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Introduction to Aerospace Vehicles

by

Prof. S.P. Govinda Raju

Topics: Types of aircraft and their flight performance Video presentation. 1. Historical introduction.

2. Atmosphere, its properties and its influence on aircraft operations

3. Basics of airplane flight lift and drag, equilibrium, stability and controllability,

airplane types and missions.

4. Fluid flow fundamentals, streamlines, Bernoullis Law, viscosity, laminar and

turbulent flow, boundary layer, transition, flow separation.

5. Basic aerodynamics Drag of some simple bodies, effect of Reynolds

number, airfoils and their characteristics, control surfaces, flaps and

spoilers, swept-back wings.

6. Wings effect of aspect ratio, compressibility effects, compressible flow,

supersonic flow, Mach number.

7. Estimation of aerodynamic characteristics, analytical tools, aerodynamic

measurements, wind tunnels and instrumentation, measurement of velocity,

pressure and forces.

8. Safety in aviation the BCAR, one engine failure on take off; design loads.

9. Aircraft propulsion principles, propeller + piston engine, turbojet, turbofan

and turboprop engines.

10. Airplane performance, estimation based on drag polar and power plant

characteristics.

11. Airplane stability and control, concepts of longitudinal and lateral stability,

handling qualities, fly by wire control systems.

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1. Historical Introduction

Ancient Indian literature contains references to flight vehicles. Valmiki Ramayana mentions Pushpaka Vimana with a brief description: A large hall with many side chambers, well decorated and provided with dining facilities. The vehicle could be flown by voice command. A somewhat later work Kathasaritasagara includes a section called Vetala Panchavimshati which is a collection of twenty five stories. In one of them there is description of an aerial combat using a chariot equipped with missiles. The flying chariot was used as a platform for shooting arrows at the enemy. However there is no material evidence of any flight vehicles of ancient times.

Manned flight was attempted in some European countries in the 18th century. Hot air balloon flights are recorded in Portugal in 1709. Montgolfier brothers (France) flew in a hot air balloon in 1783. Following these flights, airships developed rapidly and were fairly successful. An airship flew over the North Pole in 1926. Airships are still used for special purposes and there are some renewed efforts to develop the as heavy transports.

Heavier than air flying machines were attempted by Cayley(1843), Lillenthal (1896), Prof. Langely (1903) before the Wright brothers succeeded in late 1903 (actually 17th Dec. 1903). The military potential of the airplane was quickly recognized and airplanes were used for surveillance very early. Airplanes equipped with machine guns fought each other and evolved into modern fighters. Larger airplanes to carry bombs and troops rapidly developed and are the fore runners of the bombers and military transport of the current time. After World War II, the pure fighter was replaced by a multi-role combat aircraft combining some features of fighters and bombers. Civil transports also developed during the time and a large variety of civil aircraft operate at current time. They cover a wide range starting with two seaters weighing less than a ton to large airplanes going up to 600 tons for the A380.

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2. Atmosphere and its properties

Air is a thin layer of a compressible fluid (primarily a mixture of oxygen and nitrogen with a small amount of water vapour especially at low altitudes) which covers the surface of the earth (a sphere of about 8000 miles diameter) to an effective depth of about 20 miles. Airplanes fly only in this layer and typical flights are at an altitude of about 35,000 feet. Properties of atmosphere of interest to flight vehicles are primarily the density, pressure and temperature of air and their variation with altitude. Typically, the atmospheric pressure at sea level is 1013 mb. Temperature of air at sea level varies depending on place and season. On a global average basis, the mean temperature at sea level is around 15oC. The temperature decreases with altitude at about 2oC for every 1000 feet. Atmosphere over India is about 15oC hotter than over temperate regions and it is normal to take ISA + 15o C as typical of India. (ISA: International Standard Atmosphere)

Hydrostatic equilibrium demands

gdhdp =

Where P = pressure of atmosphere at height h above sea level = air density at the height h g = acceleration due to gravity One may define a pressure altitude Z as the height in a standard atmosphere where P corresponds to the pressure in the atmosphere, i.e.

gdzdp

z=

Tables are available for calculating other air properties as a function of Z. it is noted that P(Z) falls off rapidly with Z and P( Z= 8000 m) = 0.373*( P at sea level). The following table is indicative of air properties over India.

Z (m) H (m) P/po /o a(m/s) 0 -20 1.0022 1.002 347

5000 5250 0.6343 0.5907 330 10,000 10,580 0.2615 0.3313 308 15,000 15,650 0.1191 0.1754 286

It may be noted that at the typical flight altitude of Jet transports (around 10

km) the atmospheric pressure is around a quarter of the sea level value. Passenger aircraft are pressurized to an internal pressure of about 0.75 of sea level pressure. Thus there is a pressure difference of about half atmosphere during cruise (relative to sea level). The structure of the fuselage is designed to withstand repeated pressurization to this level as, each time the airplane files, the passenger cabin is pumped up to the pressure which is released during landing.

