ftc atg notes & questions

ATP Technical & General FLIGHT TRAINING COLLEGE ATP DOC 01 Revision : 1/1/2001 Version 4

ATP TECHNICAL & GENERAL

ATP Technical & General FLIGHT TRAINING COLLEGE ATP DOC 01 Revision : 1/1/2001 Version 4

INDEX

ATP TECHNICAL & GENERAL

1. Revision 01 2. Transonic Aerodynamics 33 3. Turbine Engines 75 4. Turbofans 131 5. Turboprops 133 6. Electrics 141 7. Cabin Pressurization 225

Annex A Sample Exams 281 Annex B Answers to Questions 293

This book should be used in conjunction with the CPL ATG book, also another good reference is the

book titled The Jet Engine by Rolls Royce.

Copyright 2001 Flight Training College of Africa All Rights Reserved. No part of this manual may be reproduced in any manner

whatsoever including electronic, photographic, photocopying, facsimile, or stored in a retrieval system, without the prior permission of Flight Training College of Africa.

ATP Technical & General FLIGHT TRAINING COLLEGE ATP DOC 01

Revision : 1/1/2001 Page 1 Version 4

CHAPTER 1

REVISION The Atmosphere The properties of the atmosphere are very important to those of us who operate aircraft with fixed or rotary wings, (i.e. aeroplanes or helicopters), and powered by air-breathing engines. The performance (efficiency) of the wing and engine is dependent on various parameters (such as pressure, density and temperature), of the atmosphere at the operating altitude. In general terms the atmosphere is made up of four concentric gaseous layers extending up to some 2,500,000 ft.

Troposphere extends from the sea level up to the tropopause. The tropopause is not at a constant height, but varies from 20,000 ft to about 60,000 ft depending on latitude. At higher latitudes (poles) the tropopause is lower.

Stratosphere extends from the tropopause up to about 120,000 ft. The main

characteristic of the stratosphere is constant temperature (isothermal), with the increasing altitude. The upper level of the stratosphere is the normally accepted limit of conventional air breathing engines.

Mesosphere extends up to 300,000 ft. The upper level of the mesosphere

represents the design altitude of the X-15 high-altitude rocket powered research aircraft.

Thermosphere extends out to about 400500 nm. The thermosphere is the outer

layer of the atmosphere, where temperature increases significantly. The above layers of the atmosphere are the main accepted method of describing various divisions of the gaseous envelope that surrounds the earth, however from time to time scientists define other spheres within the four listed above to specify a particular phenomenon or characteristic. The ionosphere is an important example:

Ionosphere extends from about 200,000 ft to 1,250,000 ft and defines the zone within the mesosphere/thermosphere, which contains significant ionization (presence of charged particles). The varying intensity of the ionosphere affects the passage of electromagnetic transmissions, both natural and man-made.



Characteristics of the Atmosphere Pressure The atmospheric static pressure is mainly a function of the amount of air that is pressing down under the effect of gravity on a given molecule of air at a given altitude. When considering a column of air with a footprint at sea level of one square foot, the total weight of that column is just under 1,000 kg (over 2,000 lb). Since air is a fluid it is compressible, and consequently the majority of air tends to squash itself into the lower part of the atmosphere under the effect of gravity. Therefore, the majority of air is contained within the troposphere. At sea level, the standard atmospheric pressure is 1013.25hPa, and that pressure reduces steadily as altitude is increased. The rate of reduction of pressure is less as altitude increases since the amount of compression of air (i.e. the weight of air) is greatest at sea level and decreases with altitude. The static pressure at the tropopause is about 23% of that at sea level and above the tropopause, the pressure rapidly approaches a vacuum. Temperature Temperature is really a means of measuring the amount of thermal energy present in a given object or volume of fluid. In air, temperature is an indication of the activity of individual molecules of air and as such is affected by the distance between molecules (mass per unit volume or density). At sea level, the molecules of air are very close (high density) and some of the heat present in a given molecule of air is readily transferred to another body because of the very large number of molecules in a given volume that can do the same. Thats why we feel hot when we open the door on the tarmac Nairobi!



As long as the density of air is of a reasonably high value the temperature we feel in a given parcel of air (by means of heat transfer one way or the other) is a fair indication of the temperature of individual air molecules. At high altitudes however, density decreases significantly and so the ability of a given volume of air to transfer or receive heat is very different. Notice that in the thermosphere individual molecule temperature increases dramatically but because there are not many molecules present, the ability of a given volume of air (say, that taken up by a space shuttle) to transfer that heat is minimal. It is important to understand this concept so that the temperatures shown above and below are taken in the correct context. Because of the changing density of air with altitude, it is only possible to record the molecule temperature. The only other way to graph heat against altitude would be show the amount of heat energy present in a specified volume. A graph made up for the space shuttle wouldnt be much good if you later got a command on the Starship Enterprise. The ICAO standard atmosphere defines a sea level temperature of +15C, which decreases at a standard lapse rate of 1.98C per 1,000 ft or 6.5 per 1,000 metres up to the tropopause where it is considered to be 56.5C at an altitude of 36,090 ft. This temperature is then constant (in the theoretical standard atmosphere at least!) for most of the stratosphere.

Performance tables for foreign aircraft are sometimes calculated against Fahrenheit. To convert F to C subtract 32 and multiply by 5/9. To convert C to F, multiply by 9/5 and then add 32. Density The concept of density has been discussed in the paragraphs under temperature. Density, or

mass per unit volume is normally indicated by the Greek letter rho () and has a defined value of 1.225 kg per cubic metre at sea level in the standard atmosphere. The relative density column above shows the density at a given altitude as a percentage of the sea level value and is useful in understanding the varying thickness of the air at various altitudes.



Density is affected by a number of variables, the main two being temperature and pressure. Humidity, or the presence of water vapour also affects the density of air since water vapour itself is less dense than standard air (nitrogen, oxygen, argon, carbon dioxide and a few other trace elements). Pure water vapour has a density of 0760 kg per cubic metre as against 1.225 for standard dry air. Consequently, air that contains water vapour is less dense than dry air at the same temperature. For a given mass of gas, there is a fundamental relationship between temperature, pressure and density, which can be expressed as follows: p

T = constant (for that particular gas)

where p = pressure in hPa, T = temperature absolute (K) and = density NOTE: Absolute temperature is based on a zero value of 273.15C, so that 15C = 288K Composition of the Atmosphere Dry air is a mixture of many gases, of which nitrogen and oxygen are the most abundant. It has the following composition, with traces of other gases including helium, hydrogen and ozone.

Aerodynamic Force When a body is moved through the air it experiences a resultant force as a reaction to that motion. The familiar terms of lift and drag are simply parts or components of that force and for the ease of understanding are considered to be at right angles and parallel to the direction of flight respectively. In conventional aerodynamics the changing pressure distribution around an aerofoil (wing) is the best way to understand the way in which this force is produced. The relevant theories are called the Equation of Continuity and Bernoullis Theorem.



The pattern of the airflow around an aircraft at low to moderate speeds depends on:

shape of aircraft; attitude (angle) to the undisturbed airflow; size of aircraft density of air; and viscosity of air.

The last three factors together make up Reynolds number (R) which will be discussed later in this chapter. Equation of continuity The equation of continuity states that mass of a fluid cannot be created or destroyed, and that when considering the flow of a given mass of air through varying sized openings: Air mass flow is a constant. When considering the flow of air through a venturi tube, the air mass flow will be the product of cross-sectional area (A), flow velocity (V) and density (p). This product is constant at all points along the tube:

AV = constant At low speeds (i.e. below Mach 04 where pressure changes are so small as to be considered negligible) density will not vary as a function of flow velocity. At these speeds, the equation of continuity is now:

AV = constant

Applying this relationship to the venturi, it can be seen that for a decrease in cross-section a corresponding increase in velocity will occur and vice-versa.



BERNOULLIS THEOREM Any gas (air) in steady motion possesses four types of energy, the total of which represents the amount of energy possessed by a given parcel of air. They are:

kinetic energy due to the velocity of the air; heat energy; pressure energy; and potential energy due to height above a given level.

