Transcript Principle of flight

PRINCIPLES OF FLIGHT
DEFINITIONS

Mass :- Mass is the quantity of matter in
a body

Density :- Density is the mass per unit
volume.

Pressure :- Pressure is the force per unit
area.
(Units:- lbs / sq inch)

Momentum :- The quantity of motion in a body is
known as momentum of the body and is equal to
the product of mass and velocity (M = m x v)

Motion :- When a body changes its position in
relation to its surroundings.

Speed :- Speed is the rate of change of position.

Velocity :- Velocity is the speed in a
particular direction.
Velocity is a vector quantity having
both magnitude and direction.

Acceleration :- Acceleration is the
rate of change of velocity.

Work :- Work is said to be done on a
body when a force acting on it physically
moves the point of application in the
direction of the force.
Work done = Force x Distance moved in the
direction of force
(Units : Foot Pounds)

Power :- Power is the rate of doing work.
(One horse power is equals to 550 lbs/sec)



Energy :- Energy is the capacity to do the work.
Energy can exist in many forms i.e
heat, light, electrical, sound, chemical, atomic,
pressure, mechanical etc...
Potential Energy :- Due to the position of a
body above ground level.
Potential Energy (PE) = Mgh
Kinetic Energy :- Due to the motion in the
body.
Kinetic Energy (KE) = ½ mv²

Couple :- A couple consists of two equal,
opposite and parallel forces not acting
through the same point.

Equilibrium :- A body is said to be in
equilibrium when
(a) Algebraic sum of all the forces acting
on the body is zero.
(b) Clockwise moment is equal to the
anticlockwise moment about any point.

Boyles’ Law :- The volume of a given mass
of a perfect gas is inversely proportional to the
pressure, provided the temperature remains
constant.
p x v = constant (temp unchanged)

Charles’ Law :- The volume of a perfect gas
increases by 1/273 of its value at 0°C for every
degree C rise in temperature, provided the
pressure remains constant.
Laws Of Motion

Newton’s First Law Of Motion :- A body
which is in a state of rest or of its uniform
motion will continue to be in the same
state unless an external force is applied
upon it.
This property of all bodies is called
inertia and a body in such a state is said to
be in equilibrium.

Newton’s Second Law Of Motion :The rate of change of momentum of a
body is directly proportional to the applied
force and takes place in the direction of
the application of the said force.

Newton’s Third Law Of Motion :- To
every action, there is an equal and
opposite reaction.
GLOSSARY OF TERMS

Aerofoil :- A body is designed to
produce more lift than drag.
A typical aerofoil section which is
cambered on top surface and is
more or less straight at bottom
surface.

Chord Line :- It is a line joining the centre
of curvature of leading and trailing edges
of an aerofoil section.

Chord Length :- It is the length of chord
line intercepted between the leading and
trailing edges.

Angle Of Attack :- It is the angle
between the chord line and the relative
airflow undisturbed by the presence of
aerofoil.

Angle Of Incidence :- The angle
between the chord line and the
longitudinal axis of the aircraft.

Angle of Incidence :- The angle between the
chord line and the longitudinal axis of the
aircraft.

Total Reaction :- It is a single force
representing all the pressures ( force per unit
area ) over the surface of the aerofoil.
It acts through the centre of pressure which
is situated on the chord line.

Lift :- The vertical component of total
reaction resolved at right angles to the
relative air flow.

Drag :- The horizontal component of the
total reaction acting parallel and in the
same direction as the relative airflow.
ATMOSPHERE
Introduction :
The word Atmosphere is derived from
the Greek ‘Atoms’ means ‘vapour’ and
‘phere’ means ‘sphere’.

Atmosphere means the gaseous
sphere surrounding the earth.
Composition :
Air is a mixture of number of gases
consisting of :Nitrogen
Oxygen
Argon
CO2 and
other gases
-
78.03 %
20.99 %
00.94 %
-
00.04 %

Apart from the above gases air also
contains some impurities like dust and salt
particles.

Water vapour and traces of other gases
are also present.
Divisions Of Atmosphere :
The atmosphere is divided in four main
regions :-

Tropo Sphere
Strato Sphere
Iono Sphere
Exo Sphere




Tropo Sphere :- It extends from the
surface to a height of about 9 km near
the poles and 17 km near the equator.

Tropo pause:- Tropo pause is the
dividing line between Tropo Sphere and
Strato Sphere.

Strato Sphere :It extends from the
Tropopause upto a height of about 3 km.