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The variation of p with altitude is useful in constructing an altimeter (which is called pressure altimeter). The principle is to use an evacuated elastic pressure sensor (bellows) whose displacement when subjected to varying pressure (due to change of z) is indicated on a dial directly calibrated in terms of altitude (the pressure altitude). It is to be noted that the true altitude can be some what different from the value indicated on a pressure altimeter. A schematic sketch of the pressure altimeter is shown below:

If not compensated, the fall of temperature and pressure will cause discomfort to the passengers in any jet transport. Therefore it is normal to condition the air (heating, dehumidification, pressurization) so that satisfactory comfort is maintained for the passengers. Aerodynamic properties of lifting surfaces (wings) and power of engines of all types are dependent on the density of air and hence decrease with altitude, other things being the same. Thus every aircraft has a ceiling beyond which it can not climb for want of lift or engine power. The altitude record for airplane flight is around 1,00,000 feet , but most aircraft can only reach half this altitude. Cruise altitude for jet transports is in the 35,000 to 40,000 feet range. The supersonic transport, the Concorde, flies at up to 60,000 feet. 2.1 Atmospheric water vapour Air can hold water vapour to an extent depending on the temperature and pressure. Typically at sea level, the water content of air at 40oC is less than 5% at a relative humidity of 100%. Humid air is lighter than dry air, but the difference is not important from the point of view of flight dynamics. However, many atmospheric phenomenon like fog, rain, snow and icing, vertical atmospheric motion including cloud formation are a result of the atmospheric water vapour. Up and down motion of air leads to gusts which are important from the point of loads acting on the wings (gust loads). Condensation of water in the form of ice on aerodynamic surfaces of propellers and wings can cause loss of performance and need to be considered. The phenomenon is important in an altitude range of 5000-15000 feet with in which only ice formation is possible. Air is too dry at higher altitudes to cause condensation.

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Protection to icing is provided in aircraft (turboprops) operating for extended periods at the critical altitudes. Piston engine aircraft are provided with heating for the carburetors to prevent icing inside it. Lightning, related to atmospheric static electricity needs to be considered specially in the case aircraft made of composites (which are poor conductors). Suitable conducting paths have to be provided to avoid the structural damage by lightning. 2.2 Winds Horizontal motion of air (wind) can affect the flight of aircraft as the performance of wing is related to relative motion with respect to air. Tail wind (in the direction of aircraft flight) can increase ground speed (desirable) and landing distance (undesirable). Head wind is favorable to landing but reduces cruise speed relative to ground. Cross wind leads to landing problems and need to be considered carefully from the point of view of aircraft control.

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3. Basics of Airplane Flight Airplane flight is fundamentally based on the aerodynamics of wings. By definition, a wing is any surface that produces a large force at right angles to the direction of motion (Lift) while suffering a small resistance (Drag) in the direction of motion. Illustrations:

Typical wings have a large Lift to Drag ratio in the region 10 to 40. The following is illustrative of airplanes.

Surface (L/D)max Smooth airfoil Up to 250 Well built gliders Up to 40 Low speed airplanes 10 20 Combat aircraft 6 9

In level flight, lift of the airplane overcomes its weight while the thrust of the engine overcomes drag. The importance of high L/D is obvious. In general an airplane is a body with six degrees of freedom corresponding to linear and angular motions about the three axes of the airplane conveniently chosen along its longitudinal axis and two others at right angles to it (as in figure). For the purpose of analysis, the coordinate axes are chosen as in figure.

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ox, oy, oz are Cartesian axes centered at aircraft center of gravity. Airplane axes and velocity vector are defined in figure. u, v, w : Components of velocity of the airplane along ox, oy, oz respectively. v, , : polar components of V: , : incidence angle

: sideslip angle V : flight velocity (magnitude)

Common notation (body fixed axes)

ox: roll axis oy: pitch axis oz: yaw axis

In general the velocity vector V has all three components u, v, w. However u is much larger than v, w. Most of the time v = 0 corresponds to = 0 i.e. the airplane flies with the velocity vector in its plane of symmetry. varies depending on flight condition, but generally is only a few degrees in level flight. Requirements of controlled flight may be stated as following:

1. Equilibrium 2. Stability 3. Controllability

Equilibrium implies balance of forces and moments i.e. the algebraic sum of all forces / moments acting along / about the three axes must be zero. For level flight without sideslip, this implies lift = weight, thrust = drag and pitching moment about C.G is zero (ensured by suitably operating the elevator).

Stability implies return to original equilibrium condition after a reasonable time following a disturbance. Controllability implies that the pilot will be able to alter tby moving some control surfaces such that the moveaccordance with his requirements. A simple example is that of a pendulum: which has onlyotherwise illustrates the principles involved. Equilibrium: Tension T = weight of bob, W Stability:

decays with time until (t ) = 0 inverted pendulum

Disturbed position

We

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he flight path of the airplane ment of the airplane is in

one degree of freedom, but

is unstable.

Time

T

ight, W

Time

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Controllability: Apply F, then can be held at any non zero value i.e. F = W tan. In applying these principles to airplanes the following points are to be noted.

1. An airplane has 6 degrees of freedom against one of the pendulum. 2. Stability is to be ensured by suitably configuring the airplane lifting

surfaces, (wings, horizontal and vertical tail surfaces), Shapes, sizes, positions and orientations are important. Airplane C.G plays an important role in this.