Bernoulli proved that the sum of these energies remains constant in a steady streamline flow. The limitations of this theory are basically that it should only be used for precise measurement below 0.4 Mach where density changes due to compression of the air will not occur. If we assume that the heat energy will not change for a given flow (a reasonable assumption) and that the flow is occurring at the same height (potential energy constant), then the theorem can be simplified to:

Pressure energy + kinetic energy = constant Since kinetic energy (1/2mV) per unit volume can be expressed as 1/2pV, and this term translates into dynamic pressure for air in motion (see Measurement of Speed next topic), then the equation takes on a more practical meaning of:

Static pressure + dynamic pressure = constant The Distribution of Airflow around and Aerofoil Pressure gauges fitted to an aerofoil at differing angles to the relative airflow (angle of attack) show pressure distributions as illustrated below. The direction and magnitude of the arrows in the diagram represent the resultant effect of the pressure change as compared with ambient static pressure. Arrows pointing away from the aerofoil show a negative pressure (compared with ambient), and arrows pointing toward the aerofoil show increased pressure. Clearly, a large arrow on the top surface represents a large reduction in pressure, which in turn will produce a force upwards (lift). This concept can be expressed in a quantitive manner by

comparing the free-stream static pressure () with the pressure at any given point on the surface (p), in the form:



A negative value of this term would be represented by an arrow away from the surface, and a positive value by an arrow towards the surface. A glance above indicates that at all angles of

attack () there is greater reduction in pressure on the top surface than below. Clearly, in the examples shown, the resultant effect is for an upwards force (lift), and the size of this lifting force appears to increase with an increase in angle of attack with the leading edge of the aerofoil having significantly more effect at the higher angles. By aerodynamic convention, the term (p p0) is converted to a non-dimensional one by dividing it by another pressure, free-stream dynamic pressure (q). This results in a pressure coefficient for each of the plotted points, equal to the term: Cp = (p-p0) Q Below shows these coefficients plotted for a particular aerofoil at a given angle of attack with each point on the upper and lower surface having its own value. In effect these are local lift coefficients, and the total lift coefficient for the entire aerofoil at that angle could be calculated by summing all those shown on the diagram. Negative values are plotted above the zero point to more easily indicate the production of lift in an upward direction. Note that at the forward stagnation point the Cp is equal to +1. The stagnation point is shown in the diagrams on the previous page by the arrows pointing towards the surface.



Aerofoil Terms Although you should be thoroughly conversant with the terms used to describe the elements of an aerofoil, we have included the following by way of revision. The terminology used in the discussions on aerofoils is illustrated, and the meanings of the terms are shown below. 1. Chordline is a straight line connecting the leading edge and the trailing edge of the

aerofoil. 2. Chord is the length of the chordline. All aerofoil dimensions are measured in terms of

the chord. 3. Mean camber line is a line drawn halfway between the upper surface and the lower

surface. 4. Maximum camber is the maximum distance between the mean camber line and the

chordline. The location of maximum camber is important in determining the aerodynamic characteristics of the aerofoil.

5. Maximum thickness is the maximum distance between the upper and lower surfaces.

The location of maximum thickness is also important.



6. Leading edge radius is a measure of the sharpness of the leading edge. It may vary from zero, for a knife-edge supersonic aerofoil, to about 2% (of the chord) for rather blunt leading edge aerofoils.

Measurement of Speed The traditional method of measuring an aircrafts speed through the air is to compare total pressure (static dynamic) with static pressure, which will result in a value of only dynamic pressure. Dynamic pressure is of course a result of an aircrafts motion through the air. This is the principle of the airspeed indicator (ASI). Dynamic pressure Because air in motion possesses mass by virtue of its density, it also has energy proportional to its speed. When brought to rest, air exchanges that kinetic energy to produce pressure energy. The amount of energy that air possesses as a result of its motion is a function of its

speed and density. The kinetic energy (KE) of one cubic metre of air of density () in kg per cubic metre, moving at V metres per second is:

V joule Converted to pressure energy when brought to rest, this dynamic pressure (q) is expressed as:

q = V Although there are a number of types of speed for various purposes, dynamic pressure can be thought of as an expression for indicated airspeed in most cases.



Types of airspeed Indicated airspeed (lAS) is the value indicated on the ASI scale. Calibrated airspeed (CAS). When IAS is corrected for pressure error correction (PEC), which is a function of the position of pitot/static, sources, and for instrument error (IE), the result is CAS. PEC will vary depending on the pressure pattern around the aircraft at varying speeds and configurations and will be tabulated in the aircraft flight manual. IE is normally very small and is the result of indicating errors within the instrument itself. Thus CAS is really a true value of dynamic

pressure ( V2).

CAS = IAS PEC + IE

Equivalent airspeed (EAS). When CAS is corrected for pressure errors due to compressibility (CEC) at higher speeds the result is EAS. CEC is sometimes included in flight manual correction tables by adjusting the PEC tables at higher speeds.

EAS = CAS + CEC

or EAS = IAS + PEC + IE + CEC

True airspeed (TAS). For the same dynamic pressure at higher altitudes where

density (p) is less, V must increase. In fact, the V in 1/2pV2 is TAS. Thus the relationship between TAS and IAS (or of course CAS and EAS) is a function of the change in density. This change in density from sea level is called relative density (a), and is expressed as:

=

0

where 0 is density at sea level and p is density at the subject altitude. The TAS at a subject altitude, for a given EAS can be found as follows:

Referring back, the value of relative density at 40,000 ft is about 0.25, so at that altitude TAS equals:



Lift During the discussion on aerodynamic force the pressure pattern around an aerofoil was shown. The total effect of this pressure pattern is to provide a net upward force (lift) at low positive angles of attack for most conventional aerofoil sections. The normal way of representing the total effect is to consider the result as a single force acting through one point on the section. This point is the centre of pressure (CP). As the angle of attack is increased the size of the force increases and the CP moves forward until the stalling angle of attack is reached when the CP moves back. The range of movement of the CP is between 2030% of the chord from the leading edge for a cambered aerofoil section. For a symmetrical section there is little movement of the CP at normal angles of attack.

Lift is the component of the total aerodynamic force acting through the CP, and is perpendicular (at right angles) to the flightpath of the aircraft. There are a number of factors, which affect the size of the total aerodynamic force, and therefore also affect the amount of lift produced:

the free-stream air velocity (or the velocity of the aircraft through the air) V; the density of the air the area of the wing S; and the angle of attack degrees.

Additionally, for different wings or when circumstances change, the following factors will affect the amount of lift produced:

condition of the wing surface; wing shape; the viscosity of the air; and the local speed of sound.



However, for a given wing in a specified air mass (constant altitude, temperature etc.) the first four factors are the ones, which determine the amount of lift. When discussing aerodynamic force it was shown that the changing pressure pattern that resulted from different angles of attack could be expressed as a different coefficient of lift for each new angle of attack. Thus, when attempting to quantify the effect of the first four factors, angle of attack can be represented as a coefficient (i.e. a coefficient of lift CL). The formula for lift is:

LIFT = CLVS Factors affecting the co-efficient of lift As discussed earlier, angle of attack is one factor that will vary the pressure pattern around a wing and thus the coefficient of lift. However, there are a number of other factors, which also determine the coefficient of lift. Anything that varies CL will of course vary the total lift produced in a given situation. The factors that determine CL are:

angle of attack; shape of the wing section (camber) and wing planform; Reynolds number; and Mach number.

The boundary layer Before discussing the factors affecting CL, we need to understand that the ability of the wing to produce lift at a given point on the wing is largely determined by the condition of the thin layer of air adjacent to the surface the boundary layer. Since air is viscous, it tends to cling or stick to an object that is moving through it. In the case of a wing, the molecules of air immediately adjacent to the surface are in fact attached to that surface and as such have a relative velocity of zero. Molecules slightly further away from the wing are dragged along by the attached molecules beneath, although not to the same degree. Thus they have a measurable velocity relative to the wing. The further from the wing, the less the air is dragged along, and hence the greater is the relative velocity. Eventually a layer of air is reached that is not affected by the wing and as such has the maximum velocity relative to the wing. This of course is the free-stream air, and the relative velocity of this free stream to the wing is the actual velocity of the wing. The layers of air that extend from the surface out to the free stream make up the boundary layer. (Of interest, aerodynamicists define the boundary layer as that region of flow in which the speed is less than 99% of the free-stream flow). Initially, the boundary layer is made up of numerous layers of air that slide relative to each other. A boundary layer characterized by this structure is classified as laminar. Further back along the surface the boundary layer changes from laminar to turbulent flow. The point of change from laminar to turbulent flow is called the transition point. These features of the boundary layer is shown below:.



