1) The document discusses the significance of the speed of sound in flight, defining subsonic, transonic, and supersonic flight based on Mach numbers. 2) It explains how air pressure and airflow behave differently depending on whether aircraft speed is below or above the speed of sound. 3) The key principles discussed include how lift is generated via pressure differences on the top and bottom surfaces of airfoils, as well as how angle of attack and airfoil shape impact lift and drag forces.

1. By
SRINATH R
ASST. PROFESSOR
BASIC PRINCIPLES OF FLIGHT

2. SIGNIFICANCE OF SPEED OF SOUND
Speed of sound
• The speed of sound in air depends only on the temperature of the air.
• As the air temperature in the atmosphere falls with height, the speed of sound
is reduced with height.
• The exact relationship between the speed of sound and temperature being
given by:
 Speed of sound, a = { EMBED Equation.3 } m/s
 = { EMBED Equation.3 } knots
 where T is the absolute temperature of the atmosphere in K.

3. TYPICAL FIGURES FOR THE STANDARD
ATMOSPHERE ARE:

4. Mach number
 The Mach Number (M) refers to the speed at which an aircraft is traveling in relation to the
speed of sound.
 Thus a Mach Number of 0.5 means that the aircraft is traveling at half the speed of sound.
Both the speed of the aircraft and the speed of sound are true speeds.
Realms of Flight
 The aerodynamic characteristics with which we must contend as we study the theory of
flight can be divided into three basic realms, or regimes, all based on Mach numbers.
(i) Subsonic flight:
 Flight below Mach 0.75 is called subsonic flight, and in this speed range all of the
airflow is subsonic.
(ii) Transonic flight:
 The most difficult realm of flight is that between Mach 0.75 and 1.20, because at
this speed some of the airflow is subsonic, while other flow is supersonic.
 At these speeds, shock waves form and move around.
(iii) Supersonic flight:
 Flight above Mach 1.20 is smooth and efficient, since all of the airflow is
supersonic and the shock and expansion waves are attached and are stationary.

5. Importance of Speed of Sound
 Sound is a pressure disturbance in the air, transmitted through the air by a
wave motion.
 Any object which moves through the air causes a disturbance, which spreads
outwards in the form of pressure waves.
 If the object moves slowly (subsonically) the pressure waves advance ahead
of the object and are able to affect the air, causing it to prepare for the arrival
of the object.
 If the object moves supersonically pressure waves cannot travel faster and do
not move ahead of the object and cannot affect the airflow.

7. Compressibility Effects
 This is another aspect that bears importance of speed of sound.
 At subsonic air flows through a restricted tube, the velocity will increase as the tube converges
and will decrease as it diverges.
 At supersonic velocities of the air flowing through the restricted tube, things are quite different, it
slows down and is compressed.

8. Critical Mach Number
 Consider a symmetrical airfoil shape moving through the air at a small positive
angle of attack at a high subsonic speed, say M = 0.8.
 As air flows over the top surface its speed first increases and then decreases again.
 The maximum speed rises very close to sonic speed. If the aircraft speed rises
slightly the maximum speed over the wing will reach sonic speed (M = 1.0).
 When the maximum speed first reaches M = 1.0 the aircraft Mach Number at that
point is called the Critical Mach Number.

9. SHOCK WAVE FORMATION AND DEVELOPMENT
 What is a Shock Wave?
 A shook wave is a very thin region in which there is a sudden decrease of
velocity and increases in the pressure, temperature and density of the air
passing through it.
 All the points on the surface of a wing produce pressure waves.
 If the airflow is subsonic, these pressure waves can all move away- ahead of the
wing, but when the critical Mach Number is reached and the speed becomes
sonic speed at some point on the wing, pressure waves move forward only as
far as this point and then “pick-up” to form a Shock Wave.
 If the speed is increased further the shock wave starts to move towards the
trailing edge as the supersonic area above the wing grows larger. Another shock
wave will form below the wing and will also move towards the trailing edge.

10. BERNOULLI'S THEOREM
• Daniel Bernoulli, an eighteenth-century Swiss scientist, discovered that as
the velocity of a fluid increases, its pressure decreases.
• How and why does this work, and what does it have to do with aircraft in
flight?
• Bernoulli's principle can be seen most easily through the use of a venturi
tube
• The venturi will be discussed again in the unit on propulsion systems, since a
venturi is an extremely important part of a carburetor.
• A venturi tube is simply a tube which is narrower in the middle than it is at
the ends. When the fluid passing through the tube reaches the narrow part, it
speeds up. According to Bernoulli's principle, it then should exert less
pressure.

