British Airways Global Learning Academy - Basic Aerodynamics PDF

British Airways Global Learning Academy – Basic Aerodynamics Form Drag This is the portion of the resistance which is due to the fact that when air flows past an aircraft, eddies are formed within the air and the flow which previously was streamline now becomes turbulent. Where CD is the drag coeff...

British Airways Global Learning Academy – Basic Aerodynamics Form Drag This is the portion of the resistance which is due to the fact that when air flows past an aircraft, eddies are formed within the air and the flow which previously was streamline now becomes turbulent. Where CD is the drag coefficient, which is a dimensionless coefficient varying with surface finish, fineness ratios etc. The turbulent flow creates a pressure which acts along the line of airflow and in the same direction. This is due to an increase in pressure in the air immediately in front of the aircraft and a decrease in pressure behind the aircraft in the turbulent zone. ρ is the density of air, V is speed of air and S is the plan area of the wing. Form drag can be reduced by ‘shaping’ the aircraft in such a way as to reduce its resistance to a minimum, some examples shown in Figure 18 This is known as ‘streamlining’.A definite relationship exists between the length and thickness of a streamlined body and its resistance. For least resistance, the length should be between three and four times greater than the maximum thickness, and the ratio between the length and maximum thickness is called the Fineness Ratio It is important to appreciate that Profile Drag will increase with velocity, within the speed range of about 30 to 400 mph, by the square of the velocity. The speed range is quoted because in the transonic and supersonic regions, the ‘square of the velocity’ law is found to be totally inaccurate, due to the effect of air compressibility. Mathematically, profile drag (Dp) may be calculated from the expression: 𝐷𝑟𝑎𝑔 Module 08B ETBN 0492 October 2023 Edition = Figure 18 – Variation In Drag Due To Form 1 × 𝜌 × 𝐶 ×𝑉 ×𝑆 2 32 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Interference Drag If we consider the aircraft as a whole, the Total Drag is greater than just the sum of the Drag on the individual parts of the aircraft. Referring to Figure 19 as an example, this is due to flow "Interference" at the junction of various surfaces such as the wing/fuselage junctions and wing/pylon junctions. This flow interference creates an additional Drag, which we call "Interference Drag". As it is not directly associated with the production of Lift it is also a form of Parasite Drag. Suitable filleting, fairing and streamlining of shapes to control local pressure gradients can aid in minimising Interference Drag Figure 19 – Examples Of Sources Of Interference Drag Module 08B ETBN 0492 October 2023 Edition 33 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Induced Drag The action of the aerofoil that gives us Lift also causes Induced Drag. Remember that the pressure above the wing is less than atmospheric, and the pressure below the wing is equal or greater than atmospheric pressure. Since fluids always move from high pressure towards low pressure, there is a spanwise movement of air from the bottom of the wing outward from the fuselage and upward around the wing tip (Figure 20). This flow of air results in 'spillage' over the wing tip, thereby setting up a whirlpool of air called a vortex. Figure 20 – Pressure Differential Above And Below A Wing The air on the upper surface has a tendency to move in toward the fuselage and off the trailing edge. This air current forms a similar vortex at the inner portion of the trailing edge of the wing (Figure 20a). These vortices increase Drag, because of the turbulence produced and constitute Induced Drag. Just as Lift increases with an increase in Angle of Attack, Induced Drag also increases as the Angle of Attack is increased, there is a greater pressure difference between the top and bottom of the wing. This causes more violent vortices to be set up, resulting in more turbulence and more Induced Drag causing a greater downflow of air behind the wing trailing edge. Sometimes, in moist air the pressure drop in the core of these vortices will cause condensation of the moisture so that the small, twisting vortices are visible as vapour, especially with large passenger aircraft on approach and landing in moist conditions (Figure 20b). Module 08B ETBN 0492 