Angle of attack Below we can see how the CL changes as angle of attack is increased for a conventional aerofoil section with a thickness/chord ratio of about 13:100. Note that at lower angles there is a linear increase in CL for a given increase in angle, but, just before the stalling angle is reached, the rate of increase of CL reduces. This is represented by the curve leaning over before reaching the stalling angle. At the stall, there is a rapid reduction of CL but note that the wing is still producing some lift.



As the turbulent flow in the boundary Layer moves back along the top surface of the wing, it will be unable to stay attached. At this point, it is said to have separated and will no longer allow the wing to generate lift. As we see the separation point (SP) moving forward as the angle of attack is increased. This movement of the SP follows behind, and in the same direction, as the centre of pressure. In fact, the movement of the SP is linked to the movement of the CP since the boundary layer separates as a result of pressure changes aft of the CP. The CP is situated in the area of lowest pressure on the upper surface of the wing and behind the point of lowest pressure the pressure increases steadily to ambient pressure. Thus the air in the boundary layer is moving against progressively higher pressures an adverse pressure gradient (APG). It is worthy of noting that the CP is not the lowest point of pressure on the upper surface of the wing, it is that point where the resultant of all pressures around the wing act through. The CP does however fall close to the point of minimum pressure on the upper surface of the wing. As the distance over which this APG increases with forward movement of the CP, and also as the total amount of pressure change increases with lowering pressure at the CP, then so the ability of the boundary layer to stay attached decreases. In effect, the boundary layer has an uphill job to stay attached and to a large extent will finally separate when it runs out of kinetic energy (see also the later section on drag). At the stalling angle the rate of forward movement of the SP increases and not enough wing is left to provide adequate lift. This sudden decrease in CL is of course the stall. Too sudden an onset of the stall is an undesirable feature of any aircraft, so many wings have either wash-out where the angle of incidence of the wingtip is less than at the wing root, or a varying wing section across the span to make the stall more progressive. Wing shape and planform There are many ways in which a wing design may be varied to change the local or total CL. The main ones are discussed below. Leading edge radius A wing leading edge has a small radius if it appears sharp. A fat or well-rounded leading edge has a large radius. Leading edge radius affects the CL at or near the point of the stall, with the small radius producing a sharper effect on the CL curve and the large radius giving a more progressive stall and flattening of the CL, curve. Below shows the effect of leading edge radius of the CL curve.



Camber Awing has positive camber if the mean camber line lies above the chord line. Most low-speed or general-purpose aerofoil sections have some positive camber, whereas some high-speed (supersonic) sections are symmetrical and as such have no camber. Below shows the effect on CL of different sections with progressively increasing camber. Note that the symmetrical section has a CL value of zero at 0 angle of attack, but has a higher stalling angle. Wing sections with greater camber give a higher value of CL for the same angle and also produce a higher maximum value of CL at the stall. These comparisons assume that all other features of the wings are the same.



Aspect ratio Because a wing has a finite length, at some point the air from the upper and lower surfaces, each of which are at a different pressure, will meet. The net result of this mixing of air is the creation of vortices at the tips and trailing edge which impart a downwards motion to the airflow known as induced downwash. This downwash affects the net direction of the free-stream air approaching the wing and in effect reduces the effective angle of attack. The coefficient of lift is determined by the effective angle of attack. A low aspect ratio wing, having the tip vortices closer together than a high aspect ratio wing will produce a greater downwash and consequently a greater reduction in the effective angle of attack. Thus the lift of a low aspect ratio wing will increase less rapidly with increasing angle than does the lift on a high aspect ratio wing. We will return to aspect ratio and the effect of downwash when considering induced drag.



Sweepback The effect of sweepback on CL is discussed in later chapters. Surface condition Roughness of the wing surface will affect the condition of the boundary layer and thus the ability of the wing to generate lift. Experimentation over the years has shown that a roughened leading edge, up to the front 20% of the chord, will significantly reduce the maximum value of CL. that can be achieved. This makes sense because it is over this section of chord length, particularly at high angles of attack, that the boundary layer is accelerating into the area of lowest pressure and thus gaining its kinetic energy for the uphill flow into the adverse pressure gradient (APG). The rougher the surface at this stage, the less kinetic energy gained by the boundary layer compared with a smooth surface. The lower the speed gained (kinetic energy), the less is the pressure reduction that produces lift. In Chapter 2, you will see that a rough surface can in fact improve the lift of a wing by delaying separation. This can happen only after the boundary layer has changed from smooth laminar flow, has become turbulent, and is about to separate as it battles through the APG! Reynolds number (R) In 1883, a physicist named Osborne Reynolds discovered that there was a relationship between the speed of flow of the fluid and the diameter of a pipe through which the fluid was moving. At a speed, which was inversely proportional to the diameter, the fluid flow changed from streamline to turbulent. This relationship, called the Reynolds number (R), applies to the airflow over a wing, and hence affects the value of CL. An increase in R will give a greater value of CL max. This is an aerodynamic term for the value of:

R = VL

R where = density, V = TAS, L = chord length, = viscosity

Viscosity is in fact a measure of the adherence quality of the airflow against the surface, such that a high value of viscosity will slow the airflow and vice versa. A high viscosity fluid is thick (honey) and a low viscosity fluid is thin (water). For most situations density, viscosity and chord length can be considered constant and the only likely variable at a given altitude is speed (TAS). If V is increased, Reynolds number will increase giving a higher value of CL max. This is because at the higher speeds, for the same angle of attack, the boundary layer will receive more kinetic energy, which will result in delayed separation, and consequently a higher maximum value of CL. Below shows this effect.



A reduction in density at higher altitude (all other factors the same as at low altitude) will reduce R and hence reduce CL max. Again the reason is linked with the energy of the boundary layer. A lower density gives lower mass and hence lower kinetic energy since kinetic energy is a function of mass as well as speed. Mach number The effect of Mach number on lift is covered later in Chapter 2. Drag Total drag on an aircraft is the sum of all forces acting parallel to the flightpath in opposition to the forward motion of the aircraft. Although there are many components to total drag, caused by a variety of reasons, at subsonic speeds it is normal to sub-divide drag into two main heading types:

parasite drag (also known as zero lift drag); and induced drag (sometimes referred to as lift-dependent drag).

As with lift, the boundary layer has a significant role to play. It is the size and behaviour of the layer that determines the drag on aircraft at most speeds. Parasite Drag Parasite drag (sometimes referred to as zero lift drag), is made up of the following types of drag.



Surface friction drag Surface (or skin) friction drag is largely determined by the total area of the aircraft that is exposed to the air flowing past it. Clearly, an aircraft with significantly more surface area than another will experience much more dragging effect of the boundary layer air flowing past. The type of boundary layer present also has significant effect with laminar flow creating less surface friction drag than turbulent flow. This is because laminar flow exposes only one layer of air to the surface, which slides past adjacent layers of air. Turbulent flow, on the other hand, with its characteristic eddies exposes more air to the surface with greater mixing of the lower layers with the faster moving air further away from the surface. This mixing creates greater drag on the surface. The third factor affecting surface friction drag is the coefficient of viscosity of the air. The greater the viscosity, the greater the dragging effect of the air. For a given size of aircraft, surface friction drag can really only be reduced by controlling the type of boundary layer present. In the previous section on lift, we saw how the adverse pressure gradient eventually causes the boundary layer to run out of energy and separate. Any area of wing without an attached boundary layer does not produce lift. For minimum surface friction drag, the transition from laminar to turbulent must be delayed as long as possible. The main factors affecting the transition are:

surface condition a rough surface, particularly in the first 20% of chord length will accelerate transition;

adverse pressure gradient (APG) once past the point of minimum pressure, the boundary layer has to negotiate the APG. Experience has shown that it is very difficult to maintain laminar flow past this point, which is normally also the point of maximum thickness of the wing.

