Basic Aerodynamics PDF - Part 66–B08

B08 AERODYNAMICS Post CIR 2023/989  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics © Air Service Training (Engineering) Ltd Aeronautical Engineering Training...

B08 AERODYNAMICS Post CIR 2023/989  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics © Air Service Training (Engineering) Ltd Aeronautical Engineering Training Notes These training notes have been issued to you on the understanding that they are intended for your guidance, to enable you to assimilate classroom and workshop lessons and for self-study. Although every care has been taken to ensure that the training notes are current at the time of issue, no amendments will be forwarded to you once your training course is completed. It must be emphasised that these training notes do not in any way constitute an authorised document for use in aircraft maintenance. Document Quality Air Service Training (Engineering) Limited are committed to improving their product and service. Consequently, if you find any errors with this document then please forward them to the document owner at the e-mail address below. [email protected] Initial Issue 3 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Amendment History Commission implementation Regulation 2023/989 – Initial Issue Amendment Details of Change Date List (AL) 0 Commission Implementation regulation 2023/989 June 2024 Initial Issue 4 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics CONTENTS CHAPTER 1: Atmospheric Physics............................................................................ 7 SECTION 1: The Atmosphere..................................................................................... 7 SECTION 2: Physics of a Moving Fluid.................................................................... 16 SECTION 3: Basic Atmospheric Instruments............................................................ 23 SECTION 4: Self Study Questions............................................................................. 27 CHAPTER 2: Flight Aerodynamics........................................................................... 29 SECTION 1: Components and Terminology............................................................. 29 SECTION 2: Lift........................................................................................................ 38 SECTION 3: Drag..................................................................................................... 60 SECTION 4: Lift/Drag Ratio...................................................................................... 79 SECTION 5: Stalling................................................................................................. 82 SECTION 6: Self Study Questions............................................................................. 92 CHAPTER 3: Theory of Flight.................................................................................... 95 SECTION 1: Level Flight Conditions......................................................................... 95 SECTION 2: Manoeuvres....................................................................................... 101 SECTION 3: Climbing............................................................................................. 105 SECTION 4: Gliding................................................................................................ 115 SECTION 5: Turning............................................................................................... 120 SECTION 6: Self Study Questions........................................................................... 127 CHAPTER 4: High-Speed Airflow............................................................................ 130 SECTION 1: General.............................................................................................. 130 SECTION 2: Transonic Flight and Raising the Critical Mach Number of the Aircraft 138 SECTION 3: Supersonic Flight............................................................................... 147 SECTION 4: Airflow in the Engine Intakes of High-Speed Aircraft.......................... 159 SECTION 5: Self Study Questions........................................................................... 165 CHAPTER 5: Stability............................................................................................... 167 SECTION 1: Introduction........................................................................................ 167 SECTION 2: Static Stability..................................................................................... 168 SECTION 3: Dynamic Stability................................................................................ 169 Initial Issue 5 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics SECTION 5: Directional Stability............................................................................. 178 SECTION 6: Lateral Stability................................................................................... 180 SECTION 7: Spiral Stability.................................................................................... 185 SECTION 8: Dutch Roll Stability............................................................................. 187 SECTION 9: Self Study Questions........................................................................... 190 Initial Issue 6 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics CHAPTER 1: ATMOSPHERIC PHYSICS SECTION 1: The Atmosphere Introduction The atmosphere is one of the four main ‘spheres’ of our planet the other three are the Biosphere, Lithosphere and Hydrosphere. In order to fly and sustain flight, an aircraft as it passes through the air must generate enough lift force to overcome its weight by doing some work on the atmosphere that surrounds it. It is important therefore, that in order for us to gain an understanding of how an aircraft flies, that we first have some knowledge of the medium that an aircraft operates in, the atmosphere, as changes in the properties of the atmosphere will affect the way an aircraft flies. The Layers of the Atmosphere The atmosphere is a region of gasses that surrounds the earth up to a height of approximately 500 miles (800 Km) and is considered to consist of five distinct gaseous layers. These layers are known as the: Initial Issue 7 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Troposphere, Stratosphere, Mesosphere, Ionosphere (Thermosphere) Exosphere. Many scientist however, do not consider the Ionosphere a distinctive layer of the atmosphere and this forth layer is more commonly known as the Thermosphere. This layer starts at the coldest part of the atmosphere above the Mesosphere and finishes at the hottest part just below the upper part of the Exosphere. In the make up of the atmosphere, the Troposphere is the smallest of all the earth’s atmospheric layers and is the closest to us here on earth, extending upwards from sea level to approximately 5 to 9 miles. Although this is the smallest of all the atmospheric layers, the Troposphere contains approximately 80% of the earth’s atmosphere, so it is the densest and is characterised by turbulent weather conditions such as storms, rain, sleet and snow. Above the Troposphere lies the atmospheric layer known as the Stratosphere. This layer extends from the upper level of the Troposphere, known as the Tropopause, to approximately 31 miles above sea level, ending at point known as the Stratopause. In the Stratosphere, the conditions are considered tranquil or non-turbulent, even though it does have high velocity winds such as the jet stream. This is because these winds are considered steady not gusty like the winds in the Troposphere. Above the Stratosphere, lies the Mesosphere that extends from approximately 31 miles to 50 miles above sea level and above this we find the final two layers, the Ionosphere, or Thermosphere and then the Exosphere. In considering the effect the atmosphere has on the aerodynamics of an aircraft. We need only consider the lower two layers of the atmosphere; the Troposphere and Stratosphere, as most aircraft normally only fly from sea level up to around 70,000 ft (13.3 miles). Most commercial aircraft fly between 33,000ft (6.25 miles) and 42,000 ft (7.6 miles). Initial Issue 8 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Characteristics of the Atmosphere The atmosphere that surrounds the earth, or air, as we know it, is made up by a number of gases principally Nitrogen and Oxygen. The exact make up of air in the lower levels of the atmosphere being 78% Nitrogen, 21% Oxygen and 1% other gases (Argon and Carbon Dioxide). These percentage values are consistent up to approximately 50 miles above sea level, although the concentration levels of air varies greatly with height, there being insufficient concentrations of air present in the atmosphere for example to sustain human life at the upper limits of the tropopause. For aerodynamics, one of the most important characteristics of the atmosphere is its density, as changes to the density of air will affect the amount of work an aircraft has to do on the air in order to sustain flight. In flight therefore as air is a gas and is easily compressed or expanded, any change in atmospheric conditions, such as pressure and temperature will alter the density of air and affect the work required to fly. To find a relationship that can be used to find changes between the factors of pressure, temperature and density, a formula is derived from the Universal Gas Law: Where: P = Pressure V = Volume T = Temperature Initial Issue 9 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics But since the volume of air can be derived from the formula for density: then This can be substituted into the Universal gas formula to give: This formula can now be simplified if the gas is considered to be perfect. As at a constant height in the atmosphere, the mass of a perfect gas is considered constant, so mass can be cancelled out on both sides of the equation leaving: Where : P = Pressure ρ = Density T = Temperature Atmospheric Pressure and its effect on Density Pressure in the atmosphere occurs because the gasses that make up the atmosphere are held in contact with the earth’s surface by the force of gravity. The closer we are therefore to the earth’s surface, the greater is the gravitational effect, so the higher is the number of air