October 2023 Edition Figure 20a – Airflow Circulation Around A Wing 34 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics This is the reverse of the case of Profile Drag and in fact it can be shown that the Induced Drag will decrease in proportion to the square of the airspeed Another effect of the wingtip vortex is to reduce lift. As the high pressure air flows from the underside to the upper, the pressure differential across the outboard section of the wing is reduced. Therefore, a larger wing is required to produce the required lift than would be necessary if vortices could be prevented. A larger wing produces more form drag. Many modern aircraft employ 'winglets', small near vertical surfaces, designed to reduce or prevent the formation of wingtip vortices. The designs vary, the object being to prevent loss of lift and reduce induced drag without generating appreciable form drag (Figure 20c). Figure 20b – Visible Vortices In Moist Air As the aircraft is also moving forwards, the air which is flowing vertically around the wing-tips will tend to be left behind and will develop a spiral motion in the form of vortices. These vortices, or whirlpools, are the source of a factor called Induced Drag which plays an important part in the behaviour of an aerofoil in flight. If the speed of the aircraft is increased, then the lift will also be increased, and in order to maintain level flight the angle of attack would have to be reduced. In reducing the angle of attack the angle of the reaction of the aerofoil to the vertical is also reduced. The effect of this is to reduce the magnitude of the component of induced drag, and it therefore follows that as speed is increased, the induced drag will decrease. Figure 20c – Winglet Vortices Reduction Module 08B ETBN 0492 October 2023 Edition 35 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Induced Drag And High Aspect Ratio The sum of Profile and Induced Drag is the Total Drag of the aircraft, and the accompanying graph (Parabola of Total Drag) in figure 21 shows how Profile, Induced and Total Drags vary with the airspeed. Induced Drag can also be reduced by having a long narrow wing. (i.e a wing of high aspect ratio). The lowest point on the total drag (Parabola) curve gives the most economical speed at which to fly the aircraft, for at this speed the total drag is at its minimum value. Compared with a short stubby wing (Low Aspect Ratio) of the same area, a long, narrow wing (i.e a wing of high aspect ratio) and therefore smaller wing tips, has weaker vortices, and therefore less induced Drag. If the spanwise flow of air over the mainplane can be restricted or stopped, the vortices created at the wing tips will be reduced. Unfortunately, a high aspect ratio wing is more difficult to build from the structural strength point of view. A tapered wing has a weaker wing tip vortices because there is less wing tip and so the induced drag is less. Total Drag As stated previously, drag is the total resistance acting on a body on its passage through the air. It is caused by the disruption of the streamline flow, which results in turbulence and skin friction. MINIMUM DRAG It can be shown that, within certain limits, the drag of an aerofoil depends upon the shape of the aerofoil, the angle of attack, the air density, the area of the aerofoil surface and the velocity of the airstream. Airspeed for MINIMUM DRAG We have seen that Profile Drag increases with the square of the airspeed, while Induced Drag decreases with the square of the airspeed. Figure 21 – Total Drag Parabola Module 08B ETBN 0492 October 2023 Edition 36 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Thrust, Weight And Aerodynamic Resultant There are four forces that act on an aircraft in flight: lift, weight, thrust, and drag. The motion of the aircraft through the air depends on the size of the various forces. The weight of an airplane is determined by the size and materials used in the airplane's construction and on the payload and fuel that the airplane carries. The thrust is determined by the size and type of propulsion system used on the airplane and on the throttle setting selected by the pilot. Lift and drag are aerodynamic forces that depend on the shape and size of the aircraft, air conditions, along with the aircrafts’ velocity. Just as the lift to drag ratio is an efficiency parameter for total aircraft aerodynamics, the thrust to weight ratio is an efficiency factor for total aircraft propulsion. 