British Airways Global Learning Academy - Basic Aerodynamics PDF

British Airways Global Learning Academy – Basic Aerodynamics This will cause the air flow to slow down and give a reduced velocity (V2). Compressibility So far all of our work on fluids has been based on the assumption that fluids are incompressible. The static pressure of the air will increase (B...

British Airways Global Learning Academy – Basic Aerodynamics This will cause the air flow to slow down and give a reduced velocity (V2). Compressibility So far all of our work on fluids has been based on the assumption that fluids are incompressible. The static pressure of the air will increase (Bernoulli’s theorem and Table 1) to become P2 in the wider section of the duct but, because air is compressible, the air density will increase as it is compressed by the rise in pressure in the divergent part of the duct. This is certainly true for the practical application of fluid theory to liquids such as water but not so for air, which is most definitely compressible! In Figure 2, For the supersonic, compressible air flow, the air entering the convergent part of the duct, consists of decreasing air pressure (P1) and velocity (V1); then as the air enters the divergent part of the duct, with the increased area, air will spread out to fill the increased area. Our theory based on the incompressible behaviour of fluids is still sufficiently valid for air when it flows below speeds of approximately 130–150 m/s. As speed increases compressibility effects become more apparent and Table 2 demonstrates the reverse effects of fluid velocity, static and dynamic pressures due to air compressibility at speeds approaching, near too or above the speed of sound (Mach 1.0). This will cause the air flow to increase and give a reduced velocity (V2). The static pressure of the air will decrease (Table 2) to become P2 in the wider section of the duct and, because air is compressible, the air density will decrease as it is de-compresses by the fall in pressure in section B of the duct. Therefore, when we study high-speed flight where aircraft fly at velocities approaching, close too, or in excess of, the speed of sound, also known as Mach 1.0 (340 m/s at sea level under standard ISA conditions), then the compressibility effects of air must be considered. Table 2 – Convergent/Divergent Duct Summary (At/above Mach1.0) This is particularly true when considering the possible inaccuracies in aircraft pitot–static instruments, where such instruments depend on true static and dynamic air pressures for their correct operation. In Figure 2, For the subsonic air flow, the air entering the convergent part of the duct, consists of increasing air pressure (P1) and velocity (V1); then as the air enters the divergent part of the duct, with the increased area, air will spread out to fill the increased area. Module 08B ETBN 0492 October 2023 Edition 7 DUCT TYPE FLUID VELOCITY DYNAMIC PRESSURE STATIC PRESSURE Converging Decreasing Decreasing Increasing Diverging Increasing Increasing Decreasing Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Fig 2 – Convergent/Divergent Sub Sonic/Supersonic comparisons Module 08B ETBN 0492 October 2023 Edition 8 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Application Of Bernoulli’s Principle We see how lift is produced, using the venturi tube in Figure 3.. If we remove the upper surface, we find that the streamlines themselves provide the upper boundary of the venturi tube since the flow is subsonic and cannot compress. The velocity of the airflow increases until it reaches the narrowest point in the tube. We know that as the velocity increases the static pressure decreases and the dynamic pressure increases. The next step is to change the lower surface of the venturi tube into an aerodynamic profile and to add some streamlines below it. The velocity decreases again after the narrowest point and returns to the inlet level by the time the airflow reaches the outlet. During this phase the static pressure increases again and the dynamic pressure decreases. Now we have a surface with an area of low static pressure above it and area of unchanged static pressure below it. We, now have a difference in pressure across the top and bottom of the wing. Now let’s imagine replacing the upper surface of the venturi tube with a straight line and see what happens to the airflow. This doesn’t change things very much. From fluid dynamics you should remember that the product of the resultant pressure acting across a given surface area creates a force in the direction of the resultant pressure hence the force of lift is produced. The streamlines are still closer to each other in the centre and the static pressure decreases in this area. Module 08B ETBN 0492 October 2023 Edition 9 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Top of tunnel replaced with flat surface Area of compressed streamlines Flat surface removed Bottom surface profile smoothed Figure 3 - Application Of Bernoulli’s Principle Module 08B ETBN 0492 October 2023 Edition 10 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Airflow Around A Body Skin Friction and Viscosity Skin Friction is caused by a tendency of the particles of air to cling to the surface of the aircraft. There are two reasons for this