Module 8- Basic Aerodynamics (1).pdf

GCAA CAR-66 CAT-A MODUĮE 08 BASIC AERODYNAMICS  PAGE INTENTIONALLY BLANK  CAR 66 CATEGORY A MODULE 8...

GCAA CAR-66 CAT-A MODUĮE 08 BASIC AERODYNAMICS  PAGE INTENTIONALLY BLANK  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS CONTENTS CONTENTS......................................................................................... I 1. PHYSICS OF THE ATMOSPHERE...............................................1-1 1.1. NATURE..............................................................................1-1 1.2. PROPERTIES......................................................................1-2 1.2.1. Pressure..................................................................1-4 1.2.2. Temperature............................................................1-6 1.2.3. Density....................................................................1-6 1.2.4. Temperature, Pressure and Density changes at altitude 1-6 1.2.5. Humidity..................................................................1-6 1.2.6. Viscosity..................................................................1-6 1.3. ATMOSPHERE 1.................................................................1-8 2. AERODYNAMICS..........................................................................2-1 2.1. AIRFLOW AROUND A BODY..............................................2-1 2.2. AEROFOILS........................................................................2-3 2.2.1. Terminology.............................................................2-3 2.3. FLOW CHARACTERISTICS................................................2-5 2.4. GENERATION OF LIFT.......................................................2-7 2.4.1. Conservation of Energy...........................................2-7 2.4.2. Conservation of Mass (The Continuity Equation)....2-7 2.4.3. Bernoulli’s Equation...................................................... 2-8 2.4.4. The Venturi Tube.....................................................2-9 2.4.5. Newtons Law’s............................................................... 2-10 2.5. PROBLEM SETS................................................................. 2-11 2.5.1. Aerodynamics 1...................................................... 2-11 2.6. AERODYNAMIC FORCES.................................................. 2-12 2.7. CENTRE OF PRESSURE.................................................... 2-14 2.7.1. Aerodynamic Centre................................................ 2-15 2.7.2. The Co-Efficient Of Lift............................................ 2-16 2.8. STALLING........................................................................... 2-18 2.8.1. Wash Out................................................................ 2-20 2.8.2. Wing Stall Patterns.................................................. 2-20 2.8.3. Stall Wedges/ Strips/Vane....................................... 2-21 2.9. CENTRE OF PRESSURE DISTRIBUTION.......................... 2-23 2.10. PITCHING MOMENT COEFFICIENT................................... 2-23 2.11. DRAG.................................................................................. 2-27 2.11.1. Profile Drag............................................................. 2-27 2.11.2. Skin Friction and the Boundary Layer...................... 2-27 2.11.3. Transition Point....................................................... 2-28 2.11.4. Reynolds Number................................................... 2-30 Module 8 Issue 0 Rev 6 – 04/2024 Page i  2.11.5. Adverse Pressure Gradient..................................... 2-32 Module 8 Issue 0 Rev 6 – 04/2024 Page ii  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.11.6. Separation............................................................... 2-32 2.11.7. Form Drag............................................................... 2-33 2.11.8. Interference Drag.................................................... 2-36 2.12. PROFILE DRAG CURVE..................................................... 2-37 2.13. INDUCED (VORTEX) DRAG................................................ 2-37 2.13.1. Ground Effect.......................................................... 2-40 2.13.2. Induced Angle of Attack.......................................... 2-40 2.13.3. Induced drag curve.................................................. 2-42 2.13.4. Aspect Ratio............................................................ 2-42 2.14. SPANWISE LIFT EFFICIENCY............................................ 2-45 2.15. COEFFICIENT OF INDUCED DRAG................................... 2-47 2.16. THE CO-EFFICIENT OF DRAG........................................... 2-47 2.17. AIRFLOW CONTROL DEVICES.......................................... 2-50 2.17.1. Wing Fences........................................................... 2-50 2.17.2. Saw Tooth Notch..................................................... 2-51 2.17.3. Winglets.................................................................. 2-51 2.17.4. Boundary Layer Control - Vortex Generators.......... 2-53 2.17.5. Vortilons.................................................................. 2-54 2.17.6. Boundary Layer Control Through Suction/Blowing 2-55 2.18. TOTAL DRAG...................................................................... 2-56 2.19. LIFT/DRAG RATIO............................................................... 2-57 2.20. DRAG POLAR...................................................................... 2-60 2.20.1. Aerofoil Contamination............................................ 2-61 2.21. PROBLEM SETS................................................................. 2-63 2.21.1. Aerofoils 1............................................................... 2-63 2.21.2. Drag........................................................................ 2-64 3. THEORY OF FLIGHT.....................................................................3-1 3.1. THE FOUR FORCES OF FLIGHT........................................3-1 3.1.1. Weight.....................................................................3-1 3.1.2. Thrust......................................................................3-1 3.2. STEADY STATE FLIGHT.....................................................3-2 3.3. AERODYNAMIC RESULTANT............................................3-3 3.4. FORCES IN CLIMB..............................................................3-5 3.5. PERFORMANCE.................................................................3-6 3.6. POWER CURVES................................................................3-8 3.6.1. Effect of Altitude...................................................... 3-10 3.7. FORCES IN GLIDE AND DESCENT.................................... 3-11 3.7.1. Glide Angle and Ratio.............................................. 3-12 3.8. THEORY OF A TURN.......................................................... 3-13 3.8.1. Centripetal Force..................................................... 3-13 3.8.2. Looping................................................................... 3-14 3.9. LOAD FACTOR.................................................................... 3-16 3.9.1. Effect of Load factor on Stalling Speeds.................. 3-17 Module 8 Issue 0 Rev 6 – 04/2024 Page iii  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 3.10. LEVEL TURNS..................................................................... 3-18 3.10.1. Effect of Weight on Stall Speeds............................. 3-19 3.11. FLIGHT MANOUEVERING ENVELOPES (V-N DIAGRAMS) 3-19 3.12. LIFT AUGMENTATION........................................................ 3-21 3.12.1. High Lift Devices..................................................... 3-22 3.12.2. Effect of Flaps and Slats on Stall Angle................... 3-25 3.12.3. Effect of Flap deployment on Pitch.......................... 3-26 3.12.4. Use of High Lift Devices.......................................... 3-26 3.13. PROBLEM SETS................................................................. 3-29 3.13.1. Theory of Flight 1.................................................... 3-29 3.13.2. Forces and Manoeuvre 1........................................ 3-30 4. FLIGHT STABILITY AND DYNAMICS..........................................4-1 4.1. BASIC CONCEPT & DEFINITION........................................4-1 4.2. STATIC STABILITY.............................................................4-1 4.3. DYNAMIC STABILITY..........................................................4-3 4.4. AIRCRAFT STABILITY........................................................4-5 4.5. DESIGN FEATURES...........................................................4-6 4.5.1. Directional Stability..................................................4-6 4.5.2. Longitudinal Stability...............................................4-8 4.5.3. Lateral Stability........................................................ 4-12 4.6. CONTROL........................................................................... 4-17 4.6.1. Pitch Control............................................................ 4-20 4.6.2. Roll Control............................................................. 4-23 4.6.3. Adverse Yaw........................................................... 4-24 4.6.4. Directional Control................................................... 4-27 4.6.5. Dutch Roll................................................................ 4-28 4.6.6. Control Surface Bias............................................... 4-29 4.7. AERODYNAMIC BALANCING............................................. 