molecules present and the greater is the weight or pressure. Conversely as we climb in the atmosphere, due to the reduction in gravity, air thins out and the number of air molecules decreases, so the weight of air decreases and so will atmospheric pressure. Thus, if a column of air 1 inch square was to extend from sea level Initial Issue 10 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics to the extremities of the atmosphere, atmospheric pressure at any point could be found as it would equal the weight of the air molecules above it. At sea level we find that the standard atmospheric pressure is equal to 14.69 PSI (1013.25 mbar) and decreases as we climb in the atmosphere at a non-uniform rate due to the reduced gravitational effect the further we move away from the surface. Atmospheric pressure becoming half its sea level value at about 18000 ft and approximately quarter of its sea level value at the tropopause (about 36,000 ft). These changes in atmospheric pressure will affect the density of air, as if a given volume of air is considered, the higher we climb in the atmosphere, as the air pressure reduces due to the decrease in the number of air molecules the less air will be compressed, so its density will decrease. Conversely as we descend in the atmosphere, for the same given volume as pressure increases the higher will be the number of air molecules present, so its density will increase. Initial Issue 11 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The density of air is therefore directly proportional to pressure, increasing or decreasing in line with atmospheric pressure. Atmospheric Temperature and its effect on Density In the lower region of the atmosphere, the temperature of air depends on the amount of heat energy from the sun that is reflected back from the surface. Therefore, the further away from the surface the air is the lower will be its temperature. Temperature affects the density of air as at a constant pressure, the cooling of air decreases the amount of movement and spacing between air molecules allowing more molecules to be contained in a given volume increasing its air density. Conversely as air is heated at a constant pressure the molecules tend to speed up and increase the spacing between them reducing the number of molecules in a given volume deceasing air density. The density of air is therefore inversely proportional to temperature. The international lapse rate for temperature in the atmosphere up to a height of 36,090 ft (the tropopause) is given at the rate of 0.65C per 100 metres or 1.98 C per 1000 ft. After this height this rate is no longer valid as temperature then remains constant at – 56.5C up to about 65,000 ft, where it then varies in different parts of the upper atmosphere, due to varying atmospheric conditions becoming hottest in the upper region of the thermosphere, just below the exosphere. Humidity in the Atmosphere and its effect on Density Humidity is the amount of water vapour suspended in the air and is found up to a height of approximately 6 miles (9.6 km) in varying quantities. The ability of air to hold water vapour increases with air temperature. The actual amount of water vapour in the atmosphere being dependent on the air temperature of the day and whether the air is near or has recently passed over a large area of water. So, on hot days air can hold more water vapour, but even at cold temperatures there is always a certain amount of water vapour in the atmosphere at lower levels. Humidity affects air density because water vapour is less dense than air. The density of water vapour under standard sea level conditions is: 0.7600 Kg/m3 Whereas for perfectly dry air the density is: 1.225 Kg/m3 Initial Issue 12 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The density of air is therefore greatest when air is perfectly dry and least dense when it holds its maximum amount of water vapour, water vapour being only 5/8 the weight of dry air. The actual amount of water vapour air can contain however is relatively small, ranging from a trace to a maximum of about 4 to 5% per unit volume at its saturation point, where it can hold no more water vapour. In expressing the amount of humidity suspended in the air, many forecasters will give it as a percentage of its saturated humidity, known as relative humidity. This is the ratio of the actual amount of water vapour suspended in air, to the amount of water vapour at which air would become saturated at a certain temperature. So, if air humidity is given at 100% then it actually means that the air per unit volume contains approximately 4 to 5% water vapour. Overall Altitude effects on Density As we have already stated, the main factors that will affect density, pressure, temperature and humidity will all decrease as altitude increases. Pressure decreasing as air thins out, temperature decreasing up to a certain height and humidity decreasing in line with temperature. The effects these factors have on density however are different as density changes directly with change in pressure and inversely with changes in temperature and humidity. Overall however, since pressure is the dominating factor in controlling the mass per unit volume, density will overall decrease in line with pressure and decrease as altitude increases. The International Standard Atmosphere (ISA) As atmospheric conditions vary around the world due to changes in the properties of the atmosphere. It was internationally agreed to have a Standard Atmosphere covering temperature, pressure and density for varying altitudes, in order to compare aircraft performance and calibrate aircraft instruments. The International Standard Atmosphere (ISA) was agreed by the International Civil Aviation Organisation (ICAO) and set at mean sea level with values of: Pressure: 1013.25 hecto Pascal (hPa) 14.69 PSI 29.92 inches of mercury or 76 cm of mercury Initial Issue 13 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Density: 1.225 kg/m3 0.077 lbs/ft3 Temperature: 15°C 59°F 288K NOTE: As the millibar as a unit does not strictly conform to the requirements of the SI system, it is being replaced internationally by the hecto Pascal (hPa) which is directly equivalent. So, 1013.25 mb equals 1013.25 hPa It is from these sea level values that all other corresponding values have been calculated and presented as the International Standard Atmosphere. In calculating the values of the International Standard Atmosphere up to the tropopause, the equation of state for a perfect gas is used, and is given by the formula: P = ρR T Where Ρ = Pressure ρ = Density T = Temperature R = Gas constant (for air = 287 J/kg.K) Initial Issue 14 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics ALTITUDE DENSITY PRESSSURE TEMPERATURE kg/m3 Millibars Degrees C feet metres 52,496 16,000 0.166 104 -56.5 45,934 14,000 0.228 142 -56.5 39,372 12,000 0.312 194 -56.5 32,810 10,000 0.414 265 -50 26,248 8,000 0.526 357 -37 19,686 6,000 0.66 472 -24 13,124 4,000 0.819 612 -11 6,562 2,000 1.007 795 2 0 0 1.225 1013.25 15 Note: It must be remembered that the ICAO International Standard Atmosphere is an assumed state for the purpose of comparing aircraft and engine performances and calibration of aircraft instruments etc. It is unlikely that the actual conditions on the day will conform to this standard. Initial Issue 15 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics SECTION 2: Physics of a Moving Fluid Introduction As we have already established the static properties of the atmosphere, its pressure, density and temperature. It is important that we now gain an understanding of how air acts when it is moving to fully understand how it affects an aircraft in flight. Types of Fluid Flow How the air of the atmospheric behaves when it moves over an object, such as an aircraft depends on a number of factors, such as the speed of the flow or the shape of the object it is passing over. The types of fluid flow experienced by air is either laminar or turbulent in nature, or when passing around an object a mixture of both. Laminar Airflow Laminar airflow, also known as linear airflow or streamline flow, exists when succeeding molecules of air follow a steady path. In this type of flow, the air flows smoothly over an object, with the molecules following an orderly pattern, as they do not mix with other streamlines. For an aircraft in flight, laminar or streamline flow produces an ideal flow pattern around an aircraft giving it the least amount of drag. In this type of flow there is no separation of the flow from the surface, so is desirable in most phases of flight. Initial Issue 16 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics To indicate the velocity of a flow around an object, the spacing between streamlines is used. Streamlines that are drawn close together indicate a high velocity, whilst streamlines with a wider spacing indicate a reduced velocity. Turbulent Flow Turbulent flow or unsteady flow occurs when succeeding molecules do not follow along a streamline but instead travel along a path different from that of the preceding molecule. In this type of flow, as the parameters are constantly changing with time, turbulent flow cannot be represented by streamlines. For an aircraft in flight, turbulent flow over an aircraft will result in an increase in drag being produced so that more energy is required to maintain flight and is therefore undesirable in most phases of flight. Airflow Patterns Around Objects The airflow pattern around a vertical plate (a) is illustrated above. The plate has a flat and wide frontal surface and the air separates to travel up and under the plate, but there is no surface behind the plate for the airflow, so it becomes very turbulent. The airflow over the sphere (b) is smoother. The airflow separates easier as it approaches the curved frontal area of the sphere, but it has a small surface for the air to attach to as is it passes over and under the surface. The airflow detaches from the surface and again becomes turbulent. The airflow over the aerofoil (c) is smoother again. As the air approaches the smaller curved frontal area of the aerofoil it will separate and flow above and below the surface of the aerofoil. Because the aerofoil has a longer more streamlined shape for the air to Initial Issue 17 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics flow over it remains laminar for longer