Physics for Aero dynamicsAERODYNAMICS

For Training Purposes Only ATA AERODYNAMICS Page FUNDAMENTALS AERODYNAMICS PHYSICS FOR AERODYNAMICS Physics for Aerodynamics The laws of physics that affect the aircraft in flight and on the ground are described using the international SI system.The SI system is based on the metric system and must be used by law throughout the world You need to use conversion tables for the English or American systems You can find conversion tables in the appendix of most technical documentation The laws of physics are described by fundamental units and basic quantities.The fundamental units can not be defined in other quantities.The basic quantities are defined in fundamental units Speed, for example, is a basic quantity It is defined by the fundamental units distance and time Speed, denoted by V is distance, denoted by m over time, denoted by s There are seven fundamental units in physics mass, length, time, temperature, current, mol number and the intensity of light The fundamental units used in aerodynamics are mass, length, time and temperature Aerodynamics Lesson 1.1.3 Time The unit of measurement for time is seconds, denoted by s Originally this was based on the length of a day However not all days are exactly the same duration so the second is now defined as the time it takes for a certain number of energy changes to occur in the caesium atom 1.1.4 Temperature The unit of measurement for temperature is kelvin, denoted by K Zero kelvin is called absolute zero because it is the lowest temperature possible The kelvin scale starts at zero and only has positive numbers One kelvin is the same size as one degree Celsius 1.1 Fundamental units For Training Purposes Only 1.1.1 Mass The unit of measurement for mass is kilograms, denoted by kg The mass of one kilogram is defined by a piece of platinum alloy at the office of weights and measurements in Paris The mass of one kilogram is also the volume of one liter of pure water at a temperature of four degrees Celsius Mass is not the same as weight The astronauts flying around in their space labs have no weight but their bodies have a mass 1.1.2 Length The unit of measurement for length is meters, denoted by m The meter was established as a standard unit of length by a commission set up by the French government in 1790 A meter is more precisely defined as a certain number of wavelengths of a particular colour of light Page FUNDAMENTALS AERODYNAMICS PHYSICS FOR AERODYNAMICS For Training Purposes Only Aerodynamics Lesson Figure Page AERODYNAMICS PHYSICS FOR AERODYNAMICS FUNDAMENTALS Aerodynamics Lesson 1.2 Speed and acceleration 1.2.1 Speed and velocity Speed is the distance that a moving object covers in a unit of time For example, we can say that an aircraft has a speed of 500 kilometers per hour Speed is denoted by V Velocity is the distance that a moving object covers in a given direction in a unit of time We can say that an aircraft has a velocity of 500 kilometers per hour northward Velocity is also denoted by V 1.2.2 Acceleration For Training Purposes Only Acceleration is the change in velocity divided by the time during which the change takes place You can see that the velocity changes from 100 m/s to 150 m/s during this ten second period In this example the acceleration is 50 m/s per ten seconds This is equal to five meters per second per one second which is m/s2 Acceleration is measured in meters per square second ( m/s2 ) Acceleration is denoted by a Page FUNDAMENTALS AERODYNAMICS PHYSICS FOR AERODYNAMICS For Training Purposes Only Aerodynamics Lesson Figure Page FUNDAMENTALS AERODYNAMICS PHYSICS FOR AERODYNAMICS 1.2.3 Acceleration due to gravity 1.3 Force and weight We begin our look at force with an experiment You can see that our friend is standing on a weighing scale in an elevator and observing his weight ( Fig below, left ) There is no change in weight if a body stays at rest or if it moves with uniform velocity But what happens to the weight if the elevator accelerates as it moves upward? As the elevator accelerates there is an additional force which increases the weight Force is measured in Newtons The term deca Newton is used in all technical manuals for force and for weight Weight is one kind of force It is mass multiplied by the acceleration due to gravity You know that gravity is the attraction exerted on any material towards the center of the earth Weight is also measured in Newtons ( Fig below, right ) For Training Purposes Only A special form of acceleration is acceleration due to