𝑇𝑊 𝑅𝑎𝑡𝑖𝑜 = 𝐹 𝑇ℎ𝑟𝑢𝑠𝑡 𝑚𝑎 = = 𝑊 𝑊𝑒𝑖𝑔ℎ𝑡 𝑚𝑔 Figure 22 – Thrust/Weight Ratio At Differing Aircraft Attitudes From Newton's second law of motion, the acceleration (a) times the mass (m) equals the external force. If we consider a horizontal acceleration and neglect the drag, net external force is the thrust (F). For most flight conditions, an aircraft with a high thrust to weight ratio will have a high value of excess thrust. High excess thrust results in a high rate of climb. If the thrust to weight ratio is greater than one and the drag is small, in theory, the aircraft can accelerate straight up like a rocket and is much less reliant on generation of aerodynamic lift. Dividing by the weight results in the thrust divided by the weight equal to the acceleration (a) divided by the gravitational acceleration (g). An aircraft with a high thrust to weight ratio has high acceleration. The generation of Lift/Drag and the relationship between Lift, Weight, Thrust and Drag is discussed further in the next section of these notes and section 8.3 (Theory of Flight) of this module respectively. Typical TW ratio’s: A320neo = 0.311, A380 = 0.227, B777 = 0.285, B737 Max 8 = 0.310, Eurofighter Typhoon = 1.15 Module 08B ETBN 0492 October 2023 Edition 37 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics The maximum air velocity and minimum static pressure occurs at a point above the aerofoil near the maximum thickness of the profile. The air velocity decreases and the static pressure increases after this point. Generation Of Lift And Drag If we consider the distribution of static pressure around an aerofoil profile, (Figure 23) the dark blue area in front of the leading edge, is where the static pressure is higher than the ambient static pressure. In the darker, grey area at the trailing edge the static pressure is higher than the ambient static pressure. This is caused by low velocity turbulent air in this area. This is because the velocity of the air approaching the leading edge, slows to less than the flight path velocity. The static pressure is highest at the stagnation point, where the airflow splits between the upper and lower surface and comes to a complete stop. The aerodynamic resultant force is the resultant of all forces acting on a profile in airflow and is considered to act through the centre of pressure. In the green and red areas above and below the profile, the static pressure is lower than the ambient static pressure and is because the air speeds up as it passes above and below the profile so that the local air velocity is greater than the flight path velocity. Since the aerodynamic resultant is a vector (fig 23a) – it has magnitude and direction; that does not always point straight up it can be separated into its two components:  Lift - Perpendicular to the relative wind (air flow)  Drag - Parallel to the relative wind (air flow) Aerodynamic Resultant Stagnation Point Chord Line Figure 23 – Aerodynamic Pressure Distribution Around An Aerofoil Figure 23a – Aerodynamic Resultant Vector with Lift and Drag Module 08B ETBN 0492 October 2023 Edition 38 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics It should be noted that as long as the direction of the aerodynamic resultant is not at 90º to the chord line of the aerofoil there will always be drag produced as an unintentional by-product of lift. We need firstly to decide what pressure is causing the lift. From previous explanations, it can be seen that it is the change in velocity and so the change in dynamic pressure that causes the aerodynamic resultant and hence lift. The aerodynamic forces of lift and drag depend on the combined effect of many variables such as the dynamic pressure the surface area of the profile the shape of the profile and the angle of attack. Given this all we need to do is replace ‘Air Density’ with the formula for Lift And Lift Co-efficient (CL) L ρ v q S = = = = = 𝐿= Lift Force. Air (fluid) Density. True Airspeed. Dynamic Pressure Wing Planform Area To achieve this, we simply multiply the lift equation by a number that represents the efficiency of the aerofoil at turning changes in pressure into a lift force – referred to as the coefficient of lift (CL). This gives us: 𝐿𝑖𝑓𝑡 𝐹𝑜𝑟𝑐𝑒 (𝐿) 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 (𝑆) 𝐿= Re-arranging the formula we obtain the simplest and most basic formula for lift: 1 𝜌𝑣2 × 𝑆 × 𝐶𝐿 2 Transposing the formulae to make CL the subject gives us: 𝐿= 𝜌 × 𝑆 𝐶 = In reality however it’s not as easy as you might think; a profile has different pressures because of different angles of attack. Module 08B ETBN 0492 October 2023 Edition 1 𝜌× 𝑣 ×𝑆 2 We have already mentioned however that this is a pretty simple view of everything that creates lift for an aerofoil and we need to take into account its’ shape, fineness ratio and the angle of attack etc. Since lift is a force, and we know the air density acting over the surface area of the wing: 𝐴𝑖𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 (𝜌) = 𝜌 × 𝑣 . This gives us: “q - Dynamic Pressure” = If we now look at how to calculate the lift produced by an aerofoil, you might think that this is simple. 