4-29 4.7.1. Horn Balance.......................................................... 4-30 4.7.2. Inset Hinge.............................................................. 4-31 4.7.3. Balance Panel (Sealed Hinge)................................ 4-31 4.7.4. Mass Balance.......................................................... 4-32 4.8. TABS................................................................................... 4-33 4.8.1. Trim Tabs................................................................ 4-33 4.8.2. Balance Tabs.......................................................... 4-36 4.8.3. Anti-Balance Tabs................................................... 4-37 4.8.4. Servo Tab................................................................ 4-37 4.8.5. Spring Tabs............................................................. 4-38 4.9. DRAG DEVICES.................................................................. 4-39 4.9.1. Spoilers and Lift Dumpers....................................... 4-41 4.9.2. Speed Brakes.......................................................... 4-42 Module 8 Issue 0 Rev 6 – 04/2024 Page iv  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS PAGE INTENTIONALLY BLANK Module 8 Issue 0 Rev 6 – 04/2024 Page v  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 1. PHYSICS OF THE ATMOSPHERE Aerodynamics is that part of the study of Fluid Dynamics which relates to the action (and reaction) of bodies in a moving stream of air. Here we will review the composition of the air which comprises Earth's atmosphere; to consider the changes which can occur with certain characteristics of the atmosphere and to learn how those changes can affect the properties of the air. Most civil aircraft operate between Sea Level (SL) and 45,000 feet. Our studies of the atmosphere concentrate on this region. 1.1. NATURE The air that surrounds the earth (the Atmosphere) is a physical mixture of gases made up of 78% Nitrogen, 21% Oxygen, 0.9% Argon, 0.03% Carbon Dioxide and a trace of hydrogen, helium and neon. These percentages are volumetric, meaning that this ratio remains constant regardless of the change in altitude. Figure 1 The atmosphere is divided into layers, the Troposphere being the layer closest to the earth and contains virtually all the water that is present in the atmosphere; it is therefore the region where we find most of the weather forms such as clouds, rain and snow. Its temperature decreases with an increase in height. The Troposphere is very important in aviation because it is where the weather patterns exist that affect operating conditions. Module 8 Issue 0 Rev 6 – 04/2024 Page 1-1  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS he upper limit of the Troposphere where the temperature stops decreasing (an Isothermal region) is called the Tropopause. This ranges in height between 20,000 feet at the poles to 60,000 feet at the equator. The Tropopause is higher in summer than winter and rises and falls as high and low pressure moves under it. Its temperature remains at a constant -56.5 ° C Figure 2 1.2. PROPERTIES Any gas will have the physical properties such as pressure, density and temperature, which can vary. These properties vary within the atmosphere depending on where you may be in the world. Because of these variations, the performance of an aircraft will vary. If meaningful comparisons between measured performances are to be made, we must have a reference for all of our aerodynamic computations, the International Civil Aviation Organisation, (ICAO), has agreed upon a “Standard Atmosphere”. This is known as the International Standard Atmosphere or ISA. The International Standard Atmosphere constitutes the standard variation of pressure, temperature, density, viscosity, etc, appropriate to mid latitudes (45°N) In order to provide a datum for aircraft performance comparison, and instrument calibration, this assumed set of conditions is used. Whilst representative, these conditions do not necessarily reflect actual conditions in the atmosphere. Module 8 Issue 0 Rev 6 – 04/2024 Page 1-2  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS When all aerodynamic computations are related to this Standard, we can compare flight test data and other information, relative to our aircraft and its performance, regardless of where the readings were taken, and the results will be meaningful. An ISA is based on the following Sea Level (SL) criteria. SL Pressure 101.3 kN/m2 (1013.2 millibars/hPa) SL Density 1.225 kg/m3 SL Temperature 288 K (15ºC) SL Temperature Lapse rate6.5K/Km (1.98ºC / 1000 feet) The ISA values vary with altitude as shown in the following table: Height above Sea Pressure (kN/m2) Temperature (K) Density (kg/m3) Level (km) Sea Level 101.3 288 1.225 1 89.9 282 1.112 2 79.5 275 1.007 3 70.1 269 0.909 4 61.7 262 0.819 5 54.0 256 0.736 6 47.2 249 0.660 7 41.1 243 0.590 8 35.7 236 0.526 9 30.8 230 0.467 10 26.5 223 0.414 (Tropopause) 11 22.7 217 0.365 12 19.4 217 0.312 13 16.6 217 0.267 14 14.2 217 0.228 15 12.1 217 0.195 16 10.4 217 0.166 17 8.8 217 0.142 18 7.6 217 0.122 19 6.5 217 0.104 20 5.5 217 0.089 Figure 3 Module 8 Issue 0 Rev 6 – 04/2024 Page 1-3  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 1.2.1. Pressure The force that the air exerts on a unit of area is the measure of pressure. Pressure that is referenced from zero pressure is called Absolute Pressure. Pressure that excludes the pressure or the atmosphere is referred to as gauge pressure, as the pressure we are reading on the face of the gauge is the pressure above the atmospheric pressure already present. The altimeter in an aircraft cannot directly measure its height, but it can measure the absolute pressure caused by the weight of air above it, and hence its height. The scale is normally marked in feet rather than in units of pressure. The weight of air above any surface produces a pressure at that surface, therefore Pressure ( P ) is the ratio of the force ( F ) applied to the surface area ( A ). Pressure = Force = Mass x Acceleration (Weight) Area Area In the atmosphere, pressure is caused by the mass of the gaseous molecules acting under the force of gravity on a given area. As all molecules act under gravity then this pressure (called Static Pressure) can also be considered to be the weight of a column of air on a unit area. Static Pressure always acts perpendicular to any surface it is in contact with. (Figure 4) Figure 4 The total pressure exerted on a system is known as absolute pressure, which is equal to atmospheric pressure plus gauge pressure, expressed as: Pabsolute = Patmospheric + Pgauge. Module 8 Issue 0 Rev 6 – 04/2024 Page 1-4  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS There are numerous systems of measuring pressure, in aviation there are three common systems in use. 1.2.1.1. Pounds per square inch This is perhaps the most common measure of pressure and simply expresses the force in pounds that the air exerts on each square inch of area. In our standard atmosphere at sea level, the air exerts a pressure of 14.69 pounds per square inch (psi.). Approximately one half of our atmosphere is below 18,000 feet (ft.) and at that altitude; the air pressure has dropped to half of that at sea level (7.34 psi.) 1.2.1.2. Inches of Mercury A manometer is a device employed to measure pressure. It is based on the principle that by filling a tube with mercury and inverting it in a bowl of mercury, the liquid in the tube will drop and create a vacuum above it. The liquid will drop until the force exerted by the air on the surface of the mercury in the bowl is exactly equal to the weight of mercury in the tube. The pressure of the air under Standard Sea Level conditions will support a column of mercury to a height of 29.92 inches or 760 mm. Both inches and millimeters of mercury (mm Hg) are used as a unit of pressure. 1.2.1.3. Millibars Weather forecasters use millibars (mb) as a measure of pressure, on weather maps for example, the standard sea level pressure is 1013.25 mb. The altimeter in an aircraft does not measure how high it is; rather, it measures the absolute pressure caused by the weight of air above it. The scale, however, is normally marked in feet rather than in units of pressure. By setting the barometric scale to sea level pressure the altimeter shows the height above sea level. This scale is either in millibars or inches of Mercury (American). 1.2.1.4. Pascal The SI unit of pressure is the Pascal (Pa). This equal’s a force of one Newton divided over an area of one square metre (Nm-2). A pressure of one bar is equal to 100,000 Pa, with one millibar being equal to 100 Pa. This makes the standard atmospheric pressure at sea level equal to 101325 Pa or 1013.25hPa. Module 8 Issue 0 Rev 6 – 04/2024 Page 1-5  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 1.2.2. Temperature Under standard conditions, temperature decreases at approximately 1.98 ºC for each increase of altitude of 1000 feet. This decrease of temperature with altitude is defined as the lapse rate and continues up until an altitude of 38,000 feet, where the temperature remains at a constant -56.5 ºC up to 65,000 feet. The ICAO Standard Temperature at sea level is + 15 ºC. (See Figure 3) 1.2.3. Density Density is defined as mass per unit volume of a substance, at specified temperature and pressure. It is represented by the Greek letter  (rho). The density of the air is a property of great importance in aerodynamics. Air is compressible at certain speeds and, although its temperature and pressure may also rise when compressed, its density rises also. 1.2.4. Temperature, Pressure and Density changes at altitude As altitude increases, temperature and pressure, as we have seen, both decrease. In relationship to density, as the temperature decreases, density will increase, whereas as pressure decreases then density will also decrease. So, although the temperature decreases, the decrease in pressure (its lapse rate) is at a greater rate and as such, proportionally allows for a greater decrease in density rather than an increase. 