Iono Sphere :- Above Stratosphere, it
extends upto a height of 24 km.

Exo Sphere :- It extends from
Ionosphere upto a height of 1126.5 km.
Temperature :


The temperature of earth’s surface depends
almost entirely upon the heat received from the
sun. As a rule, temperature decreases with
height. The hotter the earth’s surface becomes,
more readily it radiates its heat back again to
space.
Heat is transferred by three methods i.e. (i)
Conduction (ii) Convection and (iii) Radiation
The
instrument
used
for
measuring
temperature is called thermometer and the
units of measure is either “Fahrenheit” or
“Centigrade” in degrees.
Variation of Temp with Height:
In the atmosphere the temperature as
a rule decreases with height.

Lapse rate :- The decrease of
temperature with height is known as
“Lapse” and the rate of decrease is
known as “Lapse Rate”.
Air Density :
The density of air is defined as the mass
of the air contained in unit volume and is
measured in “grams per cubic meter”.

Presence of water vapour in the
atmosphere decreases the air density.
Also the air density decreases if pressure
decreases or its temperature increases.
Variation of Density :

Variation of air density at the surface :- At
the surface, variations of air density are due to
temperature variations. When temperature is
maximum, air density is minimum and viceversa.
Variation of density with height :- Air density
decreases with height mainly due to the effect
of the pressure. The decrease in air density with
height due to fall in pressure is much more than
the increase in air density due to fall in
temperature with height.
BERNAULI’s THEOREM &
VENTURI EFFECT
Bernauli’s Theorem :In the early days of the Industrial revolution, Daniel
Bernauli, an Italian physicist, discovered certain
properties relating to fluids in motion, which he
summarized as follows:The total energy in a moving fluid is the total sum of
three forms of energy i.e. Potential, Kinetic and
Pressure Energy.
In a stream line flow of an ideal fluid, the sum of all
these three energies remains constant.
Venturi Tube :-

A tube which has inlet portion
gradually narrowing then a throat or
neck followed by an out let which
widens gradually is called a venturi
tube or convergent / divergent duct.
Venturi Tube :-
Venturi effect and Bernauli’s Theorem :


In the previous chapter, we have seen that for a
flow of air to remain streamlined, the volume
passing at a given point in unit time’ must
remain constant.
If a venturi tube is placed in such an air stream,
then the mass flow in the venturi tube must also
remain constant and streamlined.
In order to achieve this and still pass through
the restricted section of the venturi, and
accompanying pressure drop is a natural
consequence according to Bernauli’s theorem.

Therefore when a wing moves through
the air, the pressure on the upper
surface is less than atmospheric and
more than atmospheric on the bottom
surface. This pressure difference
existing between the top and bottom
surface, is the main lifting force of a
flying aircraft.
Venturi Effect :

When a stream line air flow is passing
through a venturi tube the mass flow
remains constant at all points in the tube.
Since the cross sectional area at throat is
less, to maintain the constant air flow
either the air should get compressed or it
should speed up.

It almost behaves like an incompressible
fluid and therefore speeds up.

Its kinetic energy is increased and
therefore according to Bernauli’s theorem
the pressure energy drops.
This phenomenon is called Venturi
Effect.
FORCES ACTING ON
AIRCRAFT
Introduction :-

An aircraft is considered to be in straight
and level flight when it is flying at a
constant altitude and speed, maintaining
lateral level and direction.
Forces Acting on Aircraft :
Weight

Lift

Thrust

Drag

Direction of Flight
Lift


Thrust


CP

CG

Weight
Drag




Weight :- Weight of the aircraft acting
vertically downwards through C.G
Lift :- Lift acting vertically upwards
through C.P
Thrust :- Thrust acting horizontally
forward along the propeller shaft.
Drag :- Drag acting horizontally
backwards along the line of total drag of
the aircraft.
Forces acting on straight
and level flight :



Weight :- Weight of the aircraft acting
vertically downwards through C.G
Lift :- Lift acting vertically upwards through
C.P
Thrust :- Thrust acting horizontally forward
along the propeller shaft.
Drag :- Drag acting horizontally backwards
along the line of total drag of the aircraft.
Equilibrium :



In a straight and level flight, the following
conditions
must
be
satisfied
for
equilibrium.
(a) Algebraic sum of forces acting
horizontally = 0
(b) Algebraic sum of forces acting
vertically = 0
It follows that L = W and T = D.