with only light turbulent flow at the end of the aerofoil. Controlled Separated Flow or Leading Edge Vortex Flow This flow is a halfway stage between laminar flow and turbulent flow and occurs when a sharp object such as a leading edge slightly separates the flow from the surface. The flow however does not turn turbulent, even though it has separated, but instead forms a vortex travelling along the leading edge. This type of flow is often found in swept and delta type planforms particularly at high angle of attack and because of the predictability and stability of the vortex it can be controlled to give a useful lift force. Free Stream Airflow (FSA) Free stream airflow is airflow that is significantly far away from a surface of a body not to be disturbed by it. The pattern of airflow round an aircraft at low speeds depends mainly on the aircraft’s shape and its attitude relative to the free stream flow. Viscosity As air is a fluid, when it is in motion, it will be subject to viscosity. This is the property of the fluid that tends to resist relative motion within the layers of a moving fluid. In a streamline flow therefore, if different layers are moving, or sliding past each other at different velocities, the viscous forces between the layers will have a direct effect on each other. The faster moving layers tending to slow down as they try to increase the speed of the slower layers. The viscosity of a liquid however is dependent on temperature, but unlike liquids, the viscosity of a gas is directly proportional to temperature, so as an aircraft climbs in the atmosphere, the viscosity of the air will decrease. The Change from Laminar to Turbulent Flow Initial Issue 18 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The change from laminar to turbulent flow was first discovered by a 19th Century physicist named Osborne Reynolds who was involved in experiments with flow of fluids in pipes. He discovered that the flow changed from streamlined to turbulent flow when the velocity of the fluid reached a critical value that was inversely proportional to the diameter of the pipe. Or simply put, the larger the pipe the lower the speed at which the fluid became turbulent. He also discovered that this rule also applied to the flow past a body placed within the stream. For example, if two spheres of different sizes were placed into the flow then the transition from laminar to turbulent flow would occur at a velocity that was inversely proportional to the diameter of the sphere and that the transition point would initially be at the point of maximum thickness relative to the flow. Reynolds’ experiments led him to produce a dimensionless formula that produces a number for a fluid passing over or through an object. The number produced determining the conditions and characteristics of the flow, which will be the same irrespective of individual factors. Reynolds No = ρ = Density = Velocity = Length (normally chord) = Viscosity Reynolds’ Number is therefore a measure of the ratio between the inertial forces and viscous forces of the fluid. His formula has been well confirmed over the years and it is an established fact that if the same Reynolds number can be achieved for the airflow over a scale model as a full size aircraft in flight, then the flow patterns over the model are similar to the flow patterns over a full size aircraft. This allows aircraft designers and engineers to use scale model in wind tunnel tests to produce the same flight characteristics of a real aircraft, as in aerodynamics it does not make any difference if the surface is moving through the air or if the air is moving over the surface. This is because it is the ‘relative velocity’ of the airflow that is important in determining its airflow pattern over an object. Equation of Continuity The equation of continuity states that when a fluid flow passes through a pipe its mass must remain constant, since mass can neither be created nor destroyed. The equation applies only to streamline or steady flow and simply states that since mass cannot be created or destroyed, when air passes through a pipe its air mass flow is a constant. Initial Issue 19 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Using this equation, if a flow passing through a pipe of varying cross-sectional area such as a venturi tube is considered, then the mass airflow entering a pipe over a given time must equal the mass airflow leaving the system in the same time period. The mass flow at any point in the pipe therefore, will be the product of air density (ρ), cross-sectional area of the pipe (A) and air velocity (V). Mass airflow = ρAV = a Constant This equation applies to both subsonic and supersonic airflow provided that the flow remains steady, but can be simplified for airflows travelling at low speeds up to approximately 0.4 Mach. This is because at speeds up to this point air is considered to be incompressible, so its density will remain constant and can be removed from the equation, leaving: Mass airflow = AV = a Constant Or for different points along a tube as: Mass airflow = Or Initial Issue 20 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Using this equation, it can be seen that for an airflow passing through a pipe, the velocity of the flow is inversely proportional to the crosssectional area. So, a reduction in area causes an increase in velocity, with streamline converging as the velocity increases. Bernoulli’s Theorem Bernoulli’s Theorem expands the equation of continuity for a fluid flow to include the principle of the Conservation of Energy. His theorem states that, when a fluid passes through a pipe in a steady state, its total energy remains constant, as energy can neither be created or destroyed. For a fluid flow passing through a pipe therefore, the energy of the fluid entering the pipe in a given time would equal the energy leaving the pipe for the same time period. In his original experiments, Bernoulli took into account all energy transfers for a fluid passing through a pipe. But for a perfect fluid however, he theorised that no energy would be lost to heat transfer or work done, so that the total energy of a fluid passing through a pipe could be considered to be a combination of its: Potential Energy - Energy due to height or position. Pressure Energy - Energy stored in a non-moving fluid. Kinetic Energy - Energy due to movement of a moving fluid. For streamline airflow, such as air passing over a streamline object or through a pipe, the changes in height and therefore its changes in potential energy can be considered negligible and ignored. This simplifies Bernoulli’s equation to the sum of the pressure energy plus the sum of kinetic energy. Total Energy = Pressure Energy + Kinetic Energy = a Constant In fluid flow, Bernoulli stated this equation in terms of pressure. The pressure energy being the non-moving pressure of the fluid called the static pressure and the moving energy of the fluid being called the dynamic pressure, which rearranges the formula for Initial Issue 21 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics kinetic energy to include density, as in a fluid flow the energy will depend on the volume moved. To rearrange kinetic energy into dynamic pressure Kinetic energy = ½ mv2 where v = velocity Transposing the formula of density to find mass (m): Density ρ = So, m = ρV But since the density of a fluid is considered at a constant volume, therefore V = 1, which now rearranges the formula as: Density ρ = So, mass (m) = ρ We can now substitute mass (m) for density (ρ) into the right hand side of the formula for Kinetic energy which rearranges it to give us the Dynamic Pressure formula: Kinetic energy = ½ mv2 Dynamic pressure = ½ ρv2 The total energy of a fluid flow or total pressure therefore can be stated as: Total Pressure (Pt) = Static Pressure (Ps) + Dynamic Pressure (½ ρ v2) = a Constant For a fluid passing through the reduced area of a pipe, such as a venturi, the reduction of area causes an increase in dynamic pressure of the fluid and a decrease in its static pressure. Conversely when the cross sectional area is increased there will be a reduction in dynamic pressure and an increase in static pressure. Initial Issue 22 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Note: The total pressure can also be known or also referred to in other text books as its: Total Head Pressure, Stagnation Pressure, or Pitot Pressure. Dynamic pressure (½ ρ v2) is commonly abbreviated to ‘q’ when no calculations are required or no factors within the formula change. SECTION 3: Basic Atmospheric Instruments Introduction In order to fly an aircraft safely, a pilot flying needs some way of knowing how fast the aircraft is travelling through the air and the high they are. The basic instruments used for determining these measurements are the airspeed indicator (ASI) and the altimeter. Airspeed Indicator (ASI) The ASI is a simple instrument that operates by measuring the difference between two pressures taken from a pitot-static system. On a simple aircraft the system normally consists of two static vents positioned on either side of the fuselage and a pitot tube placed in a position pointing forwards towards the free stream airflow. These two pressures are fed into the ASI, which reads the difference between the two measured pressures and indicates dynamic pressure (½ ρ v2) in terms of airspeed. Initial Issue 23 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics To maintain the accuracy of the indicator, the instrument is checked when new and at regular intervals to ensure it does not have an error greater than 2 knots or 2 MPH. During calibration however, any errors found that are within limits are recorded at different points on the indicator scale and used as part of a correction scale to obtain calibrated airspeed. Calibrated Airspeed (CAS) Calibrated Airspeed (CAS) is IAS corrected for position error, which is the error due to the location of the pitot and static vents on the aircraft. As this error would be the same for all aircraft of the same type, these figures can be obtained by experimental data. The resulting pressure errors figures being published in the aircraft flight manuals and when combined with any instrument errors are recorded on a correction card, which is used by pilots to make the conversion between IAS and CAS. NOTE: CAS is also known as Rectified