1.2.5. Humidity The condition of moisture or dampness in the air is called Humidity. The maximum amount of water vapour that the air can hold depends on the temperature of the air. The higher the temperature the more water vapour it can absorb. Air with water vapour in it, is lighter than air containing no vapour, so that on damp days the air density is lower than on dry days. Humidity is normally stated as a percentage. If the humidity is specified as 60%, it means that the air is holding 60% of the maximum vapour that can be held at that temperature. 1.2.6. Viscosity Viscosity is a measure of the resistance of fluid to an applied stress. In everyday terms it is like the “thickness” of a fluid. For example, water has a low viscosity, so it appears “thin”. In comparison, honey has a higher viscosity, so it appears “thick” (See Figure 5). As air is classed as a fluid in aerodynamics, this means the tendency of one layer of air to move with the layer next to it. Viscosity essentially describes the airs internal resistance to flow and may be thought of as a measure of its internal friction. Module 8 Issue 0 Rev 6 – 04/2024 Page 1-6  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 5 Module 8 Issue 0 Rev 6 – 04/2024 Page 1-7  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS PROBLEM SETS 1.3. ATMOSPHERE 1 (1) Most civil aircraft operate within what altitude region? (2) What is the typical physical mixture of gases that make up dry air? (3) What does the term ICAO represent? (4) What are the ISA standard temperature, pressure and density values at sea-level? (5) Define the term pressure. (6) Absolute pressure is a combination of what pressures? (7) If the temperature is 275K at 2km above sea-level in the ISA, what is the temperature at 7km above sea-level? (8) What is the temperature at 45,000 feet above sea-level in ISA? (9) Name the 3 common systems of measuring pressure used in aviation? (10) What is the sea-level value of pressure in millibars (ISA)? (11) Define the term humidity. (12) Define the term density. (13) Define the term viscosity, and what happens to the viscosity of a gas with increasing temperature? Module 8 Issue 0 Rev 6 – 04/2024 Page 1-8  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2. AERODYNAMICS Aerodynamics is the study of air in motion, which includes changes in the physical characteristics, such as pressure and density. Because the air is in motion, changes in velocity and mass flow-rates are also important. We must also consider the option when the air is stationary, and an object moves through it as in the case of an aircraft in flight. In reality it makes little difference if the air is flowing around an object at a certain velocity, or the object is moving at the same velocity in still air. Aerodynamics also involves the study of forces being generated (e.g. the "lift" force on a wing), and so a brief mention must be made of some basic principles. 2.1. AIRFLOW AROUND A BODY We need to examine the aerodynamic forces of an aircraft, but before doing so we will consider the forces of any object moving through the air. We will eventually consider a specific aerodynamic shape or aerofoil and consider how lift and drag are produced. Lift and drag are both forces, but how are they produced? If a random shaped object is placed in the path of a uniform airflow as shown in Figure 6, the airflow will be undisturbed until it meets the object. The presence of the object will seriously disturb or disrupt the airflow and in doing so create forces in all directions. How is this force produced? Air, like all fluids, possesses a property called pressure. This pressure normally exerts a pushing force on any object it contacts. This force always acts at right angles (or normal) to the object. In Figure 6 the forces normal to the object are shown as small vector arrows at right angles to the surface of the object. Figure 6 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-1  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS There is also a frictional force present acting along the surface of the object as the air flows over it. As represented by the smaller arrows this force is less than the normal force and is tangential to the surface. Just as the forces normal to the surface are pressure forces, then those tangential are viscous forces, or a force due to the viscosity of the air. (Remember aerodynamics is concerned with fluid dynamics). At the moment we do not have one force, but instead a large number of small forces, represented by the small vector arrows. If we produce a single force by adding all of these vectors, we can produce a resultant force which we call the total reaction. The magnitude and direction of the total reaction will depend on the two forces already mentioned, pressure and viscous. Figure 7 This total reaction is shown in the diagram and acts at an angle θ to the direction of the airflow. We can resolve the total reaction vector into two separate vectors, one parallel to the airflow and one perpendicular to it. (Figure 7) By convention we define these two forces as: Drag, which is the component of total reaction force acting parallel to the free stream airflow Lift, which is the component of total reaction force acting perpendicular to the free stream airflow The free stream airflow is the undisturbed airflow a long way from the object. This needs to be so because if an object is placed in the path of airflow, the airflow will begin to be disturbed before it reaches the object. The use of the term ‘lift’ can be misleading, for under certain conditions of flight, such as a dive, it may act horizontally, and in other circumstances vertically downwards. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-2  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.2. AEROFOILS The earliest serious work on the development of aerofoil sections began in the late 1800's. Although it was known that flat plates would produce lift when set at an angle of incidence, some suspected that shapes with curvature, that more closely resembled bird wings would produce more lift or do so more efficiently. The erroneous belief that efficient aerofoils had to be thin and highly cambered was one reason that some of the first aeroplanes were biplanes. 2.2.1. Terminology An aerofoil is any surface such as a wing, rotor blade or propeller which produces an aerodynamic force when it is passed through a stream of air. Consider the wing of an aircraft, the cross-sectional shape obtained by the intersection of the wing is called an aerofoil. Such an aerofoil is shown below, (Figure 8) which illustrates some basic terminology. Figure 8 Leading Edge is the foremost point on the aerofoil. Trailing Edge is the rear-most point on the aerofoil. Chord Line is the straight line joining leading and trailing edges. Chord Length (C) is the length of the chord line. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-3  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Mean Camber Line is the line drawn through points equidistant from the upper and lower surfaces. (The camber line is usually a curved line; the greater the curvature, the greater will be the aerodynamic forces generated). Camber is the maximum distance between the mean camber line and the chord line, measured perpendicular to the chord line. Thickness of an aerofoil is the greatest distance between the upper and lower surfaces. (generally, between ⅓ and ½ way along the chord line). Thickness / chord ratio is normally expressed as a percentage. Angle of Attack () - the angle formed between the chord-line and relative airflow. By changing the angle of attack of the wing, two things can happen: The pressure difference between the upper and lower surfaces is greater (the fundamental cause of lift) due to the air having to speed up in order to flow through a tighter constriction and A greater downwash is produced from the deflected airflow. These two events will increase the Lift force on the wing. Relative Airflow (RAF) - Relative airflow is created by movement of an aerofoil through the air. The ‘relative airflow’ is parallel to the flightpath but in the opposite direction. (Figure 9) If a wing moves forwards horizontally the relative wind moves backwards horizontally. Figure 9 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-4  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS The particular aerofoil above can be seen to have more cross-sectional area above the chordline than below. That is, it is not symmetrical about the chordline. This is known as a Cambered design. In this instance, the chord is always straight, whereas the camber line is bent. If, however there is no camber attached to the design of the aerofoil then this is known as a Symmetrical design. Here, both the chord and the camber line are straight. This is seen most often on aerobatic aircraft where lift must be produced when inverted. (Figure 10) Figure 10 2.3. FLOW CHARACTERISTICS The patterns of lines around the aerofoil are known as Streamlines. Streamlines indicate the instantaneous direction of flow, and if flow is steady, they also show the path that a particle of air would follow. Streamlines are imaginary lines across which there is no flow. They can be artificially created (e.g. using smoke in a wind tunnel). The closeness of the lines gives an indication of flow speed. The closer they are then the faster the air flow. Because of the “layered” appearance, such flow is termed laminar and a characteristic is that unless a change is deliberately introduced, it will be unchanged from one instant to another. As can be seen, at the leading edge of the aerofoil there is a distinct ‘upwash’ of the air, whereas at the trailing edge a ‘downwash’ can be seen. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-5  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Just below the leading edge, where the airflow has separated, there is a point where the velocity of the free stream air has decreased to zero. Here the full force and pressure is felt and at its highest. This point is called the ‘Stagnation’ point and the total pressure is a combination of both the static pressure and the dynamic pressure on the aerofoil. Figure 11 Figure 11 above shows the airflow around an aerofoil section at a small angle of attack. At some point, the laminar flow will cease and be replaced by a mixture of both translational and rotational pattern of flow, whose pattern changes continuously. (Figure 12). This unsteady pattern is termed Turbulent flow, the creation of turbulence results in the creation of Drag. Figure 12 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-6  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.4. GENERATION OF LIFT There are several theories used to describe how a lifting force is generated by the action of air in motion past an aerofoil. Lift is generated in accordance with the fundamental principles of physics, the most relevant being: Conservation of Energy, which says that energy is neither created nor destroyed. Conservation of Mass, including the common assumption that the aerofoil’s surface is impermeable for the air flowing around. Conservation of Momentum, which is a direct consequence of Newton's laws of motion, especially Newton's second law which relates the net force on an element of air to its rate of momentum change. 2.4.1. Conservation of Energy The term energy may be defined as the capacity for doing work. The law of conservation of energy suggests that unless extra energy is introduced into a system the overall energy content must remain unchanged. 2.4.2. Conservation of Mass (The Continuity Equation) This is a simple algebraic equation that relates the values of density, velocity and area at one section of a stream tube to the same quantities at any other section. Since mass can be neither created nor destroyed, we have mass in = mass out. For steady fluid flow this can be expressed as: ρ1 A1V1 = ρ2A2V2 As flow is virtually incompressible at low speeds then ρ1 = ρ2. The equation now reads A1V1 = A2V2 If A2 is less than A1, then the velocity of the fluid must increase for the equation to be valid. (Similar to the egg timer principle, where sand travels through the throat of the timer quicker) This is valid for aerodynamics up to about ⅓rd the speed of sound. (Figure 13) Module 8 Issue 0 Rev 6 – 04/2024 Page 2-7  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 13 2.4.3. Bernoulli’s Equation In the previous chapter it was shown that the atmosphere exerts pressure at all times. This type of pressure, which exerts a force on all bodies, is called Static pressure (P) and acts equally in all directions. When air is in motion, however, it possesses an additional energy (kinetic energy) due to the fact that it is moving, and the faster it moves the more kinetic energy it has. If moving air is now brought to rest against some object, the kinetic energy is turned into pressure energy. This pressure on the surface of the body which causes the moving air to stop is called Dynamic pressure. The value of dynamic pressure depends on the density of the air and its speed and may be expressed as: Dynamic pressure = ½  V2 Bernoulli’s equation highlights the relationship between speed and pressure and can be expressed as: P + ½  V² = constant Static Dynamic Total pressure pressure pressure By applying the conservation of energy, the above equation can be expressed as: P1 + ½  V²1 = P2 + ½  V²2 This implies that if V2 is greater than V1, then P2 must be less than P1 (i.e. there will be a subsequent drop in pressure P). This principle can be applied to aerodynamics, as the flow through a venturi has similar characteristics to the flow over an aerofoil. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-8  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.4.4. The Venturi Tube An application of Bernoulli’s equation is seen during experiments using a Venturi tube. This simple instrument is a tube which gradually narrows to a throat, then expanding at the exit. It can be used to demonstrate an approximate relationship between pressure and velocity for low flow speeds. Figure 14 As air flows (dynamic pressure) into a constriction, that is between the surface of the aerofoil below and the weight of the static air above, due to the continuity equation, the air is squeezed and the streamlines move closer together and therefore must speed up in order that the mass of air can flow through the constricted area in a set period of time. As discovered by Bernoulli, this speeding up of the air will reduce the static pressure in the converging throat part of the venturi. (Figure 14) Figure 15 shows in a wind tunnel experiment, how the air flowing over the top of the aerofoil shape is travelling faster than below. This accelerated air is producing the relative lower pressure on the upper surface. The end result of this effect is a greater lowering of pressure on the upper surface compared to that of the lower. This imbalance of pressure between the upper and lower surfaces of the aerofoil creates a net force in the upward direction. As discussed in the last paragraph, the overall effect of this pressure difference is an upward force felt by the aerofoil leading to the fundamental cause of Lift. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-9  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 15 2.4.5. Newtons Law’s Lift can also be generated by the upper and lower surfaces of the wing when air flows around the wing and it is deflected downwards. A mass of air moving at a certain speed has a certain amount of momentum defined by the physical quantity of mass x velocity. Whenever this momentum changes over a period of time, a force is exerted that is: Force = Rate of change of Momentum This can be seen in Figure 16, where the flow of air has been turned to follow the shape of the wing and ends up being deflected downwards. To do this a force must be applied and according to Newton's Third Law of Motion, ‘for every action there is an equal and opposite reaction. Air that is deflected downwards will produce an upward or lifting reaction on the wing. Figure 16 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-10  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.5. PROBLEM SETS 2.5.1. Aerodynamics 1 (1) Explain how force acts on a body. (2) What is the perpendicular component of the total reaction force called? (3) What is the parallel component of the total reaction force called? (4) Define the term free-stream airflow. (5) Define the term conservation of energy. (6) For a steady state fluid what variables does the continuity equation relate to? (7) State Bernoulli’s equation, and describe its meaning. (8) Draw a simple venturi-tube and briefly describe the flow through it Module 8 Issue 0 Rev 6 – 04/2024 Page 2-11  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.6. AERODYNAMIC FORCES Whatever the theory, the lift force results from a difference between the pressures acting in the upper and lower surfaces. Figure 17 Figure 17 shows how the pressure varies around an aerofoil section. The length of the arrows shown represent the pressure difference; the direction of the arrows represents the sense; towards the surface indicates pressure greater than static, away from the surface indicates pressure less than static. It can be seen that the difference in pressures between the upper and lower surfaces is greatest over the front portion of the aerofoil. Therefore, most of the lift force generated must come from this region. At a point just behind the leading edge on the underside of the aerofoil the relative airflow speed reduces to zero. The full force of the dynamic pressure is felt at this point and so it follows that the pressure there must have its highest possible value. This maximum value is called the stagnation pressure. Figure 18 shows how the lift distribution varies with angle of attack and how negative angles can create negative lift on a cambered wing shape. Additionally, it shows how more lift can be generated at higher angles of attack by comparing 40 and 100. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-12  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Angle of -80 Attack Angle of Attack +40 Angle of Attack +100 Figure 18 The pressure distribution can be determined by experimentation, where pressures acting at several points on the aerofoil can be measured using manometers. A manometer will indicate the difference in static pressure (P) acting at a particular point and the free-stream static (ρ0). The difference (P – ρ0) / q0 is known as the pressure coefficient Cp. The pressure distribution of a particular aerofoil can be plotted in terms of Cp against % of chord (Figure 19) Here, negative values indicate pressures less than atmospheric. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-13  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS -1.0 UPPER SURFACE CP = LOWER SURFACE P 0 q0 / 20 40 60 80 100 % CHORD +1.0 STAGNATION POINT Figure 19 The pressure coefficient is an important quantity; for example, the distribution of Cp over the aerofoil surface leads directly to the value of the co-efficient of lift (CL - which will be discussed later on in the chapter). Different distributions will result from different aerofoil shapes, velocities and angle of attack. 2.7. CENTRE OF PRESSURE As an object moves through a fluid, the velocity of the fluid varies around the surface of the object. The variation of velocity produces a variation of pressure on the surface of the object. It has been stated that pressure acting on an area produces a force. The force (F) resulting from the air in motion is termed aerodynamic force. If all the distributed forces due to pressure were replaced by a single resultant force, this single force would act less than halfway back along the chord. The position on the chord at which this resultant acts is called the Centre of Pressure (CofP). Therefore, one way of looking at CofP is the point at which Lift is said to act. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-14  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS BECOMES. Figure 20 The vector representing lift through the centre of pressure passes through the point of minimum pressure on the upper surface, usually the point of maximum thickness of the aerofoil. (Figure 20) The idea of the centre of pressure is very similar to that of centre of gravity. 2.7.1. Aerodynamic Centre As mentioned previously, both the upper and lower surfaces have differing pressure distribution and as such each have their own CofP. As the pressure distribution is different between the two surfaces, then the centres of pressure could also be located at different places. In fact, on a cambered wing the lower surface CofP is forward of the upper surface CofP. These two opposing forces create a ‘couple’ resulting in a rotation of the aerofoil. This rotation is caused by the application of a moment known as a pitching moment. The pitching moment depends on the magnitude of the force creating it and the position of the centres of pressure with respect to a pivot. (We shall discuss later how this resultant is balanced by the tailplane). With changes in the angle of attack, we have seen that both the lift force and the centre of pressure will change. So, there must be some point along the chord about which there is no change in the pitching moment as the angle of attack is changed. (Figure 21) This point is known as the Aerodynamic Centre (AC). (Refer to Figure 30) Module 8 Issue 0 Rev 6 – 04/2024 Page 2-15  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 21 2.7.2. The Co-Efficient Of Lift Results of wind-tunnel testing show that within certain limitations the forces of lift and drag of an aerofoil depend on: Density of the air Square of the velocity Plan area of the aerofoil The shape of the aerofoil The basic factor controlling the value of lift is the dynamic pressure represented by: ½  V2. This pressure, exerted over an area (the aerofoil surface), will yield a force proportional to the amount of the area – i.e. lift force = pressure x area. So, the size or plan area of a wing will obviously affect the amount of lift produced and this must therefore be added to the above equation: Lift  ½  V2 S, where S is the wing area. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-16  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS How the wing transforms this into the Lift force will depend on the geometry of the aerofoil (the shape). Different aerofoils will fare better at transforming dynamic pressure into lift then others, and so designers give each aerofoil shape a ‘Co- efficient’ to express this. The coefficient of lift (CL) can be thought of as being a measure of the lifting effectiveness of the aerofoil. This co-efficient depends on the aerofoil geometry and its angle of attack. It varies with the flight conditions but its value changes primarily with the angle of attack. (α) Remembering that lift is proportional to ½ ρ V² S the full lift equation has now been arrived at by including a co-efficient of lift the factor (CL ) which takes into account changes in angle of attack: Lift = ½  V2 S CL As lift is considered a force then its values in SI terms are in Newtons (N) To attain a value of the co-efficient, transpose the formula about to make CL the subject: CL = …………Lift……… ½ V2 S. A 737 has an area of 105m2. Its takeoff speed is 82m/s. This would yield a dynamic pressure of 4118Pa. At sea level this would give a lift force of 865 kN. The co-efficient would then be determined to be: CL = ………865 000…… = 2 4118 x 105 As both aspects of the equation are in fact forces (Lift is a force and Pressure x Area is a force) the value of CL is unitless. This value holds true at takeoff – that is at a certain angle of attack and velocity. A higher angle of attack will give a greater value of CL. So, by varying the angle of attack, the pilot has the ability to alter the amount of lift produced. By using wind tunnel experimentation, aircraft designers can produce graphs of the value of CL against differing angles of attack. The shape of the lift curve for any wing will be more or less the same but it should be noted that the greater the camber of the wing the greater the lift it will develop This is illustrated in Figure 22 where a cambered section is compared to a symmetrical section. A point of interest is that although the cambered section still generates lift at a zero angle of attack the symmetrical section does not. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-17  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 22 2.8. STALLING For most wing sections, the amount of lift generated is directly proportional to the angle of attack, for small angles; the graph of CL against angle of attack is a straight line. However as shown in the graph of Figure 22, a point is reached where the lift starts to fall off. This effect is known as the critical angle of attack leading to a phenomenon known as Stalling. Stalling occurs when the airflow fails to follow the contours of the aerofoil and breaks away or separates from the top surface forming vortices similar to those behind a flat plate. The onset of stall is accompanied by a loss in lift and an increase in drag. As the angle of attack increases the ‘Stagnation Point’ moves farther along the lower surface of the aerofoil effectively creating a longer upper surface for the air to flow over. Due to the air’s viscosity, friction is created with the surface giving rise to drag (see the chapter on Skin Friction Drag). This slows down the speed of the air reducing its kinetic energy. When the angle of attack reaches a certain value, the air runs out of kinetic energy and breaks away from the surface of the wing in a random manner (Figure 23). There is no longer a mechanism to reduce the pressure over the upper surface, thereby creating a lift force. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-18  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS It should be noted that there is a definite angle of attack associated with the stall point for each aerofoil. This point is not affected by the speed of the aircraft. So, an aerofoil will stall at a particular angle of attack not a certain speed. To recover from a stall the smooth airflow must be restored. The aircraft will automatically pitch nose down (due to the centre of pressure moving back towards the trailing edge) when it has stalled but it may not be wings level. It requires both altitude and pilots input to correctly recover from a stall condition as they must reinstate a smooth flow of air over the aerofoil in order to achieve a pressure differential once again. The stalling characteristics of a wing depend not only on aerofoil shape, but also wing geometry, since not all the wing will stall at the same angle of attack. Also, not all wing planforms stall at the same point. The lift does not go to zero as lift is still being produced by the lower surface, but with a sudden loss of necessary lift, the aircraft will descend due to weight now being greater than lift. Figure 23 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-19  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.8.1. Wash Out To maintain a wings level flying attitude when stall occurs, it is important that lift is maintained over the control (ailerons) surfaces. Various design features can be incorporated in the wing which will assist in maintaining control. The ideal place on the wing for stall to first occur would be the root, as this will still allow aileron control. Although this may happen on some aircraft, on others a design feature is employed to counter this. One such design is known as Wash Out. The term wash out refers to wings designed