gravity An object, such as this ball, which falls freely under the force of gravity has uniform acceleration if there is no air resistance Acceleration which is due to gravity is denoted by g The value of this acceleration varies across the earth’s surface but on average it is nine point eight meters per square second For ease of calculation ten meters per square second is often used Aerodynamics Lesson Page FUNDAMENTALS AERODYNAMICS PHYSICS FOR AERODYNAMICS For Training Purposes Only Aerodynamics Lesson Figure Page AERODYNAMICS PHYSICS FOR AERODYNAMICS FUNDAMENTALS Aerodynamics Lesson 1.4 Work and Power 1.4.1 Work For Training Purposes Only Work is done when an object is moved over a distance It is force multiplied by distance Work = N x m Work is denoted by joule and is measured in Newton meters You can see that the object with a force of six hundred Newton is moved a distance of thirty meters The work is six hundred Newton multiplied by thirty meters which is eighteen thousand Newton meters Page AERODYNAMICS PHYSICS FOR AERODYNAMICS FUNDAMENTALS Aerodynamics Lesson 1.4.2 Power For Training Purposes Only Power is work over time or more specifically force multiplied by distance over time Power is measured in Watts which is Newton meters per second You probably know the term horse power When steam engines were first used their power was compared to the power of horses because they were used for work which was previously done by horses Now the international SI system uses watts and kilowatts instead of horsepower You can see that the object with a force of 600 N is moved a distance of 30 m in 10 seconds The power is six hundred Newton multiplied by thirty meters divided by ten seconds which is 1800 watts or 1.8 kilowats Page FUNDAMENTALS AERODYNAMICS PHYSICS FOR AERODYNAMICS Aerodynamics Lesson 1.5 Pressure 1.5.1 Static pressure Pressure is the force acting on a unit of area It is denoted by Pascal ( Pa ) and measured in Newtons per square meter ( N/m2 ) Static pressure acts equally in all directions It is denoted by a small ’p’ and measured in Newtons per square meter ( N/m2 ) Static pressure is calculated as height multiplied by density multiplied by gravity Pstat = h x H x g 1.5.2 Dynamic pressure ” bar ” and has the unit daN cm bar = daN2 cm bar = 100 000 Pa For Training Purposes Only Dynamic pressure acts only in the direction of the flow It is denoted by a small ’q’ and sometimes called q pressure and, like static pressure, measured in Newtons per square meter ( N/m2 ) Dynamic pressure is calculated as half the density multiplied by the velocity squared q = ½ x H x v2 The static pressure for aircraft technical systems is denoted by ’bar’ and measured in decaNewtons per square centimeter ( daN/cm2 ) One bar is equal to one hundred thousand PASCAL The STATIC PRESSURE for technical systems e g for AIRCRAFT HYDRAULIC SYSTEMS is denotet by Page 10 AERODYNAMICS TRANSSONIC FUNDAMENTALS Aerodynamics Lesson For Training Purposes Only 9.5 Transonic Profiles Different profiles are used in the different speed ranges In previous chapters you’ve seen conventional subsonic profiles You know that the conventional subsonic profile becomes inefficient when the airflow is above the critical Mach number We refer to the airflow above the critical Mach number as the supercritical airflow Profiles which perform well within the transonic range used to be called supercritical profiles and are now mostly called transonic profiles The term ’transonic’ is easier on the passengers ear than the term ’supercritical’!! Here a conventional subsonic profile, is compared to a transonic profile You can see that the transonic profile has a flatter upper surface, a more curved leading edge and a thinner trailing edge With the subsonic profile we have a large build up of supersonic airflow and a large shock wave The flow separation behind the shock wave increases the drag With the transonic profile the airflow immediately accelerates to supersonic because of the rounded leading edge The supersonic airflow decelerates because of the flat upper surface and this gives a much smaller shock wave There is no flow separation behind the shock wave This area can be used to generate lift You can see that the aft lower surface on the transonic profile has a negative camber The local velocity in this area is reduced because of the defuser effect When the velocity of the airflow is reduced the static pressure increases The higher static pressure on the lower surface of the transonic profile increases the lift in this