Airspeed or in the USA as True indicated airspeed True Airspeed (TAS) True airspeed (TAS) is the actual speed of the aircraft relative to the air passing over it and is often required when making navigational calculations. In flight, as the airspeed indicator and the correction figure were obtained under standard sea level conditions, the ASI and its correction figures, will only give the true airspeed of the aircraft at sea level conditions. To obtain an accurate airspeed at any other height therefore, the actual atmospheric conditions must be considered, as air density will reduce altering the dynamic pressure. In fact, indicated airspeed reduces at the square root of the atmospheric density. Alternatively, if an aircraft was to climb at a constant IAS, then as density decreases, with increasing altitude, TAS will gradually increase due to IAS being obtained from the dynamic pressure (½ ρ v2). Initial Issue 24 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics NOTE: TAS will only be true for the time of calculation is made, as the actual flight conditions are constantly changing. Equivalent Airspeed (EAS) Equivalent Airspeed is IAS corrected for both position and compressibility errors. The latter error is due to compressibility of the air in front of the pitot head at airspeed greater than 300 knots (TAS). As this speed has universal implication the correction factor uses a standard atmosphere and is the ratio of ambient density to standard density. The following flowchart shows the steps required to make the appropriate airspeed conversion. Initial Issue 25 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Initial Issue 26 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics SECTION 4: Self Study Questions Chapter 1 Section 1: Name the 5 distinct gaseous layers. Which layers do aircraft normally fly in? What type of gases are found in the atmosphere and what percentages are they? What is the formula derived from the universal gas law? What is the standard pressure at sea level? Atmosphere reduces by ½ its sea level value at? Atmosphere reduces by ¼ its sea level at? Density of air is______________ proportional to pressure? What is the international lapse rate? Humidity in the air is found up to a height of approximately? The ability to hold water vapour increases or decreases with an increase in air temperature? What is the density of water vapour at standard sea level conditions? What is the density of perfectly dry air at standard sea level conditions? What is the maximum amount of water vapour air can hold as a percentage? The international standard atmosphere (ISA) was agreed by? Initial Issue 27 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Chapter 1 Section 2: What are the two types of fluid flow? What is controlled separated or leading edge vortex flow? Viscosity of a gas is ____________ proportional to temperature? What is the Reynolds Number formula? Equation of continuity states? The equation of continuity applies to low speeds up to _______ mach? Bernoulli’s theorem states? What is the formula for dynamic pressure? Total pressure is also known as? Chapter 1 Section 3: An ASI indicates what pressure? An ASI is checked for accuracy at which points and what are the limits? What is CAS? What is TAS? What is EAS? Initial Issue 28 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics CHAPTER 2: FLIGHT AERODYNAMICS SECTION 1: Components and Terminology Basic Aircraft Components. The Fuselage: The fuselage forms part of the main structure of the aircraft to which the wings and tail section are attached. The fuselage also provides the space for the crew, passengers and cargo to be carried and is designed to be as aerodynamically efficient as possible. The Wings: The wings or mainplane of an aircraft are designed to generate sufficient lift to support the weight of the aircraft in flight. In most passenger aircraft they are also designed to carry the weight of the engines and fuel and must be capable of taking local loads well in excess of the total aircraft weight, which can exist during manoeuvres. The Tail Section: The tail section consists of a vertical fin and horizontal tailplane. The function of these surfaces is to provide stability and manoeuvrability of the aircraft and will be explained in later sections. The Control Surfaces: These surfaces control aircraft movement and are categorised as either primary or secondary. The ailerons, elevator and rudder are termed primary; the spoilers, flaps and other high lift devices being termed secondary control surfaces. Initial Issue 29 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Wing Position Terminology Wings are attached to an aircraft fuselage in either a low, high or mid position. The actual wing position on the aircraft is determined by some of the following design parameters: Engine positioning and size or Propeller blade length. Undercarriage positioning. Short Take-off and Landing Capacity. In practice the wings of an aircraft are inclined above, or below the horizontal. The inclination of the wings affects the stability of the aircraft and will be described later chapters. Wings inclined above the horizontal are termed dihedral, where as those inclined below the horizontal are termed anhedral. Initial Issue 30 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Wing Planform Terminology The following terminology is associated with the wing planforms: Gross Wing Area (S): The plan view area of the wing including the portion of the wing cut out to accommodate the fuselage. Net Wing Area: The plan view area of the wing excluding the fuselage portion. Initial Issue 31 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Wingspan (b): The straight-line distance between wing tips. Average Chord (Cav): The average chord of the wing is the average length between the leading and trailing edge of the wing. The product of the span and average chord gives the gross wing area (S = b x Cav). Initial Issue 32 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Aspect Ratio (AR): The ratio of the wingspan to the average chord. Aspect Ratio = Can Also be expressed as: Aspect Ratio = or Aspect Ratio = Initial Issue 33 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Long thin wings are of high aspect ratio, whilst short stubby wings are of low aspect ratio Taper Ratio (λ): The ratio of tip chord (C tip) to chord root (C root) Taper Ratio = The Angle of Sweepback: Measured by the angle between a lateral axis perpendicular to the aircraft centreline and a constant percentage chord line along the semispan of the wing. This percentage is usually taken to be a quarter chord (25%) of the wing, as taken from the leading edge. Initial Issue 34 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Mean Aerodynamic Chord (MAC): The chord line drawn through the centre of area of the half span area. NOTE: That MAC and Cav are not the same and that Aspect ratio, taper ratio and sweepback are some of the main factors in determining the aerodynamic characteristics of a wing. Wing Shape High Lift Wing: A high lift wing has a high thickness/chord ratio; a pronounced camber and a well rounded leading edge. This type of wing produces high lift at low speeds. Its maximum thickness being found between 25 – 30% of the chord line behind the leading edge. General Purpose Wing: A general-purpose wing has a lower thickness/chord ratio, less camber and a sharper leading edge than a high lift wing. The maximum thickness of the wing is still found at about 25 – 30% of the chord line behind the leading edge. This type of wing produces less drag than a high lift wing at higher speed. Initial Issue 35 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Supercritical Wing: A supercritical wing has a very slight curvature on the upper surface and has its point of maximum thickness positioned close to the trailing edge. This type of wing is found on many modern transport aircraft as it gives low drag characteristics near supersonic or transonic speeds. High Speed Wings: High-speed wings are normally symmetrical shaped wings that have their point of maximum thickness at the 50% chord point. The wing has a very low thickness/chord ratio normally between 5 -10% and has normally no camber and a sharp leading edge. This type of wing gives a very low drag characteristic at transonic and supersonic speeds, but has however poor lift capabilities at low speeds. Wing Section Terminology Chord Line: A straight line joining the leading and trailing edges of a wing. Initial Issue 36 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The Chord: The length of the chord line is used as a reference for all other dimensions relating to the wing. The Mean Camber Line: A line drawn at an equal distance between the upper and lower surfaces of an aerofoil. Maximum Camber: The maximum distance between the mean camber line and the chord line. It is one of the variables that determine the aerodynamic characteristics of a wing. Maximum Thickness: The maximum distance between the upper and lower surfaces. Maximum Thickness Chord Ratio: The ratio of maximum thickness to chord. This is normally expressed as a percentage, for subsonic wings the ratio is generally about 12 – 14 %. Aerodynamic Terminology Free Stream Flow: The region of air where pressure, temperature and relative velocity are unaffected by the passage of the aircraft through it, free stream flow is also known as Relative Air Flow (RAF). Total Reaction (TR): The Resultant of all the aerodynamic forces acting on the wing or aerofoil section, which acts perpendicular to the chord line. Centre of Pressure (CP): The point on the chord line through which the TR is considered to act. Lift: The component of the TR, which is perpendicular to the flight path or RAF. Drag: The component of the TR, which is tangential to the flight path, i.e. parallel to the RAF. Angle of Attack: The angle between the chord line and the flight path or RAF. Streamline: The path traced by a particle in a steady fluid flow. Fineness Ratio: The ratio of the chord to the maximum thickness of an aerofoil. Wing Loading: The weight per unit area of the wing. Initial Issue 37 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Load Factor (g or n): The total lift produced to the weight of the aircraft. SECTION 2: Lift Introduction In order to fly, an aircraft must generate a force that is at least