At any instant, the weight of an aircraft is a
certain quantity and the aircraft is flown at such
an angle of attack and air speed that it
produces lift equal to weight. Under these
conditions, the aircraft has certain amount of
drag which is counteracted by the pilot
adjusting his engine controls so that T = D
The position of CG is always kept ahead of the
CP so that if the engine cuts, the aircraft
assumes a gliding attitude without difficulty.
GLIDE

Glide :- Glide is that condition of flight
in which the aircraft is losing height
without power at a constant speed
maintaining lateral level and direction.

Gliding Angle :- Gliding angle is the
angle between earth’s horizon and the
path of the aircraft.
Forces Acting On Glide :
The forces acting on an aircraft in a glide
are

Weight

Lift

Drag

Weight :- Weight acting vertically
down wards.

Lift :- Lift acting at right angles to the
glide path.

Drag :- Drag acting backwards along
the glide path.
Gliding Speed :
It has been shown that the angle of glide is the
least when L/D is maximum. Thus if we fly at a
speed corresponding to the optimum angle of
attack, we will get the flattest glide. This speed
is the best gliding speed given in the pilots
notes for the aircraft. Gliding at any speed
higher or lower than this speed will mean a
reduction in L/D ratio and hence the glide path
will be steeper.
LIFT
Lift :


The lift (L) is the force which acts on
the main plane vertically upwards
through the centre of pressure.
It helps in taking off the aircraft from the
ground and then to maintain the aircraft in
level flight.
The shape of an aerofoil is such that it is
convex on top side and more or less plain
on the bottom side.


When the aircraft moves on the forward
direction, the air coming from front side of
aircraft passes over the aircraft.
Due to the curve nature of the aerofoil, the
velocity of incoming air is much more on top
side as compared to the bottom side. As a
result of this the pressure on the top side
decreases as compared to the bottom side.
Consequently the aerofoil is being lifted due to
the high pressure on the bottom side.
Factors Governing Lift :
The different factors governing the lift
of an aerofoil are as follows :(a) Angle of attack
(b) The air speed
(c) Area of aerofoil
(d) Density of air

Angle of attack :- It is defined as the angle
between the chord line and the relative air
flow. If it is properly adjusted that is at angle
between 3° and 4°, the lift will be maximum.

Air Speed :- It is the speed of airflow over the
aerofoil. When the air speed is more over the
aerofoil, the pressure decreases considerably
and the lift is more convenient.

Area of the Aerofoil :- It is the total area of an
aerofoil over which the air passes. By increasing
the surface area to the airflow the lift can be
increased.

Density of Air :- As the pressure is directly
proportional to the density, a difference in
pressure gives rise to the difference in density of
air on both the side of an aerofoil. If the
difference is more then the lift also will be more.
DRAG
Drag :




The drag (D) is the force which acts
horizontally backwards.
It is the resistive force of the incoming airflow
from the front side of an aircraft which retard
the forward motion of the aircraft.
It is an unwanted force which tries to reduce
the thrust of an aircraft.
The greater the drag, the greater is the power
needed to over come it.
For an economical flight every effort must be
taken to reduce the drag.
Factors Affecting Drag :
The different factors affecting drag are as
follows :(a) The shape of the body
(b) The surface
(c) Frontal area of the body exposed
(d) Square of the velocity of the airflow
(e) The density of the air
(f) The acceleration due to gravity

The shape of the body :- The shape of
the aircraft is made in such a way that
minimum portion of the body is exposed to
the airflow. It helps in reducing the drag.

The Surface :- The less is the surface
exposed to the airflow, the less will be the
drag.

Frontal area of the body exposed :The frontal area of the body is made in
such a way that it is a streamlined one
which will reduce the drag.

Velocity of airflow :- The force due to
drag is directly proportional to the square
of the velocity of the airflow. In order to
minimise the drag, the aircraft is flown
when the velocity of the airflow is less.

Density of Air :- The aircraft is made to fly in
the air, when its density is relatively low due to
the changing weather condition in order to
reduce the drag.