3. Control surfaces are to be provided to create moments about the three

axes on demand. Typically elevator, aileron, and rudder are used. A typical aircraft plan form is as below:

The configuration is dictated by performance as well as by stability and control requirements. It may be noted that the airplane has many modes of instability (typically 4 major ones) and keeping them in control is possible by suitable choice of C.G location, horizontal and vertical fin sizes & wing dihedral (the angle by which a

W F

W

T

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wing is tilted upwards). Sometimes, deliberately mild instability is desired in the case of combat aircraft. These will be considered later. 3.1 Airplane Types and Missions Airplanes come in a great variety depending on their application. One may broadly consider than under military and civil categories, Military aircraft can be classified under trainers, multi role combat aircraft and transport. Multi role combat aircraft are used for various missions like interception, close air support, interdiction and deep penetration. Missions are defined in terms of weapons carried (canon, missiles, bombs) and range and nature of airspace (friendly or hostile). Deep penetration demands the maximum in terms of weapons, range and capacity for autonomous navigation. Interceptors are light and powerful. Deep penetration aircraft are heavy, have large range and good navigation capability. Typical aircraft operating in India are as below: Trainers : HJT 16 (Kiran), HJT 36 Interceptor : MIG 21

MRCA with deep penetration capability : Mirage 2000, Jaguar

Transports : HS 748, IL 76 Civil aircraft come in various seating capacities (from 10 to 700) and range (a few hundred km to several thousand). Speed of flight is normally around 250 knots for short range aircraft to about 500 knots for large range aircraft (knot is a unit of speed and corresponds to 1.15 miles per hour). Other flight vehicles of interest are general aviation aircraft (of up to 10 seats) rotary wing aircraft, airships, paraplanes etc. Unmanned aircraft are also being used for surveillance purposes.

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4. Fluid Flow Fundamentals Some basic concepts indicated below are very useful in understanding and interpreting fluid flows. A streamline is a curve whose direction at each point coincides with the direction of the velocity of the fluid at that point. All streamlines passing through a small closed curve form a stream tube. The concept is particularly useful in steady flows in which case the stream tubes behave like solid tubes through which the fluid passes. From the law of conservation of matter, it follows that the amount of fluid flowing through each section of the stream tube per unit time must be a constant. Referring to the figure, it , w, A are respectively the fluid density, the velocity and the cross-section area of stream tube, it follows that: Aw = constant.

For an ideal fluid (fluid of constant density and no viscosity) there are no shear stresses in the fluid and the forces on fluid elements are entirely due to inertia and fluid pressure (neglecting body force due to gravity). In this case we can derive an important relation between velocity and pressure (the Bernoulli law) as below:

Forces on an element of ideal fluid Momentum flux increase over the element is

Stream Tube

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ss

A

(Mass flux x change of velocity)

This is balanced by the pressure force increase in s direction which is

sspA

Thus we have

sp

s

+ = 0

i.e. (s 0)

2

2

=+ p

or ap =+2

2 constant along a steam line. This is the Bernoulli law which relates

the changes of pressure to changes of velocity along a streamline. Thus, along a stream line, if velocity increases, the pressure decreases. Thus regions of high velocity correspond to regions of low pressure. Real fluids have viscosity, a fluid property which implies friction forces between layers of fluid. Referring to a fluid between two parallel plates, one of which is sliding relative to the other, there is a shear stress - given by

dydu =

Flow between a fixed and a sliding plate

= coefficient of viscosity and is a property of the fluid. It generally depends on temperature. For liquids it falls with increase of temperature. For air, it increases with increase of temperature. One may define (/) as , the kinematic viscosity of the fluid. The value of for air is very small and 1/ is around 70,000 at sea level in metric units. Similarity considerations indicate that a dimensionless parameter, the Reynolds number ( /D where D is a typical body dimension) which is a measure of the

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relative magnitude of the inertia forces in relation to viscous forces, is very important. The number typically is over a million for air flow over practical bodies like airplanes. Reynolds number plays a very important role in fluid flows. At low Reynolds numbers (R) the flow is laminar in the sense that fluid particles move in smooth curves. For flow in a pipe, laminar flow implies that fluid particles move in layers parallel to the wall. This happens at R < 1000. For higher Reynolds numbers, the flow becomes turbulent in the sense that fluid particles move chaotically and the flow is only steady when averaged over time. Turbulent flow results in a higher level of skin friction as compared to laminar flow. For flow past bodies in a fluid of low viscosity (like air), the effect of viscosity is only felt in a thin layer of fluid near the surface of the body (called the boundary layer). The boundary layer is laminar at low Reynolds numbers but becomes turbulent at high Reynolds numbers, through a process of transition which is a complex phenomenon involving the stability of the boundary layer. However, in the absence of any pressure gradient (like in a flat plate) the boundary layer is close to the body all along its length. As bodies do induce a pressure gradient on the boundary layer, the flow can reverse direction close to the surface leading to separation of low as indicated in the figure. The phenomenon of laminar flow, transition, turbulent flow and flow separation in the boundary layers are very important in understanding and interpreting the flow over practical bodies like airfoils.

