Introduction to Aerospace Engineering E-Book

Ethirajan Rathakrishnan

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 436

Veröffentlichungsjahr: 2021

Beschreibung

Provides a broad and accessible introduction to the field of aerospace engineering, ideal for semester-long courses  

Aerospace engineering, the field of engineering focused on the development of aircraft and spacecraft, is taught at universities in both dedicated aerospace engineering programs as well as in wider mechanical engineering curriculums around the world-yet accessible introductory textbooks covering all essential areas of the subject are rare. Filling this significant gap in the market, Introduction to Aerospace Engineering: Basic Principles of Flight provides beginning students with a strong foundational knowledge of the key concepts they will further explore as they advance through their studies.  

Designed to align with the curriculum of a single-semester course, this comprehensive textbook offers a student-friendly presentation that combines the theoretical and practical aspects of aerospace engineering. Clear and concise chapters cover the laws of aerodynamics, pressure, and atmospheric modeling, aircraft configurations, the forces of flight, stability and control, rockets, propulsion, and more. Detailed illustrations, well-defined equations, end-of-chapter summaries, and ample review questions throughout the text ensure students understand the core topics of aerodynamics, propulsion, flight mechanics, and aircraft performance. Drawn from the author’s thirty years’ experience teaching the subject to countless numbers of university students, this much-needed textbook:  

• Explains basic vocabulary and fundamental aerodynamic concepts  
• Describes aircraft configurations, low-speed aerofoils, high-lift devices, and rockets  
• Covers essential topics including thrust, propulsion, performance, maneuvers, and stability and control 
• Introduces each topic in a concise and straightforward manner as students are guided through progressively more advanced material 
• Includes access to companion website containing a solutions manual and lecture slides for instructors 

Introduction to Aerospace Engineering: Basic Principles of Flight is the perfect "one stop" textbook for instructors, undergraduates, and graduate students in Introduction to Aerospace Engineering or Introduction to Flight courses in Aerospace Engineering or Mechanical Engineering programs.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