so that the outboard (tip) sections have a smaller angle of incidence, and thus a lower angle of attack than the inboard (root) sections. (Figure 24) This will ensure that the inboard section reaches its stalling angle before the outboard section, so ensuring control is maintained. (This feature becomes important on swept-wing planforms where stall begins at the wing tips) Figure 24 2.8.2. Wing Stall Patterns A wing does not normally stall over its entire length simultaneously. The stall begins at one part of the wing and then spreads. The main factor governing where the stall begins is the shape of the wing. It is plainly undesirable that a wing stalls from its tip first as this can lead to control difficulties. Any tendency to drop a wing at the stall may well lead to spinning. Different wing planforms though have differing stall patterns. (Figure 25) Module 8 Issue 0 Rev 6 – 04/2024 Page 2-20  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 25 2.8.3. Stall Wedges/ Strips/Vane We have seen previously that washout on a wing permits the root of the wing to stall first, allowing the pilot to retain roll control during the stall. Even with a degree of washout, the aircraft will ‘drop a wing’ on occasions due to adverse boundary layer air causing the outer part of the wing to stall first. This can be overcome with the use of stall wedges, or stall strips, as they are sometimes known. Stall Wedges are small, wedge-shaped strips mounted on the leading edge of the wings at about one third span. They are designed to disrupt the boundary layer airflow, at large angles of attack approaching the stall, thus ensuring the airflow breaks away (stalls), at the root end of the wing first. (Figure 26) Additionally, they produce a similar effect to a wing fence at smaller angles of attack resulting in a smoother airflow over the ailerons, thus retaining optimum roll control. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-21  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 26 Another device employed is a vane-type stall warner (Figure 27). This takes advantage of the fact that the stagnation point moves to the lower surface as α is increased. At normal angles the vane is held down. As the stall angle approaches the airflow moves the vane upwards. The vane is connected to a stall warning in the flight deck, giving the pilot warning of an impending stall. Figure 27 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-22  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.9. CENTRE OF PRESSURE DISTRIBUTION Experiment shows that as angle of attack is altered the pressure distribution over an aerofoil changes. Consequently, there will be movement of the centre of pressure. (Figure 28) Figure 28 As the angle of attack is increased up to about 12º the centre of pressure gradually moves forward until it is less than ⅓ of the chord from the leading edge. Above this angle (the stalling angle) the centre of pressure begins to move backwards again. So now it can be understood that both the lift force and the centre of pressure vary as angle of attack varies. 2.10. PITCHING MOMENT COEFFICIENT We have seen how the pressure distribution on a wing differs between the top surface and lower surfaces. We have also seen that there is a point on these surfaces where we can simulate this pressure distribution by a single force. This is known as the Centre of Pressure (CofP) As the pressure distribution is different between the two surfaces, then the centres of pressure could also be located at different places. In fact, on a cambered wing the lower surface CP is forward of the upper surface CP. (Figure 29) Module 8 Issue 0 Rev 6 – 04/2024 Page 2-23  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 29 The result of these two forces move the wing nose down. This particular principle was not understood by the early aviators, leading to many mishaps and untimely deaths. We will come to how this is resolved in later chapters. This rotation is caused by the application of a moment known as a pitching moment (M). The pitching moment depends on the magnitude of F and the position of the centre of pressure with respect to the pivot. Just as the coefficient CL was introduced to create the lift equation, so a pitching moment coefficient CM is introduced. M = CM ½ ρ V² S c Since the pitching moment is a moment, i.e. force x distance, and ½ ρ V² S represents a force, its necessary to introduce a length into the equation, this is in the form of the chord, c. As with CL, it is usual to draw graphs using CM rather than M. (Figure 30) Module 8 Issue 0 Rev 6 – 04/2024 Page 2-24  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 30 The pitching moment is considered positive when it tends to push the nose upwards, negative when the nose tends to go downwards. From the graph (Figure 30) we can see that the pitching moment which was slightly nose down at the angle of zero lift, increases or decreases as near as matters in proportion to the angle of attack. Looking at the dashed line we can see that at an angle of attack of 4°, there is a greater moment of coefficient about the leading edge ( -0.2 - a greater negative pitch) then there is at the trailing edge. (+0.04) About the leading edge, CM becomes more and more nose down as angle of attack is increased. At a point about the trailing edge, although starting at the same slightly nose down moment at zero lift, CM becomes less nose down and finally nose up with increased angle of attack. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-25  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS There are now two possible ways of thinking about the effects of increased angle of attack on the pitching moment: One way is to think of lift changing and the point of application (centre of pressure) changing (Figure 31 upper) The other is to think of the point of application (aerodynamic centre) being fixed and only the lift changing, (Figure 31 lower) because although there has been a change in the amount of lift generated, there has been no change in the moment at the point about which it has taken place (the aerodynamic centre). At subsonic speeds the aerodynamic centre is about ¼ of the chord from the leading edge. At supersonic speeds the aerodynamic centre is about ½ of the chord from the leading edge. Figure 31 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-26  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.11. DRAG We have already given Drag a definition in the previous chapters. That is, the component of the total reaction force that acts parallel to the free stream airflow. In fact, it is the resistance to the airflow and the faster we fly then the greater the drag on the aircraft. Drag itself is best studied by breaking it down into two distinct headings: Profile or 'zero-lift' drag Induced or 'Lift dependant' drag 2.11.1. Profile Drag This particular type of Drag (also known as Parasite Drag in the U.S.) is made up of three components. SKIN FRICTION (VISCOUS) DRAG FORM DRAG INTERFERENCE DRAG 2.11.2. Skin Friction and the Boundary Layer Consider a flat smooth surface over which air is flowing. What may seem to be a smooth surface to an observer, will, to a molecule of air, seem a very rough one. Air is a viscous medium, and so as air flows over a solid surface, the air will try to drag the surface along with it due to friction between the air and the solid surface. The presence of this friction creates a drag force known as skin friction. Any surface subjected to a moving airstream will inevitably have, through viscous adhesion, a minutely thin layer of air at its surface which has zero relative velocity. The layers of air near the surface retard the layers farther away owing to shearing action between them. Succeeding layers adjacent to the surface will, through the same viscous action, be subject to retardation, but to a lesser degree with increasing distance (albeit a very small one) from the surface. A point is therefore reached where the airflow will be unaffected, and its velocity will be that of the 'free stream‘ airflow. This layer of air from the surface where there is zero velocity, to the point where there is no retardation, is referred to as the 'Boundary Layer‘ and is normally defined as the region in which the velocity of flow is less than 99% of the free stream value. (Figure 32) Module 8 Issue 0 Rev 6 – 04/2024 Page 2-27  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS The Boundary Layer is thus the mechanism by which skin friction drag is created. The amount of drag created depends on the shape and thickness of this layer. Figure 32 The distance above the surface in which velocity regains a value close to that of the free stream velocity may be no more than a few millimetres over an aerofoil. Surface friction drag depends on the rate at which air adjacent to the surface is trying to slide relative to it. It is also worth noting that the type of material the aeroplane is made of does not affect viscous drag. i.e. air does not stick any more or less to an aluminium aeroplane than a carbon-fibre one. However, some types of material are more suited to promoting laminar as opposed to turbulent boundary layers. 