Form drag Form drag is also known as pressure drag. When the boundary layer finally separates, or in areas where surface features prevent it from forming (drain holes etc.), the separated flow still impacts against the aircraft surface causing drag. This is form drag. A given area subjected to separated flow will give more drag (form drag) than the same area subjected to the skin friction drag of a turbulent boundary layer. Consequently, efforts are made to delay separation of the boundary layer in an attempt to reduce form drag. Of interest when attempting to retain the boundary layer, the favoured type of flow within the layer is turbulent in preference to laminar flow. This is due to the higher amount of kinetic energy contained in a turbulent boundary layer as a result of greater molecular activity. With greater kinetic energy, the boundary layer can resist the effects of the adverse pressure gradient for longer, thus reducing drag and delaying separation. Another major benefit of delaying separation of the boundary layer is the greater lift achieved. Since the separation point moves forward with increase in angle of attack, the effect of delayed separation is to increase CL at the higher angles and most importantly to increase CL max. Below shows the relationship between the boundary layer and separated flow.



Interference drag It has been found that the total parasite drag of an aeroplane is greater than the sum of surface friction and form drag. The additional drag is caused by mixing, or interference, of the boundary layer airflow at the junction of the wings, fuselage, nacelles etc. Interference drag is minimized by the provision of fairings. Interference drag is not directly associated with the production of lift, and as such is a component of the total parasite drag. Summary of parasite drag Parasite drag increases with airspeed, and at very high airspeeds nearly all the total drag (i.e. parasite + induced) is caused by it. The predominance of parasite drag at high speeds shows the need for aerodynamic cleanness to obtain maximum performance. Parasite drag is proportional to the square of EAS, thus doubling the speed will quadruple the amount of parasite drag.



Induced Drag Induced drag is a direct result of the aircraft producing lift. If the wing is flown at an angle of attack such that it produces no net force perpendicular to the direction of flight, then it is not producing any induced drag. It will of course be producing parasite drag as we have already seen. Induced drag is the major component that some aerodynamicists term lift-dependent drag. The other components of lift-dependent drag are additional increments of surface friction drag, form drag and interference drag caused by the changing pressure pattern around the aircraft as a result of changes in lift. But regardless of how they are caused, they are still form drag etc.

As you can see above shows the difference in pressure between the upper and lower surfaces of the wing as viewed from behind. This difference in pressure causes air to spill around the tip, deflecting the upper surface flow towards the fuselage and the lower surface flow toward the tips. As the two flows meet at the trailing edge a series of vortices is formed, which accumulate at the tip to form a large wingtip vortex. When the pressure difference between the upper and lower surfaces is increased, such as when the wing is producing more lift, then the size of the vortex will increase also.



Having left the trailing edge of the wing, the net effect of the vortex is to impart a downward flow to the air, known as induced downwash. Energy is clearly needed to impart this change of direction to the air, and is taken from the energy gained as a result of the wing producing lift. This cost of energy lost is in the form of additional drag induced drag.

Because the lift produced is in reality a result of flow, which is deflected down due to the induced downwash, the effective lift at right angles to the free stream flow must be increased slightly. This can only be achieved by increasing the size of the total force, which while it increases lift, will also increase drag as the other component induced drag. The next diagram shows the two components of the total aerodynamic force in relation to desired direction of flight (horizontal).

Of course, in practice the wing does not go through this step-by-step approach to end up with induced drag. This is merely a way of explaining the phenomenon. Whenever the wing is producing lift it will be creating a vortex, deflecting the air down and producing induced drag. Under the right conditions, the vortices are one of the few ways that we can see aerodynamics and marvel at the physics of it all. On take-off, all aircraft produce their first vortices of the flight as they increase angle of attack at rotation in an effort to produce the necessary lift to counter weight at such a low speed. If the air is moist enough, the pressure drop in the vortex may be enough to cause condensation. The same thing can be seen (again, providing the air is moist enough) when an F-18 pulls g in a low-level turn at an air show. All it is doing is increasing the angle of attack and in so doing increasing the pressure differential between the wing surfaces that then form the vortices.



There are a number of variables that affect the amount of induced drag. These are listed below. The first two factors are clearly design considerations. For a given aircraft then, the main factors affecting the amount of induced drag are the amount of lift being produced and the speed that it is flying. Factors affecting induced drag:

wing shape, particularly planform aspect ratio lift, and of course weight speed

Planform The ideal planform for minimum drag is an elliptical one, however there are considerable manufacturing problems in using this shape and consequently very few aircraft have been produced with this shape. Also, aircraft that fly at higher subsonic speeds have certain design requirements that are more important than absolute minimum induced drag. As with many things, a compromise is needed. Out of interest, but do not commit it to memory, the equation for coefficient of induced drag for an elliptical planform is:

The elliptical planform is the most efficient because it provides the same local coefficient of lift at each point along the span. Thus the ratio of local coefficient of lift to wing average coefficient of lift at any point is always 1. With rectangular wings, significant efficiency is lost at the tips due to the vortex problem. Thus the ratio of local lift coefficient to wing average is very low at the tips. Although such wings may have a root ratio slightly better than 1, the inefficiency of the wingtips (due to the presence of large vortices) significantly reduces overall wing efficiency compared with the elliptical wing. In an attempt to improve tip efficiency, designers often use taper, or a different wing section towards the tips. The equation for coefficient of induced drag for any other shape wing (other than elliptical) is the same as above but multiplied by a constant (k) which is different for each wing shape. Aspect ratio Aspect ratio can be found by dividing the wing span by the mean chord length, or more commonly by the expression:

AR = span or span x span = span chord chord x span area



Thus aspect ratio is more an expression for wing shape rather than wing size. Thus long thin wings will have a high aspect ratio and short stubby wings a low aspect ratio. The vortices shed along the length of the wing tend to roll up into a large wingtip vortex at a distance of approximately 5 to 20 chord lengths behind the wing. For a long thin ( high aspect ratio) wing, the tip vortex is thus much smaller than for a short stubby ( low aspect ratio) wing. It therefore imparts less downwash onto the wing and has less induced drag If two wings of the same area but different aspect ratio are producing the same total lift (to counter the same weight), then the low aspect ratio wing, with the greater downwash must increase its total angle of attack to the freestream flow to achieve the same lift. This is due to the reduction in effective angle of attack caused by greater downwash. Remember that a wing of low aspect ratio will always need to be flown at a higher angle of attack to the free-stream flow to achieve the same lift as a wing of high aspect ratio (for a given area).

Effect of lift and weight The induced downwash angle, and consequently the amount of induced drag, depends on the pressure difference between the upper and lower surfaces of the wing. This difference in pressure is of course the lift per unit area provided by the wing. Thus, at a given speed, an increase in lift (which at a given speed would need to be provided by an increase in CL) will increase induced drag. This increase in CL. may be needed by an increase in weight or in a manoeuvre. Effect of speed As speed changes in level flight, a wing must produce the same lift at each speed for a given weight. To do this, it must be flown at a varying angle of attack to maintain the required value of CL. An increase in angle of attack inclines the total aerodynamic force more rearwards, thus increasing the induced drag component.



To summarize, the slower we fly the greater the angle of attack required and hence the greater the downwash angle. This in turn increases the value of induced drag. Conversely, the faster we fly, the less the amount of induced drag. You will note that this is the opposite to parasite drag, where the faster we flew, the greater the drag. This combination will be discussed in more detail shortly.

Summary of induced drag - its causes and effects

Wingtip vortices form as higher-pressure air below the wing spills into the area of lower pressure above the wing.

Downwash is caused by the wingtip vortices. This downwash deflects the original remote airflow down by the amount called the

downwash angle. The average direction of the remote airflow is changed and the angle of attack is

reduced. The effective lift vector is then tilted backwards by the induced angle of attack, which

is equal to half the downwash angle; this maintains the lift at right angles to the relative airflow at the CP.

