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STABILITY

AND CONTROL



INTRODUCTION

How well an airplane flies and how easily it can be controlled are subjects

studied in aircraft stability and control. By stability we mean the tendency of

the airplane to return to its equilibrium position after it has been disturbed.

The disturbance may be generated by the pilot's control actions or by

atmospheric phenomena. The atmospheric disturbances can be wind gusts,

wind gradients, or turbulent air. An airplane must have sufficient stability th

the pilot does not become fatigued by constantly having to control the airplan

owing to external disturbances.



• A classic airplane has three basic controls:

1. ailerons,2. elevator, and

3. rudder.

• They are designed to change and control the moments about the roll, pitc yaw axes. These control surfaces are flap like surfaces that can be deflec and forth at the command of the pilot.

• Rolling The ailerons control the roll or lateral motion and are therefore often called the lateral control

• Pitching The elevator controls pitch or the longitudinal motion and thus often called the longitudinal control

• Yawing The rudder controls yaw or the directional motion and thus is called the directional control



STATIC STABILITY

Stability is a property of an equilibrium state. To discuss

stability we must first define what is meant by equilibrium. If an airplane is t

remain in steady uniform flight, the resultant force as well as the resultant

moment about the center of gravity must both be equal to zero. An airplane

satisfying this requirement is said to be in a state of equilibrium or flying at a

trim condition. On the other hand, if the forces and moments do not sum to

zero, the airplane will be subjected to translational and rotational

accelerations.



STATIC STABILITY

Statically stable. If the forces and moments on the body caused by a distur

initially to return the body toward its equilibrium position, the body is stati



Statically unstable. If the forces and moments are such that the body continues

away from its equilibrium position after being disturbed, the body is statically u

Neutrally stable If the body is disturbed but the moments remain zero, the bod

equilibrium and is neutrally stable



DYNAMIC STABILITY A body is dynamically stable if, out of its own accord, it eventually returns toa

remains at its equilibrium position over a period of time. It is important to not

static stability does not imply dynamic stability. The plane is dynamically uns

still statically stable



after initially responding to its static stability, the airplane may oscillate with in

amplitude, as shown in Figure . Here, the equilibrium position is never maintai

period of time; the airplane in this case is dynamically unstable

Dynamically unstable



LONGITUDINAL STATIC STABILITY



If the airplane is flying at its trim angle of attack and suddenly encounters a d

that causes it to pitch up or down (e.g., due to a wind gust), the moment will b

the plane will return to its equilibrium position. To see that, imagine a wind gu

the plane up from ae to some larger a. By looking at the plot in Fig. , you can s

moment coefficient (and hence the moment) will be negative, which makes the

down and return to equilibrium



If the gust pitches the nose downward a negative (counterclockwise) moment

results, which also tends to pitch the nose further away from its equilibriumposition. Therefore, because the airplane always tends to diverge from equilibriu

when disturbed, it is statically unstable



CRITERION

To have static longitudinal stability

1. Cmo must be positive.

2. the aircraft pitching moment curve must have a negative slope, i.

dCm/dCα <0



CONTRIBUTION OF AIRCRAFT COMPONENT

COMPONENTS such as

WING

TAIL etc



WING CONTRIBUTION

Wing contribution to the pitching moment:

If we sum the moments about the center of gravity, the following equobtained:



.



TAIL CONTRIBUTION

There are two interference effects that influence the tail aerodynamic

1. The airflow at the tail is deflected downward by the downwash due

finite wing i.e., the relative wind seen by the tail is

not in the same direction as the relative wind

V∞ seen by the wing.

2. Due to the retarding force of skin friction and pressure drag over th

the airflow reaching the tail has been slowed. Therefore, the velocity o

relative wind seen by the tail is less than V∞



Flow and force diagrams in the viscinity of the tail.

the sum of moments about the center of gravity of the tail is



,



On simplifying,



TOTAL PITCHING MOMENT

.In terms of angle of attack,



EQUATIONS FORLONGITUDINAL STATIC

STABILITY By definition, CM0 is the value of CM cg When αa = 0, that is,whenzero. Substituting αa= 0 into above equation we directly obtain

Consider now the slope of the moment coefficient curve. Differentimoment equation w

ith respect to αa, we obtain



THE NEUTRAL POINT

There is one specific location of the center of gravity such that

dCM cg/dαa= 0. The value of h when this condition holds is define

neutral point, denoted by hn.

The location of the neutral point is readily obtained from Eq. (7.28)

setting h = hn and dCM cg/d α a = 0, as follows.