2.11.3. Transition Point The boundary layer exists in two forms: as laminar flow and turbulent flow. Near the leading edge of the aerofoil the air is laminar and flows in a smooth layered streamlined manner. These streamlines remain in their respective positions to each other giving rise to a 'Laminar' flow. (Think of this as a multi-lane motorway where the cars stay in their respective lanes. Although the cars in the different lanes are travelling at different speeds, they stay in their in their own lanes. Now imagine a set of road works up ahead. This will inevitably slow the flow down. The cars will now start to move between lanes in order to avoid crashing into each other. So, what starts out as a nice smooth flow of traffic turns into a disorganised flow). At a point on the aerofoil there is a change or transition, where instability in flow develops, and the flow in the layer becomes turbulent. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-28  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS This transformation in the flow can be seen with smoke rising from a cigarette. Initial smoke flow is laminar, but as it passes through the air it encounters friction, slows down (loses inertia) subsequently turning turbulent. This same effect takes place over the surface of the wing. Figure 33 In Figure 33 important features of the transition from laminar to turbulent flow are that: (i) The depth of the laminar layer is typically given as 0.07in. (ii) The depth of the turbulent layer is typically given as 0.7in. (iii) The velocity gradients of the two layers being different leads to the greater shearing or friction effect occurring in the turbulent layer. In the turbulent layer, eddies form that are relatively large compared to molecules, and a rapid mixing of fast- and slow-moving masses of air occurs. The turbulent eddies extend the influence outwards from the surface, so the boundary layer effectively becomes thicker. Note the velocity gradients of the two layers being different leads to greater friction effect occurring in the turbulent layer. This in turn creates more drag. Generally speaking, the transition point (that point at which the laminar flow turns turbulent) for an aerofoil section will be at the point of maximum section depth where the velocity of flow is greatest (refer to the Venturi effect). So therefore, designers need to maintain a laminar boundary layer flow as long as possible over an aerofoil section in order to reduce drag. One method of ensuring a greater percentage of laminar flow is to maintain an increasing depth of section as far back from the leading edge as possible, thereby locating the point of maximum velocity farther aft. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-29  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS This results in a wing section known as a laminar flow wing. Note the velocity gradients of the two layers being different leads to greater friction effect occurring in the turbulent layer. The main variable which dictate the change from the laminar state to turbulent are: Surface condition The surface area The viscosity of the fluid The rate of change of velocity 2.11.4. Reynolds Number In wind tunnel tests it is important to know what factors control the transition from laminar to turbulent boundary layer flow. As testing is normally carried out on small scale models instead of full-size objects, designers must ensure that when looking at the airflow over the wing any aerodynamic effects must be similar to that of the full scale object. (That is, both must be dynamically similar). As we have discussed there are two forms of flow of importance to aircraft designers - laminar and turbulent. Also, we have seen that turbulent air causes more drag then laminar. So one important factor is where the transition point appears on the wing. The position of transition to turbulent flow on an aerofoil moves forwards with increasing speed and also if the air density is increased. It moves rearwards if the coefficient of viscosity of the air increases. The transition point will also depend on the distance along the chord from the leading edge for a given aerofoil. This dependence on speed, density, viscosity and chord can be expressed as a single quantity known as Reynolds number (Re), where: Re = ρ V l μ p = density, V = velocity, l = diameter of the pipe, μ = viscosity coefficient The number itself is dimensionless like a ratio and was formulated by Osborne Reynolds in 1883 during his experiments with fluids flowing through a pipe into which he injected a coloured dye. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-30  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS By varying certain parameters (velocity, density, diameter of pipe), he found that a change in flow (from laminar to turbulent) came about when these parameters crossed a value threshold: If the number calculated was: Below 2000 – Then we have Laminar flow. Between 2000 to 4000 – Then we have Transitional flow. Above 4000 – We have Turbulent flow. So therefore, a low Re will result in laminar flow because the viscous forces dominate and the airflow adheres to the surface. A high Re will result in turbulent flow as the inertia forces dominate. A suitable combination of density and velocity can be used to obtain the same Re for the model as for the full-size aircraft. This enables the flow characteristics and force coefficients for the model to be the same as for the actual aircraft. (Dynamic similarity) By using the above formula (but substituting the diameter of the pipe with the chord of the wing) designers can use the value of the Reynolds number obtained and, by applying this value to a scale model calculate different forces on a full- scale wing/aircraft model. So now we have a formula: Re = ρ V c μ p = density, V = velocity, c = chord length, μ = viscosity coefficient Aircraft designers found that as the Re increased the transition point between laminar and turbulent flow moves forward. In essence, the Reynolds number is a comparison between the forces which propel the fluid forward and the forces which slow the fluid down. Thus, the Reynolds number is used to determine the type of flow that is occurring in a system. The Reynolds Number for full-scale flight varies from about 2,000,000 for small slow-speed aircraft to 20,000,000 for large high-speed aircraft. Unfortunately, if we test a 1/10th scale model under sea level conditions, it will be found that to keep the same Re the velocity of the air must be increased 10 times. This can cause problems due the fact that the model would be using speeds where density would be affected. To overcome this wind tunnels have been designed so that the density can be altered by either using compressed air or lowering the temperature of the air to extreme temperatures. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-31  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.11.5. Adverse Pressure Gradient On a typical low speed aerofoil at a normal angle of attack, pressure reaches its minimum value at a point somewhere around the position of maximum thickness on the upper surface. (due to greater velocity) After this the pressure gradually rises (velocity decreases) until it returns to a value close to the original free stream pressure at the trailing edge. This means that over the rear part of the upper surface, the air has to travel from low to high pressure. A pressure gradient now exists that is not assisting, but impeding flow (a bit like trying to cycle into wind)- it is known as an Adverse Pressure Gradient. This is opposite to the pressure gradient at the leading edge whereas air is going from high to low then we have a favourable pressure gradient that assists the flow over the wing - cycling with the wind behind you. (Figure 34) Figure 34 2.11.6. Separation Consider a fluid particle close to the surface of the wing. Due to viscosity the particle starts to lose its kinetic energy. Once all its kinetic energy is lost and encountering the adverse pressure gradient the particle starts to move backwards due to the pressure acting upon it - flow reversal. (See Figure 35) This results in the flow becoming separated from the wing which, if severe enough, will result in loss of lift and even stall. If the rate of pressure increase is gradual, then the process of turbulent mixing allows the outer layers to pull the inner ones along (the boundary layer merely thickens). In fact, a turbulent boundary layer can, under certain circumstances resist the pressure gradient and stay attached to the wing. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-32  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS If the rate of pressure increase is rapid, the mixing process is too slow to keep the layer moving. The boundary layer stops following the direction of the surface and starts to separate. Figure 35 Re-circulating flow tends to move towards the lower pressure in the reverse direction to the main flow. This mechanism is the primary cause of stalling. As an aerofoil’s angle of attack is increased, pressure differences between the front and rear of the aerofoil increases, and the separation position moves forwards. 