tendency. Firstly, the aircraft has a certain amount of roughness, relatively speaking, it is impossible to make the skin perfectly smooth. It could also be dirty which would have the same affect. Secondly, the air tends to cling to the surface and this is due to the air having viscosity. Technically, viscosity is the resistance to flow. It is commonly used to describe the adhesive or sticky characteristics of a fluid (see figure 4 with the effect of air layers). Figure 4 – Effect Of Viscosity On Airflow Think of oil and water; oil is much more viscous than water. The oil finds it more difficult to flow than water, therefore has a higher viscosity. Viscosity is generally a function of temperature alone; a decrease in temperature increases the viscosity (thickness). Therefore, viscosity usually increases with altitude. Fig 4a – Effect Of Viscosity Around An Aerofoil Module 08B ETBN 0492 October 2023 Edition 11 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Free Stream Flow When a fluid, liquid or gas is flowing steadily over a smooth surface, narrow layers of it follow smooth paths that are known as streamlines. This smooth flow is also known as laminar flow and will be discussed later in this section. When air flows around a non-streamlined object the air swirls into eddies, the streamlines distort and intermingle, and finally disappear. The airstream has now become turbulent. If this stream meets large irregularities, the streamlines are broken up and the flow becomes irregular or turbulent, as may be seen when a stream comes upon rocks in the river bed. The effort required to force a flat plate through the air is about 20 times that required for a streamlined shape for the same speed and with a similar frontal area presented to the air. By introducing smoke into the airflow in a wind tunnel (as we can see in figure 4b) or coloured jets into water tank experiments, it is possible to see and photograph these streamlines and eddies. Much of the difference arises from the energy needed to form air eddies behind the flat plate. A tube, which comes smoothly to a narrow constriction and then widens out again is known as a venturi tube. The following rules apply to streamlines:  Streamlines never cross  The closer streamlines are together the faster the fluid velocity and conversely the lower the static pressure. Module 08B ETBN 0492 October 2023 Edition 12 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics REAL LIFE STREAMLINES COMPUTER GENERATED STREAMLINES Figure – 4b – Free Streamline Flows Module 08B ETBN 0492 October 2023 Edition 13 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Boundary Layer Laminar And Turbulent Flow The term laminar flow describes the situation when air is flowing in thin sheets, or layers, close to the surface of an aircraft's wing with no disturbance between the layers of air, that is there is no cross flow or sideways movement of the air particles with respect to the direction of the airflow. Normally the airflow at the leading edge of a wing will be laminar, but as the air moves toward the trailing edge of the wing, the boundary layer becomes thicker and turbulent. (Fig 5a) Laminar flow is most likely to occur where the surface is extremely smooth. The area where the airflow changes from laminar to turbulent is called the transition point or region. It is desirable to keep the air flow as laminar or as smooth as possible over the aerofoil. The boundary layer (Fig 5) is that layer of air adjacent to the aerofoil surface and is approximately 1/16 of an inch thick. The air velocity in the boundary layer varies from zero, on the surface of the aerofoil, to the velocity of the free air stream at the outer edge of the boundary layer. The boundary layer is caused by the viscosity of the air sticking to the surface of the wing and the succeeding layers of air. Fig 5a – Laminar to Turbulent Airflow over An Aerofoil Figure 5 - Variation In Airflow Speed in the Boundary Layer Module 08B ETBN 0492 October 2023 Edition 14 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Due to the friction and pressure gradient existing within the boundary layer, the boundary layer, itself, may be brought to rest. This is due to the fact that the turbulent air produces an increase in static pressure above that of the boundary layer in front of it. At this point the streamlined flow will now not have the energy to push through this area of high pressure. When this occurs, the layer will break away from the surface to form a turbulent wake. The point at which this takes place is called the Separation Point We can now define the Boundary Layer as that area where shearing takes place between successive layers of air or between the surface and the full flow velocity of the airstream. It is worth noting that the boundary layer can be either ‘lamina’ or turbulent. We can see the full range of Boundary Layer behaviour in figure 5b Figure 5b – Boundary Layer Behaviour Module 08B ETBN 0492 October 2023 Edition 15 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Relative Airflow (RAF) The Relative Airflow (Wind) is the angle or direction that air passes over or across an aerofoil surface (wing) of an aircraft. As can be seen in figure 6 and 6a the Relative Air Flow is not the angle at which the aircraft is climbing