The horizontal rearward component of the tilted lift vector is the induced drag. The higher the angle of attack, the greater the downwash angle, and hence the

greater the induced drag.



Total Drag The graph below shows the variation of total drag with EAS, which is made up of the two main components:

parasite drag (which varies as the square of EAS); and induced drag (which varies as the inverse of the square of EAS).

The result is a graph which has a minimum point known as minimum drag speed (Vmd) which for a given weight is also the speed for maximum value of lift to drag (L/D) and as such is the most efficient speed. A total drag curve can only be shown for a certain set of conditions, if any one of the conditions changes, it will alter the shape of the curve, and consequently the minimum point. Effect of weight Looking below the drag curve for two weights. Note that an increase in weight moves the curve up and to the right. This gives a higher total drag at the higher weight for any speed and also an increase in minimum drag speed.



Configuration Selection of landing gear and speed brakes in any aircraft will increase parasite drag without an increase in induced drag. Thus only one of the two component curves is affected. An increase in parasite drag for each speed will move the parasite drag curve up which will move the total drag curve up and to the left. The effect is to give a lower Vmd with the configuration change as shown below. Effect of aerofoil shape The in-flight efficiencies that are demanded of modern airliners dictate the need for minimum drag in the cruise configuration. Apart from attempts to reduce induced drag as much as possible by employing optimum aspect ratio etc., designers use aerofoil sections that give the lowest parasite drag at the cruise angle of attack. This is normally done by attempts to retain a laminar boundary layer for as long as possible and so reduce surface friction drag. All aerofoils will have a range of angles of attack where the transition point has not moved significantly forward and thus the percentage of chord covered by a laminar flow is greatest. These are the angles of attack (normally fairly low) where coefficient of drag does not change significantly for a given change in angle of attack (and therefore change in CL). The result is a characteristic of the Cn curve called the laminar bucket. By employing an aerofoil that has the laminar bucket at angles used for cruise, a designer can achieve great fuel savings. This normally means a cambered section and is the basis of the supercritical aerofoil concept discussed later in the course.



As you can see, the change in laminar bucket position (CL or angle of attack) for two sections with the same thickness/chord ratio. Effect of compressibility (Mach number) Up to now, we have been considering relatively low speeds. Effects of high speed on drag will be covered in the next chapter. Airframe Efficiency As with any machine, the measure of efficiency of an aircraft is determined by a comparison of output to input. Since the output is lift, to overcome weight and thus be able to fly, and the input is thrust to counter drag, then efficiency can be expressed as:

Lift or more easily Lift Thrust Drag

Both lift and drag are components of the same total aerodynamic force, and consequently the efficiency of an aerofoil (its lift/drag ratio) depends on the angle of the total aerodynamic reaction to the free-stream flow. This curve can be compared with the angle of attack of CLmax. Note that the angle of attack for maximum lift/drag is significantly lower than that for maximum lift. Although the wing is capable of producing high values of CL. at high angles of attack, it will also suffer higher induced drag as previously discussed. Thus a compromise angle needs to be flown.



Note also that the graph shown plots values of CL., CD and CL/CD, and that a specific value of the coefficient or coefficient ratio occurs at one specific angle of attack. Consequently, if we are able to determine what value of a specific coefficient we need to satisfy a particular requirement (range, glide angle etc.), we can easily see what angle of attack should be flown to achieve that objective.



CHAPTER 2

TRANSONIC FLIGHT Compressibility Theory Aircraft that are flying at speeds well below the speed of sound send out pressure waves (by disturbing the air) in all directions. This creates the sound that we hear as an aircraft approaches and also gives warning to the air ahead. These waves are in fact the result of one molecule of air moving and striking an adjacent molecule which strikes the next one and so on. The air does not flow as the waves move away from the aircraft, but rather the molecules of air vibrate about a mean position. The amount of vibration depends on the amount of disturbance or pressure the air is subjected to in the first place. Because air is compressible, the change in pressure that goes with the disturbance also creates a change in density and temperature. Consequently, the changing characteristics of the air will vary the speed of wave movement (speed of sound) by altering the ability of one part of air to pass the message of the disturbance on to the next parcel. This concept, that the speed of sound varies depending on the condition of the air, is a very important one to understand and memorize. Wave Propagation A stationary source of pressure waves gives off a pattern much like the radiating ripples from a stone thrown in a pond. If the pressure source is moving at subsonic speed, the waves ahead of the source (an aircraft) tend to bunch up. Although they bunch up ahead of the source, they can never catch up with one another since they all emanate from the same source travelling at a constant speed. Notice that the distance between the waves ahead of the aircraft is the same. This distance, although constant will get progressively smaller as the speed of the aircraft approaches the speed of sound. When the aircraft is travelling at the speed of sound all the pressure waves bunch up together to form a Mach wave.

Although an aircraft could be travelling at any speed in relation to the speed of sound, the speed of sound will vary from one air mass to another. Thus the tendency of the pressure waves to bunch up will not always be to the same amount for a given aircraft speed. It all depends on what the speed of sound is for that air mass, and more importantly, it depends on the speed of the aircraft in relation to the speed of sound. Before we go any further then, we must know how the speed of sound is determined, and how it can vary.



The speed of sound in a given mass of air is the speed at which sound waves move from one part of the air to another. The ability of the waves to move is dependent on the ability of the message to be passed between air molecules. This in turn will be determined by how much the air is compressed and how much energy (or speed) the individual molecules have. Molecular speed in turn is determined by the compression of the air and the air temperature. If the air temperature is increased, the added increase in molecular speed as the air is compressed is sufficient to cause an increase in the rate of expansion, and therefore an increase in the speed of propagation of the pressure wave. Thus, the speed of sound will have been increased by an increase in temperature. Mathematically, the relationship between speed of sound and temperature has been shown to be the only one that matters, since variation in pressure and density (both affected by temperature) have been found to virtually cancel each other. If a is the speed of sound, then in terms of pressure and density:

is the ratio of specific heats R is the gas constant T is absolute temperature

Since both the ratio of specific heats (specific heat at constant pressure to specific heat at constant volume) and the gas constant are all fixed, the relationship can be rewritten to:

Clearly then, there is a direct relationship between the speed of sound and temperature. In practical aviation, we do not really need to calculate the speed of sound, but we must know how the relationship between our speed and that of sound will vary. This relationship makes it clear that flying into a warmer air mass will increase the speed of sound and vice versa. If needed, the formula allows us to calculate the speed of sound in knots. For such exercises remember that T is in absolute degrees and absolute zero occurs at 273C. Thus +15C converts into 273 + 15 = 288 absolute for use in the formula. As discussed earlier, the speed of sound is the speed at which pressure waves will radiate out from an aircraft moving through the air, but that speed will vary as a function of temperature. This means that as we climb in the atmosphere, the only factor that will vary the speed of sound is the temperature, despite the changes in pressure and density that also occur. The table below shows the value of a speed of sound for various altitudes in the standard atmosphere.



Mach Number The need to devise some other method of measuring an aircrafts speed (other than TAS) as it approaches the speed of sound is due to the significant changes in airflow characteristics at these speeds, and the consequent effect on aircraft handling and performance. A knowledge of aircraft speed through the air (TAS) in relation to the speed of sound is necessary. Although aircraft have been traveling at these speeds only since the late 1940s, the system of speed measurement had been devised last century by the Austrian physicist, Ernst Mach. From his name has come the term Mach number, which is the ratio of:

speed of the aircraft (TAS) local speed of sound (a)

Mach number is designated by the letter M and since it represents a ratio of one speed to another, it has no units. The mathematics of the ratio clearly show that if an aircraft is travelling at the same speed as the speed of sound, then the ratio will cancel down to 1, i.e. Mach 1. An aircraft travelling at half the speed of sound has a Mach number of 0,5 and one travelling at twice the speed of sound has a Mach number of 2. For Mach numbers less than 1 it is usual to forget about the zero and express it as say Mach point seven, for Mach .7. Mach numbers are normally written with the M after the figures, so that this would be written as .7M. For clarity, throughout this text Mach numbers will be written as follows, 0.7M and 1.2M. Although we may initially think that an aircraft has one Mach number at a given time that is the ratio of its TAS at that time to the local speed of sound, it is important to remember that the speed of the airflow around an aircraft is not the same at every point. The discussion of Bernoullis theorem in Chapter 1 showed that as pressure changed around an aerofoil, so too did the speed of flow. For all the different speeds around an aircraft (different local true airspeeds if you like), it follows that there are different local Mach numbers. Consequently, there is a need to define certain types of Mach number.