Acceleration due to Gravity :- When the
aircraft is made to fly in a less height that is
under the influence of acceleration due to
gravity, then the drag is minimum.
CLIMB
Climb :
Introduction :A climb is that
condition of flight in which an aircraft
gains altitude at a steady rate and a
constant airspeed maintaining lateral
level and direction
Forces Acting in a Climb :
The forces acting on an aircraft during
a climb are as follows :(a)
(b)
(c)
(e)
Weight (W)
Lift (L)
Drag (D)
Thrust (T)




Weight :- Weight acting vertically
downwards.
Lift :- Lift acting at right angles to the
path of climb.
Drag :- Drag acting backwards along
the path of climb.
Thrust :- Thrust acting forward along
the path of climb.
Ceiling :

Service aircrafts are required to give their
best efficiency at certain pre - determined
operating altitudes and the engine, propeller
and aircraft are designed accordingly. The
rate of climb is an important factor in its
consideration.
Beyond its best operating altitude, an
aircraft can climb upto its service ceiling
where its rate of climb drops off to a
predetermined rate (normally 100'/min).

The absolute ceiling of an aircraft is
that altitude beyond which the aircraft
will not climb. At this altitude, there is
only one possible level speed and the
power required to fly straight and level
is equal to the power available from
the engine.
Effect of Wind :
When an aircraft is climbing, the wind
effects its path of climb in relation to
the ground. When climbing in to wind,
the ground speed being less greater
height is gained for the same amount
of ground covered than if the climb
were made down wind. Hence a better
obstacle clearance when near the
ground.
STALL AND SPIN
How an aircraft stalls :
From the airflow pattern observed over an aerofoil
at varying angles of attack, it is observed that
beyond 15° (approx) angle of attack, the airflow
over the top surface breaks up and the turbulent
airflow spreads over to the leading edge from the
trailing edge.

The CP moves, suddenly back at this stage, and
the aircraft nose drops, in spite of all efforts to keep
it up. This phenomenon, where the aircraft is out of
control along with a sudden loss of height by an
increase in angle of attack is called a STALL.
Stalling Angle :
The angle of attack at which the lift of an
aerofoil is maximum and beyond which
there is a sudden loss in lift and rapid
increase in drag due to airflow over the
aerofoil becoming turbulent instead of
remaining streamlined, is called the
‘Stalling Angle’.
Symptoms of Stall :
The following symptoms indicate the
approach of stall :(a) High attitude
(b) Decreasing speed
(c) Sluggish controls
(d) Sink
(e) Nose drop
(f) Wing drop

High attitude :- As the pilot keeps on increasing
the angle of attack in trying to maintain height.

Decreasing Speed :- Due to increase in drag
as a result of increase in angle of attack.

Sluggish controls :- All controls start becoming
less effective as the speed is decreased.

Sink :- Just after the point of stall, the lift
obtained from the wing decreases and sink may
be felt.

Nose drop :- Inspite of the pilot trying to ease
back on the stick, the nose drops, because the
CP moves sharply back, thus causing the nose
to go down.

Wing drop :- In some aircrafts it occurs because
one wing stalls just before the other one. This
can also be due to slight yaw at the point of stall.
Recovery from stall :
(a) The obvious method is to decrease
the angle of attack by easing the stick
forward.

(b) Use of power will effect a much
quicker recovery with a much lesser loss
of height.
Types of stall :
Stalls can be generalized under the
following three main headings :(a) Basic Stall
(b) Shock Stall
(c) High speed Stall

Basic Stall :- It can be further sub-divided as
follows :
(i) Stall : Clean aircraft
(ii) Stall : With flaps and under carriage down
(iii) Stall with power on.

Shock Stall :- This occurs at very high Mach
numbers due to compressibility effects. Here the
angle of attack can be any figure.

Recovery action lies in lowering the Mach No.

High Speed Stall :- The aircraft can, in fact,
stall in any attitude relative to the horizon as it
is the relative flow that is significant and which
gives the angle of attack. The aircraft thus can
be made to stall in a climb, in glide, in turn, in
fact any time when the wings are presented at
the stalling angle to the airflow. Further, harsh
movement of stick can also result in a stall at
any speed.

To recover, the backward pressure on the
stick must be relaxed.
SPINNING :
Introduction :Spinning is that
stalled condition of flight in which the
aircraft rapidly loses height in a spiral
path while auto-rotating and autopitching.
Conditions for a Spin :



Mishandling of controls at the point of stall
causes a spin.
A yaw at the point of stall initiates a spin.
A yaw will cause a wing drop and auto
rotation begins.
An aircraft can get into a spin from any
attitude of flight. e.g.: gliding turn, steep turn,
aerobatics...