region A wing with a transonic profile is also called a ’rear loaded wing’ We can compare the conventional and the transonic profile on the graph at the top of the picture On the horizontal axis we have the thickness to cord ratio and on the vertical axis we have the cruise Mach number First we assume that the conventional profile and the transonic profile have the same thickness to cord ratio of point one two In this case the wind tunnel data shows, that the cruise Mach number for the transonic profile is 15% higher than it is for the conventional profile In reality most aircraft fly with a cruise Mach number of approximately 0.8 At this cruise Mach number you can see that the thickness to cord ratio for the transonic profile is 42% higher than it is for the conventional profile This difference is shown by the wind tunnel data and by the flight data of an experimental aircraft The higher thickness of the transonic profile means that the total weight of the wing is reduced if the wing span is unchanged Page 98 AERODYNAMICS TRANSSONIC FUNDAMENTALS Aerodynamics Lesson For Training Purposes Only There are other advantages of a wing with a transonic profile Greater lift means that the wing can be smaller than the conventional wing and higher Mach numbers means that the sweepback angle can be reduced This reduction in the sweepback angle and the rounded leading edge improves the low speed characteristics of the wing and allows simpler lift devices to be used Here you can see that the conventional profile needs thick material to withstand the bending moment on the root of the wing and the thicker transonic profile needs less material to withstand the same bending moment The greater thickness also gives greater fuel capacity We can also increase the wing span of a wing with a transonic profile and keep the weight unchanged This has the advantage of reducing the drag The transonic profile also has it’s disadvantages You can see that in the range from well below the critical Mach number to just above it , the drag on the transonic profile is greater than on the conventional profile As you know the great advantage of the transonic profile is in the transonic region Page 99 AERODYNAMICS TRANSSONIC FUNDAMENTALS Aerodynamics Lesson 9.6 Control Surfaces in Transonic Region For Training Purposes Only In this segment we see what happens with some of the control surfaces in the transonic range The shock wave appears on the wing root first because this is the thickest part of the wing The aircraft reaction is the same as a stall due to a high angle of attack Here the angle of attack is in the normal range and the shock wave causes a flow separation This flow separation is called a shock stall or a high speed stall When we have a shock stall the center of lift moves towards the tip of the wing and, because of the sweepback, towards the rear of the aircraft The aircraft has a nose down reaction after passing the critical Mach number This reaction is known as the ’tuck under‘ effect The horizontal stabilizer is used to correct the tuck under effect This system works automatically and is known as the Mach trim system The horizontal stabilizer must increase the downward acting force to compensate the tuck under effect Page 100 AERODYNAMICS TRANSSONIC FUNDAMENTALS Aerodynamics Lesson For Training Purposes Only The control surface on the horizontal stabilizer is called the elevator It is dangerous to operate the elevator to compensate the tuck under effect Let’s see why The deflection of the elevator in subsonic flight increases the downward forces because of the higher acceleration of the airstream on the lower side of the horizontal stabilizer The deflection of the elevator in transonic flight has a different effect The airspeed accelerates above the speed of sound and a shock wave appears The flow separation behind the shock wave reduces the horizontal stabilizer forces and the aircraft reaction is the opposite of the normal reaction The nose down reaction increases dramatically and the aircraft goes out of control The nose down reaction increases dramatically and the aircraft goes out of control ! Some aircraft are equipped with an elevator lock to prevent this dangerous situation This lock operates automatically at high Mach numbers You will learn more about this in the chapter on elevators in Primary Flight Controls Shock Wave origination due to the increased camber when the elevator is deflected Page 101 FUNDAMENTALS AERODYNAMICS SUPERSONIC Aerodynamics Lesson 10 10 Supersonic Flight We begin