11. APPLICATION
• Bernoulli's principle states that within a steady airflow of constant energy,
when the air flows through a region of lower pressure it speeds up and vice
versa.
• Thus, there is a direct mathematical relationship between the pressure and the
speed, so if one knows the speed at all points within the airflow one can
calculate the pressure, and vice versa.
• For any airfoil generating lift, there must be a pressure imbalance, i.e. lower
average air pressure on the top than on the bottom.
• Bernoulli's principle states that this pressure difference must be
accompanied by a speed difference

12. • The streamlines divide the flow around the airfoil into stream tubes as
depicted by the spaces between the streamlines.
• By definition, fluid never crosses a streamline in a steady flow.
• Assuming that the air is incompressible, the rate of volume flow (e.g. liters
or gallons per minute) must be constant within each stream tube since matter
is not created or destroyed.
• If a stream tube becomes narrower, the flow speed must increase in the
narrower region to maintain the constant flow rate. This is an application of
the principle of conservation of mass

13. STREAM LINES

14. PRESSURE FORCE
• Pressure is the normal force per unit area exerted by the air on itself and on
surfaces that it touches.
• The lift force is transmitted through the pressure, which acts perpendicular
to the surface of the airfoil.
• The air maintains physical contact at all points.
• Thus, the net force manifests itself as pressure differences
• The direction of the net force implies that the average pressure on the upper
surface of the airfoil is lower than the average pressure on the underside.
• These pressure differences arise in conjunction with the curved air flow.
• Whenever a fluid follows a curved path, there is a pressure gradient
perpendicular to the flow direction with higher pressure on the outside of the
curve and lower pressure on the inside

15. AIRFOIL
 The lift force depends on the shape of the airfoil, especially the amount of camber
curvature such that the upper surface is more convex than the lower surface,
Increasing the camber generally increases lift.
 Cambered airfoils will generate lift at zero angle of attack.
 When the chord line is horizontal, the trailing edge has a downward direction and
since the air follows the trailing edge it is deflected downward.
 When a cambered airfoil is upside down, the angle of attack can be adjusted so that
the lift force is upwards.
 This explains how a plane can fly upside down.
 The wings of birds and most subsonic aircraft have spans much larger than their
chords.
 Most of the discussion in this article concentrates on two-dimensional airfoil flow.
However, the flow around a three-dimensional wing involves significant additional
issues, and these are discussed below under Lift of three dimensional wings.
 For a wing of low aspect ratio, such as a delta wing two-dimensional airfoil flow is
not relevant, and three-dimensional flow effects dominate.

16. AIRFOIL AND LIFT
• The airfoil shape and angle of attack work together so that the airfoil exerts a downward force on
the air as it flows past.
• According to Newton's third law, the air must then exert an equal and opposite (upward) force on
the airfoil, which is the lift.
• The force is exerted by the air as a pressure difference on the airfoil's surfaces
• Pressure in a fluid is always positive in an absolute sense, so that pressure must always be
thought of as pushing, and never as pulling.
• The pressure thus pushes inward on the airfoil everywhere on both the upper and lower
surfaces.
• The flowing air reacts to the presence of the wing by reducing the pressure on the wing's upper
surface and increasing the pressure on the lower surface.
• The pressure on the lower surface pushes up harder than the reduced pressure on the upper
surface pushes down, and the net result is upward lift.[54]
• The pressure difference that exerts lift acts directly on the airfoil surfaces.

19. AIRCRAFT FORCES AND LIFT
 Aircraft are kept in the air by the forward thrust of the wings or aerofoils,
through the air.
 The thrust driving the wing forward is provided by an external source, in this case
by propellers or jet engines.
 The result of the movement of the wing through stationary air is a lift force
perpendicular to the motion of the wing, which is greater than the downwards
gravitational force on the wing and so keeps the aircraft airborne.
 The lift is accompanied by drag which represents the air resistance against the
wing as it forces its way through the air.
 The drag is dependent on the effective area of the wing facing directly into the
airflow as well as the shape of the aerofoil.
 The magnitudes of the lift and drag are dependent on the angle of attack between
the direction of the motion of the wing through the air and the chord line of the
wing.

20. LIFT AND DRAG OVER AIRFOIL

21. ANGLE OF ATTACK
 For an aircraft wing, it is the angle between the direction of motion of the
wing and the chord line of the wing.
 At very low angles of attack, the airflow over the aerofoil is essentially
smooth and laminar with perhaps a small amount of turbulence occuring at
the trailing edge of the aerofoil.
 The point at which laminar flow ceases and turbulence begins is known as
the separation point.
 Increasing the angle of attack increases the area of the aerofoil facing
directly into the wind.

22. CONTD..
 This increases the lift but it also moves the separation point of laminar flow
of the air above the aerofoil part way up towards the leading edge and the
result of the increased turbulent flow above the aerofoil is an increase in the
drag.
 Maximum lift typically occurs when the angle of attack is around 15 degrees
but this could be higher for specially designed aerofoils.
 Above 15 degrees, the separation point moves right up to the leading edge of
the aerofoil and laminar flow above the aerofoil is destroyed.
 The increased turbulence causes the rapid deterioration of the lift force while
at the same time it dramatically increases the drag, resulting in a stall.

23. PICTORIAL VIEW

24. LIFT AND DRAG CURVE

25. AERODYNAMIC DRAG COMPONENTS
 Drag is the force experienced by an object representing the resistance to its
movement through a fluid.
 Sometimes called wind resistance or fluid resistance, it acts in the opposite
direction to the relative motion between the object and the fluid.
 The example opposite shows the aerodynamic drag forces experienced by an
aerofoil or aircraft wing moving through the air with constant angle of attack
as the air speed is increased..