The concept of the neutral point is introduced as an alternative stabil

Criterion.

For longitudinal static stability, the position Of the center of gravity m

always be forward of the neutral point.



THE STATIC MARGIN

ILLUSTRATION OF STATIC MARGIN



Equation above shows that the static margin is a direct measure of

nal static stability. For static stability, the static margin must be pos

Moreover, the larger the static margin, the more stable is the airplan



LONGITUDINAL CONTROL

Control of an airplane can be achieved by providing an incremental li

on one or more of the airplane's lifting surfaces. The incremental lift f

be produced by deflecting the entire lifting surface or by deflecting a fl

incorporated in the lifting surface. Owing to the fact that the control

movable lifting surfaces are located at some distance from the center

gravity, the incremental lift force creates a moment about the airplan

of gravity. Figure below shows the three primary aerodynamic control



Primary aerodynamic controls:



Factors affecting the design of a control surface arecontrol effectiv

hinge moments, and aerodynamic and mass balancing.



ELEVATOR EFFECTIVENESS

When the elevator is deflected, it changes the lift and pitching moment of

the airplane. The change in lift for the airplane can be expressed as follows

The influence of the elevator on the Cm vs α

curve.



the pitching moment equation yields

By simplifying, we get

Flap effectiveness parameter.



ELEVATOR ANGLE TO TRIM

Setting the pitching moment of equation equal to zero

(definition of trim) we can solve for the elevator angle required to trim

airplane:

By simplifying, we get the final equation for elevator angle to trim:



DIRECTIONALSTABILITY



The directional stability and control, deal with the equilibrium and its ma

about the z-axis

Static directional stability is a measure of the aircraft's resistance to slipping. T

static directional stability, the appropriate positive or negative yawing moment

generated to compensate for a negative or positive sideslip angle .

The greater the static directional stability the quicker the aircraft will turn into

wind which is not aligned with the longitudinal axis

Directional stability



Sideslip is the angle between the plane of symmetry of the airplane and the di

motion. It is taken as positive in the clockwise sense.

It is denoted by ‘β’.

a positive β is due to a positive sideslip velocity which is the component of airpl

velocity along the y-axis.

Cit i f di ti ltti tbilit



Criterion for directional static stability

Considerthatinequilibriumflighttheairplaneisflyingwithβ 0



Consider that in equilibrium flight, the airplane is flying with β =0.

Now, let a disturbance cause the airplane to develop positive sideslip of ∆β. It is

that to bring the airplane back to equilibrium position i.e. β = 0, a positive yaw

(∆N) should be produced by the airplane. Similarly, a disturbance causing a n

should result in – ∆N i.e. for static directional stability

Cnβ > 0 for static directional stability

= 0 for neutral directional stability and

< 0 for directional instability.



C ib i f i C β



Contribution of wing to Cnβ



Consider an airplane with wings which have sweep Λ. When this wing is subject

β, the components of the free stream velocity

normal to the quarter chord line on the two wing halves will be unequal i.e. V co

right wing and V cos (+β) on the left wing. Consequently, even if the two winɅ

are at the same angle of attack, they would experience unequal effective

pressures and their drags will be different. This will

cause a yawing moment.

The yawing moments due to the right and the left wing halves (Nw)r and (Nw)



It may be noted that the contribution of wing to Cnβ is positive. Since, Cnβ sh

positive for directional static stability, a positive contribution to Cnβ is called

contribution

Contribution of fuselage to Cnβ

A fuselage at an angle of attack produces a pitching moment and also contrib

Cmα. Similarly, a fuselage in sideslip produces a yawing moment and contrib

of the airplane.

However, in an airplane, the flow past a fuselage is influenced by the flow pasHence, instead of an isolated fuselage, the contributions of wing and fuselage

estimated together. It is denoted by Cnβwf



Contribution of vertical tail

A vertical tail at an angle of attack (αv) would produce a side force (Yv) and a

moment (Nv)

The side force Yv is perpendicular to the

velocity Vvt. However, the angle αv is small

and Yv is taken perpendicular to FRL



Influence of wing-body combination on contribution of vertical tail

The wing body combination has the following influences.

