to the pilot. Control

forces are provided by the stick centering

lateral bungee or spring.

A problem particular to the high speed is

due to the interaction of aerodynamic forces

and the elastic deflections of the wing in

torsion. The deflection of ailerons creates

twisting moments on the wing which can cause

significant torsional deflections of the wing.

At the low dynamic pressures of low flight

speeds, the twisting moments and twisting

deflections are too small to be of importance.

However, at high dynamic pressures, the

deflection of an aileron creates significant

NAVWEPS 00-807-80

STABILITY AND CONTROL

P,

RAl ^,

r%“LL

O/SEC.

,/ <EiECT

0 OF ADDED

POWER

BOOST

V. KNOTS

4 ROLL .lD

HELIX

ANGLE

pb

TT

-

V, KNOTS

AILERON ----- DEFLECTlON

8,

V.KNOTS

SPEED CORRESPONDING

TO LIMIT OF PILOT EFFORT

TO MAINTAIN MAXIMUM DEFLECTION

A (3 z 3 is

1.0

0 c 5 ELASTIC WING TWISTING

REVERSAL

Figure 4.30. Control in Roll

twisting deflections which reduce the effec-

tiveness of the aileron, e.g., downward deflec-

tion of an aileron creates a nose down twist of

the wing which reduces the rolling moment

due to aileron deflection. At very high speeds,

the torsional deflection of the wing may be

so great than a rolling moment is created

opposite to the direction controlled and “aile-

ron reversal” occurs. Prior to the speed for

aileron reversal, a serious loss of roll helix

angle may be encountered. The effect of this

aeroelastic phenomenon on rolling perform-

ance is illustrated in figure 4.30.

To counter the undesirable inceractiuo be-

tween aerodynamic forces and wing torsional

deflections, the trailing edge ailerons may be

moved inboard to reduce the portion of the

span subjected to twisting moments. Of

course, the short span, highly tapered wing

planform is favorable for providing relatively

high stiffness. In addition, various configura-

tions of spoilers may be capabIe of producing

the required rolling performance without the

development of large twisting moments.

CRITICAL REQUIREMENTS, The critical

conditions for requiring adequate lateral con-

trol power may occur at either high speed or

low speed depending on the airplane configura-

tion and intended use. In transonic and super-

sonic flight, compressibility effects tend to

reduce the effectiveness of lateral control de-

vices to produce required roll helix angles.

These effects are most significant when com-

bined with a loss of control effectiveness due to

aeroelastic effects. Airplanes designed for

high speed flight must maintain suflicient

lateral control effectiveness at the design dive

speed and this is usually the predominating

requirement.

During landing and takeoff, the airplane

must have adequate lateral control power to

contend with the ordinary conditions of flight.

The lateral controls must be capable of achiev-

ing required roll helix angles and acceleration

through prescribed roll dispIacements. Also,

the airplane must be capable of being con-

NAVWEPS OO-UOT-80

STABILITY AND CONTROL

trolled in a sideslip to accomplish crosswind

takeoff and landing. The lateral control dur-

ing crosswind takeoff and landing is a par-

ticular problem when the dihedral effect is

high. Since the sweepback contributes a large

dihedral effect at high lift coefficients, the

problem is most important for the airplane

with considerable sweepback. The limiting

crosswind components must be given due re-

spect especially when the airplane is at low

gross weight. At low gross weight the speci-

fied takeoff and landing speeds will be low and

the controlled angle of sideslip will be largest

for a given crosswind velocity.

MISCELLANEOUS STABILITY PROBLEMS

There are several general problems of flying

which involve certain principles of stability as

well as specific areas of longitudinal, direc-

tional and lateral stability. Various condi-

tions of flight will exist in which certain

problems of stability (or instability) are un-

avoidable for some reason or another. any

of the following items deserve consideration

because of the possible unsafe condition of flight

and the contribution to an aircraft accident.

LANDING GEAR CONFIGURATIONS

There are three general configurations for the

aircraft landing gear: the tricycle, bicycle, and

“conventional” tail wheel arrangement. At

low rolling speeds where the airplane aerody-

namic forces are negligible, the “control-fixed”

static stability of each of these configurations

is determined by the side force characteristics

of the tires and is not a significant problem.