or descending but the direction the airflow passes over the aerofoil, relative to the aerofoil and is a critical distinction as the Relative Airflow provides the lift for an aerofoil. A very high or low Relative Airflow (Wind) is a crucial factor on the lift or drag produced by the aerofoil and this will be discussed later. Relative Airflow is always in the opposite the direction to the aircrafts’ forward flight path velocity Fig 6a – Relative Airflow with respect to the Aerofoil Fig 6 – Relative Airflow (Wind) with respect to an aircraft Module 08B ETBN 0492 October 2023 Edition 16 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Up-Wash, Downwash & Stagnation Point As air flows towards an aerofoil it will be turned towards the lower pressure at upper surface, this is termed up-wash. After passing over the aerofoil the air flow returns to its original position and state, this is termed downwash. Figure 8 – Wing Tip Vortices Upper and Lower Surfaces Direction Fig 7 - Up-wash and Downwash The point on the leading edge of an aerofoil (A) and trailing edge (B) where the airflow separates, some going over the surface and some below. This is known as stagnation point. Vortices Wing tip vortices are formed because the wing develops lift. That is to say the pressure on the top of the wing is lower than on the bottom; and near the tips of the wing this pressure difference causes the air to move around the edge from the bottom surface to the top (Fig 8). This results in a rotational movement of the fluid (air) forming the trailing vortex. As viewed from the rear, they rotate clockwise from the left wing and anti-clock wise from the right wing (Fig 8a and 8b). Module 08B ETBN 0492 October 2023 Edition Figure 8a – Wing Tip Vortices Being Generated 17 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics The strength of the vortex is related to the amount of lift generated by the wing so they become particularly strong in high-lift conditions such as take-off and landing. Aerodynamics Terminologies They also increase in strength with the size of the airplane, because the lift is equal to the weight of the aeroplane. For a large transport aeroplane such as an Airbus A380 or Boeing 747, the vortices are strong enough to roll a small aeroplane onto its back if it gets too close. Aerofoils The aerofoil is a shaped surface designed to produce a reaction when moved through an airstream. Present day aerofoils are devised to produce a high reaction force with as little resistance as possible. When comparing the flat plate to the aerofoil, it was discovered that a curved instead of a flat plate produced a much greater lift force than the drag. Thus the modern aerofoil was developed. As stated, an aerofoil is a surface designed to obtain a desirable reaction from the air through which it moves. Therefore, we can say that any part of an aircraft, which converts air velocity into a force useful for flight, has an aerofoil shape. The blades of a propeller are so designed that when they rotate, their shape and position cause a low pressure to form in front of them and a higher pressure behind them so they pull the aircraft forward. Likewise, the blades on a helicopter and also those used in a jet engine are aerofoil shaped. Figure 9 shows a selection of aero foil designs Figure 8b – Wing Tip Vortices On Starboard Wingtip PORT Module 08B ETBN 0492 October 2023 Edition 18 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics m Figure 9 – Aerofoil Design Shapes Module 08B ETBN 0492 October 2023 Edition 19 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Chord Line The straight line joining the centres of curvatures of the leading and trailing-edges (Figure 10a). Chord length is the distance between the leading and the trailing edge measured along the chord line Camber And Wing Shape The curvature of the aerofoil from the leading edge to the trailing edge; "upper camber” refers to the curvature of the upper surface, "lower camber" refers to the curvature of the lower surface (Fig 10). my On the upper surface a large camber will give good lift (increased area), but high drag (greater mass) and therefore, low speed (Fig 10) The Mean Camber Line is the line joining the leading and trailing edges of the section equidistant from the upper and lower surfaces (Fig 10). Fig 10. – Aerofoil Key Terminologies If the upper camber is larger than the lower camber the wing is said to be asymmetrical and the velocity differential increases (Fig 9). If the upper and the lower camber are the same, the wing is said to be symmetrical. This type of wing relies on a positive angle of attack to generate lift and is generally used on high performance, acrobatic aircraft (Figure 9). Angle of Attack The angle between the chord line of the section and the direction of the oncoming airflow (Figure 10a) This should not be confused with the Angle of Incidence, which is the angle between the chord line and the longitudinal axis of the aircraft (Fig 10a). Module 08B ETBN 0492 October 2023 Edition Figure 10a – Angle of Incidence And Chord Line 20 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Fineness Ratio & Thickness/Chord Ratio Two ratios used for discussing the cross section of a wing. The Fineness ratio looks at the length of the chord compared to the maximum