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5. Basic Aerodynamics It is convenient to define a force coefficient as;

F = CF v2 * (Area) Where F = force acting on a body

= fluid density far from the body (constant for Incompressible fluids) V = fluid velocity far from the body

(Area) = a characteristic reference area of the body.

i.e. Fx = CFX ( v2 ) A (Drag) Fy = CFY ( v2) A (Lift) The coefficients CFX, CFY depend on the orientation of the body relative to the stream, flow Reynolds number R and flow Mach number M defined as below: Reynolds number R = V d/ Mach number M = V/ a Where d = a characteristic length of body = Kinematic viscosity of the fluid (1 / 70,000 in SI units for air) a = velocity of sound ( 300 350 m /s for air)

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A simple calculation show that R for airplanes is in the range of 106 to 108 while civil aircraft fly at M < 0.85. We shall primarily consider bodies in this range of R & M. Typical ranges or R are shown in the figure:

The force coefficients for typical bodies are illustrated below: 5.1 A circular disc placed normal to stream

The CD is practically constant for all R more than 103 (CD nearly 1)

Flow corresponding to disc Note: (1) separation at sharp edge

(2) Large wake (3) CD nearly constant ~ 1. 5.2 Flat plate along flow direction

Note: 1. no sepa

2. thin bou3. small C4. CD dec

5.3 Sphere Note: 1. C

2. C3. T

Flow undergoes sudd

0.1

0.4

ration 16

ndary layers D ( < 0.01 ) reases with increase of R

D is moderately high. D drops suddenly from 0.4 to 0.1 at R 2 x 105 he transition is sharp

en change as below:

R 105 106

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5.4 Airfoils

Note: 1. sudden improvement in L / D around R = 105

2. importance of smooth surface at R > 105 Tests should be conducted at higher than critical R so that the results are useful for actual flight conditions (there is a need for large wind tunnels)

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6. Basic Aerodynamics 6.1 Wing sections: Properties of wing sections (also called airfoils) depend on their profile and incidence. Wings have finite span and an airfoil is the limit of a wing with span tending to infinity. Properties of airfoils are useful in designing wings. Typical geometric properties of airfoils are as follows:

tmax / c : 12 to 18% max camber : 2 to 4% location of tmax : 30 60 % of chord Typical aerodynamic properties of airfoils are as below: Cl max 1.4 to 1.6 at 15o, Aerodynamic center at 1/4th chord. Cdmin .004 dCl / d ~ 0.1 per degree Cm = 0 to 0.1 about aerodynamic center. Aerodynamic center is a point on the airfoil such that Cm is independent of Ct for all Cl in the linear range (some what below stall). Various airfoils and their properties are given in the following book: Ira. H. Abbot and Albert E. Von Doenhoff theory of Wing Sections Dover Publications, New York 1959. For a specific airplane, the wing profile is chosen depending on speed of flight (flight Mach number) and type of airplane. The final choice of wing profile involves complex considerations including structural strength, sensitivity to profile errors, location and type of control surfaces (flaps, slats), flight Mach number (low mach no. or mach no. close to 1.0 say 0.8 to 0.85).

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6.2 Flaps and Spoilers Flaps are a means of changing the lift coefficient of the airfoil at the same incidence. A simple flap consists of hinging a part of the airfoil near the rear and rotating the same.

Flaps are used for the control surface to create moments about the three axes of the airplane (ox, oy, oz) for flight control. Flaps are also used for enhancing the lifting capacity of a wing during take off and landing of any airplane. Clmax for an airfoil (around 1.6 without flaps) can be increased to about 2.4 with simple flaps and to about 3.0 with a combination of slat and multi-slotted Fowler type flaps. These are used on large civil transports. Spoilers are used for decreasing lift of airfoils and also to create drag. These are used primarily just after landing for dumping lift as well as air brakes to dissipate the kinetic energy of the airplane without using mechanical brakes (which are used for lower speeds only).

Typical flaps / spoilers: Spoiler deflected upwards on landing Spoilers are also used for control purposes (ex: spoiler aileron).

Flaps also cause an increase of drag and they have to be used carefully for take off. Generally full flap deflection is used for landing, but only partially deflected for take off. 6.3 Effects of compressibility on properties of wing sections Large civil aircraft operate at 0.80 to 0.85 Mach number. Effects of compressibility are important at these speeds and the design of wings for these aircraft is carefully done to ensure good performance (i.e. low drag) at these speeds. Unswept airfoils feel the adverse effects of compressibility (increase of CD at constant CL) at around 0.5 to 0.7 (depending on profile and thickness) and an effective way of postponing these is to use wing sweep. For an unswept wing, effect of mach no. on Cl is adequately given by the Prandtl-Glauert rule, i.e.

21 M

CC lilc

=

where Clc = lift coefficient accounting for compressibility Ta S

N 20

Cli = lift coefficient in incompressible flows M = free stream Mach number

he above holds good below the critical mach no. Mcr (defined as the Mach number t which local sonic flow is produced.)

weep on an airfoil affects the lift as the free stream velocity is effectively the component normal to airfoil span direction as in figure.

ote: = angle of attack along stream direction.

N = angle of attach with respect to airfoil chord = / cos

= sweep angle.

V = free stream velocity Vs = lateral component VN = normal component

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It can be shown that in this case.

