Aerodynamics

Foreword
Preface
About This Book
Contents
Part I Fundamentals of Aerodynamics
1 Introduction
1.1 Aerodynamics Research Tasks
1.2 History of Aerodynamics
1.2.1 Qualitative Knowledge and Practice
1.2.2 Low Speed Flow Theory
1.2.3 High-Speed Flow Theory
1.3 The Leading Role of Aerodynamics in the Development of Modern Aircraft
1.4 Aerodynamics Research Methods and Classification
1.5 Dimension and Unit
Exercises
2 Basic Properties of Fluids and Hydrostatics
2.1 Basic Properties of Fluids
2.1.1 Continuum Hypothesis
2.1.2 Fluidity of Fluid
2.1.3 Compressibility and Elasticity of Fluid
2.1.4 Viscosity of Fluid (Momentum Transport of Fluid)
2.1.5 The Thermal Conductivity of the Fluid (The Heat Transport of the Fluid)
2.1.6 Diffusivity of Fluid (Mass Transport of Fluid)
2.2 Classification of Forces Acting on a Differential Fluid Element
2.3 Isotropic Characteristics of Pressure at Any Point in Static Fluid
2.4 Euler Equilibrium Differential Equations
2.5 Pressure Distribution Law in Static Liquid in Gravitational Field
2.6 Equilibrium Law of Relative Static Liquid
2.7 Standard Atmosphere
Exercises
3 Foundation of Fluid Kinematics and Dynamics
3.1 Methods for Describing Fluid Motion
3.1.1 Lagrange Method (Particle Method or Particle System Method)
3.1.2 Euler Method (Space Point Method or Flow Field Method)
3.2 Basic Concepts of Flow Field
3.2.1 Steady and Unsteady Fields
3.2.2 Streamline and Path Line
3.2.3 One-Dimensional, Two-Dimensional and Three-Dimensional Flows
3.3 Motion Decomposition of a Differential Fluid Element
3.3.1 Basic Motion Forms of a Differential Fluid Element
3.3.2 Velocity Decomposition Theorem of Fluid Elements
3.4 Divergence and Curl of Velocity Field
3.4.1 Divergence of Velocity Field and Its Physical Significance
3.4.2 Curl and Velocity Potential Function of Velocity Field
3.5 Continuous Differential Equation
3.5.1 Continuity Differential Equation Based on Lagrange View
3.5.2 Continuity Differential Equation Based on Euler’s Viewpoint
3.6 Differential Equations of Ideal Fluid Motion (Euler Equations)
3.7 Bernoulli's Equation and Its Physical Significance
3.7.1 Bernoulli Equation
3.7.2 Application of Bernoulli Equation
3.8 Integral Equation of Fluid Motion
3.8.1 Basic Concepts of Control Volume and System
3.8.2 Lagrangian Integral Equations
3.8.3 Reynolds Transport Equation
3.8.4 Eulerian Integral Equations
3.8.5 Reynolds Transport Equation of the Control Volume with Arbitrary Movement Relative to the Fixed Coordinate System
3.9 Vortex Motion and Its Characteristics
3.9.1 Vortex Motion
3.9.2 Vorticity, Vorticity Flux and Circulation
Exercises
4 Plane Potential Flow of Ideal Incompressible Fluid
4.1 Basic Equations of Plane Potential Flow of Ideal Incompressible Fluid
4.1.1 Basic Equations of Irrotational Motion of an Ideal Incompressible Fluid
4.1.2 Properties of Velocity Potential Function
4.1.3 Stream Functions and Their Properties
4.1.4 Formulation of the Mathematical Problem of Steady Plane Potential Flow of Ideal Incompressible Fluid
4.2 Typical Singularity Potential Flow Solutions
4.2.1 Uniform Flow
4.2.2 Point Source (Sink)
4.2.3 Dipole
4.2.4 Point Vortex
4.3 Singularity Superposition Solution of Flow Around Some Simple Objects
4.3.1 Flow Around a Blunt Semi-infinite Body
4.3.2 Flow Around Rankine Pebbles
4.3.3 Flow Around a Circular Cylinder Without Circulation
4.3.4 Flow Around a Cylinder with Circulation
4.4 Numerical Method for Steady Flow Around Two-Dimensional Symmetrical Objects
Exercises