equal to its weight to maintain level flight, and a force greater than the weight in order to manoeuvre. This force is called lift and acts perpendicular to the relative airflow (RAF). Airflow and Lift Whenever an aircraft moves through the air, or if an object is placed into a moving airstream. The air moving around the aircraft, or the object, will undergo a change in direction, which causes a change in its velocity. As this will either speed up or slow down the airflow passing over an object, it will also affect its static pressure, as explained by the equation of continuity and Bernoulli’s theorem. Using Bernoulli’s theorem, the definite relationship between velocity and the static pressure can be used to explain how lift is generated. This is because it can be proven that for an airflow passing around an aerofoil section, the flow will resemble the flow passing through a venturi tube, due to its wings geometrical shape. The convergent part of the tube resembling the upper surface of the wing as the velocity increases and static pressure decreases. Whilst the divergent part resembles the lower surface of the wing as the velocity is travelling at a lower speed than the upper surface so its static pressure is increasing. Initial Issue 38 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics These changes in velocities over the upper and lower surfaces results in a pressure differential occurring between the two surfaces that will produce an upward force known as lift. Airflow Around an Aerofoil For an aerofoil surface that is placed into an airstream, the air approaching the aerofoil will develop a dividing stream, which separates the flow between the upper and lower surfaces. In order to separate the flow, the dividing stream as it approaches the aerofoil is slowed down by the surface and momentarily comes to a rest near the leading edge, forming a stagnation point. At this point the velocity of the airflow is reduced to zero and the static pressure reaches its maximum (Bernoulli’s equation), this is known as stagnation pressure of the airflow and is above that of ambient pressure. A further stagnation point will also exist at the rear of the aerofoil, due to the pressure gradient over the aerofoil, but this point will be dealt with later in the sections dealing with stalling, as it affects the air at the rear of the aerofoil. On a typical aerofoil section, the forward stagnation point occurs just below the leading edge of the wing, so that the airflow passing over the upper surface has to move forward first. In moving forward, the air imparts an upward acceleration to the airflow passing over the upper surface, which along with the pressure differential (negative pressure gradient) associated with the upper surface helps draw the air locally upwards producing an upwash. Initial Issue 39 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics At the rear of the aerofoil the air leaving the upper surface will be moving faster relative to the air leaving the lower surface. This will tend to force the streamlines downwards producing a downwash. Angle of Attack (AOA) The attitude that an aerofoil surface presents to an oncoming airflow is known as its angle of attack (α), and is the angle measured between the chord line of the aerofoil and the relative airflow (RAF). In flight, changes in the angle of attack will cause the velocity and static pressure of the flow to vary as the air passes over and under an aerofoil surface. This change in the pattern of the airflow around the surface affects the pressure differential between the upper and lower surfaces either increasing or decreasing it, affecting the amount of lift developed. The Effect of Angle of Attack (AOA) on Airflow Around an Aerofoil For a symmetrical aerofoil placed in a steady airstream, lift is only produced when the aerofoil has a positive angle of attack. This occurs because when a symmetrical aerofoil is placed at zero degrees AOA to the relative airflow, the stagnation point forms on the leading edge, so that the change in velocity above and below the aerofoil are equal so there is no pressure differential and no lift will be generated. Initial Issue 40 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics If the aerofoil is now given a positive AOA, the stagnation point will move below the leading edge causing an upwash to develop. Initial Issue 41 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics This brings about an increase in velocity of the air passing over the upper surface of the aerofoil compared to the air passing below the lower surface The changes in velocity over the aerofoil therefore will change the static pressure above and below the surface producing a pressure difference between the two surfaces allowing lift to be generated. On an asymmetrical aerofoil however, at zero degrees AOA, the stagnation point will form below the leading edge and an upwash will occur. This will therefore produce lift at this angle, as the air passing over the more curved upper surface will be travelling faster than the air passing below the aerofoil. Initial Issue 42 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Increasing the angle of attack on an asymmetrical wing will now cause the stagnation point to move further along the lower surface creating more upwash and increasing the distance that the air over the upper surface has to travel. As this will further increase the velocity of the air over the upper surface, a larger pressure differential will be created so more lift is generated. For an airflow passing over an aerofoil shape therefore, the angle of attack in conjunction with the actual shape of the aerofoil are the principal factors in determining how air moves around it and how lift is generated. Any changes to either of these two factors will affect how an airflow moves over an aerofoil and the amount of lift it generates. Chordwise Pressure Distribution For an aircraft in flight, although the whole aircraft contributes towards the lift and drag of the aircraft, it may be assumed that the wings since they are specifically designed to produce lift will produce the necessary lift for the whole aircraft. A wing generates lift whenever an airflow passing over and under it, creates a pressure differential between the two surfaces due to local changes in its velocity and static pressure. These changes to the static pressure over the wing can be shown diagrammatically by a series of pressure vectors drawn from the surfaces of the wing that are joined at their ends to produce a pressure envelope. Initial Issue 43 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics By convention pressure above ambient is given a (+) sign towards the surface and those below ambient given a (–) sign and plotted away from the surface. The length of the pressure vector is proportional to the difference between absolute pressure ( ) and the freestream static pressure (p0) i.e. ( ). This is then converted to a pressure coefficient ( ) by comparing it to dynamic pressure ( ). One of the most important values of is the value at the stagnation point on a wing, where air brought to rest. Since the air is not moving the value of absolute pressure ( ) is equal to the freestream static pressure (p0) plus the dynamic pressure ( ). Therefore p = p0 + q. Substituting in the equation gives: By cancelling this equation down, we end up with: The value therefore of the pressure coefficient at any stagnation point is: +1 Variation of Pressure Differential with Changes of Angle of Attack For different angles of attack the size and position of the pressure envelope will alter and the actual pressure changes, during the design stage can be measured using manometers. These instruments show that increasing the angle of attack will increase the pressure differential between the upper and lower surfaces, due to a greater decrease in pressure on the upper surface than the change in pressure on the lower surface and the pressure envelope increases in height and on an asymmetrical wing moves forward towards the leading edge. Initial Issue 44 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The size and direction of the vectors in the pressure envelope therefore indicates the amount of lift that can be produced and as can be seen from the above examples the envelopes and therefore lift increases up to a certain angle, known as the stalling angle of attack. Beyond this angle, which is this is typically between 15 to 18 for a general aerofoil, the majority of flow over the upper surface breaks down into heavy turbulent flow, which causes an increase in pressure, and the relationship between velocity and static pressure no longer applies, since Bernoulli’s theorem only applies to streamline flow. On studying the pressure distribution diagrams, it can be seen that at a certain angle of attack the pressure distribution is the same both above and below the aerofoil so no net lift will be generated. This is known as the Zero lift angle of attack, which for an asymmetrical aerofoil, will always be negative. Initial Issue 45 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The zero lift angle of attack for most asymmetrical wings being approximately - 4 angle of attack, but for a symmetrical aerofoil, this angle will always be 0º angle of attack. Zero Lift Angle of Attack Centre of Pressure and Total Reaction Force In contrast to the complicated pressure plots of the pressure envelope, it is possible to show the overall effects of changes to the static pressure over a wing with a single force. This single force is termed the total reaction force (TR) and acts through a single point on the chord line called the centre of pressure (CP). The force represents all of the forces acting over the wing and acts perpendicular to the chord line. Initial Issue 46 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The direction of the total reaction force (TR) is the resultant of all the forces acting on the wing, its lift force that acts perpendicular to the relative air flow (RAF) and the drag force that acts parallel to the RAF. Therefore, as both lift and drag vary in size, during flight, the lift force changing with changes in the angle of attack and the drag force changing with changes in speed and lift, the size and direction of the TR alters. In level flight the CP is positioned on an asymmetrical wing about a