( )2cos1cos.2

MClc

=

The lift coefficient is reduced due to sweep effect, but the effective Mach number is also less (M Cos). Compressibility effect is thus delayed considerably. A sweep angle of 30 35o degrees is used on large civil transports. 6.4 Benefit of a swept wing Let us compare the weight of two wings designed with the same span and area. If the wing has no sweep, for a critical mach number of 0.8, its thickness will be 9%. If we consider a profile of double the thickness (18%), then Mer = 0.7. But if we sweep the profile of 18% thickness by an angle of 290 ( 875.0cos = ), the same Mer is maintained. However, the wing length is increased to 1/0.875 or 1.14 of the original value. The chord wise thickness of the wing is increased by 2 x 0.875 or 1.75. The sheet cross-section area for resisting bending is decreased to 1.14/1.75 or 0.65. Thus the wing weight decreases by 1.14 x 0.65 = 0.74. This is a significant benefit. If the wing weight is held constant a large increase in Mer is obtained. The above analysis is due to George Schairer (May 5, 1945) and led to use of swept wing on Boeing B-47 bomber.

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7. Performance of wings Wings are lifting surfaces of finite size. Typical wing planforms are shown in figure.

7.1 Wings in incompressible flow Theory of wings is well developed. Prandtls lifting line theory adequately explains many properties of wings. A simple version of Max Munks analysis is given below to explain the effect of aspect ratio on drag. A finite wing deflects fluid in a region roughly corresponding to the area with the wing span as the diameter. The flow in this region has a downward component as shown in figure below. It is called the downwash.

Distribution of downwash Distribution over the area In longitudinal direction Momentum balance indicates:

Lift = flux of normal momentum

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!componentvelocity

fluxmass

wbvL""#""$%

=

4

2

or w = 4L / b2 Due to downwash, the lift vector tilts backwards by an angle w/2Vas in figure

This results in an induced drag, Di = L. w/v = 2L2 / v2 b2 Note that the induced drag depends only on span loading of the wing L/b and flight dynamic pressure ( v2). Wings of small span loading (large span) have a small induced drag. The above equation could be written in dimensionless form as

CDi = (CL2/ () x Aspect Ratio)

Wings of small aspect ratio have to operate at smaller values of CL to avoid excessive induced drag and hence maximum CL is seldom an important parameter for such wings. Further, wings of small aspect ratio have a small dCL/d and stall at higher angles of attack. 7.2 Supersonic flow Flow properties at M > 1 are radically different from flow at subsonic mach numbers. Density changes which are small in subsonic flow play a dominant role. A small disturbance in a compressible medium travels at the speed of sound. Thus at M < 1, the whole fluid is covered by the disturbance generated at any point. However in supersonic flow, disturbances and their effects are confined as indicated in figure

= sin-1(1/M)

Di = induced drag = Lift * w/2V

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Disturbances in stagnant fluid (above), Disturbances due to moving source, v> a (below)) Typical flows at supersonic speeds are indicated below

Pressure distribution

Note that there is drag (component along flow) due to the N- shaped pressure distribution. This is called the wave drag. This is in addition to friction on the walls which exists in all domains of flow. Flow past a wedge in shown in figure:

Pressure on the wedge surface is given by

12

2

=

Mq

p

p

25

Using the previous result one can show

.,1

42 LDL

CCM

C =

=

Note that there is wave drag equal to L. In subsonic flow (inviscid)

0,12

2=

= DL CM

C

This clearly shows that there is an additional drag due to lift. Lift Drag ratio in supersonic flow is generally much lower than in subsonic flow. Airplanes operate at supersonic speeds only at high altitudes. Supersonic speeds are avoided at lower altitudes due to the enormous dynamic pressure that would be produced at these altitudes. These large dynamic pressures would induce large loads on the wings due to even small gusts and thus overload the structure.

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8. Aerodynamic Measurements Aerodynamic characteristics of an airplane configuration are required for estimating the performance and stability of the airplane and also for designing simulators used for training pilots. These are generally obtained by testing suitable models in wind tunnels as the calculations based on theoretical methods are not sufficiently accurate. The tests are conducted in suitable wind tunnels capable of simulating the flight of the airplane in terms of Reynolds number and Mach number as closely as possible. Wind tunnels have to be quite large to achieve a reasonably high Reynolds number for tests. 8.1 Types of Wind Tunnels Low speed wind tunnels typically running at less than 100 m/s are suitable for studying the aerodynamic characteristics of aircraft in their take off and landing configurations. As the Mach number of these tests is low (around 0.2) the results are not applicable to flight at higher Mach numbers (typically 0.8 for civil aircraft). Additional tests of these configurations may be required in transonic and supersonic wind tunnels. Low speed wind tunnels can generally run continuously while most of high speed wind tunnels are of the intermittent type due to the enormous power required to operate them. We shall only consider low speed wind tunnels here. To achieve high Reynolds numbers, some large wind tunnels use pressurization (ambient pressure of 4 5 atmospheres). A few are cooled to cryogenic temperatures to reduce the kinematic viscosity. But a large bulk of low speed wind tunnels run at atmospheric pressure. 8.2 Typical Wind Tunnel

The goal of the wind tunnel designer is to have uniform velocity in the whole test section. However, variations of the order of +/- 0.25% in the velocity and turbulent fluctuations of the order of 0.1% are tolerable. The honeycomb, screens and