Free-stream Mach number This is the Mach number at a point in the flow at sufficient distance to be unaffected by the aircraft. Free-stream Mach number is designated by Mfs and is found by:

Mfs = TAS local speed of sound Local Mach number For a given Mfs, the flow around the aircraft is accelerated at some places and decelerated at others. Also, because the temperature changes around the aircraft, so too will the local speed of sound. Thus, there will be a range of local Mach numbers for a given Mfs. Critical Mach number Mcrit As the Mfs of an aircraft increases, there will come a stage when the highest local Mach number reaches unity. Since the flow may be accelerated over a wing with an increase in angle of attack, Mcrit will be lower in that situation. Mcrit marks the lower end of the band of Mach numbers (Mfs) where a local Mach number may be supersonic, thus marking the boundary between subsonic and transonic speeds. Detachment Mach number Mdet Mdet is that Mfs where the bow shockwave (discussed later) attaches to the leading edge and above which there is only a small movement of the bow shockwave for an increase in speed. Above Mdet all values of local Mach number are supersonic except in the lowest layers of the boundary layer. Critical drag rise Mach number Mcdr Mcdr is that Mfs above which, due to the formation of shockwaves, there is a significant rise in drag. It is also referred to as the Drag Divergence Mach Number, Mdd Speed Divisions Because of the changing response of air at different speeds, it is important to define the various divisions of speed so that we can anticipate the type of reaction to a particular speed. The picture below shows diagrammatically the various speed divisions listed below.



Subsonic Subsonic flow starts at zero and has its upper limit at Mcrit. Remember that Mcrit is that Mfs at which the highest local Mach number reaches unity. So the subsonic band contains no flow whatsoever that is sonic (equal to the speed of sound) or supersonic (faster than the speed of sound). Transonic Transonic flow begins at Mcrit (that is the Mfs that is Mcrit) and extends up to Mdet. This is the stage at which the bow shockwave attaches to the leading edge and above which all local Mach numbers are supersonic. Therefore the transonic band is where there is a mixture of both subsonic and supersonic flow around the aircraft. Supersonic When all the local Mach numbers surrounding an aerofoil are supersonic (i.e. greater than Mach 1), the Mfs is considered to be supersonic. In general terms the subsonic band extends up to about 0.75M and the transonic band from 0.75M to about 1.2M. The Formation of Shockwaves Previously we looked at the accumulation of pressure waves ahead of a moving source (such as an aircraft) that is moving at subsonic speeds. As previously noted, the pressure waves are equally spaced with the distance between waves determined by the speed of the aircraft. The distance moved by the waves in a given time at subsonic speeds is greater than the distance moved by the aircraft because the speed of sound is greater than the aircrafts TAS.



Above, the pattern of pressure waves is shown when V is equal to the speed of sound -Mach 1. In this case a different pattern is shown with all the waves forming a single line ahead of the moving source. This line, the Mach wave, is formed and represents the limit of influence of the source. No pressure waves emanating from the source can travel ahead of the Mach wave because the speed of sound is not faster than the speed of the source. In other words, V is equal to a. Below shows the pressure pattern from a supersonic source, where the pressure pattern forms an oblique Mach wave or limit of influence of the source. As can be seen from the diagram, the wave pattern is three-dimensional and the Mach wave, or boundary, becomes a surface called a Mach cone.



The Bow shockwave In practical terms, the formation of shockwaves around an aircraft is in fact more complex than the simple pressure patterns shown, because there are many variables that alter the speed of flow and also the speed of sound at different points around an aerofoil. Of particular importance is the compression of air immediately in front of the aircraft, which raises the air temperature. The effect of this increase in temperature is of course to increase the local speed of sound in this area which results in the propagation of waves ahead of the aircraft at a rate faster than the normal rate (speed of sound). This increased local speed of sound extends ahead of the aircraft to a point where temperature is restored to ambient. As the aircraft speed approaches Mach 1 the waves ahead of the object tend to bunch up as previously discussed but they will do this well ahead of the object to form the bow wave. As the aircraft speed exceeds Mach 1 the increased speed of wave propagation ahead of the aircraft is offset by the increased speed of the aircraft, now travelling at a Mfs faster than Mach 1. So although the forward waves are projected out faster than a Mfs equal to Mach 1, due to the increased speed of sound, the aircraft partly catches up. The effect of all this is to bring the bow wave closer to the aircraft until the aircraft is travelling at such a speed that the bow wave attaches to the leading edge (remember, this is Mdet). The ability of the bow wave to attach is determined by the flow ahead of the aircraft, which in turn is determined by the shape of the aircraft or wing. The blunter the leading edge, the greater the compression and temperature rise, and consequently the greater the increase in local speed of sound. The greater the increase in the local speed of sound, the more difficult it is for the bow wave to attach. In reality, some shapes will not allow the bow wave to attach and it will stand off slightly at all speeds. To encourage bow wave attachment (which is desirable at higher Mach numbers to achieve stable flow), a sharp leading edge radius is used which reduces the compression effect ahead of the wing at transonic speeds. Once attached (or as near as it is going to get), an increase in Mach number into the supersonic band causes a further rearward slope of the bow wave. Below shows a bow wave not attached at a Mach number in the transonic band (i.e. less than Mdet).



Wing shockwaves At the same time that the bow wave is forming as the aircraft approaches Mach 1, shockwaves are forming on the wing itself. As the speed of the flow over the wing is accelerated to a speed faster than Mfs, wing shockwaves will of course form well before a Mfs of 1. The formation of wing shockwaves above O85M is quite common, although this can be delayed by using a thinner wing section which will of course reduce the amount of flow acceleration. Conversely, the use of thick, highly cambered sections will encourage the formation of shockwaves at lower Mfs values. With all wings, wing shockwaves can be induced to form at even lower values of Mfs if the flow is accelerated by an increase in angle of attack such as when manoeuvring. Another different feature of the wing shockwave is that, at its base, is the boundary layer. Part of the boundary layer must of course be subsonic. The presence of the boundary layer enables the effect of the shockwave to be transmitted forward at its base, which in effect thickens both the boundary layer and shockwave. Pressure disturbances from behind the shockwave leak forward in the boundary layer under the shockwave (remember that this area will be subsonic). The thickening of the boundary layer forms an oblique shockwave, which leans back and merges with the main shockwave. This shape at the base of a wing shockwave is sometimes called a lambda foot since it resembles the Greek letter lambda. Below shows a diagram of both upper and lower wing shockwaves at a representative subsonic Mach number (about 0.85M Mfs for that wing). The Mfs at which shockwaves form on a given aerofoil will vary from one to another depending on the shape of the aerofoil, particularly the thickness/chord ratio.

The Nature of Supersonic Flow In Chapter 1 the equation of continuity was used to demonstrate the pressure changes that accompany a velocity change through a venturi. In that situation where the flow is subsonic, pressure reduces as speed increases. For a similar flow through a venturi at supersonic speed, considerable changes to pressure occur because of the problem of pressure wave patterns above the speed of sound. The result is that supersonic flow through a convergent duct results in an increase in pressure with a consequent decrease in velocity. However, the reverse is true for a divergent duct (where the cross-sectional area is increased).



For ducted flow the following characteristics apply

For unducted flow the following characteristics apply

Supersonic flow always decelerates through a shockwave

Supersonic flow always decelerates to subsonic flow through a normal (90 to the flow) shockwave unless the flow is subjected to very bizarre thermodynamic conditions.