39 𝐿 1 𝜌𝑣 2 ×𝑆 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Beyond 16° AoA, the detached airflow forms swirls and eddies of turbulence and the value of the lift produced falls rapidly. This is known as aerofoil 'Stall'. The angle at which it occurs varies slightly with each aerofoil section but the effect is the same. It should be noted that the aerofoil still produces positive lift at a negative AoA. Angle of Attack (AoA) It can be seen from the previous descriptions that the amount of lift derived is dependent on the velocity of the air approaching the aerofoil, and the acceleration of the air over the upper surface in relation to the air flowing under the lower surface, the latter is dependent on the camber of the surfaces. A wing section is selected to give sufficient lift at the aircraft's cruising speed. It is, however, necessary to generate the same or more lift at lower speeds during take-off and landing. Point of Stall This is achieved by changing the effective camber of the wing. Whilst this can be achieved by changing the physical shape of the aerofoil section (we will discuss this in a later section of these notes), the simpler method is to change the angle of attack at which the aerofoil is presented to the air flow. The angle of attack (AOA) or sometimes “α” (Greek letter alpha), is measured between the airflow streamline and the aerofoil chord line (as previously seen in figure 23a). Increasing the “α” angle of attack increases the camber of the upper surface in relation to the airflow and also increases the downwash produced. For an individual aerofoil shape, tests are carried out during the design that allow you to plot the efficiency of the aerofoil at producing lift – the coefficient of lift (CL) against different angles of attack. As the graph (Figure 24) of Coefficient of Lift (CL) against Angle of Attack (AoA) shows that lift rises in a linear manner from the angle of zero lift (approximately - 2° in this case) to around 12°. At this point the laminar flow over the upper surface of the aerofoil begins to break down. Module 08B ETBN 0492 October 2023 Edition Fig 24 – CL against AoA 40 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics The stalling angle is normally in the region of 15º (illustrated in figure 24a), although this varies, depending on the type of wing considered. Aerodynamic Stall As previously discussed, the lift produced by a wing is steadily increased as the angle of attack is increased, up to the stalling angle. Beyond this angle the amount of lift produced decreases rapidly. This occurs because, at the high angle of attack involved in the stall, the airflow has separated from most of the upper surface of the wing (Figure 24a). The reason that the stall occurs is that the air is unable to travel over the upper surface of the wing against the adverse pressure gradient which occurs behind the point of minimum pressure. Aerodynamic Stall And Centre of Pressure (CoP) The point of minimum pressure above the aerofoil surface, known as the Centre of Pressure (CoP) is a point usually on the chord line through which, the maximum Total Reaction (TR) may be considered to act and provide the most effective aerodynamic lift for the aerofoil. It is important to appreciate that the wing (and therefore the aircraft) stalls at a given angle of attack (incidence) rather than at a given airspeed. Referring to Figures 24a and 24b we study what happens as the AoA of the aerofoil is increased. R1 = 40 At a low Angle Of Attack (AoA) the CoP is set further back on the aerofoil Chord line with minimum or no airflow separation and turbulent airflow with a positive pressure gradient. R2 = 140 An increasing AoA sees the CoP moves forward toward the Leading Edge of the aerofoil surface with airflow separation at the Transition point producing turbulent airflow at the