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contraction are designed to ensure the above quality flow in the test section. Diffuser helps in recovering the kinetic energy of the stream by converting it into pressure rise. Motor power depends on wind tunnel size and speed. A typical; wind tunnel of 10 sq.m test section area running at 80 m/s absorbs about a MW. Models to be tested are placed in the test section. Permissible model size is only a small fraction of the area of the test section due to the blockage error. Typical wing area of an aircraft model is only about 5% of the test section area. 8.3 Model Mounting and Instrumentation Typically, an aircraft model is mounted on a sting which carries a balance at the model end and attaches to a pitch and yaw mechanism at the other. The pitch and yaw mechanism permits orienting the model at any desired incidence and sideslip in the test section. Typical range of incidence is 5o to +30o and sideslip is 10 deg. However, combat aircraft models are tested even at high incidence values as there is a recent trend towards maneuvers at very high angles of attack. Measurements in wind tunnels relate to velocities (magnitude and direction) pressures (distribution on various surfaces like wings etc.) and forces (on overall aircraft configurations as well as on parts like stores, armament and rotodomes etc.) Velocity at a point can be measured using a pitot-static tube. A typical design is shown below.

The design has negligible error in the range of of 20o. The velocity V is calculated from: Pt - Ps = v2 Where = density of air (assumed constant and Independent of pressure. This relation is good only up to Mach 0.5). The speed in the test section is measured by measuring the pressure drop across the contraction and calibrating it against the wind tunnel speed in the test section without any body in it (empty tunnel). The pressure drop is measured using a manometer or a pressure transducer.

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The Pitot - static tube can also be used for measuring the flight speed of an aircraft. In this case the air density is function of altitude and temperature. However, the dynamic pressure v2, is directly measured and one can define an equivalent air speed Ve (EAS) as:

Ve2 = Pt - Ps

where, o = sea level standard density As the airplanes lifting characteristics depend only on dynamic pressure, it is enough to indicate Ve on the pilots instruments. The true air speed V can be calculated if altitude and temperature are also measured. On modern aircraft different sensors are used for measuring these and a computer calculates all the desired quantities like equivalent air speed, true airspeed, Mach number etc. Measurement of force in wind tunnels is generally done using a strain gauge based six-component balance. The principle used here is to measure strains at suitable locations on an elastic body and calculate the forces using the measured strains. A schematic of a strain gauge balance is shown in figure:

Sections A & B are moment measuring stations. C consists of thin parallel bending strips sensitive to axial force. Six strain gauge bridges produce six outputs (R1..R6) related to the six applied forces / moments (Normal force, side force, axial force pitching moment, yawing moment and rolling moment). The relation is linear and is written as

=

6

1

66

11

6

1

..........

F

F

C

C

R

R&&

C11C66 are established by calibration. Once this is done one can use the balance to measure forces using the inverse relation

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=

6

1

66

11

6

1

..........

R

R

U

U

F

F&&

where [U] is the user matrix and is the inverse of the calibration matrix [C] Qualitative studies of flow can be done using flow visualization by tufts or by using smoke. The second method generally needs a separate wind tunnel specially designed for the purpose. Careful introduction of smoke and appropriate lighting to illuminate the smoke and not the tunnel walls are essential for good visualization of the streamline pattern in a complex flow.

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9. Safety in Aviation The level of safety expected in civil aviation is extremely high. Safety is defined as freedom from accident and is a statistical concept. The British Civil Aviation Regulations (BCAR) expects aircraft to be designed for a level of safety of about 1 accident or less in 107 flights. (This corresponds to roughly 10,000 years of average use on a civil airplane). Actual level of safety in commercial operation is about a tenth of this value. BCAR defines various types of events having a bearing on safety. Ex: engine shut down in flight, hard landing, fire warning in flight etc. These are more frequent them the level quoted above. Major accidents involving fatalities are expected to reach the BCAR level of safety. Design for safety therefore involves statistical calculations and book keeping of various events having a bearing on safety. 9.1 An illustration: Consider the take off of a twin engine airplane from a runway of well defined length. It is assumed that there are obstacles of various sorts (buildings, towers, power lines etc) outside the airport, but these are below a certain surface (called the take off surface) generally defined as having a slope of 1.6%. Normal take off using both engines provides adequate performance for the airplane to clear the take off surface by a wide margin. But if an engine fails during take off, there is a possibility of the airplane falling below the take off surface and thus creating an accident by hitting an obstacle. BCAR demands that the possibility of this event should be less than once in 107 flights. The airplane designer / manufacturer/ operator together must make sure that this level of safety is assured to the satisfaction of the certifying authority. It implies that take off conditions of the airplane (all up weight, engine power, flap setting) for the airfield conditions (length of runway, altitude of airport, air temperature at airport etc) are such that, if an engine fails during any point of take off run, the airplane can either safely stop within the available runway length or continue further, take off clear the obstacles and climb to 1500 ft go round and come back and land safely. The problem is complex, but safety is ensured by defining clearly all the parameters at take off and laying down an operating procedure which ensures safely. BCAR demands clear definition of maximum permissible weight at take off for any given airfield (altitude, temperature) conditions, rotation speed, decision speed, take off speed and enroute climb speed etc., relevant to the flight of the aircraft on one engine and the minimum performance in terms of climb gradient in the various take off segments. (2.4% in third segment, 0.8% enroute) Being based on statistical reasoning these numbers have to be interpreted in a statistical sense and words like gross and net have only a statistical meaning. Typical extracts of the relevant performance capability of a typical airplane designed as per BCAR is enclosed as an illustration.