with a segment on shock waves and expansion waves Then we look at supersonic profiles and at supersonic engine inlets Here we look briefly at aerodynamic heating 10.1 Shock- and Expansion Waves For Training Purposes Only Before we look at the development of supersonic lift we see what happens to the density, the pressure, the temperature and the velocity in supersonic flight When a supersonic airflow passes through a shock wave we have sudden changes in density, pressure, temperature and velocity We also have sudden changes in flow direction When a supersonic airflow passes through a shock wave the density increases, the pressure increases, the temperature increases and the velocity decreases A shock wave wastes energy Some of the useful energy, indicated by the sum of static and dynamic pressure is turned into unavailable heat energy Supersonic Airflow Supersonic Airflow Supersonic Airflow Supersonic Airflow Page 102 AERODYNAMICS SUPERSONIC FUNDAMENTALS Aerodynamics Lesson 10 Two main types of waves are formed in supersonic flow: Shock Waves Expansion Waves 10.1.1 Shock Waves For Training Purposes Only There are two types of shock waves: : Normal Shock Waves : Oblique Shock Waves Normal Shock Waves First we look at normal shock waves Here you see a blunt nosed object placed in a supersonic airstream The shock wave is detached from the leading edge and forms a right angle to the airstream Note that a normal shock wave is only formed in front of this object Oblique shock waves are formed above and below the object When a supersonic airstream passes through a normal shock wave there is no change in the airflow direction The velocity of the airflow is slowed to subsonic The static pressure, the density and the temperature of the air increase by large amounts and the useful energy, or the total pressure is greatly reduced Oblique Shock Waves An oblique shock wave consumes less energy than a normal shock wave Here you see a sharp nosed object placed in a supersonic airstream The shock wave touches the leading edge An oblique shock wave is formed where the supersonic airstream turns into a new flow direction You can see in this example that we also have an oblique shock wave at the trailing edge When a supersonic airstream passes through an oblique shock wave there is a change in the airflow direction, the velocity of the airflow decreases but it is still supersonic, the static pressure and the density and temperature of the air all increase but not by as much as with a normal shock wave and the useful energy or total pressure is reduced, again not by as much as with a normal shock wave Page 103 AERODYNAMICS SUPERSONIC FUNDAMENTALS Aerodynamics Lesson 10 Expansion Wave An expansion wave is formed where the supersonic airstream turns away from the preceding flow direction Unlike a shock wave, this flow around a corner doesn’t cause sharp or sudden changes in the airflow When a supersonic airstream passes through an expansion wave, the airflow direction follows the surface as long as there is no flow separation The velocity of the airflow increases, the static pressure, the density and thetemperature of the air decrease and there is no change in the useful energy or in total pressure For Training Purposes Only 10.2 Supersonic Profiles Here you can see the pressure distribution on a thin flat plate in a supersonic airflow The airflow over the upper surface passes through an expansion wave at the leading edge and this gives a uniform suction pressure on the upper side The airflow under the plate passes through an oblique shock wave at the leading edge and this gives a uniform positive pressure on the lower side In this example the center of lift is at fifty percent of the cord because of the constant pressure distribution The net lift is produced by the distribution of pressure on a surface You know that the profile lift is the force from the perpendicular to the free airstream The inclination of the net lift from the profile lift produces drag In this segment we look at the aerodynamic characteristics of different types of profile in supersonic flight First we see a thin flat plate at a positive angle of attack The airstream above and below the surface passes through expansion waves and oblique shock waves Here you can see the wave pattern on a thin flat plate in a supersonic airflow The airflow over the upper surface passes through an expansion wave at the leading edge and then an oblique shock wave at the trailing edge The airflow under the plate passes through an oblique shock