trailing edge of the Aerofoil. This has the effect of creating an adverse pressure gradient and aerodynamic drag. R3 = 160 The CoP has moved to its’ furthest point forward toward the Leading Edge with the adverse pressure gradient at near maximum and the turbulent airflow has now completely separated from the upper aerofoil surface with a dramatic increase in drag. As the aerofoil enters into a stall, the CoP moves rapidly rearwards, toward the Trailing Edge, causing a pitch down moment. Figure 24a – Aerofoil AoA Lift to Stall Transition Module 08B ETBN 0492 October 2023 Edition 41 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Figure 24b – CoP Movement along an Aerofoil Chord line Module 08B ETBN 0492 October 2023 Edition 42 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Another aerofoil CoP movement example is shown in Figure 24c, which has a stall α AoA of 140 when the CoP direction reverses. Since the coefficient of lift is constant (it depends on the wing shape which is a constant, and on the angle of attack, which we know is a constant for the point of stall), the point at which the stall occurs is governed by ½pV2, and this is of course the dynamic pressure. Since dynamic pressure gives us indicated airspeed, we therefore have a situation whereby any aircraft will stall at a constant IAS, regardless of altitude. This of course assumes constant weight and aircraft configuration, and straight and level flight. The statement also ignores the very small variations in the difference between equivalent and indicated airspeed as altitude is changed. In light aircraft warning of approach to the stall is usually achieved aerodynamically in the form of buffet. Where this is absent, or could be confused with turbulence, the stall warning is artificially induced. In heavy aircraft with powered controls it is normal to incorporate a stick shaker. This device shakes the stick in order to simulate the effect of the turbulent airflow over the elevators which would normally be felt at the stick a pre-stall buffet, but which is masked by the electrohydraulically powered control system. Stick shakers are operated from a detector which senses incidence (angle of attack) and rate of change of incidence. Chord Line Having gone this far it is normal to incorporate also a stick pusher. If the pilot doesn't respond to the stick shaker, the stick pusher automatically ensures that the correct incipient stall recovery procedure is initiated. Module 08B ETBN 0492 October 2023 Edition Figure 24c – CoP Movement With AoA 43 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Stall Conditions Wing Tip Stall The total wing lift is the resultant of the lift distribution. It is represented by the two large red arrows in Figure 24d.The total wing lift acts on the centre of lift. A flow separation at the tip of the wing is extremely dangerous. The centre of lift moves towards the root and also forward of the centre of gravity illustrated in figure 24e. The cord line through the centre of lift is known as the Mean Aerodynamic Chord, or MAC for short, discussed previously. Since there is now a turning moment produced between the centre of gravity (CoG) and the centre of lift (CoP) the aircraft rotates to the nose up position. The position of the centre of lift can be described in percentage terms. The leading edge corresponds to 0 % and the trailing edge to 100 % so in this example we can say that the centre of lift is located at approximately 30 % MAC. The angle of attack increases as the aircraft rotates nose up and the stall condition gets worse. Pilot input is required to keep the aircraft under control and reduce the AoA. Wing Root Stall A stall strip is a knife edge like device, which is used on smaller aircraft to prevent the wing tip from stalling first. During a wing root stall (see figure 24d) the stall occurs at the root, by the body-to-wing fairings. The loss of lift that results from the flow separation in the area of the wing root. Here the stall strip is mounted at the leading edge of the wing root. The disadvantage of this device is that it disturbs the lift distribution under normal conditions When we have a flow separation at the root of the wing, the centre of lift moves outwards towards the tip and also behind the centre of gravity. Preventing Early Wing Tip Stall A tendency to stall at the tip section first has dangerous implications for the lateral control and stability of the aircraft. Since the distance between the CoG and the