Dedication

Preface

About the Author

About the Companion Website

1 Basics

1.1 Introduction

1.2 Overview

1.3 Modern Era

1.4 Conservation Laws

1.5 Incompressible Aerodynamics

1.6 Compressible Aerodynamics

1.7 Vocabulary

1.8 Aerodynamics in Other Fields

1.9 Essence of Fluid Mechanics

1.10 Summary

Notes

2 International Standard Atmosphere

2.1 Layers in the ISA

2.2 Pressure Modelling

2.3 Density Modelling

2.4 Relative Density

2.5 Altimeter

2.6 Summary

3 Aircraft Configurations

3.1 Structure

3.2 Propulsion

3.3 Summary

4 Low‐Speed Aerofoils

4.1 Introduction

4.2 The Aerofoil

4.3 Aerodynamic Forces and Moments on an Aerofoil

4.4 Force and Moment Coefficients

4.5 Pressure Distribution

4.6 Pressure Distribution Variation with Incidence Angle

4.7 The Lift‐Curve Slope

4.8 Profile Drag

4.9 Pitching Moment

4.10 Movement of Centre of Pressure

4.11 Finite or Three‐Dimensional Wing

4.12 Geometrical Parameters of a Finite Wing

4.13 Wing Geometrical Parameters

4.14 Span‐Wise Flow Variation

4.15 Lift and Downwash

4.16 The Lift Curve of a Finite Wing

4.17 Induced Drag

4.18 The Total Drag of a Wing

4.19 Aspect Ratio Effect on Aerodynamic Characteristics

4.20 Pitching Moment

4.21 The Complete Aircraft

4.22 Straight and Level Flight

4.23 Total Drag

4.24 Reynolds Number Effect

4.25 Variation of Drag in Straight and Level Flight

4.26 The Minimum Power Condition

4.27 Minimum Drag‐to‐Velocity Ratio

4.28 The Stall

4.29 The Effect of Protuberances

4.30 Summary

Note

5 High‐Lift Devices

5.1 Introduction

5.2 The Trailing Edge Flap

5.3 The Plain Flap

5.4 The Split Flap

5.5 The Slotted Flap

5.6 The Fowler Flap

5.7 Comparison of Different Types of Flaps

5.8 Flap Effect on Aerodynamic Centre and Stability

5.9 The Leading Edge Slat

5.10 The Leading Edge Flap

5.11 Boundary Layer Control

5.12 Boundary Layer Suction

5.13 The Jet Flap

5.14 Summary

6 Thrust

6.1 Introduction

6.2 Thrust Generation

6.3 Turbojet

6.4 Turboprop and Turboshaft Engines

6.5 Ramjet and Scramjet

6.6 The Ideal Ramjet

6.7 Rocket Propulsion

6.8 Propeller Engines

6.9 Thrust and Momentum

6.10 Bypass and Turbofan Engines

6.11 The Propeller

6.12 The Slipstream

6.13 Gyroscopic Effect

6.14 Swing on Take‐Off

6.15 Thermodynamic Cycles of Jet Propulsion

6.16 Summary

7 Level Flight

7.1 Introduction

7.2 The Forces in Level Flight

7.3 Equilibrium Condition

7.4 Balancing the Forces

7.5 Range Maximum

7.6 Altitude Effect on Propeller Efficiency

7.7 Wind Effect on Range

7.8 Endurance of Flight

7.9 Range Maximum

7.10 Endurance of Jet Engine

7.11 Summary

8 Gliding

8.1 Introduction

8.2 Angle of Glide

8.3 Effect of Weight on Gliding

8.4 Endurance of Glide

8.5 Gliding Angle

8.6 Landing

8.7 Stalling Speed

8.8 High‐Lift Aerofoils

8.9 Wing Loading

8.10 Landing Speed

8.11 Short and Vertical Take‐Off and Landing

8.12 The Helicopter

8.13 Jet Lift

8.14 Hovercraft

8.15 Landing

8.16 Effect of Flaps on Trim

8.17 Summary

Notes

9 Performance

9.1 Introduction

9.2 Take‐Off

9.3 Climbing

9.4 Power Curves: Propeller Engine

9.5 Maximum and Minimum Speeds in Horizontal Flight

9.6 Effect of Engine Power Variation

9.7 Flight Altitude Effect on Engine Power

9.8 Ceiling

9.9 Effect of Weight on Performance

9.10 Jet Propulsion Effect on Performance

9.11 Summary

10 Stability and Control

10.1 Introduction

10.2 Longitudinal Stability

10.3 Longitudinal Dihedral

10.4 Lateral Stability

10.5 Directional Stability

10.6 Lateral and Directional Stability

10.7 Control of an Aircraft

10.8 Balanced Control

10.9 Mass Balance

10.10 Control at Low Speeds

10.11 Power Controls

10.12 Dynamic Instability

10.13 Summary

11 Manoeuvres

11.1 Introduction

11.2 Acceleration

11.3 Pulling Out from a Dive

11.4 Correct Angles of Bank

11.5 Other Problems of Turning

11.6 Steep Bank

11.7 Aerobatics

11.8 Inverted Manoeuvres

11.9 Abnormal Weather

11.10 Manoeuvrability

11.11 Summary

12 Rockets

12.1 Introduction

12.2 Chemical Rocket

12.3 Engine Design

12.4 Thrust Generation

12.5 Specific Impulse

12.6 Rocket Equation

12.7 Efficiency

12.8 Trajectories

12.9 High‐Exhaust‐Velocity, Low‐Thrust Trajectories

12.10 Plasma and Electric Propulsion

12.11 Pulsed Plasma Thruster

12.12 Summary

Note

References

Appendix A

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Common systems of units.

Table 1.2 Units of some secondary variables.

Chapter 2

Table 2.1 Different layers in standard atmosphere, along with the temperature...

Table 2.2 Some representative values of pressure and temperature in the ICAO ...

Table 2.3 Pressure altitude versus pressure.

a

Table 2.4 Properties of standard atmosphere.

Chapter 6

Table 6.1 Typical range of thermal, propulsive, and combustion efficiency.

Chapter 12

Table 12.1 Some liquid and solid propellants and their specific impulse

Table 12.2 Rocket development events

2

Table A.1 SI units and their conversion to US units.

List of Illustrations

Chapter 1

Figure 1.1 Flow through a constant area pipe.

Figure 1.2 Force variation with time.

Chapter 2

Figure 2.1 Temperature variation in the standard atmosphere.

Figure 2.2 An element in atmosphere.

Chapter 3

Figure 3.1 Schematic views of Boeing 747 aircraft.

Chapter 4

Figure 4.1 Section of an aerofoil.

Figure 4.2 Aerodynamic force on an aerofoil.

Figure 4.3 Lift, drag, and pitching moment acting on an aerofoil.

Figure 4.4 Surface pressure distribution over an aerofoil.

Figure 4.5 Pressure coefficient (

) distribution over an aerofoil.

Figure 4.6 An aerofoil at an angle of attack.

Figure 4.7 Pressure distribution around a cambered aerofoil.

Figure 4.8 Lift curve for a two‐dimensional aerofoil.

Figure 4.9 Variation of profile drag coefficient and

with incidence.

Figure 4.10 Variation of drag coefficient with lift coefficient.

Figure 4.11 Variation of

with

for an aerofoil section.

Figure 4.12 Illustration of force and moment at

,

, and a general referenc...

Figure 4.13 Movement of centre of pressure with increase of incidence.

Figure 4.14 Movement of

with incidence for positive and negative lifts.

Figure 4.15 Geometric parameters of some wing planforms: (a) rectangular win...

Figure 4.16 (a) Gross and (b) net areas of a wing.

Figure 4.17 Unswept, tapered wing with geometric twist (washout).

Figure 4.18 Span‐wise pressure gradient on the wing surfaces.

Figure 4.19 Flow pattern on the upper and lower surfaces of a finite wing.

Figure 4.20 Vortex shedding from the trailing edge of a finite wing.

Figure 4.21 Counter rotating vortices at the tips of a finite wing.

Figure 4.22 Span‐wise variation of the strength of the combined bound vortex...

Figure 4.23 A control volume for uniform flow past an aerofoil.

Figure 4.24 Lift curves for wings of different aspect ratio.

Figure 4.25 The forward speed (

) of aerofoil and the resultant velocity (

)...

Figure 4.26 Lift and drag caused by the downwash around an aerofoil.

Figure 4.27 Elliptical load distribution over a wing.

Figure 4.28 Drag polar for a typical wing at low incidence.

Figure 4.29 Variation of

with

and &LWx1f707;.

Figure 4.30 Variation of

with

for different aspect ratio.

Figure 4.31 Variation of aerodynamic efficiency with

.

Figure 4.32

variation with

as a function of aspect ratio.

Figure 4.33 Drag curve for a wing for which stall is (a) sudden and (b) grad...

Chapter 5

Figure 5.1 An aircraft wing with flap.

Figure 5.2 Effect of flap deflection on lift curve.

Figure 5.3 Pressure distribution around the wing with flap in neutral and de...

Figure 5.4 Profile with split flap in (a) neutral and (b) deflected position...

Figure 5.5 A slotted flap in (a) deflected and (b) neutral positions.

Figure 5.6 A Fowler flap in neutral and deflected positions.

Figure 5.7 Lift coefficient variation with flap deflection angle.

Figure 5.8 Drag polar for different flaps.

Figure 5.9 Variation of maximum lift coefficient increment with flap deflect...

Figure 5.10 A zap flap in neutral and deflected positions.