2.11.7. Form Drag Without the influence of viscosity, streamlines would close up behind all parts of an object and there would be no wake. For a symmetrical shape the streamline pattern and pressure distribution would also be symmetrical. (Figure 36) Figure 36 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-33  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS When an object is placed in a viscous fluid, such as air, which is moving relative to the object, it will experience a resistance owing to the formation of vortices which create turbulent as opposed to streamlined flow, due to the fact that when a viscous fluid flows past a solid object, vortices are formed and there is no longer a smooth streamline flow. As we saw in the previous chapter, a smooth streamline flow produced by a laminar boundary layer will create less drag than a turbulent one. But a turbulent boundary layer will have more energy associated with it, giving it greater resistance to separation due to an adverse pressure gradient. In reality viscous flow past a body will produce a resistance. Some shapes produce considerable turbulence; others minimise it. Some recognisable shapes are shown below, and a comparison made of the resulting resistance. (Figure 37) Figure 37 On the non-symmetrical shapes shown in Figure 37, the air pressure reaches its minimum value at about the position of maximum section depth. Over the rear portion there is an adverse pressure gradient, which promotes rapid degradation of available energy in the boundary layer, resulting in a reduction in pressure over the rear. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-34  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS The pressure on the forward-facing part of an object is on average higher than that on the rearward facing part. This results in a net drag force, which is known as form (pressure) drag. It is essential that form drag is reduced to a minimum in those parts of an aircraft that are exposed to the air. 2.11.7.1. Fineness Ratio It is clear from the extreme case of the flat plate at right angles to the airflow, that it represents the maximum generation of vortices and turbulence; in other words, maximum resistance or drag. The production of vortices requires the expenditure of energy in order to generate them, this energy being provided by the object causing the wake and this of course, is wasteful. By substituting a cylindrical section for the plate, we produce a less abrupt change in the path which the airflow is trying to follow. In this case, fewer vortices are generated: there is less difference in pressure from the front to the rear of the shape, and a degree of 'streamlining’ has been achieved. Figure 37 showed by reducing the frontal area of the object the airflow has a much more gradual passage from the front of the section to the rear than in the case of the cylinder. The end result, therefore, of streamlining, is to produce much less vortex generation, reduced turbulence, and so therefore greatly reduced drag. In order to reduce form drag it is important to ensure that the pressure gradient is not strongly adverse. This means the tail of the body should be reduced in depth or cross-sectional area gradually, a ratio which is known as streamlining. Streamline shapes which give the least resistance at subsonic speeds have a ratio of overall length to maximum thickness of between 3 and 4. Figure 38 This ratio is known as the Fineness Ratio, i.e. a/b. The maximum value of b should be about ⅓ of the way back from the nose. Module 8 Issue 0 Rev 6 – 04/2024 Page 2-35  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Although this gives the ideal shape for any separate body, it does not follow that that two streamlined bodies (e.g. wing and fuselage) will, when joined together give the least resistance. 2.11.8. Interference Drag Interference drag is generated by the collision of airstreams creating eddy currents, turbulence, or restrictions to smooth flow. For instance, the airflow around a fuselage and around the wing meet at some point, usually near the wing’s root. These airflows interfere with each other causing a greater drag than the individual values. This is often the case when external items are placed on an aircraft. That is, the drag of each item individually, added to that of the aircraft, are less than that of the two items when allowed to interfere with one another. Interference leads to modifications of the boundary layers and creates greater pressure differences between fore and aft areas on the surfaces concerned. This leads to greater total drag. Interference drag can be reduced by the addition of fairings and fillets in the areas concerned. (Figure 39) Figure 39 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-36  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS 2.12. PROFILE DRAG CURVE In conclusion, as we have seen, Profile drag is a combination of drag types due to skin friction, form and interference. Profile drag is directly proportional to the square of the air speed. (ZERO-LIFT DRAG) PROFILE DRAG SPEED Figure 40 The curve above (Figure 40) shows how profile drag increases with increasing air speed. 2.13. INDUCED (VORTEX) DRAG Induced drag is also known as ‘Lift Dependant Drag’, although the term vortex drag might be more descriptive. The presence of regions of different pressure (as happens when lift is generated) will cause a flow to develop from high to low pressure. This flow travels from the high pressure below the wing to the low-pressure area on the upper surface with the main flow around the wing tips. (Figure 41) As we have seen previously, the larger the lift being produced by the wing, the bigger the pressure difference between the lower and upper surfaces. The larger the pressure difference the stronger the vortex around the wing tips produced and so it can therefore be said that induced drag is proportional to lift. (So called 'Lift Dependant Drag') Module 8 Issue 0 Rev 6 – 04/2024 Page 2-37  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS Figure 41 This results in a spanwise component forming in addition to the chordwise component. This spanwise flow moves root to tip on the lower surface and tip to root on the upper surface. (Figure 42) Figure 42 When the two airflows, from the top and bottom surfaces, meet at the trailing edge they are flowing at an angle to each other and cause rotating vortices. (Figure 43) Figure 43 Module 8 Issue 0 Rev 6 – 04/2024 Page 2-38  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS All the vortices on one side tend to join up and form one large vortex which is shed from each wing tip. These are called wing tip vortices. (Figure 44) Figure 44 The effect of the vortex is to deflect the air upwards before the leading edge and downwards as it passes over the trailing edge of the wing; in other words, producing a downwash. (Figure 45) Figure 45 As the maximum strength of this movement is close to the vortex, as the air moves from the wing tip towards the fuselage the downwash steadily decreases. (See Figure 43) Module 8 Issue 0 Rev 6 – 04/2024 Page 2-39  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS So, for a given strength of vortex, the larger the wingspan the less will be the effect of this downwash velocity. (We will look at this later on) The air leaving the trailing edge does so at a certain angle and a certain velocity and this angular deflection of the airflow will depend on the speed. For a given downwash velocity the deflection angle will be greater at low speeds than at high speeds due to a higher CL to maintain lift 2.13.1. Ground Effect As we have seen, vortices are produced by the pressure differential between the upper and lower surfaces. This being strongest at the wingtips where the air spills around the tip. As an aircraft approaches the ground during the landing phase, the vortices and the downwash that is produced by them, are interrupted. (Figure 46) The product of this is that induced drag is reduced whereas the lift is increased. This gives rise to an increase in the velocity of the aircraft and an increase in lift. While in the ground effect, the wing will require a lower angle of attack to produce the same amount of lift. If the angle of attack and velocity remain constant, an increase in the lift coefficient will result, which accounts for the "floating" effect of the aircraft and will allow it to keep flying farther down the runway. Figure 46 2.13.2. Induced Angle of Attack The angle the airflow leaves the wing as compared to the freestream relative wind is called the induced angle (αi). The aerofoil itself 'sees' this induced angle as a reduction in the geometric angle of attack – α (as discussed before – this is the angle between the chord line and the relative wind). This is known as its effective angle of attack (αe) and is equal to the geometric angle of attack minus the induced angle of attack. (αe = α - αi). Module 8 Issue 0 Rev 6 – 04/2024 Page 2-40  CAR 66 CATEGORY A MODULE 8 AERODYNAMICS As we know from previous chapters, the total reaction force of a wing (the Lift force) is at right angles, but this time not to the initial direction of the airflow, but to the resultant between the original direction and the final direction - the effective angle of attack. (αe) Moreover, the resulting force exerted by the air on the wing, now perpendicular to the local flow direction, is tilted backwards by an angle equal to the induced angle of attack (αi) and then is no longer perpendicular to the free stream velocity. So, there is now a component of the resulting force parallel to the relative wind and as we know, this is known as 'Drag' or more precisely 'Induced Drag'. What we can say is that the more the final flow is deflected downwards — in other words at slower speeds which will give rise to bigger downwash — the more the total reaction is tilted rearwards, giving rise to greater induced drag.(Figure 47) Figure 47 As we see in Figure 47, the angle of attack relative to the modified local airstream directions is now red