quarter way along the chord line of the aerofoil section, but moves along the chord line as the angle of attack changes. Increasing the angle of attack up to the stalling angle causes the CP and the low-pressure peak to move towards the leading edge (LE), but beyond this angle the low-pressure peak rapidly collapses causing the size of the TR to decrease and the CP to move quickly rearwards towards the trailing edge (TE), pitching the aircraft nose down. For a typical asymmetrical aerofoil, the range of CP movements over the normal working range of AOA is between the 20 to 30% of the chord line rear of the leading edge. However, with a symmetrical aerofoil, there is virtually no CP movement over the working range of AOA at subsonic speed, and the CP stays approximately central as the TR tilts. Spanwise Pressure Distribution So far, the pressure distribution around an aerofoil has only been considered in the chordwise direction. To fully understand how lift is developed over an aerofoil or wing, it is also necessary to consider its spanwise pressure distribution as airflow passes over a wing. For an airflow passing over a wing with a positive angle of attack, a pressure differential between the upper and lower surfaces of the wing will produce lift. The greatest differential occurring at the root of the wing, where the largest proportion of lift is generated with the smallest differential at the wing tip; where the least amount of lift is generated. Initial Issue 47 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Beyond the wing tips however, as air is nominally at atmospheric pressure, this causes a spanwise flow away from the fuselage on the lower surface and towards the fuselage on the upper surface. The airflow over the wing will therefore flow in both a chordwise and spanwise direction. The effect of airflow moving in both a chordwise and spanwise direction is to create vortices at both the trailing edge of the wing and at the wing tips, creating a downwash behind the wing that reduces the overall lift and increases the drag on the aircraft. To recover the lost lift, due to a spanwise flow, the angle of attack must be increased to increase the lift over the wing. This will however, cause a corresponding increase in spanwise flow and induced drag that this tilting of the lift force produces. The formation of trailing edge and wing tip vortices will be discussed later in the chapter covering drag. Wing Shape and its Effect on Lift The shape of a wing affects the amount of lift generated as it has a major influence on the way air moves around it, in both a chordwise and spanwise direction. In the chordwise direction, the pressure differential between the upper and lower surface will depend on its cross section shape i.e. its amount of camber, an asymmetrical wing producing more lift than a symmetrical wing for a given angle of attack. In the spanwise direction, the planform shape of the wing affects the way lift is generated as it not only changes the area of the wing by changing in its chord length, but it also affects the way tip vortices are produced. Initial Issue 48 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics In a spanwise direction, the actual amount of lift developed by each section of a wing varies according to its angle of attack. In practice therefore, it is the wing section effective angle of attack that determines the amount of lift each section of the wing produces, which will depend on the strength of wing tip vortices. On a rectangular wing the effective angle of attack stays fairly constant over the inner half of the wing but reduces rapidly over the outer half lift due to large wing tip vortices produced by having a large wing tip chord. By comparison a tapered wing with a reduced wing tip chord produces only small wing tip vortices. This allows this wing to have an increasing effective angle of attack to approximately three quarters of its length, before decreasing over its last quarter. The most effective wing however in producing virtually no wing tips vortices, is an elliptical wing, due to its constant downwash. This wing therefore has a constant effective angle of attack, but as will be explained later on is not commonly used due to manufacturing problems. The effectiveness of a wing to generate lift therefore will depend on both its section and planform shape along with its angle of attack. These factors are combined with other factors to form a wings coefficient of lift. Initial Issue 49 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics It follows therefore that in flight, any changes in a wings coefficient of lift will be mainly due to changes in the angle of attack, as the section and planform shape is fixed. Lift Formula As already seen in this chapter, in order to calculate the actual lift produced by a wing a number of factors have to be considered including the: AOA. Shape of wing and planform. Condition of wing surface. Reynolds’ No. Speed of Sound (Mach). Air density (ρ). Free stream air velocity squared (V2). Surface wing area (S). Having to take all these factors into account every time, will make the calculation of lift difficult. So, to simplify the calculations many of the factors are grouped together, making it easier to calculate. It has already been established that the lift force produced by a wing will depend on the pressure differential between the upper and lower surface. So, a basic formula for lift can be derived from the formula of pressure: Pressure = Force ÷ Area Transposing this formula for Force (which in the case of aerodynamics is Lift): Force (Lift) = Pressure x Area But since the pressure over the wing depends on the velocity or dynamic pressure (Pdyn = ½ ρ V2) of air over the wing, (Bernoulli’s Theorem) and that the area that the pressure acts over is fixed in a certain configuration, substituting these two into the formula for lift gives: Initial Issue 50 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Lift = ½ ρ V2 x S To take into account the remaining factors: AOA. Shape of wing and planform. Condition of wing surface. Reynolds’ No. Speed of Sound (Mach No). A coefficient, known as the coefficient of lift (CL) is established and when inserted into the formula gives us a general lift formula. Lift = CL x ½ ρ V2 x S This formula can also be rearranged in terms of the coefficient of lift (CL) Rearranging the formula this way shows that the coefficient of lift is a ratio between the lift force per unit area, at a single height or speed. Or that it is a ratio between the lift pressure and the dynamic pressure, which will vary with angle of attack. Variation of CL with Angle of Attack To establish the effect of changing the angle of attack has on the lift produced by a wing; a graph of the coefficient can be plotted against angle of attack. This is known, as a lift curve. Initial Issue 51 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The lift curve for an asymmetrical wing shows that the greatest part of the curve is linear (a straight line) so that the value of CL, and hence lift is directly proportional to the angle of attack in this region. At the far end of the curve between 12º and 16º AOA, the curve starts to lean over slightly indicating a loss of lifting effectiveness until it eventually forms a peak. At the peak the maximum value of CL or CL MAX for the aerofoil is obtained, and hence the greatest lift for a given configuration. The angle of attack at which the CL MAX is obtained is known as the critical or stalling angle AOA for the aerofoil. As beyond this AOA, as can be seen in the graph above, that lift decreases rapidly causing the CP to move towards the trailing edge causing a nose down pitching moment. The stalling of an aircraft in flight will be discussed in later chapters. In practice each aerofoil possesses its own lift curve for each configuration, so it is possible to compare the performances of both asymmetrical and symmetrical type aerofoils Initial Issue 52 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Wing Comparison In comparing these curves, the lift curves show that an asymmetrical wing will produce more lift at any given angle of attack, than a symmetrical one of the same surface area, but has a lower stalling angle. The curves also show that the zero lift angle for an asymmetrical wing is always a minus, whereas for a symmetrical aerofoil zero lift angle is always zero. Lift Augmentation Devices As aircraft have got larger and heavier, it has become necessary for aircraft to incorporate some form of supplementary lifting during the landing and take off phase. The most common lift augmentation devices falling into either one of two categories: Leading edge devices. Trailing edge devices. Leading Edge Devices The requirement for leading edge devices is to cause an increase in velocity of the airflow over the upper surface of the aerofoil in order to delay separation of the boundary layer. The result of this delayed separation allows an increase in stalling angle of attack, which allows the centre of pressure (CP) to move further forward towards the leading edge, increasing the lift at lower forward airspeeds and giving the aircraft a nose up pitching effect. Initial Issue 53 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The devices used to achieve this are: Leading edge slats. Leading edge flaps. Leading Edge Slats Slats are small auxiliary aerofoils attached along the leading edge of the wing. When selected the slat extends to form a slot between the slat and the leading edge upper surface of the wings. This allows air to pass through the slot from the high-pressure area under the wing into the low-pressure area above the wing, thereby accelerating the flow by the venturi effect, re-energising the boundary layer. The re-energised boundary layer over the front part of the wing helps maintains a smooth flow of air over the upper surface, delaying the transition from laminar to turbulent and pushing back the separation point. This will substantially increase the coefficient of lift (CL) and delaying the stall to a much higher angle of attack. Initial Issue 54 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics When the slat is closed (retracted) the slot is closed and the slat forms the leading edge of the wing. Leading Edge Flaps Leading edge flaps like slats are used to improve the lifting capability of the wing