The instability which allows ground loops

in an aircraft with a conventional tail wheel

landing gear is quite basic and can be appre-

ciated from the illustration of figure 4.31. Cen-

trifugal force produced by a turn must be

balanced and the aircraft placed in equilibrium.

The greatest side force is produced at the main

wheels but to achieve equilibrium with the

NAVWEPS oo-SOT-80

STABILITY AND CONTROL

-

“CONVENTIONAL’

TAIL WHEEL

CONFIGURATION

SIDE FORCE ON

MAIN WHEELS

CENTRIFUGAL FORCE

TRICYCLE

\\ CONFIGURATION

--BALANCING

NOSE WHEEL

SIDE FORCE

CENTRIFUGAL FORCE

BICYCLE CONFIGURATION

FORCE

Figure 4.31. Landing Gear Configurations

center of gravity aft of the main wheels a bal-

ancing load on the tail wheel must be produced

toward the center of turn. When the tail

wheel is free to swivel, the equilibrium of the

turn requires a control force opposite to the

direction of turn-i.e.. control force insta-

bility. The inherent stability problem exists

because the center of gravity is aft of the point

where the main side forces are developed. This

condition is analogous to the case of static

longitudinal stability with the center of

gravity aft of the neutral point.

The conventional tail wheel configuration

has this basic instability or ground loop tend-

ency which must be stabilized by the pilot.

At high rolling speeds where aerodynamic

forces are significant, the aerodynamic direc-

tional stability of the airplane resists the

ground looping tendency. The most likely

times for a ground loop exist when rolling

speeds are not high enough to provide a con-

tribution of the aerodyhamic forces. When the

tail wheel is free to swivel or when the normal

force on the tail wheel is small, lack of pilot

attention can allow the ground loop to take

place.

The tricycle landing gear configuration has

an inherent stability d,ue to the relative posi-

tion of the main wheels and the center of

gravity. Centrifugal force produced by a

turn is balanced by the side force on the main

wheels and a side force on the nose wheel in

the direction of turn. Note that the freeing

the nose wheel to swivel produces moments

which bring the aircraft out of the turn. Thus,

the tricycle configuration has a basic stability

which.is given evidence by control displace-

ment and a wheel side force in the direction

of turn. Because of the contrast in stability,

the tricycle configuration is much less difficult

to maneuver than the tail wheel configuration

and does not provide an inherent ground loop

tendency. However, a steerable nose wheel

is usually necessary to provide satisfactory

maneuvering capabilities.

NAVWEPS DD-BDT-80

STABILITY AND CONTROL

The bicycle configuration of landing gear

has stability characteristics more like the

automobile. If directional control is ac-

complished with the front wheels operated

by power controls, no stability problem exists

at low speeds. A problem can exist when the

airplane is at high speeds because of a distribu-

tion of normal force being different from the

ordinary static weight distribution. If the

airplane is held onto the runway at speeds

well above the normal takeoff and landing

speeds, the front wheels carry a greater than

ordinary amount of normal force and a tend-

ency for instability exists. However, at these

same high speeds the rudder is quite powerful

and the condition is usually well within

control.

The basically stable nature of the tricycle

and bicycle landing gear configurations is best

appreciated by the ease of control and ground

maneuvering of the airplane. Operation of

a conventional tail wheel configuration after

considerable experience with tricycle cohfigu-

rations requires careful consideration af the

stability that must be furnished by the pilot

during ground maneuvering.

SPINS AND PROBLEMS OP SPIN

RECOVERY

The motion of an airplane in a spin can

involve many complex aerodynamic and in-

ertia forces and moments. However, there are

certain fundamental relationships regarding

spins and spin recoveries with which all

aviators should be familiar. The spin differs

from a spiral dive in that the spin always

involves flight at high angle of attack while

the spiral dive involves a spiral motion of

the airplane at relatively low angle of attack.

The stall characteristics and stability of

the airplane at high lift coefficients are im-

portant in the initial tendencies of the airplane.