thickness, whilst the Thickness/Chord ratio looks at it the other way around, as shown (Figure 11). A thick aerofoil section with a large cambered top surface will give high lift characteristics accompanied with high drag characteristics also but is suitable where high forward speeds are not required. The large camber also allows the use of deep spars. The maximum thickness is about 25% to 30% of the chord aft of the leading-edge. Where high forward speed is of more importance, the high lift aerofoil section can be modified. The maximum thickness remains at about 25% to 30% chord, but the thickness/chord ratio is reduced whilst the top surface is given a less pronounced camber. This results in a section which possesses smaller lift and drag characteristics than that of a high lift section. Where speed is the only criteria, drastic changes in the section are made. The Chord/Thickness ratio is somewhere in the region of 5% to 10%, the leading edge is given a knife-edge whilst the top surface has little or no camber. These changes, of course, lead to low lift and drag characteristics, but experiments to improve the air circulation around the section are continuously in progress to increase the lift whilst retaining the low drag. Module 08B ETBN 0492 October 2023 Edition Figure 11 – Fineness Ratio 21 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Wing Planforms And Characteristics Aspect Ratio (AR) And Wing Planforms       The Aspect Ratio (AR) of a wing is the ratio of the wing span to the average chord. It is determined with this formula. The greater number of times the chord will divide into the span the higher the aspect ratio will be. Wing Area (S) - The plan surface area of the wing. Wing Span (b) - The distance from tip to tip. Average Chord (c) - The geometric average. Root Chord (CR) - The chord length at the wing centre line Tip Chord (CT) - The chord length at the tip. Taper Ratio (CT/CR) - The ratio of the tip chord to the root chord. The taper ratio affects the lift distribution and structural weight of the wing. A rectangular wing has a taper ratio of 1.0 while the point tip delta wing has a taper ratio of 0.0. The wing with a high aspect ratio gives a better lift/drag ratio than the wing with a low aspect ratio for reasons to do with drag which are dealt with later. As can be seen in Figures 12 and 12a, a wing with high Aspect Ratio is ideal for a non-powered aircraft, which requires lower speeds, higher lift/drag ratio but lower manoeuvrability. Conversely the lower Aspect Ratio wing is for higher speeds and higher manoeuvrability but has a lower lift/drag ratio. The aspect ratio is one of the primary factors in determining wing lift/drag characteristics. Sometimes it is expressed as the ratio of the square of the wing-span to the wing area. Figure 12 – Wing Planforms Module 08B ETBN 0492 October 2023 Edition 22 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Fig 12a – Wing-Shape And Aspect Ratio Comparisons Module 08B ETBN 0492 October 2023 Edition 23 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Dihedral/Anhedral The Dihedral of the wing is the angle formed between the wing and the horizontal plane passing through the root of the wing. We have a positive dihedral when the tip of the wing is above the horizontal plane and a negative dihedral when the tip of the wing is below the horizontal plane – also known as Anhedral. Ior Sweep Angle The sweep angle is the angle between the quarter cord, or the 25 % line and the pitch axis.  Positive sweep = Backwards  Negative sweep = Forwards Figure 12b – B787 with Dihedral Wing Design Figure 12d illustrates positive sweep angle, its’ measurement datum and some typical swept wing design configurations. Fig 12c – BAe146 with Anhedral Wing Design Module 08B ETBN 0492 October 2023 Edition 24 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Low sweep angle Moderate sweep angle High sweep angle Figure 12d – Sweep Angle Illustrations Module 08B ETBN 0492 October 2023 Edition 25 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Mean Aerodynamic Chord (MAC) The MAC is the mean (average) chord of the wing. This measurement is actually the determining factor used by the manufacturer to select the C of G location on aircraft Today, on transport aircraft, irregularly shaped wings are used almost exclusively. In most cases a taper, crescent, swept back or swept forward wing or a combination of these types are used. For this reason it is advantageous to express the C of G range in MAC percentages rather than in inches from the datum (Figure 13). Figure 13a - MAC Position On a Taper Wing Figure 13b - MAC On A Straight Wing Figure 13 – C of G MAC Range On Aircraft Module 08B ETBN 0492 October 2023 Edition 26 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Wash-In This is a condition in which a wing has an increase in its angle of incidence near the tip (Figure 14 Lower). Wash-Out A tendency to stall at the tip section first has dangerous implications for the lateral control and stability of the aircraft. The wing can be designed so that the root stalls before the tip and the aircraft remains controllable. This is achieved by physically, geometrically twisting the wing. (Figure 14 Upper), or by aerodynamically twisting the wing (camber of the profile at the root