5 Fundamentals of Viscous Fluid Dynamics
5.1 The Viscosity of Fluid and Its Influence on Flow
5.1.1 Viscosity of Fluid
5.1.2 Characteristics of Viscous Fluid Movement
5.2 Deformation Matrix of a Differential Fluid Element
5.3 Stress State of Viscous Fluid
5.4 Generalized Newton’s Internal Friction Theorem (Constitutive Relationship)
5.5 Differential Equations of Viscous Fluid Motion—Navier–Stokes Equations
5.5.1 The Basic Differential Equations of Fluid Motion
5.5.2 Navier–Stokes Equations (Differential Equations of Viscous Fluid Motion)
5.5.3 Bernoulli Integral
5.6 Exact Solutions of Navier–Stokes Equations
5.6.1 Couette Flow (Shear Flow)
5.6.2 Poiseuille Flow (Pressure Gradient Flow)
5.6.3 Couette Flow and Poiseuille Flow Combination
5.6.4 Vortex Column and Its Induced Flow Field
5.6.5 Parallel Flow Along an Infinitely Long Slope Under Gravity
5.7 Basic Properties of Viscous Fluid Motion
5.7.1 Vorticity Transport Equation of Viscous Fluid Motion
5.7.2 Rotation of Viscous Fluid Motion
5.7.3 Diffusion of Viscous Fluid Vortex
5.7.4 Dissipation of Viscous Fluid Energy
5.8 Laminar Flow, Turbulent Flow and Its Energy Loss
5.8.1 Force of Viscous Fluid Clusters and Its Influence on Flow
5.8.2 Reynolds Transition Test
5.8.3 The Criterion of Flow Pattern—Critical Reynolds Number
5.8.4 Resistance Loss Classification
5.8.5 Definition of Turbulence
5.8.6 Basic Characteristics of Turbulence
5.8.7 The Concept of Reynolds Time Mean
5.8.8 Reynolds Time-Averaged Motion Equations
5.9 Turbulent Eddy Viscosity and Prandtl Mixing Length Theory
5.10 Similarity Principle and Dimensionless Differential Equations
5.10.1 Principles of Dimensional Analysis-π Theorem
5.10.2 Dimensionless N–S Equations
Exercises
6 Boundary Layer Theory and Its Approximation
6.1 Boundary Layer Approximation and Its Characteristics
6.1.1 The Influence of the Viscosity of the Flow Around a Large Reynolds Number Object
6.1.2 The Concept of Boundary Layer
6.1.3 Various Thicknesses and Characteristics of the Boundary Layer
6.2 Laminar Boundary Layer Equations of Incompressible Fluids
6.2.1 Boundary Layer Equation on the Wall of a Flat Plate
6.2.2 Boundary Layer Equation on Curved Wall
6.3 Similar Solutions to the Laminar Boundary Layer on a Flat Plate
6.4 Boundary Layer Momentum Integral Equation
6.4.1 Derivation of Karman Momentum Integral Equation
6.4.2 Derivation of Boundary Layer Momentum Integral Equation from Differential Equation
6.5 The Solution of the Momentum Integral Equation of Laminar Boundary Layer on a Flat Plate
6.6 Solution of the Momentum Integral Equation of the Turbulent Boundary Layer on a Flat Plate
6.7 Boundary Layer Separation
6.7.1 Boundary Layer Separation Phenomenon of Flow Around Cylinder
6.7.2 Airfoil Separation Phenomenon
6.7.3 Velocity Distribution Characteristics of the Boundary Layer in Different Pressure Gradient Areas
6.8 Separated Flow and Characteristics of Two-Dimensional Steady Viscous Fluid
6.8.1 Separation Mode-Prandtl Image
6.8.2 Necessary Conditions for Flow Separation
6.8.3 Sufficient Conditions for Flow Separation
6.8.4 Flow Characteristics Near the Separation Point
6.8.5 Singularity of Boundary Layer Equation (Goldstein Singularity)
6.8.6 Critical Point Analysis of Two-Dimensional Steady Separated Flow
6.9 Introduction to the Steady Three-Dimensional Separated Flow Over any Object
6.9.1 Overview
6.9.2 Limit Streamlines and Singularities
6.9.3 The Concept of Three-Dimensional Separation
6.9.4 Topological Law of Three-Dimensional Separation
6.10 Resistance Over Objects