at low airspeeds, but unlike slats they do not create a slot when they are lowered. The effect of deploying a leading edge flap increases the stalling angle of attack by changing the effective chord line against the relative airflow that increases the camber of the wing and its coefficient of lift, generating more lift over the front part of the wing, allowing the aircraft to pitch more nose up before it stalls. Leading edge flaps are normally found fitted on high speed, thin winged aircraft instead of slats, due to the thickness or profile of the wing, as they do not have the room to accommodate the mechanisms required for the installation of leading edge slats. Initial Issue 55 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The main types of leading edge flaps are: Drooped leading edges. Krueger flaps. Drooped Leading Edges Drooped leading edge flaps normally cover the complete span of the leading edge and are lowered to increase the camber when the aircraft is approaching its stalling angle. At high speeds the flap is retracted to give the required profile for a high-speed wing. Krueger Flaps Krueger flap are similar to drooped leading edges in that when they are lowered they change the camber over that section of the wing. Unlike leading edge flaps, Krueger flaps do not normally extend the length of the leading edge but are fitted in certain sections. When retracted a Krueger flap forms part of the under wing surface. Initial Issue 56 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Trailing Edge Devices The trailing edge devices used to increase the lift over the wing are known as trailing edge flaps. These devises like leading edge flaps increase the camber of the wing when deployed, by changing the effective chord line. The actual position of trailing edge flaps on an aircraft, is determined by the positioning of other control surfaces along the trailing edge, but will normally be positioned at the root of the wing, or split between the root and the centre section where the majority of the lift of the wing is generated. On deployment, trailing edge flaps will increase the lift coefficient but will also increase the drag coefficient, so are normally deployed in stages. Small-scale deployment at take- off and climb out, where at low speed they provide extra camber giving a small increase in the coefficient of lift, that is greater than the increase in the coefficient of drag. On landing, trailing edge flaps are fully deployed to give a large increase in the maximum coefficient in lift but also increases the drag, which helps retard the aircraft to shorten the landing distance. To maintain level flight when flaps are fully deployed, the increase in drag is balanced by increasing engine thrust. Initial Issue 57 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Types of Trailing Edge Flaps Plain Flaps Plain flaps are hinged to rear of the wing, but unlike flying control surfaces they only normally move downwards. In common with all flaps they are fitted inboard at the root of the wings and both port and starboard flaps move symmetrically at the rate to avoid producing a rolling moment. Split Flap On a split flap only the lower aerofoil surface is hinged. The protrusion of the flap into the airflow causes the air to flow over the top surface at an increased velocity. Although the split flap presents some structural problems, these flaps are useful as there is very little movement of the centre of pressure when they are deployed. Extension Flaps There are a number of variations of this type of flap, from a single extension flap to a flap with up to three extending elements. Extension flaps also commonly known as Fowler Initial Issue 58 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics flaps expose slots when they are lowered, which accelerates the air over the upper surface of the extended flap segments to delay separation. With extension flaps, not only is the coefficient of lift directly increased by the increase in camber and angle of attack, but the wing area is also increased which increases the overall lift. A drawback with deploying extension flaps is that by increasing the wing area, the centre of pressure moves rearwards tending to give the aircraft a nose down pitching moment, which would require greater rearward movement of the control column on take-off and greater sensitivity by the pilot on landing. To prevent this happening in most aircraft an input to the pitch trim system, either mechanical or electrical, is a standard feature, which adjust the pitch of the aircraft accordingly as the extension flap is deployed. Combination of Flaps and Slats on Lift The ultimate system, which can result in an increase in the lift coefficient of as much as 120% on that part of the wing to which they are fitted is a combination of slotted extension flaps and leading edge slats. Initial Issue 59 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Deploying a combined system can also prevent a pronounced nose-up or nose-down attitude that occurs when deploying either slats or flaps alone. This is because as leading edge slats tend to move the centre of pressure forward and extension flaps the centre of pressure rewards. With careful design around any particular section therefore, as both these devices are extended, the movement of the centre of pressure can be reduced so that there are practically no adverse pitching moments in a critical phase of flight. SECTION 3: Drag Introduction During the movement of aircraft through the air (i.e. flight), all parts of the aircraft exposed to the airflow will produce an aerodynamic force that opposes the forward motion of the aircraft. This opposing force is known as DRAG, and it acts parallel to and in the same direction as the relative airflow (RAF). Total Drag For an aircraft in flight, drag is the resistance to forward motion that an aircraft experience as it moves through the air. Initial Issue 60 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics In steady level flight therefore, this resistance must be balanced by the thrust of the engine, so it follows that for any given airspeed the lower the drag the less thrust is required to balance it. Drag on an aircraft can therefore be considered as wasted energy, as the aircraft will have to expend thrust energy from the engines in order to overcome it. This makes aircraft that produce low levels of drag commercially attractive to aircraft operators, as the lower the drag, the lower is the amount of fuel used during a flight, so the cheaper it is to operate the aircraft. Components of Total Drag In flight, the size of the drag that acts on an aircraft depends on a number of things including, shape, speed, type of manoeuvre etc. To help us understand what makes up the total drag on an aircraft it is usual and convenient to group these different components into categories so that total drag can be more easily studied and understood. Some textbooks categorise the components of total drag as belonging to either one of two distinct groups, these being: Zero lift Drag, the drag produced when the aircraft is flying at the zero lift angle of attack. And Initial Issue 61 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Lift dependent drag, the drag produced whenever an aircraft is producing lift. Other textbooks consider that the total drag is made up of either: Profile drag Induced drag Interference drag In this course we will consider this latter grouping in explaining total drag, indicating which of the components make up either zero lift or lift dependent drag. Profile Drag As an aircraft moves through the air, the amount of drag it creates depends upon on how easily the air moves around it. The shape or profile therefore, that an aircraft presents to the oncoming airflow is important as it influences the way the air moves around and will be a major factor in determining the amount of drag created. The amount of profile drag created when the aircraft is flying at the zero lift angle of attack is also known as zero lift drag. For an aircraft in flight, profile drag can be broken down into two forms of drag: Form drag Skin friction drag Before considering the makeup of profile drag in detail however, it is important to firstly consider the layers of air closest to the surface, known as the Boundary Layer. This is because it is the conditions of the air within the boundary layer that produces profile drag. Boundary Layer In the boundary layer, as an airflow passes over aircraft and the wing in particular, it slows down due to the roughness of the surface and the viscous properties of the air itself. For the particles of air that are directly adjacent to the surface of the wing, viscous adhesion will adhere the air to the surface reducing its relative velocity to zero. Initial Issue 62 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics For other streamlines of air slightly further away from the surface, only the viscosity between different layers of air particles will cause the air to slow down, so it will not bring the air completely to rest. This means that the further away from the surface, subsequent layers of air will be slowed down but by lesser amounts. The velocities of the air within a boundary layer therefore, vary the further away the airflow is from the surface. The extent of the boundary layer being defined as the region of airflow flow in which the speed of the airflow is below 99% of the free stream velocity. Conditions within the Boundary Layer Within the boundary layer, the normal conditions are a mixture of both laminar and turbulent airflow. The usual tendency is for it to start by being laminar at the leading edge and then become turbulent as it passes over the wing, the change from laminar to turbulent airflow taking place in the transition region over the wing, at a point known as the transition point. Initial Issue 63 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics The thickness of the boundary layer is however, comparatively small only being about 10 mm in depth, starting from zero at the leading edge and increasing in thickness as it moves rearwards over the aircraft wing. After its transition to turbulent airflow the boundary layer thickens and grows at a more rapid rate, growing to approximately 10 times the thickness of the laminar boundary layer under the same free stream velocity. After the air