Figure 5.11 Sectional view of a wing with leading edge slat.

Figure 5.12 Illustration of leading edge slat on

.

Figure 5.13 A separation bubble just behind the leading edge of an aerofoil....

Figure 5.14 An aerofoil with leading edge camber.

Figure 5.15 An aerofoil with leading edge flap.

Figure 5.16 Variation of

with incidence for wings with and without leading...

Figure 5.17 Illustration of boundary layer blowing through a slit near the n...

Figure 5.18 A blown flap ahead of a flap.

Figure 5.19 An aerofoil with suction ports over its upper surface.

Figure 5.20 A jet flap.

Chapter 6

Figure 6.1 Illustration of flow through gas turbine engine.

Figure 6.2 Schematic diagram illustrating the components of a jet engine.

Figure 6.3 A view of complete engine.

Figure 6.4 A view of turbojet engine.

Figure 6.5 A view of turboprop engine.

Figure 6.6 A view of turbofan engine.

Figure 6.7 A view of turboshaft engine.

Figure 6.8 A view of ramjet engine.

Figure 6.9 Schematic diagram illustrating the components of a jet engine.

Figure 6.10 Schematic of a ramjet engine. (

) Freestream; (1) oblique shock;...

Figure 6.11

–

diagram of an ideal ramjet process.

Figure 6.12 A simple rocket motor.

Figure 6.13 A typical propeller engine.

Figure 6.14 Schematic of a turbofan engine.

Figure 6.15 Lift and drag acting on a moving propeller blade.

Figure 6.16 Thrust and resistance acting on a moving propeller blade.

Figure 6.17 Helical path travelled by various sections of propeller blade.

Figure 6.18 Variation of blade angle.

Figure 6.19 Blade angle.

Figure 6.20 Blade angle.

Figure 6.21

–

diagram of Brayton cycle.

Figure 6.22 Schematic diagram of supersonic ramjet engine. (1) Freestream; (...

Figure 6.23

–

diagram of turbojet cycle without afterburner.

Figure 6.24

–

diagram of turbojet cycle with afterburner.

Chapter 7

Figure 7.1 Forces acting on an aircraft in steady level flight.

Figure 7.2 An aircraft in flight with forces acting through a single point....

Figure 7.3 Moment due to lift and weight balanced by moment due to drag and ...

Figure 7.4 Lift generated by the tailplane.

Figure 7.5 Down load from tail balancing the effect of rearward location of ...

Figure 7.6 Up load from tail balancing the nose‐up moment caused by the wing...

Figure 7.7 Effect of downwash on the tail.

Figure 7.8 The forces acing on the aircraft in level flight.

Chapter 8

Figure 8.1 Forces acting on an aircraft during a glide.

Figure 8.2 Wind effect on glide.

Figure 8.3 Some popular air brakes: (a) spoiler on wing top, (b) spoiler at ...

Figure 8.4 Attitudes of (a) maximum speed, (b) normal cruise flight, (c) nor...

Figure 8.5 Different attitudes of aircraft during landing: (a) tail hitting ...

Figure 8.6 The concept of Custer Channel Wing.

Figure 8.7 Illustration of landing phases of flight.

Figure 8.8 Flow around a wing with flap (a) neutral and (b) deflected down....

Chapter 9

Figure 9.1 Forces acting on an aircraft during a climb.

Figure 9.2 Power available and power required curves as a function of flight...

Figure 9.3 Altitude effect on the available and required power.

Chapter 10

Figure 10.1 Illustration of flight modes an aircraft left to itself would ex...

Figure 10.2 Longitudinal dihedral angle.

Figure 10.3 An aircraft with dihedral angle.

Figure 10.4 An aircraft with rolling tendency.

Figure 10.5 An aircraft sideslipping.

Figure 10.6 Resultant force on a high‐wing aircraft in sideslip.

Figure 10.7 An aircraft with sweepback in sideslip.

Figure 10.8 A high‐fin aircraft in sideslip.

Figure 10.9 Flow due to sideslip on a low‐slung fuselage.

Figure 10.10 An aircraft in level flight (a) before disturbance and (b) afte...

Figure 10.11 (a) Main control surface of aircraft. (b) Flow past a fin with ...

Figure 10.12 A hinged control surface.

Figure 10.13 (a) Horn balance and (b) inset hinge balance.

Figure 10.14 Movements of control tab.

Figure 10.15 Location of control tab.

Figure 10.16 Mass balancing of an aircraft wing.

Figure 10.17 Forces on an aircraft during a turn at large angle of attack.

Figure 10.18 Fraise ailerons.

Figure 10.19 Differential ailerons.

Figure 10.20 Slot‐cum‐aileron control.

Figure 10.21 Spoiler.

Chapter 11

Figure 11.1 Illustration of translational and rotational motions of an aircr...

Figure 11.2 Pulling out of a dive.

Figure 11.3 Forces acting on an aircraft in turn.

Figure 11.4 An aircraft in climbing turn.

Figure 11.5 (a) An aircraft in loop and (b) the accelerometer diagram for th...

Figure 11.6 Illustration of path by an aircraft during spin.

Figure 11.7 Flattening of the spinning aircraft due to centrifugal force.

Figure 11.8 Illustration of one full rotation of an aircraft in spin.

Figure 11.9 An aircraft in sideslip.

Figure 11.10 Forces on an aircraft during nosedive.

Figure 11.11 Loads on an aircraft in upside‐down flight.

Figure 11.12 Inverted loop.

Chapter 12

Figure 12.1 Illustration of rocket thrust.

Figure 12.2 Thrust produced by the combustion gases.

Figure 12.3 Schematic diagram of liquid‐propellant rocket.

Figure 12.4 Schematic diagram of solid‐propellant rocket.

Figure 12.5 Control volume surrounding a rocket engine.

Figure 12.6 A moving rocket.