6.10.1 The Resistance Over Any Object
6.10.2 Two-Dimensional Flow Resistance Around a Cylinder
6.11 Aircraft Drag and Drag Reduction Technology
6.11.1 Composition of Aircraft Drag
6.11.2 Technology to Reduce Laminar Flow Resistance
6.11.3 Technology to Reduce Turbulence Resistance
6.11.4 Technology to Reduce Induced Resistance
6.11.5 Technology to Reduce Shock Wave Resistance
Exercises
7 Fundamentals of Compressible Aerodynamics
7.1 Thermodynamic System and the First Law
7.1.1 Equation of State and Perfect Gas Hypothesis
7.1.2 Internal Energy and Enthalpy
7.1.3 The First Law of Thermodynamics
7.2 Thermodynamic Process
7.2.1 Reversible and Irreversible Processes
7.2.2 Isovolumetric Process
7.2.3 Constant Pressure Process
7.2.4 Isothermal Process
7.2.5 Adiabatic Process
7.3 The Second Law of Thermodynamic and Entropy
7.4 Energy Equation of Viscous Gas Motion
7.4.1 Physical Meaning of Energy Equation
7.4.2 Derivation Process of Energy Equation
7.5 Speed of Sound and Mach Number
7.5.1 Propagation Velocity of Disturbance Wave in Elastic Medium
7.5.2 Micro-Disturbance Propagation Velocity—Speed of Sound
7.5.3 Mach Number
7.5.4 Assumption of Incompressible Flow
7.6 One-Dimensional Compressible Steady Flow Theory
7.6.1 Energy Equation of One-Dimensional Compressible Steady Adiabatic Flow
7.6.2 Basic Relations Between Parameters of One-Dimensional Compressible Adiabatic Steady Flow
7.6.3 Relationship Between Velocity and Cross Section of One-Dimensional Steady Isentropic Pipe Flow
7.7 Small Disturbance Propagation Region, Mach Cone, Mach Wave
7.8 Expansion Wave and Supersonic Flow Around the Wall at an Outer Angle
7.8.1 Mach Wave (Expansion Wave)
7.8.2 The Relationship Between the Physical Parameters of the Mach Wave
7.8.3 Flow Around the Outer Corner of the Supersonic Wall (Prandtl–Meyer Flow)
7.8.4 The Calculation Formula for the Flow Around the Outer Corner of the Supersonic Wall
7.9 Compression Wave and Shock Wave
7.9.1 Compression Wave
7.9.2 The Formation Process of Shock Waves
7.9.3 Propulsion Speed of Shock Wave
7.9.4 Normal Shock Wave
7.9.5 Oblique Shock Wave
7.9.6 Isolated Shock Wave
7.9.7 The Internal Structure of Shock Waves
7.10 Boundary Layer Approximation of a Compressible Flow
7.10.1 Temperature Boundary Layer
7.10.2 Recovery Temperature and Recovery Factor of Adiabatic Wall
7.10.3 Boundary Layer Equation of Adiabatic Wall
7.11 Shock Wave and Boundary Layer Interference
7.11.1 Interference Between Normal Shock Wave and Laminar Boundary Layer
7.11.2 Interference Between Oblique Shock Wave and Boundary Layer
7.11.3 Head Shock and Boundary Layer Interference
7.12 Compressible One-Dimensional Friction Pipe Flow
7.12.1 The Effect of Friction in Straight Pipes on Airflow
7.12.2 Distribution of Flow Velocity Along the Length of the Pipe
7.13 Working Performance of Shrinking Nozzle, Laval Nozzle, and Supersonic Wind Tunnel
7.13.1 Working Performance of Shrink Nozzle
7.13.2 Working Performance of Laval Nozzle
7.13.3 Working Performance of Supersonic Wind Tunnel
Exercises
Part II Applied Aerodynamics
8 Aerodynamic Characteristics of Flow Over Low-Speed Airfoils
8.1 Geometric Parameters of Airfoil and Its Development
8.1.1 Development of Airfoil
8.1.2 Definition and Geometric Parameters of Airfoil
8.1.3 NACA Airfoil Number and Structure
8.1.4 Supercritical Airfoil
8.1.5 Typical Airfoil Data
8.2 Aerodynamics and Aerodynamic Coefficients on Airfoils
8.2.1 Relationship Between Airfoil Aerodynamics and Angle of Attack
8.2.2 Aerodynamic Coefficient