(a)The angle of attack (αv) at vertical tail is different from β and

(b) The dynamic pressure (½ ρVvt2) experienced by it (vertical tail) is different f

Theangleofattackismodifiedas:



The angle of attack is modified as:

αv = β + σ

σ is called side wash

The dynamic pressure experienced by

tail is expressed as:



Differentiating by β gives

Di ti l t l f



• Directional controlis achieved by a control surface called a rudder which is

on the vertical tail. The rudder is a hinged flap which forms the aft portion of

vertical tail. By rotating the flap, the lift force (side force) on the fixed vertical

can be varied to create a yawing moment about the center of gravity

Directional control by means of the rudder

Rudder requirements



When an airplane is banked, in order to execute a turning maneuver, the ailer

a yawing moment that opposes the turn (i.e. adverse yaw). The rudder must bovercome the adverse yaw so that a coordinated turn can be achieved. The crit

for adverse yaw occurs when the airplane is flying slow (i.e. high CL)

• Adverse yaw

• Cross-wind landings

To maintain alignment with the runway during a crosswind landing requires tfly the airplane at a sideslip angle. The rudder must be powerful enough to pe

pilot to trim the airplane for the specified crosswinds. For transport airplanes,

may be carried out for cross-winds up to 15.5 m/s or 51 ft/s

A i dii



• Asymmetric power condition

The critical asymmetric power condition occurs for a multiengine airplane wh

engine fails at low flight speeds. The rudder must be able to overcome the yaw

moment produced by the asymmetric thrust arrangement

• Spin recovery

The primary control for spin recovery in many airplanes is a powerful rudder

rudder must be powerful enough to oppose the spin rotation

ROLL STABILITY CONTROL



ROLL STABILITY CONTROL

• An airplane possesses static roll stability if, when it is disturbed from a win

attitude, a restoring moment is developed. The restoring rolling moment can

be a function of the sideslip angle • The requirement for stability is that

• The roll moment created on an airplane when it starts to sideslip depends u

dihedral , wing sweep, position of the wing on the fuselage, and the vertical



The major contributor to Clβ is the wing dihedral angle T. The dihedral angle is

span wise inclination of the wing with respect to the horizontal. If the wing tip

the root section, then the dihedral angle is positive; if the wing tip is lower tha

section, then the dihedral angle is negative. A negative dihedral angle is comm

anhedral.

• When an airplane is disturbed from a wings-level attitude, it will begin to side

the airplane starts to sideslip a component of the relative wind is directed tow

side of the airplane. The leading wing experiences an increased angle of attac

consequently an increase in lift. The trailing wing experiences the opposite eff

net result is a rolling moment that tries to bring the wing back to a wings-leve

This restoring moment is often referred to as the "dihedral effect"

Wing dihedral

• Theadditionalliftcreatedonthedownward-movingwingiscreatedbythecha



The additional lift created on the downwardmoving wing is created by the cha

of attack produced by the side slipping motion. If we resolve the sideward velo

component into components along and normal to the wing span the local chan

attack can be estimated as



• Wing sweepalso contributes to the dihedral effect. In the case of a sweptback

windward wing has an effective decrease in sweep angle while the trailing wing

an effective increase in sweep angle. For a given angle of attack, a decrease in

angle will result in a higher lift coefficient. Therefore, the windward wing (less

sweep) will experience more lift than the trailing wing. It can be concluded tha

adds to the dihedral effect. On the other hand, sweep forward will decrease th

dihedral effect .

• A simplified estimate of the wing sweep contribution to Cl bis presented in Eq

•

• Fuselagecontribution



• Fuselage contribution

• The sideward flow turns in the vicinity of the fuselage and creates a local ch

angle of attack at the inboard wing stations. For a low wing position, the f

contributes a negative dihedral effect; the high wing produces a positive dihe

In order to maintain the same C,p a low-wing aircraft will require a consider

wing dihedral angle than a high-wing configuration

The horizontal tailcan also contribute to the dihedral effect in a manner simila

H igtth i fth h i tltil ith ttth igit



However, owing to the size of the horizontal tail with respect to the wing, its con

usually small.

The vertical tail

The contribution to dihedral effect from the vertical tail is produced by the side

tail due to sideslip. The side force on the vertical tail produces both a yawing an

moment. The rolling moment occurs because the center of pressure for the vert

located above the aircraft's center of gravity. The rolling moment produced by th

tends to bring the aircraft back to a wings-level attitude.

An estimate of the vertical tail contribution to Cl b



ROLL CONTROL Roll control is achieved by the differential deflection of small flaps called aileron

located outboard on the wings, or by the use of spoilers.

The basic principle behind these devices is to modify the span wise lift distrib

a moment is created about the x axis

Spoilers when used for roll control are usually deflected on one side only.

High wing-sweep angles make spoilers and ailerons less effective.



Figure showing both types of roll control devices.