wave at the leading edge and then an expansion wave at the trailing edge Page 104 FUNDAMENTALS AERODYNAMICS SUPERSONIC Aerodynamics Lesson 10 In reality a wing is not a flat plate it must have a profile There are two typical profiles, the double wedge profile and the circular arc profile Double Wedge Prfile Here you can see the wave pattern on a double wedge profile at zero angle of attack You can see the airflow over the surface passes though an oblique shock wave at the leading edge, an expansion wave and then another oblique shock wave at the trailing edge The wave pattern on the double wedge profile produces an increase in pressure on the forward half of the cord and a decrease in pressure on the aft half of the cord This means we have no net lift For Training Purposes Only α = 0E α = 3E Circular Arc Profile Here you see the wave pattern for the circular arc profile in supersonic flight You can see from the graphic at the left, why it is called the circular arc profile The airflow passes an oblique shock wave at the leading edge then undergoes a gradual and continuous expansion until it passes through another oblique shock wave at the trailing edge In general if the flow on a profile is supersonic the center of lift is located at approximately 50% cord position This contrasts strongly with the situation if the flow on a profile is subsonic In this case the center of lift is located at approximately 25% cord position You can imagine that the position of the center of lift in supersonic flight has an effect on the aerodynamic trim and stability Aircraft stability increases during supersonic flight because the distance between the center of gravity and the center of lift is reduced This is the wave pattern and the resulting pressure distribution for the double wedge profile at a small positive angle of attack You can see that the pressure distribution produces an inclined net lift and that the inclination of the net lift from the profile lift produces drag Page 105 FUNDAMENTALS AERODYNAMICS SUPERSONIC 10.3 Supersonic Engine Inlets The air entering the compressor section of a jet engine must be slowed to subsonic velocity The slowing down of the air must be accomplished with the least possible waste of energy At flight speeds just above the speed of sound we only need slight modifications to the ordinary subsonic inlet design to produce satisfactory performance At higher supersonic speeds the required modifications are more complicated The inlet design must slow the air with the weakest possible series or combination of shock waves in order to minimize the energy losses caused by temperature increases On the next picture you see one of the least complicated engine inlet designs, a normal shock diffuser inlet You can see that this type of inlet employs a single normal shock wave at the inlet to slow the air to subsonic velocity This type of inlet is suitable for low supersonic speeds where the normal shock wave is not too strong It is not suitable at higher supersonic speeds because the normal shock wave is very strong and causes a great reduction in the total pressure recovered by the inlet Aerodynamics Lesson 10 Here you see a single oblique shock inlet This design employs an external oblique shock wave to slow the supersonic airflow before the normal shock occurs Oblique Shock Inlet A more complicated variation of the single oblique shock inlet is the multiple oblique shock inlet This design employs a series of very weak oblique shock waves to gradually slow the supersonic airflow before the normal shock occurs The normal shock wave doesn’t have to be very strong This combination of weak shock waves leads to the least waste of energy and the highest pressure recovery The optimum shape of supersonic inlets varies with the inlet flow direction and with the Mach number In other words to derive the highest efficiency and stability of operation the geometry of the inlet would be different at different angles of attack and at different speeds For Training Purposes Only Normal Shock Inlet Multiple Oblique Shock Inlet Page 106 FUNDAMENTALS AERODYNAMICS SUPERSONIC Here you see and example of an inlet which can be varied to suit different conditions You can see that it is equipped with actuator operated panels At flight speeds below Mach one the engine inlet is fully open and the aircraft flies with a high angle of attack At flight speeds just above Mach one the actuators change the position of the panels slightly and the inlet employs a single normal shock wave This is similar to