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A second problem of interest from safety point of view is the possibility of engine failures in cruise. In the event of one engine failure, the airplane can look for a landing airfield so that the possibility of the second engine failing before landing is minimized. In the case of long range flights over an ocean, there is a real possibility of second engine failure before finding a landing strip and the probability of this happening should be calculated and demonstrated to be better in 10-7. If this cannot be satisfactorily proved, aircraft with three or more engines will have to be flown on such routes. Indeed, long range flights are performed with 3 or 4 engined aircraft for this reason. 9.2 Structural safety The concept of safety as defined by BCAR can be extended to cover structural strength. Interpreted this way probability of structural failure of an airplane in flight should be less than BCAR design level (10-7) In this context one may define design loads on structural members. Maximum applied load for a component (the limit load) with a suitable margin for uncertainty is defined as the design load for the component. The strength of a component is defined in terms of the proof load and the ultimate load. The proof load is the load at which there is barely noticeable permanent deformation of the structure. The structure is still airworthy. The ultimate load is the load at which the component fails completely or collapses, this load is roughly around 1.5 times the proof load for aluminum structures. The designer has to ensure that the proof load for a structural element is not exceeded by design load in flight to a probability of 10-7. It is also insisted upon (for aluminium structures) that 1.5 times the design limit load does not exceed the ultimate load for the element. The above statements are on a statistical basis and to apply them, information is required about statistics of applied loads and variability of structural strength. These

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are established based on actual test data. If test results are insufficient to conclusively establish these, margins may be required for allowing for them. BCAR provides guide lines for determining applied loads on structural elements in the form V-n diagrams for maneuver loads and gust loads. Calculations and Structural tests on components and / or complete structures are required for establishing proof and ultimate loads of structural elements. The above design philosophy is inadequate to meet the needs of fatigue failure of components. Safety in fatigue is ensured by the concept of safe life within which structural failure is unlikely (to a probability of 1 in 107). Inspections of structures are carried out at intervals so that the smallest detectable crack, if present during one inspection, will not grow to catastrophic proportions before the next inspection. Thus fatigue life calculations and tests and crack propagation tests are required for certifying a structure for fatigue life.

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10. Aircraft propulsion Aircraft propulsion is based on production of thrust by imparting additional momentum to air entering the propulsion unit. Propulsive efficiency is the efficiency with which mechanical energy of the power plant is converted into propulsive work and is derived from momentum and energy considerations as below: vo vw vo = in coming stream velocity ( flight speed ) vw = wake velocity ( relative to propulsion unit )

m = air mass flow rate into the unit then,

thrust =

m ( vw vo)

Thrust work =

m ( vw vo) vo

Mechanical energy input =

m ( vw vo)2

propulsive efficiency = useful work / energy input

=

m ( vw vo) vo /

m ( v2w v2w) = 2 vo / (vw + vo)

Note that for high propulsive efficiency, vw should not be much larger than vo. Thus, turbojet engines with vw > 500 m/s would be quite inefficient at low speeds (say 50 m/s).

1.0

0.5

0 1.0 2.0 3.0

Vw / Vo

5.0

Vw / Vo Vw / Vo

4.0

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10.1 Propellers A propeller basically consists of blades in the form of rotating wings driven by an engine. The component of lift on the rotating wing produces thrust. Propeller theory is based on blade element properties and momentum considerations.

Axial flow velocity = (vo + vw)/ 2 The figure above indicates the general flow near a propeller. Note that the flow at the propeller disc is (vo + vw)/ 2 Propeller characteristics are defined by the following parameters J = V / nD or = V / n D (J = ) CT = T / n2 D4 CP = P / n3 D5, = propeller efficiency Here V = flight speed n = engine RPS T = Thrust P = power absorbed D = Prop. Diameter = air density The above dimensionless characteristics for a typical propeller are indicated in figure

max ~ 70% to 80%

() ()

CT

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Propellers with variable pitch (the blades are rotatable about radial axes so that the incidence of the blades i.e. pitch can be adjusted) running at constant speed have superior characteristics and are generally used on large aircraft. (Fine pitch is good for low speed take off and climb while coarse pitch is more suitable for cruise.) 10.2 Power Plants for Driving Propellers Piston engines using aviation gasoline (100 octane) are generally used to power small airplanes. To improve their altitude performance, supercharging is used. Exhaust driven turbo superchargers are common. A few aviation diesel engines exist and they are primarily for large range applications. There seems to be some current interest in developing them for general aviation applications. More commonly turbo-shaft engines are coupled to propellers using large ratio gear boxes ( to match the typical rotation speed of prop (1000 to 2000 rpm) to turbine engine speeds (10000 20000 rpm or even higher ). Propellers are suitable for flight mach numbers of 0.6 or less. At higher speeds the propellers tips have to run at supersonic speeds and the efficiency is very much reduced and noise level increases. 10.3 Propulsion using the Gas Turbine Engine The first turbine based propulsion unit to displace the piston engine + propeller was the turbojet, the principle is given below.