becomes turbulent, as the airflow no longer follows an orderly pattern, its velocity increases as the air is constantly changing direction. The kinetic energy therefore, of the airflow in the turbulent region is higher than in the laminar region at the same distance from the surface. This fact is extremely important, as the increased energy of the turbulent air will help delay separation over the wing by overcoming the adverse pressure gradient. Form Drag Form drag is the drag produced whenever the airflow that is passing over an object separates away from the surface becoming heavily turbulent. The separated flow behind the object producing a reduction in pressure that tries to pull the object back. Initial Issue 64 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics An extreme example of separated airflow and form drag can be seen when a flat plate is placed at right angle to the airflow. The pressure immediately in front of the plate is above atmospheric pressure, due to the formation of stagnation points, whilst behind the plate the pressure will be below atmospheric due to the formation of vortices. This results in a sucking effect behind the plate pulling it backwards. To reduce the amount of form drag produced by an airflow passing over an object therefore, it is necessary to make it less flat plate than the example above by streamlining. This reduces the rapid change of direction an airflow undergoes as it passes over an object, so that it stays attached longer delaying separation and reducing the amount of form drag produced. Initial Issue 65 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics As can be seen from the above diagram, the amount of form drag reduces quite drastically when aerodynamic fairings are fitted to both the back and front of an object as it reduces the amount of separation. This increase of the length of the object to its thickness is known as the fineness ratio of an object and for a general-purpose aerofoil, that is travelling at low subsonic speed it will produce the least amount of form drag when an object has a fineness ratio of around 4 to 1. This figure however can vary between higher speed wing designs without increasing the drag to any great extent. Initial Issue 66 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Skin Friction Drag The skin friction or skin friction drag of an aircraft is the drag associated with the retardation of air within the boundary layer, as the retarded air will try to drag the surface along with it. In practice the extent of retardation and skin friction drag depends on the rate at which air adjacent to the surface is trying to slide relative to it. This produces a shear stress between adjacent air particles, which is directly proportional to the speed of the airflow. Therefore, the gradual velocity change associated with laminar airflow will produce a low shear stress near the surface that results in low skin friction drag. Whereas the rapid velocity change associated with turbulent boundary airflow will produce a high skin friction drag. It follows then that forward movement of the transition point increases the size of the turbulent region over the wing and increases the skin friction drag. The viscous drag force between streamlines within the boundary layer are not sensitive to pressure and density variation and is therefore is unaffected by the variations in pressure at right angles (normal) to the surface of the body. Viscous drag forces are however, sensitive to temperature changes as the viscosity of a gas varies directly with temperature and will therefore increase and decrease with changes in altitude. The more viscous the air becomes the greater the retardation will be in the boundary layer, so the greater the skin friction drag. Initial Issue 67 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Other Factors Affecting Skin Friction Drag Others factors that will affect the amount of skin friction over an aerofoil are: Surface condition and size of area. Forward speed of the aircraft. Surface Area and Condition The size of the surface area will have an effect on the amount of skin friction drag produced, as the whole of the aircraft in flight will have an airflow passing over it, so each part the airflow touches will produce a boundary layer. It follows then, that by increasing the surface area of an aircraft it will increase the amount of boundary layer over the aircraft and produce a greater amount of skin friction drag. The condition of the surface area will also have an effect on the amount of skin friction drag produced, as the laminar layer near the front of the aircraft is extremely sensitive to surface irregularities. Irregularities over the wing such as damage or contamination, which alter the smooth flow over the wing, will bring about an earlier or premature transition point increasing the amount of turbulent flow and skin friction drag. It should also be noted that contamination by ice, snow or frost, would not only result in an increased drag but also an increase in weight that requires an increased lift in order to maintain level flight. Ice formation on a wing Initial Issue 68 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics Effect of Forward Speed on Skin Friction Drag The effect of changing the forward speed of an aircraft affects the amount of skin friction drag produced, as an increase in the relative speed of the airflow over a wing will cause the airflow to change from laminar to turbulent at an earlier point. As this will cause a greater part of the aerofoil to be covered in turbulent airflow, it follows then that the skin friction drag will be greater. Interference Drag For an aircraft flying in level flight, the total drag acting on the aircraft is often found to be greater than the sum of the profile drag of individual components. This occurs because airflow over the aircraft is disturbed where various components are joined together, particularly between the wing and the fuselage. The disturbance leads to a modification of the boundary layers, either turning the local flow turbulent or causing local separation which produces additional drag known as Interference drag. For subsonic flight, the interference drag and total drag can be reduced by the addition of fairing or fillets, which smooth out the airflow. NOTE: In many text books the sum of the profile drag and interference drag can be referred to as parasite drag or the total zero lift drag as it is the drag produced even when the aircraft is producing no net lift. Induced Drag Whenever a wing is producing lift, a pressure differential exists between the upper and lower surfaces that will produce a spanwise flow and concentrated vortices at the extremities of the wing as air tries to flow from the lower to upper surfaces. Initial Issue 69 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics These vortices are strongest at the wing tip and become progressively weaker towards the centre line. Behind the wing, the wing tip vortices induce a downwash to the airflow, which deflects the relative airflow down away from the horizontal through an angle known as the angle of induced downwash (ε). This deflection of air behind the wing influences the relative airflow of the air approaching the wing deflecting it upwards by the same angle (ε). This in effect reduces the angle of attack on the wing reducing the overall lift, as the lift, which acts perpendicular to the local relative airflow, is tilted rearwards. To recover the lost lift, due to vortex formation, the Initial Issue 70 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics angle of attack must be increased to increase the lift, which will increase the drag on the aircraft. It follows then that the larger the vortex the greater the induced drag. Factors Affecting Induced Drag The main factors that affect vortex formation and therefore induced drag are: Wing planform. Aspect ratio. Weight and speed. Wing Planform Wing planform is the one of the principal factors affecting induced drag, as the size of the wing tip chord length directly affects the size of wing tip vortex. A rectangular planform with a large cord length at the wingtip will allow more air to flow from the lower to upper surface producing much larger vortices than a tapered one. So, tapering a wing towards the tip it reduces the amount of air flowing from the lower surface to the upper surface thereby reducing the size of wing tip vortices. Initial Issue 71 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics An elliptical planform has unique properties, as the downwash remains constant across the complete wingspan, but this type of wing gives manufacturing and structural difficulties so is not a design commonly used in modern commercial aircraft. A good compromise that maintains the aerodynamic efficiency as close as possible to the properties of an elliptical wing, is a straight tapered wing that is tailored by wing twist and section variation. This type of wing is the design found used in most modern commercial aircraft. Aspect Ratio (AR) The aspect ratio of a wing is the ratio of its wingspan to its chord length and has an affect the amount of induced drag produced, as the higher this ratio is (the longer the wingspan is) the lower will be the pressure differential at the wing tips. This occurs because on a longer wing the spanwise pressure differential between the upper and lower surfaces can even each other out. In fact, induced drag is inversely proportional to the aspect ratio, e.g. if Aspect Ratio (AR) is doubled then induced drag is halved. Weight and Speed The weight and speed of an aircraft affects the amount of induced drag produced as both factors affect the amount of lift produced. Initial Issue 72 June 2024  © Air Service Training (Engineering) Limited Part 66–B08 Basic Aerodynamics For an aircraft flying in level flight the amount of lift produced can be calculated from the formula. Lift = CL ½ ρV2 S It can be seen therefore that if the original speed is halved, then the dynamic pressure (½ ρ V2) of the formula will be reduced by four times. So, to restore the lift required and maintain level flight, the coefficient of lift CL must be increased fourfold by increasing the angle of attack. This however, increases the spanwise flow around the wing tips and the size of the wing tip vortices. In level flight therefore, the size of th