As previously mentioned, it is desirable to

have the wing initiate stall at the root first

rather than tip first. Such a stall pattern

prevents the undesirable rolling moments at

high lift coeGients, provides suitable stall

_~. ,,

.

warning, and preserves lateral control effec-

tiveness at high angles of attack. Also, the

airplane must maintain positive static longi-

tudinal stability at high lift coe&ients and

should demonstrate satisfactory stall recovery

characteristics.

In order to visualize the principal effects of

an airplane entering a spin, suppose the air-

plane is subjected to the rolling and yawing

velocities shown in figure 4.32. The yawing

velocity to the right tends to produce higher

local velocities on the left wing than on the

right wing. The rolling velocity tends to

increase the angle of attack for the downgoing

right wing (a,) and. decrease the angle of

attack for the upgoing left wing (al). At

airplane angles of attack below the stall this

relationship produces roll due to yaw, damping

in roll, etc., and some related motion of the

airplane in unstalled flight. However, at

angles of attack above the stall, important

changes take place in the aerodynamic char-

acteristics.

Figure 4.32 illustrates the aerodynamic

characteristics typical of a conventional air-

plane configuration, i.e., moderate or high

aspect ratio and little-if any-sweepback.

Ifs this airplane is provided a rolling displace-

ment when at some angle of attack above

the stall, the upgoing wing experiences a

decrease in angle of attack with a correspond-

ing increase in C, and decrease in C,,. In other

words, the upgoing wing becomes less stalled.

Similarly, the downgoing wing experiences

an increase in angle of attack with a corre-

sponding decrease in CL and increase in CD. Es-

sentially, the downgoing wing becomes more

stalled. Thus, the rolling motion is aided

rather than resisted and a yawing moment is

produced in the direction of roll. At angles

of attack below stall the rolling motion is

resisted by damping in roll and adverse yaw

is usually present. At angles of attack above

the stall, the damping in roll is negative and

a rolling motion produces a rolling moment

in the direction of the roll. This negative

NAVWEPS OO-BOY-BO

STABIUTY AND CoMml

damping in roll is generally referred to as

“autorotation.”

When the conventional airplane is stalk4

and some rolling-yawing displacement takes

place, the resulting autotiotation rolling mo-

ments and yawing moments start the airplane

into a self-sustaining rolling-yawing motion.

The autorotation rolling and yawing tenden-

cies of the airplane at high angles of attack

are the principal prospin moments of the

conventional airplane configuration and these

tendencies accelerate the airplane into the

spin until some limiting condition exists.

The stabilized spin is not necessaray a simple

steady vertical spiral but may involve some

coupled unsteady oscillatory motion.

An important characteristic of the mote

conventional airplane configuration is that the

spin shows a predominating contribution of

the autorotation tendency. Generally, the

conventional configuration has a spin motion

which is primarily rolling with moderate yaw.

High directional stability is favorable since it

will limit or minimize the yaw displacement

of the spinning airplane.

The fundamental requirement of the spin is

that the airplane be placed at an excessive

angle of attack to produce the autorotation

rolling and yawing tendencies. Generally

speaking, the conventional airplane must be

stalled .before a spin can take place. This

relationship establishes a fundamental p&r-

ciple of recovery-the airplane must be un-

stalled by decreasing the wing angle of attack.

The most dfective procedure for the conven-

tional configuration is to use opposite rudder

to stop the sideslip, then lower the angle of

attack with the elevators. With sufficient

rudder power this procedure will produce a

positive recovery with a minimum loss of

altitude. Care should be taken during pullout

from the ensuing dive to prevent excessive

angle of attack and entry into another spin.

It should be appreciated that a spin is always

a possible corollary of a stall and the self-

sustaining motion of a spin will take place at

NAVWEPS OO-BOT-80

STABILITY AND CONTROL

YAWING

VELOCITY

ROLLING

VELOCITY

AERODYNAMIC CHARACTERISTICS TYPICAL OF AERODYNAMIC CHARACTERISTICS TYPICAL OF

A CONVENTIONAL CONFIGURATION A CONVENTIONAL CONFIGURATION

I--- I---

STALL STALL

CL CL

AND AND

CD CD

I 0, ANGLE OF ATTACK QL OR

t TYPICAL Q’ . ..I,.” cncrn lr H “lU” a-LL” A CD

AERODYNAMIC CHARACTERISTICS

co NFIGURATION

a, ANGLE OF ATTACK OL aR

Figure 4.32. Spin Characteristics

excessive angles of attack. Of course, a low

speed airplane could be: designed to be spin-

proof by making it stallproof. By limiting

the amount of control deflection, the airplane

may not have the longitudinal control power

to trim to maximum lift angle of attack. Such

a provision may be possible for certain light

planes and commercial aircraft but would

create an unrealistic and impractical limita-

tion on the utility of a military airplane.