CoP is now increased there is an increased turning moment and the aircraft rotates to the nose down position. The wing can be designed so that the root stalls before the tip and the aircraft remains controllable. The aircraft loses altitude rapidly, the airspeed increases and the angle of attack decreases. This is achieved by geometrically twisting the wing, or by aerodynamically twisting the wing to cause “Wash Out” as shown and explained earlier in the Aerodynamic Terminologies section of these notes. The aircraft recovers from the stall without pilot input since the decrease in AoA reduces and then removes the stall condition whilst the increased airspeed generates more lift. Module 08B ETBN 0492 October 2023 Edition 44 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Resultant Lift CoP moving rewards and towards wing tip Wing Root Stall Longitudinal Axis CoG Increased nose down turning moment Resultant Lift Loss of lift due to flow separation CoP moving rewards and towards wing tip 30% MAC Excessive wing tip structural loading Fig 24d – Wing Root Stall Module 08B ETBN 0492 October 2023 Edition 45 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Resultant Lift CoP moving forwards and towards wing root Longitudinal Axis Wing Tip CoG CoP moving forwards and towards wing root Loss of lift due to flow separation Increased nose UP turning moment Resultant Lift 30% MAC Figure 24e – Wing Tip Stall Module 08B ETBN 0492 October 2023 Edition 46 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics We need firstly to decide what pressure is causing the drag. From previous explanations, it can be seen that it is the change in velocity and so the change in dynamic pressure that causes the aerodynamic resultant and hence drag. Drag And Drag Co-efficient (CD) Given this all we need to do is replace ‘Air Density’ with the formula for If we now look at how to calculate the drag produced by an aerofoil, you might think that this is simple. DP ρ v q S = = = = = Drag Profile/Force. Air (fluid) Density. True Airspeed. Dynamic Pressure Wing Planform Area 𝐷 = 1 𝜌× 𝑣 ×𝑆 2 We have already mentioned however that this is a pretty simple view of everything that creates drag for an aerofoil and we need to take into account its’ shape and the angle of attack etc. Since drag is a force, and we know the air density acting over the surface area of the wing: 𝐴𝑖𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 (𝜌) = 𝜌 × 𝑣 . This gives us: “q - Dynamic Pressure” = To achieve this, we simply multiply the drag equation by a number that represents the shape, surface finish, fineness ratio etc of the aerofoil at turning changes in pressure into a drag force – referred to as the coefficient of drag (CD). This gives us: 𝐷𝑟𝑎𝑔 𝑃𝑟𝑜𝑓𝑖𝑙𝑒 (𝐷 ) 𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐴𝑟𝑒𝑎 (𝑆) 𝐷 = Re-arranging the formula we obtain the simplest and most basic formula for Drag Profile/Force (Dp): 1 𝜌𝑣2 × 𝑆 × 𝐶𝐷 2 Transposing the formulae to make CD the subject gives us: 𝐷 = 𝜌 × 𝑆 𝐶 = In reality however it’s not as easy as you might think; a profile has different pressures because of different angles of attack. 𝐷 1 𝜌𝑣 2 ×𝑆 Some examples of Drag Co-efficient (CD) are shown in Fig 25 Module 08B ETBN 0492 October 2023 Edition 47 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Note that, as with lift, drag is directly proportional to each of the following; a) b) c) Drag coefficient (CD) Dynamic pressure (q) Wing planform area (S) The relationship between drag and angle of attack is not as simple as was the case with lift. In the drag coefficient against angle of attack curve (see figure 25) we see the drag is lowest at 0°, or even a small negative angle, and increases on both sides of this angle, up to about 16° However, the increase in drag is not very rapid, then it gradually becomes more and more rapid, especially after the stalling angle, when the airflow separates from the surface. Figure 25 – Comparisons Of Drag Co-efficient (CD) Module 08B ETBN 0492 October 2023 Edition Figure 25 – CD against AoA 48 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Drag Polar Curve The drag polar is a curve that shows the relationship between the drag coefficient and lift coefficient for a full aircraft. This relationship is expressed by an equation that can be represented by a graph called drag polar. From inspection of Figure 26 it is evident that both CDO (shown in the graph as CDP) and CDi vary with lift coefficient. However, the part of parasite