is greater than the camber at the tip and the angle of incidence is constant across the wing span). The outboard sections (toward the wing tips) will reach the stalling angle after the inboard sections, thus allowing effective wing flight control the stall progresses. Figure 13c – MAC On A Swept Wing To determine the MAC on a typical sweptback wing as in Figure 13c, it would be measured chord wise at the root and the tip. These measurements would be used to determine the average aerofoil section. For example: the root measurement of a certain wing is 144 inches and the tip is 72 inches. The MAC would be 108 inches. The leading edge of the mean aerodynamic chord is abbreviated LEMAC. The trailing edge of the mean aerodynamic chord is abbreviated TEMAC. The centre of gravity will always lie between LEMAC and TEMAC. The centre of gravity is expressed as a percentage behind LEMAC. Figure 14 – Twisted Wing Geometric Wash-In And Wash-Out Module 08B ETBN 0492 October 2023 Edition 27 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics POSSIBLE Total Reaction (TR) The result of all the aerodynamic forces acting on the wing or aerofoil section is shown in Figure 15. Centre of Pressure (CoP) A point, usually on the chord line through which the total reaction (minimum pressure) may be considered to act. At a low Angle Of Attack (AOA) the Centre Of Pressure is set further back on the Chord line when compared to an increasing AoA when the Centre Of Pressure moves forward toward the Leading Edge of the aerofoil (Figure 16). This will be explained in more detail under the Generation of Lift And Drag section of these notes. Figure 16 - Centre of Pressure Figure 15 - Total Reaction Module 08B ETBN 0492 October 2023 Edition 28 Basic Aerodynamics – Aerodynamics Q British Airways Global Learning Academy – Basic Aerodynamics Total Drag Aerodynamic Drag Drag is the aeronautical term for the air resistance experienced by the aircraft as it moves relative to the air. Subsonic It acts in the opposite direction to the motion through the air. i.e. It opposes the motion and acts parallel to and in the same direction as, the relative airflow. Total Drag is the total resistance to the motion of the aircraft through the air. Induced Drag Supersonic Profile Drag The total Drag is the sum total of the various Drag forces (Figure 17) acting on the aircraft. These forces may be divided up to:  Subsonic Drag  Supersonic Drag Supersonic Drag will be discussed in the “High Speed Flight”, section of module 11 notes. So let us consider Subsonic Drag and its component parts. Profile Drag is made up from, Skin Friction, Form Drag and Interference Drag. Let us look at these types of Drag in more detail. Figure 17 – Types Of Drag Forming Total Drag Module 08B ETBN 0492 October 2023 Edition 29 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Profile/Parasite Drag The layer or layers in which this shearing action takes place, i.e. between the surface and that point of the flow which is travelling at the full velocity of the flow, is called the Boundary Layer (Figure 17a) When an aircraft is passed through an airflow, the air offers a resistance to the passage of the aircraft. This aerodynamic resistance is known as drag. The initial airflow on a smooth surface gives evidence of a very thin boundary layer with the flow occurring in smooth laminations of air sliding smoothly over one another. Therefore, the term for this type of flow is the laminar boundary Layer. Experiments show that this aerodynamic resistance or drag that is present whether or not the aircraft produces lift – unlike induced drag; may be divided into 3 parts: Referring to Figure 17a - As the flow continues back from the leading edge, friction forces in the boundary layer continue to dissipate the energy of the airstream, slowing it down. The laminar boundary layer increases in thickness with increased distance from the wing leading edge.  Skin friction  Form drag  Interference drag Induced drag will be discussed in more detail in the Generation Of Lift and Drag section later in these notes. Some distance back from the leading edge, the laminar flow begins an oscillary disturbance which is unstable. Skin Friction A waviness occurs in the laminar boundary layer which ultimately grows larger and more severe and destroys the smooth laminar flow. This is due to the surface roughness of the aircraft. The velocity of the air decreases as it nears the surface concerned, i.e. the ‘layers’ of air tend to shear due to the internal viscosity of each layer. Its effect is dependent upon: 1. 2. 3. Thus, a transition takes place in which the laminar boundary layer decays into a turbulent boundary layer. The same sort of transition can be noticed in the smoke from a cigarette in still air. At first, the smoke ribbon is smooth and laminar, then develops a noticeable waviness and decays into a random turbulent smoke pattern. The area over which the air flows The velocity of the flow The viscosity of the air Module 08B ETBN 0492 October 2023 Edition 30 Basic Aerodynamics – Aerodynamics British Airways Global Learning Academy – Basic Aerodynamics Figure 17a - Airflow Transitions Module 08B ETBN 0492 October 2023 Edition 31 Basic Aerodynamics – Aerodynamics 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 abo