8.2.3 Dimensional Analysis of Lift Coefficient
8.3 Overview of Flow and Aerodynamic Characteristics of Low-Speed Airfoil
8.3.1 Phenomenon of Flow Over a Low-Speed Airfoil
8.3.2 Curve of Aerodynamic Coefficient of Airfoil Flow
8.3.3 Separation Phenomenon of Flow Around Airfoil
8.3.4 Stall Characteristics of Airfoil Flow
8.4 Kutta–Joukowski Trailing-Edge Condition and Determination of Circulation
8.4.1 Kutta–Joukowski Trailing-Edge Condition
8.4.2 Incipient Vortex and the Generation of Circulation Value
8.5 Lift Generation Mechanism of Airfoil
8.6 Development of Boundary Layer Near Airfoil Surface and Determination of Circulation Value
8.6.1 Characteristics of Boundary Layer and Velocity Circulation Around Airfoil in a Viscous Steady Flow Field
8.6.2 Vorticity Characteristics in Boundary Layer of Upper and Lower Wing Surfaces
8.6.3 Evolution Mechanism of Boundary Layer During Airfoil Starting
8.7 General Solution of the Steady Incompressible Potential Flow Around Airfoil
8.7.1 Conformal Transformation Method
8.7.2 Numerical Calculation of Airfoil—Panel Method
8.8 Theory of Thin Airfoil
8.8.1 Decomposition of Flow Around Thin Airfoils
8.8.2 Potential Flow Decomposition of Thin Airfoil at Small Angle of Attack
8.8.3 Problem of Angle of Attack and Camber
8.8.4 Solution of Thickness Problem
8.9 Theory of Thick Airfoil
8.9.1 Numerical Calculation Method of Flow Around Symmetrical Thick Airfoil Without Angle of Attack
8.9.2 Numerical Calculation Method of Flow Around Arbitrary Thick Airfoil with Angle of Attack
8.10 Aerodynamic Characteristics of Practical Low-Speed Airfoils
8.10.1 Wing Pressure Distribution and Lift Characteristics
8.10.2 Longitudinal Moment Characteristics of Airfoils
8.10.3 Pressure Center Position and Focus (Aerodynamic Center) Position
8.10.4 Drag Characteristics and Polar Curve of Airfoil
8.11 Exercises
9 Aerodynamic Characteristics of Low Speed Wing Flow
9.1 Geometric Characteristics and Parameters of the Wing
9.1.1 Plane Shape of the Wing
9.1.2 Characterization of the Wing Geometry
9.2 Aerodynamic Coefficient, Mean Aerodynamic Chord Length, and the Focus of the Wing
9.2.1 Aerodynamic Coefficient of the Wing
9.2.2 Mean Aerodynamic Chord Length of the Wing
9.2.3 The Focus of the Wing
9.3 Low-Speed Aerodynamic Characteristics of Large Aspect Ratio Straight Wing
9.3.1 Flow State
9.3.2 Vortex Structure of 3D Wing Flow at Low Speed
9.4 Vortex System Model of Low-Speed Wing Flow
9.4.1 Characteristics of Vortex Model
9.4.2 Aerodynamic Model of the Superposition of Straight Uniform Flow and a Single Π-Shaped Horseshoe Vortex
9.4.3 Aerodynamic Model of the Superposition of Straight Uniform Flow, Attached Vortex Sheet and Free Vortex Sheet
9.4.4 Aerodynamic Model of the Superposition of Straight Uniform Flow, Attached Vortex Line and Free Vortex Sheet
9.5 Prandtl’s Lifting-Line Theory
9.5.1 Profile Hypothesis
9.5.2 Downwash Speed, Downwash Angle, Lift, and Induced Drag
9.5.3 Differential–Integral Equation on the Intensity of the Attached Vortex
9.5.4 Aerodynamic Characteristics of a Straight Wing with Large Aspect Ratio in General Plane Shape
9.5.5 Influence of Plane Shape on Spanwise Circulation Distribution of Wing
9.5.6 Aerodynamic Characteristics of General Non-Twisted Straight Wing
9.5.7 Effect of Aspect Ratio on the Aerodynamic Characteristics of the Wing
9.5.8 Application Range of Lifting-Line Theory
9.6 Stall Characteristics of a Straight Wing with a Large Aspect Ratio
9.6.1 Stall Characteristics of an Elliptical Wing