Figure 12.7 Exhaust velocity variation with payload fraction.

Figure 12.8 Propulsive efficiency variation with

.

Figure 12.9 Approximate positions for the Earth–Moon or Sun–Earth Lagrange p...

Figure 12.10 Energy per unit mass on the circular orbit and Hohmann trajecto...

Figure 12.11 Jupiter flight path at one Jovian radius, starting from an Eart...

Figure 12.12 Payload fraction variation with

.

Guide

Cover

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Introduction to Aerospace Engineering

Basic Principles of Flight

Ethirajan Rathakrishnan

Indian Institute of Technology, Kanpur

This edition first published 2021

© 2021 John Wiley & Sons, Inc.

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Library of Congress Cataloging‐in‐Publication Data

Names: Rathakrishnan, Ethirajan, author.

Title: Introduction to aerospace engineering : basic principles of flight /

    Ethirajan Rathakrishnan.

Description: First edition. | Hoboken, NJ : Wiley, 2022. | Includes

    bibliographical references and index.

Identifiers: LCCN 2021003268 (print) | LCCN 2021003269 (ebook) | ISBN

    9781119807155 (cloth) | ISBN 9781119806844 (adobe pdf) | ISBN

    9781119806868 (epub)

Subjects: LCSH: Aerodynamics. | Aerospace engineering.

Classification: LCC TL570 . R3295 2022 (print) | LCC TL570 (ebook) | DDC

    629.132/3–dc23

LC record available at https://lccn.loc.gov/2021003268

LC ebook record available at https://lccn.loc.gov/2021003269

Cover Design: Wiley

Cover Image: © guvendemir/iStock/Getty Images

This book is dedicated to my parents,

Mr. Thammanur Shunmugam Ethirajan

and

Mrs. Aandaal Ethirajan

Ethirajan Rathakrishnan

Preface

This book has been developed to introduce the subject of Aerospace Engineering to the beginners. Introduction to aerospace engineering is a compulsory course for Aerospace Engineering students. This book, being the manuscript developed using the course material used in teaching this course for a long period, precisely presents the basics of theoretical and application aspects of the subject.

This book is developed based on the class tested material for the course Introduction to Aerospace Engineering, at BS and MS levels, taught by the author at Indian Institute of Technology Kanpur. The topics covered are; Basics, International Standard Atmosphere, Aircraft Configurations, Low‐Speed Aerofoils, High‐Lift Devices, Thrust, Level Flight, Gliding, Performance, Stability and Control, Manoeuvres, Rockets. All these topics are introduced in such a manner that the students studying these for the first time could comfortably follow and assimilate the material covered.

The material covered in this book is so designed that any beginner can follow it comfortably. The book is organised in a logical manner and the topics are discussed in a systematic manner.

My sincere thanks to my undergraduate and graduate students at Indian Institute of Technology Kanpur, who are directly and indirectly responsible for the development of this book.

My special thanks to Dr. S.M. Aravindh Kumar, Department of Aerospace Engineering, S.R.M. Institute of Science and Technology, Chennai, for critically checking the manuscript and giving some useful suggestions.

For instructors only, a companion Solutions Manual is available from John Wiley that contains typed solutions to the end‐of‐chapter problems.

Chennai, IndiaMarch 23, 2021

Ethirajan Rathakrishnan

About the Author

Ethirajan Rathakrishnan is professor of Aerospace Engineering at the Indian Institute of Technology Kanpur, India. He is well known internationally for his research in the area of high‐speed jets. The limit for the passive control of jets, called the Rathakrishnan Limit, is his contribution to the field of jet research, and the concept of breathing blunt nose(BBN), which simultaneously reduces the positive pressure at the nose and increases the low pressure at the base is his contribution to drag reduction at hypersonic speeds. Positioning the twin‐vortex Reynolds number at around 5000, by changing the geometry from cylinder, for which the maximum limit for the Reynolds number for positioning the twin‐vortex was found to be around 160, by von Karman, to flat plate, is his addition to vortex flow theory. He has published a large number of research articles in many reputed international journals. He is a Fellow of many professional societies including the Royal Aeronautical Society. Rathakrishnan serves as the Editor‐in‐Chief of the International Review of Aerospace Engineering (IREASE) and International Review of Mechanical Engineering (IREME) journals. He has authored 13 other books: Gas Dynamics, 7th ed. (PHI Learning, New Delhi, 2020); Fundamentals of Engineering Thermodynamics, 2nd ed. (PHI Learning, New Delhi, 2005); Fluid Mechanics: An Introduction, 4th ed. (PHI Learning, New Delhi, 2021); Gas Tables, 3rd ed. (Universities Press, Hyderabad, India, 2012); Theory of Compressible Flows (Maruzen Co., Ltd. Tokyo, Japan, 2008); Gas Dynamics Work Book, 2nd ed. (Praise Worthy Prize, Naples, Italy, 2013); Elements of Heat Transfer (CRC Press, Taylor & Francis Group, Boca Raton, FL, USA, 2012); Theoretical Aerodynamics (John Wiley, NJ, USA, 2013); High Enthalpy Gas Dynamics (John Wiley & Sons Inc., 2015); Dynamique Des Gaz (Praise Worthy Prize, Naples, Italy, 2015); and Instrumentation, Measurements and Experiments in Fluids, 2nd ed. (CRC Press, Taylor & Francis Group, Boca Raton, FL, USA, 2017), Helicopter Aerodynamics (PHI Learning, New Delhi, 2019); Applied Gas Dynamics 2nd ed. (John Wiley & Sons Inc., 2019).

About the Companion Website

This book is accompanied by a companion website:

www.wiley.com/go/Rathakrishnan/IntroductiontoAerospaceEngineering

The website has solutions manual and lecture slides.