Air is first compressed and then heated by burning fuel in it. The hot gas is partially expanded in a turbine and the work produced is used to drive the compressor. The extra pressure is converted into kinetic energy of the jet which is used directly for propulsion. As materials cannot withstand the adiabatic flame temperature of about 2500oC (Nickel alloys can stand about 1100oC; other alloys are worse) maximum gas temperature in the cycle is limited by this and excess air is used in the combustion chambers. Thus extra oxygen is available in the exhaust and additional power (at lower thermodynamic efficiency) can be obtained by burning fuel after the turbine but before the nozzle. This is called after burning or reheat and is used on combat aircraft for short periods or at high speeds.

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The propulsive efficiency of a turbojet is enhanced by using a front mounted ducted fan or bypassing some air to the nozzle after partial compression. These engines thus have two streams of gas flow relatively cold flow in the bypass stream and the core flow which is hot. Bypass ratios of 0.5 to 5 (in relation to the core flow are used). Low bypass engines are used on combat aircraft. High bypass units are used in civil transports. Thrust reversers which partially deflect propelling jet into the flight direction to produce negative thrust are used on civil aircrafts during landing. Engine noise is an important problem in civil aviation. Noise rises as a high power of vw (~vw6) and turbojets are the most noisy. Turbofans used in civil aircraft are much less noisy. Noise absorption devices are used in the intake ducts of these engines to reduce compressor generated noise. Combat aircraft use vectoring nozzles to change the thrust direction without moving the engine. Vectored thrust is useful for producing control moments about pitch and yaw axes of the airplane, particularly at the low end of the speed envelope when aerodynamic controls are weak.

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11. Airplane Performance Airplane performance can be calculated based on the drag polar of an airplane which is of the form CD = A + B CL2 Where A and B constants depending on airplane configuration and flap setting. As an illustration, rate of climb of an aircraft can be calculated from equilibrium considerations as below,

= climb angle Clearly sin = (T-D) / W or rate of climb, R/C = V sin = (T-D)V/W Here D and L are related to aircraft as D = V2CDS L = V2CLS = W and CD = A + B CL2 Using the above equation one can calculate rate of climb at any flight speed. The principle is illustrated below.

Range of an aircraft can be calculated using Breguets formula derived as below.

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R = V t where R = range w/t = -T C where w/t = rate of weight change due to fuel consumption. = (-D/L) WC where C = s.f.c. T= D, W = L for equilibrium implies that R = L/D. V/C. ln (Winitial/ Wfinal) V = flight speed, L/D = lift to drag ratio in cruise. The formula is accurate to a few percent typically.

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12. Airplane Stability in the Longitudinal Plane

We now introduce the concept of static stability. If a small disturbance is given to incidence , the resulting aerodynamic forces must tend to restore the original .

For small change in , the aerodynamic forces along lift direction act at a point on the axis of the airplane called the neutral point.

Neutral point is property of the aerodynamic configuration of the airplane. For static stability, the airplane C.G. must be ahead of the neutral point so as to produce a returning moment (negative pitching moment) after an increase of . Control of the airplane in pitch (choice of equilibrium ) is possible when the elevator is deflected to create a pitching moment to overcome the moment due to static stability. The figure below is illustrative.

= elevator deflection Note: Cm = 0 corresponds to steady flight

= 0 (elevator neutral) leads to steady flight at = 0 = -ve max leads to steady flight at = max etc.

Lw M

L

LT

e = +ve Max

e = -ve Max

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Note: Cm Vs curves need not be linear. Some times Cm - curves have stable equilibrium at very high as in figure below. This leads to what is called deep stall.

Stable equilibrium at high (deep stall)

T Tail configurations are prone to deep stall. V Tail or twin tail configurations are better 12.1 Lateral Stability and Control Lateral stability is affected by fin area and location (weathercock stability) as well as dihedral effect (rolling moment due to side slip). Sweep and dihedral angle affects this property. Rudder produces a strong yawing moment (required during an engine failure on twin engine aircraft). 12.2 Control of Aircraft in Normal Flight The pilot controls the motion of the aircraft using four primary controls (throttle, elevator. rudder, and aileron). Manual controls are suitable for small aircraft. Large aircraft need power assistance. Aircraft operating over a wide flight envelope (loading, speed, altitude etc.) have poor handling characteristics over part of their flight envelope. (Poor response to pilot input in terms of frequency content and damping of the ensuing motion). Stability augmentation systems (e.g. yaw damper) are used on many civil aircraft. Full fly by wire control systems offer enhanced maneuverability and superior handling qualities.

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12.3 Fly by Wire (FBW) Control Systems These systems use active control technology (ACT). The technology offers the following benefits.

Improved flying qualities Improved performance by use of the concept of control configure vehicle.

Unstable configurations can be used Enhanced safety due to envelope protection. Enhanced stealth due to smaller control surfaces. Enhanced maneuver capability. ( using additional control concepts like

thrust vectoring )

The ACT is based on the use of sensors for flight variables and using the sensed motion for actuating the control surfaces using a computer generated control law. A typical FBW control system is shown below.

u = k * (y-yc) + uc : control law p = pilot command vector = p(xp, xq, xr)

y = y( p,q,r, , ) : sensed feedback vector u = u(e, a, r, tv, c ) : yc = fy. where tv is thrust vector control and c is canard control Sensors include air data variables and inertial rotation rates.

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The flight control system can include many failure modes as below

Typical failure modes

Basic mode

Inertia measuring unit disengage

Fixed gain mode

Loss of inertial sensors

Nose boom and , Sensor failure

Surface