9.6.2 Stall Characteristics of a Rectangular Wing
9.6.3 Stall Characteristics of a Trapezoidal Wing
9.6.4 Common Methods of Controlling Wing Separation
9.7 Low-Speed Aerodynamic Characteristics of a Swept-Back Wing
9.7.1 Flow Around a Swept-Back Wing
9.7.2 Load Distribution Characteristics of a Swept-Back Wing
9.7.3 Aerodynamic Characteristics of an Oblique Wing with Infinite Span
9.8 Lifting-Surface Theory of Wing
9.8.1 Aerodynamic Model of Lifting-Surface
9.8.2 Integral Equation of Vortex Surface Intensity γ(ξ,ζ)
9.8.3 A Numerical Method
9.9 Low-Speed Aerodynamic Characteristics of a Wing with a Small Aspect Ratio
9.9.1 Vortex Lift
9.9.2 Leading-Edge Suction Analogy
9.9.3 Potential Flow Solution of a Small Aspect Ratio Wing
9.9.4 Vortex Lift Coefficient CLv
9.9.5 Determination of Kp and Kv
9.10 Engineering Calculation Method for Low-Speed Aerodynamic Characteristics of a Wing
9.11 Aerodynamic Characteristics of Control Surfaces
9.11.1 Moment and Tails
9.11.2 Horizontal Tail Design
9.11.3 Vertical Tail Design
9.11.4 Requirements of the Lateral Control Surface for Aircraft Static Balance
9.11.5 Aerodynamic Requirements for Aileron Configuration
9.11.6 Basic Requirements for Spoiler Configuration
Exercises
10 Aerodynamic Characteristics of Low-Speed Fuselage and Wing-Body Configuration
10.1 Overview of Aerodynamic Characteristics of Low-Speed Fuselage
10.1.1 Introduction
10.1.2 Geometric Parameters of Axis-Symmetric Body
10.2 Theory and Application of Slender Body
10.2.1 Linearized Potential Flow Equation in Cylindrical Coordinate System
10.2.2 Cross-Flow Theory at High Angles of Attack
10.3 Engineering Estimation Method for Aerodynamic Characteristics of Wing-Body Assembly
10.4 Numerical Calculation of Wing Flow
Exercises
11 Aerodynamic Characteristics of Subsonic Thin Airfoil and Wing
11.1 Subsonic Compressible Flow Around an Airfoil
11.2 Velocity Potential Function Equation of Ideal Steady Compressible Flow
11.3 Small Perturbation Linearization Theory
11.3.1 Small Disturbance Approximation
11.3.2 Linearization Equation of Perturbed Velocity Potential Function
11.3.3 Pressure Coefficient Linearization
11.3.4 Linearization of Boundary Conditions
11.4 Theoretical Linearization Solution of Two-Dimensional Subsonic Flow Around the Corrugated Wall
11.5 Prandtl-Glauert Compressibility Correction of Two-Dimensional Subsonic Flow
11.5.1 Transformation of Linearized Equations
11.5.2 Compressibility correction based on linearization theory
11.6 Karman-Qian Compressibility Correction
11.6.1 Characteristics of Karman-Qian Compressibility Correction
11.6.2 Governing Equations for Perfectly Compressible Planar Flows
11.6.3 Transformation in Velocity Plane
11.6.4 Relation Between Compressible and Incompressible Flow Velocity Planes
11.7 Laitone Compressibility Correction Method
11.8 Aerodynamic Characteristics of Subsonic Thin Wing
11.8.1 Compressibility Correction of Sweep Wing With Infinite Span
11.8.2 Transformation Between Planform Shapes of Wings
11.8.3 Prandtl-Glauert Law
11.9 Effect of Mach Number of Incoming Flow on Aerodynamic Characteristics of Airfoil
11.9.1 Effect of Mach Number on Wing Lift Characteristics
11.9.2 Effect of Mach Number on the Position of the Pressure Center of the Wing
11.9.3 Effect of Mach Number on Drag Characteristics of Airfoil
11.10 Exercises
12 Aerodynamic Characteristics of Supersonic Thin Airfoil and Wing
12.1 Phenomena of the Thin Airfoil at Supersonic Flow
12.1.1 Shock Wave Drag of Thin Airfoil at Supersonic Flow