An aircraft however, does not go directly from a stall
into a spin. It is a transition period, the duration of
which varies considerably with different conditions of
stall in some type of aircraft, and also with different
conditions of stall in some type of aircraft.
When a wing drops at the point of stall, the aircraft
nose begins to yaw towards the dropped wing, and as
the angle of bank increases, it will drop sharply below
the horizon and the aircraft begins a spiral decent.
The condition immediately precedes the spin and is
referred to as an INCIPIENT SPIN.
Auto Pitching :
In a spin, the aircraft is auto-pitching. As
the aircraft stalls, the centre of pressure
moves rapidly back causing the nose of
the aircraft to drop. Then the CP tends to
move forward causing the nose to move
up and this keeps repeating as long as
the aircraft is spinning. This is called
AUTO-PITCHING.



The following points about spinning are
worth noting :Use of power during recovery will only increase
the loss of height and if the spin was initiated
with power, the throttle should be closed.
Use of aileron is undesirable during a spin,
because if used in the natural sense, they
increase the drag on the inner wing and tend to
keep the aircraft in the spin.

LIFT AUGMENTATION
Introduction :
The problem of augmenting (increasing) the
maximum lift co-efficient to the speed of the
lower speed range aircrafts has always been
as much attention as the search for the high
speeds. The use of high speed aerofoil
sections helps the designer to achieve higher
speed by reducing the drag. As most aircrafts
using these aerofoils also have high wing
loading, the stalling speed are proportionately
higher. This requires longer landing run.
Lift augmentation devices :
The following are the chief devices used
to augment the lift co-efficient :
(a) Slats
(b) Flaps
(c) Boundary layer control
Slats :
Slats are the small auxiliary aerofoil
surfaces of highly cambered section is
fixed to the leading edge of the wing
along the complete span and adjusted
so that a suitable slot is formed between
the two. The lift coefficient is increased
by so much as 70% and more. At the
same time the stalling angle is increased
by 10°.
Types of slats :
There are mainly three types of slats:
(a) Fixed Slats
(b) Controlled Slats
(c) Automatic Slats

Fixed Slats :- In this case the slats are kept
permanently opened with a slot and it was
found that the extra drag at a high speed would
be a greater disadvantage than the advantage
gained by the extra lift at low speeds.

Controlled Slats :- In this the slats would be
moved to open the slot and close the slot by
control mechanism attached to a lever in the
cockpit which gains the advantage at high and
low speeds.

Automatic Slats :- In this case when
the slat is not in use it lies flush against
the edge of the wings. At high angles of
attack the low pressure peak near the
leading edge of the upper surface of the
wing and the lift generated by the
cambered slot itself lift the slat upward
and forwards to the open position, thus
forming the required slot.
Flaps :



Introduction :- The plain or cambered flap
works on the same principle as on aileron or
other control surface, it is truly a ‘variable
camber’.
Flaps, like slats can also increase the drag.
Lowering of flaps produce an increase in the
lift co-efficient at given speed but at the same
time the greater camber also causes an
increase in the total drag.
The best lift drag ratio is obtained with the flap
at some angle between 15° and 35°.
Types of Flaps :
There are various types of flaps in use and
they are mainly :(a) Plain or Camber Flaps
(b) Split Flaps
(c) Slotted Flaps
(d) Fowler Flaps
(e) Jet Flaps
(f) Zap Flaps
(g) Variable camber Flaps
 STABILITY
Stability :


Introduction :- Stability of aircraft means its
ability to return some particular condition of
flight (after having been slightly disturbed from
that condition) without any effort on the part of
the pilot.
The stability of an aircraft can be defined as its
tendency to return to the original trimmed
position after having been displaced.
The term is applicable in all the three axes of
rotation. i.e. longitudinal, lateral, and normal.
The three Axes of Aircraft :
An aircraft can rotate about three axes
at right angles to each other. The three
axes are:
(a) Longitudinal Axis
(b) Lateral Axis
(c) Normal Axis
FLYING CONTROLS
Longitudinal Axis :
The axis running fore and aft through Centre of gravity
is known as the longitudinal axis of the aircraft.
(or)
It is the axis passes through Centre of Gravity of
the aircraft and runs from nose to tail of the aircraft is
called longitudinal axis of the aircraft.


This is the axis about which aircraft rolls.
The stability about this axis is known as lateral
stability.
Lateral Axis :


The lateral axis is a line running span
wise through the CG at the right angles
to the other Longitudinal and Normal
axis.
Movement about this axis is Pitching.
Stability about this axis is called
longitudinal stability.
Normal Axis :


The normal or directional axis is a line
running vertically through Centre of
Gravity and at right angles to both
lateral and longitudinal axis.
Stability about this axis is known as
directional stability.
It is the axis about which aircraft yaws.