1Basics

1.1 Introduction

Aerodynamics is the study of forces and the resulting motion of objects through the air. This word is coined with the two Greek words: aerios, concerning the air, and dynamis, meaning force. Judging from the story of Daedalus and Icarus,1 humans have been interested in aerodynamics and flying for thousands of years, although flying in a heavier‐than‐air machine has been possible only in the last century. Aerodynamics affects the motion of high‐speed flying machines, such as aircraft and rockets, and low‐speed machines, such as cars, trains, and so on. Therefore, aerodynamics may be described as a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a solid object. Aerodynamics is a subfield of fluid dynamics and gas dynamics. It is often used synonymously with gas dynamics, with the difference being that gas dynamics applies to all gases.

Understanding the flow field around an object is essential for calculating the forces and moments acting on the object. Typical properties calculated for a flow field include velocity, pressure, density, and temperature as a function of spatial position and time. Aerodynamics allows the definition and solution of equations for the conservation of mass, momentum, and energy in air. The use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations forms the scientific basis for heavier‐than‐air flight and a number of other technologies.

Aerodynamic problems can be classified according to the flow environment. External aerodynamics is the study of flow around solid objects of various shapes. Evaluating the lift and drag on an airplane or the shock waves that form in front of the nose of a rocket are examples of external aerodynamics. Internal aerodynamics is the study of flow through passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow through a jet engine.

Aerodynamic problems can also be classified according to whether the flow speed is below, near or above the speed of sound. A problem is called subsonic if all the speeds in the problem are less than the speed of sound, transonic if speeds both below and above the speed of sound are present, supersonic if the flow speed is greater than the speed of sound, and hypersonic if the flow speed is more than five times the speed of sound.

The influence of viscosity in the flow dictates a third classification. Some problems may encounter only very small viscous effects on the solution; therefore the viscosity can be considered to be negligible. The approximations made in solving these problems is the viscous effect that can be regarded as negligible. These are called inviscid flows. Flows for which viscosity cannot be neglected are called viscous flows.

1.2 Overview

Humans have been harnessing aerodynamic forces for thousands of years with sailboats and windmills [1]. Images and stories of flight have appeared throughout recorded history [2], such as the legendary story of Icarus and Daedalus [3]. Although observations of some aerodynamic effects such as wind resistance (for example, drag) were recorded by Aristotle, Leonardo da Vinci, and Galileo Galilei, very little effort was made to develop a rigorous quantitative theory of airflow prior to the seventeenth century.

In 1505, Leonardo da Vinci wrote the Codex (an ancient manuscript text in book form) on the Flight of Birds, one of the earliest treatises on aerodynamics. He was the first to note that the centre of gravity of a flying bird does not coincide with its centre of pressure, and he describes the construction of an ornithopter with flapping wings similar to birds.

Sir Isaac Newton was the first to develop a theory of air resistance [4], making him one of the first aerodynamicists. As a part of that theory, Newton considered that drag was due to the dimensions of the body, the density of the fluid, and the velocity raised to the second power. These all turned out to be correct for low‐speed flow. Newton also developed a law for the drag force on a flat plate inclined towards the direction of the fluid flow. Using for the drag force, for the density, for the area of the flat plate, for the flow velocity, and for the inclination angle, his law was expressed as

This equation is incorrect for the calculation of drag in most cases. Drag on a flat plate is closer to being linear with the angle of inclination as opposed to acting quadratically at low angles. The Newton formula can lead one to believe that flight is more difficult than it actually is, due to this overprediction of drag, and thus required thrust, which might have contributed to a delay in human flight. However, it is more correct for a very slender plate when the angle becomes large and flow separation occurs or if the flow speed is supersonic [5].

1.3 Modern Era

In 1738, the Dutch‐Swiss mathematician Daniel Bernoulli published Hydrodynamica. In this book Bernoulli described the fundamental relationship among pressure, density, and velocity, in particular Bernoulli's principle, which is one method to calculate aerodynamic lift [6]. More general equations of fluid flow – the Euler equations – were published by Leonhard Euler in 1757. The Euler equations were extended to incorporate the effects of viscosity in the first half of the eighteenth century, resulting in the Navier–Stokes equations.

Sir George Cayley is credited as the first person to identify the four aerodynamic forces of flight – weight, lift, drag, and thrust – and the relationships between them [7,8]. Cayley believed that the drag on a flying machine must be counteracted to enable level flight to occur. He also looked into the nature of aerodynamic shapes with low drag. Among the shapes he investigated were the cross sections of trout. This may appear counterintuitive; however, the bodies of fish are shaped to produce very low resistance as they travel through water. Their cross sections are sometimes very close to that of modern low‐drag aerofoils.

Air resistance experiments were carried out by investigators throughout the eighteenth and nineteenth centuries. Drag theories were developed by Jean le Rond d'Alembert [9], Gustav Kirchhoff [10], and Lord Rayleigh [11]. Equations for fluid flow with friction were developed by Claude‐Louis Navier [12] and George Gabriel Stokes [13]. To simulate fluid flow, many experiments involved immersing objects in streams of water or simply dropping them off the top of a tall building. Towards the end of this time period, Gustave Eiffel used his Eiffel Tower to assist in the drop testing of flat plates.

A more precise way to measure resistance is to place an object within an artificial, uniform stream of air where the velocity is known. The first person to experiment in this fashion was Francis Herbert Wenham, who in doing so constructed the first wind tunnel in 1871. Wenham was also a member of the first professional organisation dedicated to aeronautics, the Royal Aeronautical Society of the United Kingdom. Objects placed in wind tunnel as models are almost always smaller than in practice, so a method was needed to relate small‐scale models to their real‐life counterparts. This was achieved with the invention of the dimensionless Reynolds number by Osborne Reynolds [14]. In 1883, Reynolds also experimentally studied laminar to turbulent flow transition.