If supersonic flow is forced to turn it forms a shockwave.

An obstacle in supersonic flow will cause a shockwave (because the flow is turned)

The strength of the shock wave is proportional to the angle of turning or the size of the obstruction

If supersonic flow is turned by more than 45,58 a detached shockwave will form

Compressive corners decelerate supersonic flow

Expansive corners accelerate supersonic flow.

dA0 dV0

Subsonic flow Supersonic flow

dV0

dP>0 dP



Although the flow through a venturi can be used to understand the changes that take place, it is necessary to examine how supersonic flow negotiates sharp corners on a real wing. Expansive corners An expansive corner is one which allows the flow to expand and thus accelerate, being convex. If such a corner is considered to be a succession of infinitely small angular changes, then a single corner can be broken down into a series of small steps as shown in the top the diagram below. Consider the two streamlines in the supersonic flow as they reach the corner. The one adjacent to the surface will sense the change as soon as it gets to the corner, the flow will accelerate and, associated with the decrease in density, the pressure will decrease. This pressure disturbance will be felt along a Mach line appropriate to the flow. The streamline further away from the surface will be unaware of the corner until it reaches the Mach line originating at the corner. This Mach line is a boundary between relatively high and low pressure, therefore a pressure gradient is felt across it such that the streamline is accelerated slightly and turned through an angle equal to the change in surface angle. It now continues parallel to the new surface at a higher Mach number since V has increased and the speed of sound is less due to a decrease in temperature. The same process will be repeated at each corner. This process will take place through an infinite number of Mach lines, and, because the lines fan out, the expansion and acceleration is smooth. The region within which the expansion takes place is limited by the Mach lines appropriate to the speed of the flow ahead and behind the corner. This is called the Prandtl-Meyer expansion and is illustrated in the lower half of the diagram. The decrease in pressure ( a favourable pressure gradient) round an expansive corner in supersonic flow allows an attached boundary layer to be maintained. This is exactly the opposite to what happens in a subsonic flow where an adverse pressure gradient would cause the boundary layer to thicken and break away. Consequently, there is no objection to such corners on essentially supersonic aircraft.



Compressive corners A compressive corner causes supersonic flow to converge, creating a shockwave whose formation can be visualized by treating the corner as a source of pressure waves creating a bow wave. The shockwave exhibits all the characteristics of a bow wave. The change of flow through a shockwave A shockwave is a very narrow region within which the air is in a very high state of compression. Supersonic flow encountering a shockwave undergoes extreme compression, which results in an increase in temperature, density and pressure; but a decrease in velocity and Mach number. Flow behind a normal shockwave is always subsonic, however shockwaves that are inclined back will support supersonic flow behind them, providing the initial flow is fast enough and the shockwave is inclined sufficiently. Transonic Changes in Lift Changes in the coefficient of lift with increasing subsonic speed are easy to predict for an aerofoil at a constant angle of attack. This is also the case for consistently supersonic flow. At the constant angle of attack, the changes in coefficient are due to the increasing velocity of the air. In the transonic region however, the presence of shockwaves, either forming or moving, creates significant changes in the flow, which vary the coefficient of lift. In extreme cases, particularly where the aerofoil is one not designed for high speed, these changes can lead to stability and control problems.

As you can see above the variation in coefficient of lift for a subsonic aerofoil with a thickness/chord ratio of about 12%. The changes in lift, discussed below, are so large that this section would not be suitable for transonic or supersonic flight. The following changes to coefficient of lift occur at the points marked on the diagram:



Point A: coefficient of lift has increased approaching Mcrit due to the

increase in velocity over the top surface of the wing (and therefore an increase in Reynolds number which changes CL)

Point B: lift has again increased due to the continued acceleration of the

top flow up to supersonic values ahead of the top shockwave (Mfs about 0.81M).

Point C: The bottom shockwave has formed. The top shockwave is stronger

and flow behind the top shock is unstable and causes boundary layer separation. This reduces lift, which is further affected by the unstable flow behind the bottom shock (Mfs 0.89M).

Point D: The top shock has moved to the rear of the wing which restores most of the wing to stable flow (all supersonic) and thus gives more lift to the wing. Because there is less unstable flow behind the top shock there is less effect of flow mixing with the flow behind the lower shock (Mfs 0.98M).

Point E: The bow shockwave has almost attached to the leading edge. However the flow behind the bow shock (which is the flow over the wing producing lift) has had its energy reduced as a result of being flow behind a shockwave. Thus although the flow over the wing is stable, it produces less lift. Notice that the end result of accelerating to supersonic flow is that the coefficient of lift is less than originally available at subsonic speed for this type of aerofoil, which is mainly designed for flight at subsonic speeds. As will be seen later, aerofoils designed for transonic flight normally have a lower thickness/chord ratio. Transonic Effects of Drag The effects of shockwaves in the transonic region produce increases in drag called Mach or wave drag. Mach drag is made up of two separate types of drag from separate sources namely - energy drag - boundary layer separation drag Energy drag As air flows through a shockwave it experiences a rise in temperature at the expense of the energy of the flow. This energy lost is drag on the airframe. The more oblique the shockwave, the less energy they absorb to provide the temperature increase. Boundary layer separation As shockwaves move, they create varying amounts of separated flow, which creates drag. The increase in this type of drag is greatest at about Mach 1, but as the top shock moves to the trailing edge, reducing the amount of separated flow, drag reduces.



These changes in drag are shown above as increments on the normal drag rise (parasite drag) for an increase in speed, except this time the speed measurement is of course Mach number. Below shows the variation in coefficient of drag for an aerofoil operating at a constant angle of attack. Aircraft Control at High Speed Longitudinal Control As an aircraft approaches its Merit it experiences a nose-down trim change caused by two factors: 1. The rearward movement of the centre of pressure due to the distribution of lift as the

accelerated flow forms the top shockwave. 2. The reduced download that is normally on the tailplane. The download is reduced due

to changing downwash from the wing caused by flow separation aft of the top shockwave. This however depends heavily on the configuration of the aircraft.

If uncorrected, the effect of this nose-down pitching moment is to cause the aircraft to accelerate more, thus increasing the Mach number and so increasing the nose-down effect. Alternatively, if the pilot corrects by applying up elevator, this may again accelerate flow over the wing due to increased angle of attack.



The nature of the nose-down trim change places a very real limiting Mach number to which an aircraft may be flown and is normally the basis for establishing an aircrafts maximum operating Mach number (Mmo). This is the red line Mach number on the combined airspeed/Mach indicator. In some aircraft, where cruise at higher Mach numbers may be desired due to favourable drag figures, Mmo may be increased by installing a Mach trimmer which is simply a Mach sensitive device which automatically deflects the tail plane or elevator slightly more than is needed to counter the nose-down trim. The reason for deflecting slightly more than is needed is so that positive longitudinal stability is maintained and so that the aircraft must still be trimmed nose-down as speed increases. Mmo for an aircraft also takes into account the Mach number at which shockwave intensity will cause enough separated flow to reduce elevator effectiveness, or cause control buzz, or both. This control buzz will become control buffet if the aircraft is accelerated further and is formally termed high-speed buffet. Eventually, the buffet leads to loss of elevator control. In the early days of high subsonic flight many aircraft experienced this high-speed buffet by inadvertently accelerating beyond Mmo in turbulence and then wrongly mistaking the buffet for low speed pre-stall buffet. Similarly, aircraft in high speed descents with speed brakes deployed (which produce buffet) have flown fast enough to get high speed buffet, but it has not been identified due to the masking effect of the speed brakes. The problem of longitudinal control caused by the formation of shockwaves is amply described in the following extract of a report of the team that first exceeded Mach 1 in the Bell X-1. Early in October Yeager reached Mach 0.94 and had a nasty surprise he pulled back on the control column and nothing happened. The plane continued to fly as if he had not touched the controls. Wisely he shut down the rocket engine. As the plane decelerated, control effectiveness returned to normal. Williams engineers later determined that a shockwave had formed on the horizontal stabilizer. As the X-1 increased its speed, the shock had moved rearward, standing along the elevator hinge line at Mach 0.94, negating its effectiveness. If an aircraft is trimmed for a given cruise speed and accelerated, a progressive push force on the elevator is required to maintain an initial pitch attitude, assuming the elevator trim is not used. However, as already described, at higher Mach numbers, the nose-down trim change commences and increases with Mach number. Consequently, at higher Mach numbers the push force turns into a pull force to maintain the set attitude. Below shows the change in stick force that is required on a typical subsonic wing/tailplane combination as the aircraft is accelerated. To ease this confusing control problem, aircraft that are designed to operate at high subsonic cruise speeds but which have wing sections not fully optimized for transonic flight are fitted with a Mach trimmer as mentioned previously. Basically the Mach trimmer provides an input in the other direction of sufficient magnitude to still give a progressive increase in push force as speed (Mach number) is increased. The second half of the diagram shows this compromise.