The stability of an aircraft so far as it concerns
pitching about the lateral axis is called
longitudinal stability.

The stability which concerns rolling about the
longitudinal axis is called lateral stability.

The stability which concerns the yawing about
the normal axis is called the directional
stability.
Factors governing Longitudinal Stability :
The three main facts which influence
longitudinal stability are :(a) Position of Centre of Gravity
(b) Movement of Centre of pressure
(c) Design of the Tailplane & Elevators.
Position of Centre of Gravity :
An aircraft is most stable at its forward limit
of CG. If this forward. If this forward position
is exceeded, the stick forces become very
high and often create undue fatigue to the
pilot. As the CG position is increased back,
the stability decreases with lesser tendency
of the aircraft to returns to its original
trimmed position after having been
disturbed.
Movement of CP :


The position of Centre of pressure depends
upon the angle of attack.
The CP moves forward with increase in
angle of attack and backward when the
angle of attack decreases.
It also follows that since the aircraft rotates
around its CG, if the CP moves ahead of the
CG, a nose up movement will result.
Similarly, a nose down change of trim will
occur if the CP moves back of the CG.
Design of Tailplane and Elevator :
The function of the tailplane is to provide a countering
force to any residual out of balance force existing
among the four main forces. If the angle of attack is
increased due to any reason the wing lift is also
increased and the CP tends to move forward. As a
result the state of equilibrium no longer exists. It also
follows that the tailplane has been subjected to same
increase in the angle of attack. In order to restore the
aircraft to its original trimmed position, the role of the
tail plane comes to play, which is so designed that the
increase in tailplane lift is greater than the unbalancing
moment caused by the above mentioned disturbance
Lateral Stability :

If the aircraft regains the lateral level,
after initial disturbance, it is said to be
laterally stable.
Lateral stability is obtained by one or a
combination of the following methods.
Factors Governing Lateral Stability:
(a) Dihedral Angle

(b) Sweepback of the wings

Placing most keel surface above the CG

Using a high wing and low CG position.
Dihedral Angle :

When a wing is inclined upwards from
its lateral axis, the angle from the
horizontal is known as dihedral angle.
(Similarly the inclination below is called
anhedral angle).
It also follows that an a/c with a
dihedral angle will have a higher angle
of attack.

When an a/c with a dihedral angle is
banked, the tilted lift vector, initiates a
side slipping action. Due to dihedral
angle, the airflow meets the lower wing
at a larger angle of attack than the
higher wing, as a result the quantom of
lift increases on the lower wing thus
setting up a balancing movement to
correct the bank.
Sweepback Of Wings :
A slide slip occurs when an a/c is
banked, In case of an a/c with swept
back wings, the lower wing offers a
shorter effective chord with a greater
effective camber than the raised wing.
This results in a greater amount of lift
on the lower wing which in turn
restores lateral level.
High Keel Surface :

During a slide slip, a considerable amount of
force is exerted on the keel surface (side
surface) of the a/c, which results in a turning
movement about the CG. If the keel surface
above the CG, produce greater movement
than below it, the same will result in a
correcting movement which will assist in
restoring lateral level.
This can be achieved by placing more keel
surface above the CG
High Wing and Low CG:
If the a/c with high wing side slips, a
pendulous effect is created. During the
side-slip, the drag of the wing above
CG allows it to swing down till the time
it is placed vertically below the lift thus
restoring lateral level.
Directional Stability :


The effect of directional and lateral stability
are very closely interlinked.
A disturbance which involves only lateral
stability, initially, will always involve
directional stability during subsequent
interactions.
The purpose of the fin is to provide
directional stability. With out a fin, an a/c will
be directionally unstable because the CP of
the tear shaped body is ahead of CG
Factors governing Directional Stability:


(a) Fin area
(b) More keel surface behind the CG
Fin Area :- When an a/c is disturbed on
yawing plane the airflow for a movement
continues to attach in the original direction.
The fin having been located far behind the
CG when affected by this airflow because of
a long leverage provides a correcting
movement tending to bring the a/c back into
original path.

More Keel Surface behind the CG:- In
the lateral stability the keel surface
above the CG level is considered, but in
the directional stability the amount of
keel surface behind the CG is important.
Greater the surface behind the CG
greater is the righting movement applied
when affected directionally.