26. Induced Drag –
 Due to the vortices and turbulence resulting from the turning of the air flow and the
downwash associated with the generation of lift.
 Increases with the angle of attack.
 Inversely proportional to the square of the air speed.
 Decreases as aircraft speed increases and the angle of attack is reduced.
 Induced drag associated with the high angle of attack needed to maintain the lift is
dominant at low air speeds.
Form Drag or Pressure Drag –
 Due to the size and shape of the aerofoil. Increases with the square of air speed.
Streamlined shapes designed to reduce form drag.

27. Friction Drag –
 Arises from the friction of the air against the "skin" of the aerofoil moving
through it. Increases with the surface area of the aerofoil and the square of
air speed.
Profile Drag or Viscous Drag-
 The sum of Friction Drag and the Form Drag.

28. Wave Drag –
 Due to the presence of shock waves occurring on the blade tips of aircraft and
projectiles. Associated with passing the sound barrier it is a sudden and dramatic
increase in drag which only comes into play as the vehicle increases speed through
transonic and supersonic speeds. Independent of viscous effects.
Parasitic Drag or Interference Drag –
 Incurred by the non-liftting parts of the aircraft such as the wheels, fuselage, tail fins,
engines, handles and rivets. Increases with the square of air speed.
 Parasitic drag becomes dominant at higher air speeds.

29. INDUCED DRAG

30. DRAG CURVE

31. CENTER OF PRESSURE
 The center of pressure is the point where the total sum of a pressure field acts on
a body, causing a force to act through that point.
 The total force vector acting at the center of pressure is the value of the integrated
vector pressure field.
 The resultant force and center of pressure location produce equivalent force and
moment on the body as the original pressure field.
 Pressure fields occur in both static and dynamic fluid mechanics.
 Specification of the center of pressure, the reference point from which the center
of pressure is referenced, and the associated force vector allows the moment
generated about any point to be computed by a translation from the reference
point to the desired new point.
 It is common for the center of pressure to be located on the body, but in fluid
flows it is possible for the pressure field to exert a moment on the body of such
magnitude that the center of pressure is located outside the body.

32. AERODYNAMIC CENTER
 The aerodynamic center is the point on the airfoil where the incremental lift
(due to change in Angle of Attack) will act.
 And, since the lift force generated due to change of angle of attack passes
through this point, the moment generated about this point will be zero.
 The concept of the aerodynamic center is important in aerodynamics.
 It is fundamental in the science of stability of aircraft in flight.
 For symmetric airfoils in subsonic flight the aerodynamic center is located
approximately 25% of the chord from the leading edge of the airfoil.
 This point is described as the quarter-chord point. This result also holds true
for 'thin-airfoils For non-symmetric (cambered) airfoils the quarter-chord is
only an approximation for the aerodynamic center.

33.  The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For
example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side –
the ratio of width to height, when the rectangle is oriented as a "landscape".
 In aerodynamics it is defined as ratio of square of wing span to the area of the wing

34. LIFT OVER 3 D WING
 For wings of moderate-to-high aspect ratio the flow at any station along the span except close
to the tips behaves much like flow around a two-dimensional airfoil,
 and most explanations of lift, like those above, concentrate on two-dimensional flow. However,
even for wings of high aspect ratio,
 the three-dimensional effects associated with finite span are significant across the whole span,
not just close to the tips.
 The lift tends to decrease in the span wise direction from root to tip, and the pressure
distributions around the airfoil sections change accordingly in the spanwise direction.
 Pressure distributions in planes perpendicular to the flight direction tend to look like the
illustration at right.
 This spanwise-varying pressure distribution is sustained by a mutual interaction with the
velocity field.
 Flow below the wing is accelerated outboard, flow outboard of the tips is accelerated upward,
and flow above the wing is accelerated inboard, which results in the flow pattern illustrated at
right.[95]

35.  There is more downward turning of the flow than there would be in a two-
dimensional flow with the same airfoil shape and sectional lift, and a higher
sectional angle of attack is required to achieve the same lift compared to a two-
dimensional flow.
 The wing is effectively flying in a downdraft of its own making, as if the free
stream flow were tilted downward, with the result that the total aerodynamic
force vector is tilted backward slightly compared to what it would be in two
dimensions.
 The additional backward component of the force vector is called lift-induced drag
 Euler computation of a tip vortex rolling up from the trailed vorticity sheet.

36.  The difference in the spanwise component of velocity above and below the wing
(between being in the inboard direction above and in the outboard direction
below) persists at the trailing edge and into the wake downstream.
 After the flow leaves the trailing edge, this difference in velocity takes place
across a relatively thin shear layer called a vortex sheet.
 As the vortex sheet is convected downstream from the trailing edge, it rolls up at
its outer edges, eventually forming distinct wingtip vortices.
 The combination of the wingtip vortices and the vortex sheets feeding them is
called the vortex wake.
 Planview of a wing showing the horseshoe vortex system.