the normal shock diffuser inlet At high Mach numbers the actuators operate the panels so that they employ three oblique shock waves and then a normal shock This is similar to the multiple oblique shock inlet Aerodynamics Lesson 10 Variable Area Inlet For Training Purposes Only Mach > Page 107 AERODYNAMICS SUPERSONIC 10.4 Aerodynamic Heating Aerodynamics Lesson 10 With subsonic flight the increase in temperature is very small but with supersonic flight the increases in temperature can affect the aircraft structure This graph shows the effect of speed and altitude on aerodynamic heating You can see that the temperature increases rapidly as the Mach number increases The graph on the right shows the approximate effect of temperature on material strength The graph shows that aluminum alloy loses approximately 80% of it’s strength if the temperature increases to 250E C Because of this, parts of Concorde and some military aircraft are made from titanium alloy For Training Purposes Only Next we have a short segment on aerodynamic heating You probably know that ceramic tiles are used to protect the body of space shuttles against the temperature increases which they experience on returning to the earth’s atmosphere These temperature increases are caused by friction between the surface of the space shuttle and the high velocity of the free airstream When air flows over an aerodynamic surface we have a reduction in velocity and a corresponding increase in temperature The greatest reduction in velocity and increase in temperature occurs at the various stagnation points on the aircraft FUNDAMENTALS Page 108 TABLE OF CONTENTS ATA AERODYNAMICS Physics for Aerodynamics 1.1 Fundamental units 1.1.1 Mass 1.1.2 Length 1.1.3 Time 1.1.4 Temperature Speed and acceleration 1.2.1 Speed and velocity 1.2.2 Acceleration 1.2.3 Acceleration due to gravity 1.3 Force and weight 1.4 Work and Power 1.4.1 Work 1.4.2 Power Pressure 10 1.5.1 Static pressure 10 1.5.2 Dynamic pressure 10 Sound waves 1.6.1 1.6.2 1.2 1.5 1.6 1.6.3 1.7 Sound regions 16 Atmosphere 18 1.7.1 19 ICAO Standard Atmosphere ( ISA ) Basic Aerodynamics 20 2.1 Continuity equation 20 2.2 Bernoulli‘ s principle 22 2.2.1 Pressure measuring 24 2.3 Lift production 26 2.4 Magnus Effect and Circulation 28 Profile and wing geometry 30 3.1 Geometry of a profile 30 3.2 Wing geometry 33 Lift and drag 4.1 36 Introduction 36 12 4.1.1 Lift Equation 39 Speed of sound 14 4.1.2 Drag Equation 39 Mach number 15 Factors Affecting Lift 40 4.2 Page i TABLE OF CONTENTS 4.3 4.4 4.2.1 Angle of Attack ( AOA ) a 40 6.2.2 Rectangular Wing 62 4.2.2 Shape of a Profile 42 6.2.3 Tapered Wing 62 6.2.4 Swept Wing 62 Wing Twist, ” Washing Out ” 63 6.3.1 Geometrically Twisted Wing 63 6.3.2 Aerodynamically Twisted Wing 63 Factors affecting Drag 43 4.3.1 Relation between a and the Drag Coefficient CD 44 Polar Diagram 46 Categories of Drag 48 6.4 Stall Conditions 64 6.5 Boundary Layer Control 66 6.5.1 Wing Fences and Saw Tooth Leading Edge 66 6.5.2 Vortex Generators 67 5.1 Introduction 48 5.2 Induced Drag 49 5.3 Parasite Drag 52 5.3.1 Form Drag 52 5.3.2 Friction Drag 54 5.3.3 Interference Drag 58 5.4 Compressible Drag 60 5.5 Total Drag 61 Lift Distribution 6.3 Theory of Flight 68 7.1 Introduction 68 7.2 Forces Acting on an Aircraft 68 7.2.1 Steady Flight Conditions 70 Theory of Turn 71 7.3.1 Aditional Lift for a Turn 72 Control Surfaces 73 7.4.1 Horn Balance and Insert Hinge 73 7.3 62 7.4 6.1 Introduction 62 7.4.2 Balance Tab 74 6.2 Wing Design 62 7.4.3 Balance Panel 74 6.2.1 62 7.4.4 Anti - Balance Tab 75 Elliptical Wing Page ii TABLE OF CONTENTS 7.4.5 Control Tab 75 7.4.6 Trim Tab 76 7.5 Lift Devices 76 7.6 Drag Devices 77 Stability 8.1 Introduction 78 8.1.1 Static Stability 78 8.1.2 Dynamic Stability 79 8.1.3 Aircraft Axes 81 8.2 Directional Stability 82 8.3 Lateral Stability 83 8.4 Lateral Directional Interactions 85 8.4.1 Spiral Dive 85 8.4.2 Dutch Roll 86 Longitudinal Stability 87 8.5 78 Transonic Flight 9.3 Wave Drag 94 9.3.1 Wave Drag Reduction by Vortex Generators 94 9.3.2 Wave Drag Reduction by Area Rule 95 9.4 Swept Wing Effect 96 9.5 Transonic Profiles 98 9.6 Control Surfaces in Transonic Region 100 10 Supersonic Flight 102 10.1 Shock- and Expansion Waves 10.1.1 102 Shock Waves 103 10.2 Supersonic Profiles 104 10.3 Supersonic Engine Inlets 106 10.4 Aerodynamic Heating 108 90 9.1 Introduction 90 9.2 Critical Mach Number 91 Page iii TABLE OF FIGURES Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 10 Figure 11 Figure 12 Figure 13 11 13 17 21 23 25 45 47 59 69 Page iv