drag above the minimum at zero lift is included with the induced drag coefficient. The equation that defines the drag polar of an aircraft can be obtained from the total drag generated in it. The total drag is obtained from the sum of parasite drag and the induced drag due to lift generation of the aircraft, thus the equation that defines the total drag of an aircraft as aerodynamic coefficients can be written to follows. CD = CDO + CDi Where;  CDO  CDi = Parasite Drag = Induced Drag The variation of parasite drag coefficient, CDP with lift coefficient, CL is shown for a typical aeroplane in Fig 26. As a reminder AR is the wing Aspect Ratio, which has a significant contribution to any induced drag coefficient CDi and Drag coefficient CD The minimum parasite drag coefficient, CDO min usually occurs at or near zero lift and the parasite drag coefficient increases above this point in a smooth curve. Figure 26 – Drag Polar Curves The induced drag coefficient is shown on the same graph for purposes of comparison. In many areas of aeroplane performance it is necessary to completely distinguish between drag due to lift and drag not due to lift. Module 08B ETBN 0492 October 2023 Edition 49 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Lift/Drag Ratio Since it is common to both the top and bottom of the equation we can remove it, giving: The first polar diagram that we plot (Figure 26) is looking at how the ratio of the lift to drag produced by an aerofoil varies as the angle of attack that the aerofoil is presented to the relative airflow changes. 1 × 𝜌 ×𝑉 ×𝑆 ×𝐶 𝐿𝑖𝑓𝑡 2 = 1 𝐷𝑟𝑎𝑔 × 𝜌 × 𝑉 ×𝑆 ×𝐶 2 If we first consider the lift equation from earlier: 𝐿𝑖𝑓𝑡 (𝑓𝑜𝑟𝑐𝑒) = 1 × 𝜌 ×𝑣 ×𝑆 ×𝐶 2 𝐿𝑖𝑓𝑡 𝐶 = 𝐷𝑟𝑎𝑔 𝐶 And the drag equation: 𝐷𝑟𝑎𝑔 = 1 × 𝜌×𝑣 ×𝑆 ×𝐶 2 Now we see that the ratio of Lift to Drag is the same of the ratio of the Co-efficient of Lift to the Co-efficient of Drag. Then to find the ratio of lift to drag all we do is to divide the first equation by the second: The flight efficiency of an aeroplane is based on its aerodynamic efficiency, in particular the lift/drag (L/D) ratio. 1 × 𝜌 ×𝑉 ×𝑆 ×𝐶 𝐿𝑖𝑓𝑡 = 2 1 𝐷𝑟𝑎𝑔 × 𝜌 × 𝑉 ×𝑆 ×𝐶 2 As you can see the term × 𝜌 × 𝑉 ×𝑆 This is known by dividing the coefficient of lift by coefficient of drag at each angle of attack. The wing is most efficient at an angle of attack which gives the maximum ratio of lift to drag. From the lift curve Figure 24, we saw that we get most lift at about 15°, from the drag curve and from Figure 25 we get least drag at about 0°. is common to both the lift and drag equation – this is because it represents the dynamic pressure around the aerofoil. Module 08B ETBN 0492 October 2023 Edition From figure 27 we see that neither 0° nor 15° gives the optimum flight condition. We need the best compromise between lift and drag which occurs at about 3° when the lift is nearly 24 times the drag. 50 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Aerofoil Contamination Ice Formation And Effects of Ice, Snow And Frost Icing on aircraft is caused primarily by the presence of super-cooled water droplets in the atmosphere. If the droplets impinge on the forward facing surfaces of an aircraft, they freeze and cause a buildup of ice which may seriously alter the aerodynamic qualities. This applies particularly to small objects, which have a higher catch rate efficiency than large ones, as small amounts of ice will produce relatively bigger changes in shape. The actual amount and shape of the ice build-up depends on surface temperature. When the temperature is less than 0ºC all the impinging water droplets are frozen and when it is above 0ºC none are frozen. Fig 27 – Lift/Drag Ratio Graph The final influencing factor of note is that icing does not occur above about 12,000 m (40,000 ft.) since the droplets are all frozen and in the form of ice crystals and will not adhere to the aircraft’s surface. We find that the lift/drag ratio increases very rapidly up to about 3°, at which angle the lift is nearly 24 times the drag, the ratio then gradually falls off because, although the lift is still increasing, the drag is increasing even more rapidly. Some examples of ice formation at differing temperatures and their impact on a wings’ aerodynamic lift and drag performance can be found in Figure 28. Until at the stalling angle the lift may be only 10 or 12 times as great as the drag, and after the stalling angle the ratio falls still further until it reaches 0 at 90°. The chief point of interest