By the late nineteenth century, two problems were identified before heavier‐than‐air flight could be realised. The first was the creation of low‐drag, high‐lift aerodynamic wings. The second problem was how to determine the power needed for sustained flight. During this time, the groundwork was laid down for modern‐day fluid dynamics and aerodynamics, with other less scientifically inclined enthusiasts testing various flying machines with little success.

In 1889, Charles Renard, a French aeronautical engineer, became the first person to reasonably predict the power needed for sustained flight [15]. Renard and German physicist Hermann von Helmholtz explored the wing loading (weight‐to‐wing‐area ratio) of birds, eventually concluding that humans could not fly under their own power by attaching wings onto their arms. Otto Lilienthal, following the work of Sir George Cayley, was the first person to become highly successful with glider flights. Lilienthal believed that thin, curved aerofoils would produce high lift and low drag.

Octave Chanute provided a great service to those interested in aerodynamics and flying machines by publishing a book outlining all of the research conducted around the world up to 1997 [16].

1.3.1 Actual Flights

With the information contained in Chanute's book, the personal assistance of Chanute himself, and research carried out in their own wind tunnel, the Wright brothers gained enough knowledge of aerodynamics to fly the first powered aircraft on 17 December 1903. The Wright brothers' flight confirmed or disproved a number of aerodynamic theories. Newton's drag force theory was finally proved incorrect. This first widely publicised flight led to a more organised effort between aviators and scientists, leading the way to modern aerodynamics.

During the time of the first flights, Frederick W. Lanchester [17], Martin Wilhelm Kutta, and Nikolai Zhukovsky independently created theories that connected circulation of a fluid flow to lift. Kutta and Zhukovsky went on to develop a two‐dimensional wing theory. Expanding upon the work of Lanchester, Ludwig Prandtl is credited with developing the mathematics [18] behind thin‐aerofoil and lifting‐line theories and the boundary layers. Prandtl, a professor at the University of Göttingen, instructed many students who would play important roles in the development of aerodynamics, such as Theodore von Karman and Max Munk.

1.3.2 Compressibility Issues

At low speeds, the compressibility of air is not significant in relation to aircraft design, but as the airflow nears and exceeds the speed of sound, a host of new aerodynamic effects become important in the design of aircraft. These effects, often several of them at a time, made it very difficult for World War II‐era aircraft to reach speeds much beyond 800 km/h.

Some of the minor effects include changes to the airflow that lead to problems in control. For instance, the P‐38 Lightning with its thick high‐lift wing had a particular problem in high‐speed dives that led to a nose‐down condition. Pilots would enter dives and then find that they could no longer control the plane, which continued to nose‐down over a distance until it crashed. The problem was remedied by adding a ‘dive flap’ beneath the wing that altered the centre of pressure distribution so that the wing would not lose its lift [19].

A similar problem affected some models of the Supermarine Spitfire. At high speeds the ailerons could apply more torque than the Spitfire's thin wings could handle, and the entire wing would twist in the opposite direction. This meant that the plane would roll in the direction opposite to that which the pilot intended and led to a number of accidents. Earlier models were not fast enough, for handling this was felt as a problem, and so it was not noticed until later models of Spitfire like the Mk.IX started to appear. This was mitigated by adding considerable torsional rigidity to the wings and was wholly cured when the Mk.XIV was introduced.

The Messerschmitt Bf 109 and Mitsubishi Zero had the exact opposite problem in which the controls became ineffective. At higher speeds the pilot simply could not move the controls because there was too much airflow over the control surfaces. The planes would become difficult to manoeuvre, and at high enough speeds aircraft without this problem could outturn them.

These problems were eventually solved as jet aircraft reached transonic and supersonic speeds. German scientists in World War II experimented with swept wings. Their research was applied on the MiG‐15 and F‐86 Sabre and bombers such as the B‐47 Stratojet used swept wings that delay the onset of shock waves and reduce the drag. The all‐flying tailplane which is common on supersonic planes also helps to maintain control near the speed of sound.

Finally, another common problem that fits into this category is flutter. At some speeds, the airflow over the control surfaces will become turbulent, and the controls will start to flutter. If the speed of the fluttering is close to a harmonic of the control's movement, the resonance could break the control off completely. When problems with poor control at high speeds were first encountered, they were addressed by designing a new style of control surface with more power. However, this introduced a new resonant mode, and a number of planes were lost before this was discovered.

All of these effects are often mentioned in conjunction with the term ‘compressibility’, but in a manner of speaking, they are incorrectly used. From a strictly aerodynamic point of view, the term compressibility should refer only to those side effects arising as a result of the change in the nature of the airflow from incompressible (similar in effect to water) to compressible (acting as a gas) as the speed of sound is approached. There are two effects in particular, wave drag and critical Mach number.

Wave drag is a sudden rise in drag on the aircraft, caused by air building up in front of it. At lower speeds this air has time to ‘get out of the way’, guided by the air in front of it that is in contact with the aircraft. However, at the speed of sound, this can no longer happen, and the air that was previously following the streamline around the aircraft now hits it directly. The amount of power needed to overcome this effect is considerable. The critical Mach number is the speed at which some of the air passing over the aircraft becomes supersonic.

At the speed of sound, the way that lift is generated changes dramatically, from being dominated by Bernoulli's principle to forces generated by shock waves. Since the air on the top of the wing is travelling faster than on the bottom, due to the Bernoulli effect, at speeds close to the speed of sound, the air on the top of the wing will be accelerated to supersonic level. When this happens the distribution of lift changes dramatically, typically causing a powerful nose‐down trim. Since the aircraft normally approach these speeds only in a dive, pilots would report the aircraft attempting to nose‐dive into the ground.