•Longitudinal – Short Period – Phugoid

•Lateral-Directional – Spiral

– Dutch Roll – Roll

Dynamic Stability Modes



• Oscillating motions can be described by two parameters, the period of time

one complete oscillation, and the time required to damp to half-amplitude, o

double the amplitude for a dynamically unstable motion.

• The longitudinal motion consists of two distinct oscillations,

1. a long-period oscillation called a phugoid mode and

2. a short-period oscillation referred to as the short-period mode

• Longitudinal modes



• The longer period mode, called the "phugoid mode" is the one in which there

amplitude variation of air-speed, pitch angle, and altitude, but almost no angl

variation. The phugoid oscillation is really a slow interchange of kinetic energ

and potential energy (height) about some equilibrium energy level as the aircr

to re-establish the equilibrium level-flight condition from which it had been d

The motion is so slow that the effects of inertia forces and damping forces are

Although the damping is very weak, the period is so long that the pilot usuall

for this motion without being aware that the oscillation even exists. Typically

is 20–60 seconds. The pilot generally can control this oscillation himself.

• Phugoid (longer period) oscillations



• With no special name, the shorter period mode is called simply the "short-per

The short-period mode is a usually heavily damped oscillation with a period o

seconds. The motion is a rapid pitching of the aircraft about the center of grav

period is so short that the speed does not have time to change, so the oscillat

essentially an angle-of-attack variation. The time to damp the amplitude to on

value is usually on the order of 1 second. Ability to quickly self damp when th

briefly displaced is one of the many criteria for general aircraft

• Short period oscillations



TIME RESPONSE OF PHUGOID AND SHORT PERIOD MODE (LONGITUSTABILITY)



• "Lateral-directional" modes involve rolling motions and yawing motions.

• Motions in one of these axes almost always couples into the other so the mod

generally discussed as the "Lateral-Directional modes".

• There are three types of possible lateral-directional dynamic motion:1.roll subsidence mode,

2.spiral mode, and 3.Dutch roll mode

• Lateral-directional modes

• Roll subsidence mode



• Roll subsidence mode is simply the damping of rolling motion. There is no dir

aerodynamic moment created tending to directly restore wings-level, i.e. there

returning "spring force/moment" proportional to roll angle. However, there is

moment (proportional to rollrate) created by the slewing-about of long wings.

large roll rates from building up when roll-control inputs are made or it damp

rollrate (not the angle) to zero when there are no roll-control inputs.

• Roll mode can be improved by dihedral effects coming from design characteris

high wings, dihedral angles or sweep angles

• Dutchrollmode



• The second lateral motion is an oscillatory combined roll and yaw motion calle

The Dutch roll may be described as a yaw and roll to the right, followed by a rethe equilibrium condition, then an overshooting of this condition and a yaw an

left, then back past the equilibrium attitude, and so on. The period is usually o

3–15 seconds, but it can vary from a few seconds for light aircraft to a minute

airliners. Damping is increased by large directional stability and small dihedra

by small directional stability and large dihedral. Although usually stable in a n

the motion may be so slightly damped that the effect is very unpleasant and un

• Dutch roll mode

• In swept-back wing aircraft, the Dutch roll is



p g ,

solved by installing a yaw damper, in effect a

special-purpose automatic pilot that damps out

any yawing oscillation by applying rudder

corrections. Some swept-wing aircraft have an

unstable Dutch roll. If the Dutch roll is very

lightly damped or unstable, the yaw damper

becomes a safety requirement, rather than a

pilot and passenger convenience. Dual yaw

dampers are required and a failed yaw damper is

cause for limiting flight to low altitudes, and

possibly lower mach numbers, where the Dutch

roll stability is improved.



• Directional divergencecan occur when the airplane does not possess direction

weathercock stability. If such an airplane is disturbed from its equilibrium sta

tend to rotate to ever-increasing angles of sideslip. Owing to the side force acti

airplane, it will fly a curved path at large sideslip angles. For an airplane that

static stability (i.e. dihedral effect) the motion can occur without any significa

in bank angle . Obviously, such a motion cannot be tolerated and can readily

by proper design of the vertical tail surface to ensure directional stability

•

Spiral divergenceis a non oscillatory divergent motion which can occur whenstability is large and lateral stability is small. When disturbed from equilibrium

airplane enters a gradual spiraling motion . The spiral becomes tighter and st

time proceeds and can result in a high-speed spiral dive if corrective action is

This motion normally occurs so gradually that the pilot unconsciously correct

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