about the lift/drag curve is the fact that this ratio is greatest at an angle of attack of about 3°, in other words, it is at this angle that the aerofoil gives its best all round results. Module 08B ETBN 0492 October 2023 Edition 51 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Fig 28 – Ice Formation At Different Temperatures Module 08B ETBN 0492 October 2023 Edition 52 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Ice on an aircraft affects its performance and efficiency in many ways. Ice build-up increases drag and reduces lift. It causes destructive vibration and hampers true instrument readings. Control surfaces become unbalanced or frozen. Fixed slots are filled and movable slots jammed. Radio reception is hampered and engine performance is affected. Ice, snow, rime formation or deteriorations of other kind having a thickness and surface roughness of a medium sandpaper on the leading edge and upper surface of the wing can reduce wing lift by around 30% and increase drag by 40% and increase overall aircraft weight and wing loading (which will be discussed in theory of flight). It is important to consider that other kind of contaminations or deteriorations also affect wing Lift and drag in the same way like explained for ice, rime and snow. Some examples of contamination and deterioration are:       Mis-rigging of control surfaces Absence of seals on movable sections Dents on surfaces (bird strikes, accidental ground damages) External repair (doubler) Paint peeling Lack of cleanliness The first 20% of the wing chord is particularly sensitive, because disturbances of air flow passing it can cause separation resulting in early stall. These changes in Lift and drag significantly increase stall speed, reduce controllability and alter flight characteristics. Fig 28a – Aerodynamic Impact of Surface Contamination Figure 28a illustrates some of the aerodynamic impacts of aircraft and wing contamination, severely reducing lift ability by increasing aircraft weight, wing loading and drag. Module 08B ETBN 0492 October 2023 Edition 53 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Types of Ice And Snow Glaze Ice Glaze/Clear ice is the glassy deposit that forms over the village pond in the depth of winter. On aircraft in flight, glaze ice forms when the aircraft encounters larger water drops in clouds or in freezing rain with the air temperature and the temperature of the airframe below freezing point. It consists of a transparent or opaque coating of ice with a glassy surface and results from the liquid water flowing over the airframe before freezing Glaze ice may be mixed with sleet or snow. It will form in greatest thickness on the leading edges of aerofoils and in reduced thickness as far aft as one half of the chord. Ice formed in this way is dense, tough and sticks closely to the surface of the aircraft. It cannot be easily shaken off and, if it breaks off at all, it comes away in lumps of an appreciable and sometimes dangerous size. Fig 29b- Glaze and Rime Ice Formation Rime Ice Rime ice is brittle and opaque and tends to grow into the airstream. It is formed as the droplets freeze immediately upon impact with the cold wing structure (Figure 29b) The main danger of glaze ice is still aerodynamic, but to this must be added that due to the weight of ice, unequal wing loading and propeller blade vibration. Pack Snow Normally, snow falling on an aircraft in flight does not settle, but if the temperature of the airframe is below freezing point, glaze ice may form from the moisture in the snow. Glaze ice is the most severe and the most dangerous form of ice formation on aircraft. It is formed when the droplets deform and/or flow along the surface prior to freezing (Figure 29b). The icing of the aircraft in such conditions, however, is primarily due to water drops, though snow may subsequently be embedded in the ice so formed. Glaze icing can be more serious to the aircraft than rime, since it tends to run back along the airframe, covering more surface area than rime icing, perhaps flowing onto and adhering to unprotected areas. Glaze icing can be hard to see from inside the aircraft, so that the pilot may be unaware of ice build-up. Module 08B ETBN 0492 October 2023 Edition 54 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Light Rime Ice Severe Glaze Ice Moderate Mixed Ice Supercooled Large Droplet Ice Fig 29c – Different Types Of Ice Module 08B ETBN 0492 October 2023 Edition 55 Basic Aerodynamics – Aerodynamics