12.1.2 Supersonic Flow Around Double-Cambered Airfoil
12.2 Linearized Supersonic Theory
12.2.1 Fundamental Solution of Linearized Theory
12.2.2 Supersonic Flow Over Corrugated Wall
12.3 Linearized Theory and Loading Coefficient of Thin Airfoil at Supersonic Flow
12.3.1 Linearized Theory of Thin Airfoil at Supersonic Flow
12.3.2 The Relationship Between Pressure Coefficient and Mach Number in Supersonic and Subsonic Flow
12.3.3 Loading Coefficient of Thin Airfoil at Supersonic Flow
12.4 Aerodynamic Force Characteristics of Thin Airfoil at Supersonic Flow
12.4.1 Lift Coefficient of Thin Airfoil at Supersonic Flow
12.4.2 Shock Wave Drag Coefficient of Thin Airfoil at Supersonic Flow
12.4.3 Pitching Moment Coefficient of Thin Airfoil at Supersonic Flow
12.4.4 Comparison of Linearized Theory and Experimental Results of Supersonic Thin Airfoil
12.5 Aerodynamic Characteristics of Oblique Wing with Infinite Wingspan at Supersonic Flow
12.6 Conceptual Framework of Thin Wing at Supersonic Flow
12.6.1 The Concept of Front and Rear Mach Cone
12.6.2 Leading Edge, Trailing Edge and Side Edge
12.6.3 Two-Dimensional Flow Region and Three-Dimensional Flow Region
12.7 Aerodynamic Characteristics of Thin Wing with Finite Wingspan at Supersonic Flow
12.8 Lift Characteristics of Rectangular Flat Wing at Supersonic Flow
12.8.1 Conical Flow in the Three Dimensional Region of Supersonic Leading Edge
12.8.2 Three-Dimensional Region of Supersonic Flow Around Rectangular Flat Wing
12.8.3 Lift Characteristics of Supersonic Flow Around Rectangular Flat Wing
12.9 Characteristic Line Theory of Supersonic Flow
Exercises
13 Aerodynamic Characteristics of Transonic Thin Airfoil and Wing
13.1 Critical Mach Number of Transonic Airfoil Flow
13.1.1 Problem of Transonic Flow
13.1.2 Critical Mach Number
13.2 Transonic Flow Over a Thin Airfoil
13.3 Aerodynamic Characteristics of Transonic Thin Airfoil Flow and Its Influence by Geometric Parameters
13.3.1 Relationship Between Lift Characteristics and Incoming Mach Number
13.3.2 Relationship Between Drag Characteristics and Incoming Mach Number (Drag Divergence Mach Number)
13.3.3 Relationship Between Pitching Moment Characteristics and Incoming Mach Number
13.3.4 Influence of Airfoil Geometric Parameters on Transonic Aerodynamic Characteristics
13.4 Transonic Small Perturbation Potential Flow Equation and Similarity Rule
13.5 Influence of Wing Geometry Parameters on Critical Mach Number of Transonic Flow
13.6 Aerodynamic Characteristics of Supercritical Airfoil Flow
13.6.1 Basic Concepts of Supercritical Airfoil
13.6.2 Expansion Mechanism of Supersonic Flow Over Supercritical Airfoil
13.6.3 Aerodynamic Characteristics of Supercritical Airfoil Flow
13.7 High-Subsonic Flow Over a Swept Wing with a High Aspect Ratio
13.8 Transonic Area Rule
13.8.1 The Concept of Area Rule
13.8.2 Slender Waist Fuselage
Exercises
14 High Lift Devices and Their Aerodynamic Performances
14.1 Development of High Lift Devices
14.2 Basic Types of High Lift Devices
14.2.1 Trailing-Edge High Lift Devices
14.2.2 Leading-Edge High Lift Devices
14.3 Supporting and Driving Mechanism of High Lift Devices
14.4 Aerodynamic Principles of High Lift Devices
14.5 Aeroacoustics of High Lift Devices
14.6 Method of Wind Tunnel and Numerical Simulation for High Lift Devices
14.7 Technology of Hinged Flap with Deflection of Spoilers
Exercises
Appendix A
Appendix Vector Operation and Control Equations in Orthogonal Curvilinear Coordinate System
Appendix B
Appendix-Atmospheric Parameter Table
Bibliography