PRINCIPLES OF FLIGHT

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PRINCIPLES OF FLIGHT
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DEFINITIONS
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• 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)

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• 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.

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• 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.

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• 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)

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• 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

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• 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.

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• 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 0C for every
  degree C rise in temperature, provided the
  pressure remains constant.

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Laws Of Motion
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• Newtons 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.

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• Newtons 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.
• Newtons Third Law Of Motion - To every action,
  there is an equal and opposite reaction.

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GLOSSARY OF TERMS
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• 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.

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• 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.

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• 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.

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• 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.

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• 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.

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ATMOSPHERE
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Introduction -

• The word Atmosphere is derived from the Greek
  Atoms means vapour and phere means
  sphere.
• Atmosphere means the gaseous sphere surrounding
  the earth.

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Composition -

• Air is a mixture of number of gases consisting of
  - Nitrogen - 78.03
  Oxygen - 20.99 Argon - 00.94
  CO2 and other gases - 00.04

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• 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.

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Divisions Of Atmosphere -

• The atmosphere is divided in four main regions -
  
• Tropo Sphere
• Strato Sphere
• Iono Sphere
• Exo Sphere

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• 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.

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• 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.

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Temperature -

• The temperature of earths surface depends almost
  entirely upon the heat received from the sun. As
  a rule, temperature decreases with height. The
  hotter the earths 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.

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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.

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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.

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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 vice-versa.
• 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.

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BERNAULIs THEOREM VENTURI EFFECT
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Bernaulis 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.

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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.

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Venturi Tube -

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Venturi effect and Bernaulis 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 Bernaulis theorem.

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• 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.

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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.

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• It almost behaves like an incompressible fluid
  and therefore speeds up.
• Its kinetic energy is increased and therefore
  according to Bernaulis theorem the pressure
  energy drops.
• This phenomenon is called Venturi Effect.

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FORCES ACTING ON AIRCRAFT
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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.

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(No Transcript)
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Forces Acting on Aircraft -

• Weight
• Lift
• Thrust
• Drag

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• Direction of Flight

• Lift

• Thrust

• CP

• Drag

• CG

• Weight

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• 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.

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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.

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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.

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• 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.

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GLIDE
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• 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 earths horizon and the path of the
  aircraft.

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Forces Acting On Glide -

• The forces acting on an aircraft in a glide are
• Weight
• Lift
• Drag

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• Weight - Weight acting vertically down wards.
• Lift - Lift acting at right angles to the glide
  path.
• Drag - Drag acting backwards along the glide
  path.

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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.

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LIFT
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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.

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• 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.

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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

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• 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.

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• 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.

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DRAG
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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.

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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

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• 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.

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• 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.

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• 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.

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CLIMB
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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

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Forces Acting in a Climb -

• The forces acting on an aircraft during a climb
  are as follows - (a) Weight
  (W) (b) Lift (L) (c) Drag
  (D) (e) Thrust (T)

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• 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.

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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).

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• 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.

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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.

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STALL AND SPIN
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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.

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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.

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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

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• 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.

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• 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.

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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.

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Types of stall -

• Stalls can be generalized under the following
  three main headings - (a) Basic
  Stall (b) Shock Stall (c)
  High speed Stall

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• 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.
  

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• 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.

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SPINNING -

• Introduction - Spinning is that stalled
  condition of flight in which the aircraft rapidly
  loses height in a spiral path while auto-rotating
  and auto-pitching.

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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...

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• 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.

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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.

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• 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.

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• LIFT AUGMENTATION

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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.

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Lift augmentation devices -

• The following are the chief devices used to
  augment the lift co-efficient (a)
  Slats (b) Flaps (c) Boundary layer
  control

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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.

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Types of slats -

• There are mainly three types of
  slats (a) Fixed Slats (b)
  Controlled Slats (c) Automatic Slats

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• 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.

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• 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.

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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.

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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

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• STABILITY

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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.

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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

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FLYING CONTROLS

• PITCHING

• LATERAL AXIS

• LONGITUDINAL AXIS

• ROLLING

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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.

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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.

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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.

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• 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.

103
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.
  

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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.

105
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.

106
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
  

107
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.

108
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.

109
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.

110

• 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.

111
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.

112
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

113
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.

114
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

115
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.

116

• 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.