The modern high speed airplane configura-

tion is typified by low aspect ratio, swept wing

planforms with relatively large yaw and pitch

inertia. The aerodynamic characteristics of

such a configuration are shown in figure 4.32.

The lift curve (C, versus U) is quite shallow at

high angles of attack and maximum lift is not

clearly defined. When this type of airplane is

provided a rolling motion at high angles of

attack, relatively small changes in C, take

place. When this effect is combined with the

relatively short span of this type airplane, it is

apparent that the wing autorotation contribu-

tion will be quite weak and will not be a pre-

dominating pro-spin moment. The relatively

large changes in drag coefficient with rolling

motion imply .a predominance of yaw for the

spin of the high speed airplane configuration.

Actually, various other factors contribute

to the predominating yaw tendency for the

spin of the modern airplane configuration.

The static directional stability deteriorates at

high angles of attack and may be so weak that

extemely large yaw displacements result. In

certain instances, very high angles of attack

may bring such a decay in directional stability

that a “slice” or extreme yaw displacement

takes place before a true spin is apparent. At

these high angles of attack, the adverse yaw

due to roll and aileron deflection can be very

strong and create large yaw displacements of

the airplane prior to realizing a stall.

The aircraft with the relatively large, long

fuselage can exhibit a significant moment con-

tribution from the fuselage alone. The cross

flow pattern on the fuselage at high angles of

NAWWEPS DO-BOT-BO

STABILITY AND CONTROL

attack is capable of producing pro-spin mo-

ments of considerable magnitude which con-

tribute to the self-sustaining nature of the

spin. Also, the large distributed mass of the

fuselage in rolling-yawing rotation contributes

to inertia moments which flatten the spin and

place the aircraft at extreme angles of attack.

The spin recovery of the modern high speed

airplane involves principles which are similar

to those of the spin recovery of the conven-

tional airplane. However, the nature of the

spin for the modern configuration may involve

specific differences in technique necessary to

reduce the sideslip and angle of attack. The

use of opposite rudder to control the sideslip

and effect recovery will depend on the effective-

ness of the rudder when the airplane is in the

spin. At high positive angles of attack and

high sideslip the rudder effectiveness may be

reduced and additional anti-spin moments must

be provided for rapid recovery. The deflection

of ailerons into the spin reduces the autorota-

tion rolling moment and can produce adverse

yaw to aid the rudder yawing moment in

effecting recovery.

There may be many other specific differences

in the technique necessary to effect spin re-

covery . The effectiveness of the rudder during

recovery may be altered by the position of

elevators or horizontal tail. Generally, full

aft stick may be necessary during the initial

phase of recovery to increase the effectiveness

of the rudder. The use of power during the

spin recovery of a propeller powered airplane

may or may not aid recovery depending on the

specific airplane and the particular nature of

the slipstream effects. The use of power during

the spin recovery of a jet powered airplane

induces no significant or helpful flow but does

offer the possibility of a severe compressor

stall and adverse gyroscopic moments. Since

the airplane is at high angle of attack and

sideslip, the flow at the inlet may be very

poor and the staI1 limits considerably reduced.

These items serve to point out possible dif-

ferences in technique required for various con-

figurations. The spin recovery specific for

31.1

NAVWEPS woT-80

STABILITY AND CONTROL

-UNSTABLE

PITCH-UP

NEUTRAL

SEPARATION OR

STALLTIP FIRST

RD SHIFT OF VORTEX

INCREASE IN LOCAL

DDWNWAM AT TAIL

: :

4b FUSELAGE CROSS-

FLOW SEPARATION

VORTICES INCREASE

LOCAL DOWNWASH AT TAIL

Figure 4.33. Pitch-up