Lateral Control Disturbances in the rolling plane are often experienced with aerofoil sections not designed for transonic flight by unequal formation of shockwaves on either wing. Apart from the varying amount of total lift available on each wing (which would produce lateral control problems), the formation of shockwaves can result in loss of aileron effectiveness due to flow separation ahead of the aileron surface. To overcome the problem of reduced aileron effectiveness at higher speeds, many aircraft are fitted with outboard spoilers, which operate through the aileron control at high speeds. By deploying a spoiler device on the down wing, drag is increased which induces a roll in the required direction. The use of spoilers at high speed is also a result of the problem experienced with early high-speed designs where the use of aileron increased the lift at the rear of the upgoing wing, which led to the wing twisting about its lateral axis. The result of this was to decrease the angle of attack of the upgoing wing which instead of increasing wing lift, and sustaining the demanded roll, in fact reduced the lift on the upgoing wing and reversed roll direction. In early high-speed flight this was known as aileron reversal. Directional Control As with other controls, the rudder will normally have reduced effectiveness at high subsonic Mach numbers due to the formation of shockwaves ahead of the control hinge line. For modern high-speed aircraft that are required to manoeuvre in the transonic region, an all moving slab fin is sometimes employed. However, for transport aircraft designed for high subsonic cruise, a conventional fin and rudder combination is normally used so that low speed directional stability requirements are also satisfied.



The use of rudder at high subsonic Mach number can result in yaw in the opposite direction. Application of rudder will cause one wing to travel faster than the other, which will then drive that wing further into higher speed flow with resulting increase in drag. This increase in drag will of course result in a yaw in the opposite direction to that demanded. As a result of this sensitivity to yaw control at high Mach number, all aircraft designed for high speed/altitude flight employ a yaw damper, which rigidly monitors directional control requirements and inputs very small amounts of rudder at the earliest possible stage when required. Aircraft Design for High-Speed Flight Modern transport aircraft have the need to operate at the highest possible subsonic speeds and also achieve the best possible operating economics. This of course means the lowest drag possible for the desired cruise speed so that fuel burn is minimal. In short, design objectives for the past 20 years have focussed on getting an aircraft to cruise at the highest possible subsonic Mach number before the effects of Mcdr are felt. The following design features have been found essential to satisfy these requirements. Supercritical Wing Section The purpose of the supercritical wing is mainly to increase Mcdr by delaying the formation of shockwaves until a higher Mfs. In doing this there is also the objective of not reducing the total lift achievable by a wing of given area. In other words it is just the wing section (camber etc) that is changed. The design difference with a supercritical wing is to flatten the top surface of the wing, thus reducing the amount of top surface deceleration and consequently delaying the deceleration of the flow and the formation of shockwaves. The shockwaves form more toward the trailing edge of the wing and consequently reduces the effect of wave drag. The end result is an increase in Mcdr for the wing, which allows a higher cruise speed for no significant increase in drag. Clearly, the flattened top surface will reduce the amount of lift available from the wing at a given speed, so to partly compensate for this a reflex camer is employed at the rear undersurface. This design feature provides lift at the rear of the aerofoil and assists in stabilizing the flow at the trailing edge of the wing. This in turn reduces drag that would normally result from separated flow. Supercritical wing sections allow increased cruising speed but also permit greater range for a given airframe/engine mix by allowing reduced fuel flow in the cruise.

Wing Thickness/Chord Ratio



One of the greatest problems in attempting to cruise at high Mach number is the drag associated with flow separation behind a strong shockwave. If the onset of shockwave formation can be delayed, or if the shockwave strength can be reduced, then drag penalties will be minimal. In the earliest days of design research for high-speed flight, it was found that a wing with a low thickness/chord ratio (t/c) had far better high speed drag characteristics than a wing of high t/c. With a low t/c the airflow over the top surface does not accelerate to Mach 1 as readily, thus delaying the formation of the shocks and increasing Mcdr. Also, the intensity of shocks is reduced which in turn reduces the degree of boundary layer separation and consequently reduces the amount of total drag when Mcdr is reached. The drag curves below readily demonstrate the benefits of low t/c ratio in terms of total drag and the delay in Mcdr.

The effects (if a high t/c ratio on transonic drag were first confirmed during US testing on the X-1 series of aircraft as the following report extract shows: NACA XS-1 testing also indicated, with shocking impact, just how much drag thick wing sections added at transonic speeds. The NACA XS-1, with its 10% thickness/chord ratio wing, had 30% more overall drag at transonic speeds than did the thinner wing of the Air Force XS-1. Thick wing sections simply imposed unacceptable penalties for transonic and supersonic airplane design Low t/c wings also exhibit significant handling benefits in the transonic speed range. The CL, curve below shows how rapid variations in lift are avoided, which greatly improves longitudinal handling and stability. Note however that the total amount of lift is reduced in the transonic range for the low t/c wing.



Despite the benefits of low t/c wings for transonic flight, there are of course some disadvantages. In the approach stage of flight these aerofoils are operating less efficiently than a wing of high t/c and consequently have higher stalling speeds and higher induced drag. To counter this problem, high-lift devices (normally leading and trailing edge flaps) must be used to achieve reasonable approach speeds and landing distances. Sweepback A brief look at all modern transport aircraft designed for high-speed cruise demonstrates that wing sweep is an essential design feature of such aircraft. Following the first exploratory flights to high Mach numbers in the late 1940s, it was soon discovered that wing sweep had a significant effect in delaying the detrimental effects of compressibility (shockwaves) and permitted higher speeds to be achieved. Below shows a wing that is swept back at an angle relative to the lateral axis of the aircraft. Shown in the diagram is the flow across the wing due to the aircrafts forward motion (V). This can be resolved into one component at right angle to the leading edge (V1), and the other parallel to the leading edge (V2). Since the flow component V2 has no effect on the flow across the wing, the component V1 will produce the entire pressure pattern over the wing. Thus it is the component of the flow across the wing that affects the value of Merit and Mcdr. Consequently, a much higher value of Mfs (V in the diagram) can be flown before V1 reaches Mach 1, so delaying the onset of compressibility effects.



Because the component of forward speed that is at right angles to the leading edge is the one that determines the amount of lift at that section, then the amount of lift for a given speed is less than for the same speed with no sweep. Consequently, the coefficient of lift (CL) for a given aerofoil is less at a specific angle of attack for a swept wing than one without sweep. It is for this reason that the swept wing lift curve has significantly less slope than a straight wing, as shown below.



The next diagram shows the effect of wing sweep on coefficient of drag. The ability to delay the onset of transonic drag rise is of course the major benefit of sweepback for high-speed transonic transport aircraft. However if the whole aircraft is considered, as must be the case for practical application, the variation of drag with increasing speed is a little different as shown below. By employing a wing sweep that delays the maximum wing drag until a later Mach number, the aircrafts total drag increase is spread over a larger range of Mach numbers. Also, the total value of maximum drag is less than if both wing and fuselage reached their respective maximum at the same Mach number.

Limitations of Wing Sweep The use of wing sweep was a crucial design step that allowed aircraft to travel faster; but more importantly for the transport category aircraft, to travel far more efficiently at higher Mach numbers. The theoretical benefits of wing sweep are unfortunately limited by two factors, and the use of sweep has resulted in other handling and performance limitations.

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