An important aspect observed at hypersonic speeds is that the process of dissociation absorbs a great deal of energy in a reversible process. This greatly reduces the thermodynamic temperature of hypersonic gas decelerated near an aerospace vehicle. In transition regions, where this pressure dependent dissociation is incomplete, both the differential, constant‐pressure heat capacity, and (the volume/pressure differential ratio) will greatly increase. The latter has a pronounced effect on vehicle aerodynamics including stability.

1.3.3 Supersonic Speeds

As aircraft began to travel faster, aerodynamicists realised that the density of air began to change as it came into contact with an object, leading to a division of fluid flow into the incompressible and compressible regimes. In compressible aerodynamics, density and pressure both change, which is the basis for calculating the speed of sound. Newton was the first to develop a mathematical model for calculating the speed of sound, but it was not correct until Pierre‐Simon Laplace accounted for the molecular behaviour of gases and introduced the heat capacity ratio. The ratio of the flow speed to the speed of sound was named the Mach number after Ernst Mach, who was one of the first to investigate the properties of supersonic flow that included Schlieren photography techniques to visualise the changes in density. William John Macquorn Rankine and Pierre Henri Hugoniot independently developed the theory for flow properties before and after a shock wave. Jakob Ackeret led the initial work on calculating the lift and drag on a supersonic aerofoil [20]. Theodore von Karman and Hugh Latimer Dryden introduced the term transonic to describe flow speeds around Mach 1 where drag increases rapidly. Because of the increase in drag while approaching Mach 1, aerodynamicists and aviators disagreed on whether supersonic flight was achievable.

On 30 September 1935, an exclusive conference was held in Rome with the topic of high velocity flight and the possibility of breaking the sound barrier [21]. Participants included Theodore von Karman, Ludwig Prandtl, Jakob Ackeret, Eastman Jacobs, Adolf Busemann, Geoffrey Ingram Taylor, Gaetano Arturo Crocco, and Enrico Pistolesi. Ackeret presented a design for a supersonic wind tunnel. Busemann gave a presentation on the need for aircraft with swept wings for high speed flight. Eastman Jacobs, working for NACA, presented his optimised aerofoils for high subsonic speeds that led to some of the high‐performance American aircraft during World War II. Supersonic propulsion was also discussed. The sound barrier was broken using the Bell X‐1 aircraft 12 years later.

By the time the sound barrier was broken, much of the subsonic and low supersonic aerodynamics knowledge had matured. The Cold War (a state of political and military tension after World War II between powers in the Western Bloc (the United States, its NATO allies, and others such as Japan) and powers in the Eastern Bloc (the Soviet Union and its allies in the Warsaw Pact)) fuelled an ever evolving line of high‐performance aircraft. Computational fluid dynamics was started as an effort to solve for flow properties around complex objects and has rapidly grown to the point where entire aircraft can be designed using a computer, with wind tunnel tests followed by flight tests to confirm the computer predictions.

With some exceptions, the knowledge of hypersonic aerodynamics has matured between the 1960s and the present decade. Therefore, the goals of an aerodynamicist have shifted from understanding the behaviour of fluid flow to understanding how to engineer a vehicle to interact appropriately with the fluid flow. For example, while the behaviour of hypersonic flow is understood, building a scramjet aircraft to fly at hypersonic speeds has seen very limited success. Along with building a successful scramjet aircraft, the desire to improve the aerodynamic efficiency of current aircraft and propulsion systems will continue to fuel new research in aerodynamics. Nevertheless, there are still important problems in basic aerodynamic theory, such as in predicting transition to turbulence, and the existence and uniqueness of solutions to the Navier–Stokes equations.

1.3.4 Continuity Concept

The foundation of aerodynamic prediction is the continuity assumption. In reality, gases are composed of molecules that collide with one another and solid objects. To derive the equations of aerodynamics, fluid properties such as density and velocity are assumed to be well‐defined at infinitely small points and to vary continuously from one point to another. That is, the discrete molecular nature of a gas is ignored. The continuity assumption becomes less valid as a gas becomes more rarefied. In these cases statistical mechanics is a more valid method of solving the problem than continuum aerodynamics. The Knudsen number can be used to guide the choice between statistical mechanics and the continuum formulation of aerodynamics.

1.4 Conservation Laws

Aerodynamic problems are normally solved using conservation of mass, momentum, and energy, referred to as continuity, momentum, and energy equations. The conservation laws can be written in integral or differential form.

1.4.1 Conservation of Mass

If a certain mass of fluid enters a volume, it must either exit the volume or change the mass inside the volume. In fluid dynamics the continuity equation is analogous to Kirchhoff's current law (that is, ‘the sum of the currents flowing into a point in a circuit is equal to the sum of the currents flowing out of that same point’) in electric circuits. The differential form of the continuity equation is

where is the fluid density, is a velocity vector, and is time. Physically the equation also shows that mass is neither created nor destroyed in the control volume. For a steady‐state process, the rate at which mass enters the volume is equal to the rate at which it leaves the volume [22]. Consequently, the first term on the left‐hand side is then equal to zero. For flow through a tube with one inlet (state 1) and exit (state 2) as shown in Figure 1.1, the continuity equation may be written and solved as

where is the variable cross‐sectional area of the tube at the inlet and exit. For incompressible flows, the density remains constant.

Figure 1.1 Flow through a constant area pipe.

1.4.2 Conservation of Momentum

The momentum equation applies Newton's second law of motion to a control volume in a flow field, whereby force is equal to the time derivative of momentum. Both surface and body forces are accounted for in this equation. For instance, could be expanded into an expression for the frictional force acting on an internal flow:

For the pipe flow in Figure 1.1, control volume analysis gives

where the force is placed on the left‐hand side of the equation, assuming it acts with the flow moving in a left‐to‐right direction. Depending on the other properties of the flow, the resulting force could be negative that means it acts in the opposite direction as depicted in Figure 1.1. In aerodynamics, air is normally assumed to be a Newtonian fluid, which posits a linear relationship between the shear stress and the rate of strain of the fluid. The equation above is a vector equation: in a three‐dimensional flow, it can be expressed as three scalar equations. The conservation of momentum equations are often called the Navier–Stokes equations, while others use the term for the system that includes conversation of mass, conservation of momentum, and conservation of energy.

1.4.3 Conservation of Energy

Although energy can be converted from one form to another, the total energy in a given closed system remains constant:

where is enthalpy, is the thermal conductivity of the fluid, is temperature, and is the viscous dissipation function. The viscous dissipation function governs the rate at which mechanical energy of the flow is converted to heat. This term is always positive since, according to the second law of thermodynamics, viscosity cannot add energy to the control volume [23]. The expression on the left‐hand side is a material derivative. Again using the pipe flow in Figure 1.1, the energy equation in terms of the control volume may be written as

where the shaft work and heat transfer rate are assumed to be acting on the flow. They may be positive or negative depending on the problem.

The ideal gas law or another equation of state is often used in conjunction with these equations to form a determined system to solve for the unknown variables.

1.5 Incompressible Aerodynamics

An incompressible flow is characterised by a constant density. While all real fluids are compressible, a flow problem is often considered incompressible if the density changes in the problem have a small effect on the outputs of interest. This is more likely to be true when the flow speeds are significantly lower than the speed of sound. For higher speeds, the flow would encounter significant compressibility as it comes into contact with surfaces and slows down.

1.5.1 Subsonic Flow

Subsonic aerodynamics is the study of fluid motion that is slower than the speed of sound. There are several branches of subsonic flow, but one special case arises when the flow is inviscid, incompressible, and irrotational. This case is called potential flow. For this case, the differential equations used are simplified version of the governing equations of fluid dynamics, thus making a range of quick and easy solutions available to the aerodynamicist [24].

In solving a subsonic problem, one decision to be made by the aerodynamicist is whether to incorporate the effects of compressibility. Compressibility is a description of the amount of change of density in the problem. When the effects of compressibility on the solution are small, the aerodynamicist may choose to assume that density is constant. The problem is then an incompressible low‐speed aerodynamics problem. When the density is allowed to vary, the problem is called a compressible problem. In air, compressibility effects are usually ignored when the Mach number in the flow does not exceed 0.3. Above 0.3, the problem should be solved by using compressible aerodynamics [24].

1.6 Compressible Aerodynamics

According to the theory of aerodynamics, a flow is considered to be compressible if its change in density with respect to pressure is more than 5%. This means that – unlike incompressible flow – changes in density must be considered. In general, this is the case where the Mach number in part or all of the flow exceeds 0.3. The Mach 0.3 value is rather arbitrary, but it is used because gas flows with a Mach number below 0.3 demonstrate the changes in density with respect to the change in pressure of less than 5%. Furthermore, a maximum of 5% density change occurs at the stagnation point of an object immersed in the gas flow, and the density changes around the rest of the object will be significantly lower. Transonic, supersonic, and hypersonic flows are all compressible.

1.6.1 Transonic Flow

The term transonic refers to a range of velocities just below and above the local speed of sound (generally taken as Mach 0.8–1.2). It is defined as the range of speeds between the critical Mach number, when some parts of the airflow over an aircraft become supersonic, and a higher speed, typically near Mach 1.2, when all of the airflow is supersonic. Between these speeds some of the airflow is supersonic, and some is not.

1.6.2 Supersonic Flow

Supersonic aerodynamic problems are those involving flow speeds greater than the speed of sound. Calculating the lift on the Concorde during cruise can be an example of a supersonic aerodynamic problem.

Supersonic flow behaves very differently from subsonic flow. Fluids react to differences in pressure; pressure changes in a flow field is ‘informed’ to the flow by the sound waves. It is known that sound is an infinitesimal pressure difference propagating through a fluid; therefore the speed of sound in that fluid can be considered the fastest speed that ‘information’ can travel in the flow. This difference most obviously manifests itself in the case of a fluid striking an object. In front of that object, the fluid builds up a stagnation pressure as impact with the object brings the moving fluid to rest. In fluid travelling at subsonic speed, this pressure disturbance can propagate upstream, changing the flow pattern ahead of the object and giving the impression that the fluid ‘knows’ the object is there and is avoiding it. However, in a supersonic flow, the pressure disturbance cannot propagate upstream. Thus, when the fluid finally does strike the object, it is forced to change its properties – temperature, density, pressure, and Mach number – in an extremely violent and irreversible fashion across a shock wave. The presence of shock waves, along with the compressibility effects of high‐velocity fluids, is the central difference between supersonic and subsonic aerodynamic problems.

1.6.3 Hypersonic Flow

In aerodynamics, hypersonic speeds are speeds that are highly supersonic. In the 1970s, the term generally came to refer to speeds of Mach 5 (five times the speed of sound) and above. The hypersonic regime is a subset of the supersonic regime. Hypersonic flow is characterised by high‐temperature flow behind a shock wave, viscous interaction, and chemical dissociation of gas.

1.7 Vocabulary

The incompressible and compressible flow regimes produce many associated phenomena, such as boundary layers and turbulence.

1.7.1 Boundary Layers

The concept of a boundary layer is important in many aerodynamic problems. The viscosity and fluid friction in the air are approximated as being significant only in this thin layer. This principle makes aerodynamics much more tractable mathematically.

1.7.2 Turbulence

In aerodynamics, turbulence is characterised by chaotic, stochastic property changes in the flow. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. Flow that is not turbulent is called laminar flow. Incorporating all the characteristics, turbulence may be described as a ‘random three‐dimensional phenomenon, exhibiting multiplicity of scales, possessing vorticity, and showing very high dissipation’.

1.8 Aerodynamics in Other Fields