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| Preface | |
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| Preface to the First Edition | |
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| Introduction and Background | |
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| Description of Fluid Motion | |
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| Choice of Coordinate System | |
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| Pathlines, Streak Lines, and Streamlines | |
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| Forces in a Fluid | |
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| Integral Form of the Fluid Dynamic Equations | |
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| Differential Form of the Fluid Dynamic Equations | |
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| Dimensional Analysis of the Fluid Dynamic Equations | |
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| Flow with High Reynolds Number | |
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| Similarity of Flows | |
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| Fundamentals of Inviscid, Incompressible Flow | |
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| Angular Velocity, Vorticity, and Circulation | |
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| Rate of Change of Vorticity | |
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| Rate of Change of Circulation: Kelvin's Theorem | |
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| Irrotational Flow and the Velocity Potential | |
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| Boundary and Infinity Conditions | |
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| Bernoulli's Equation for the Pressure | |
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| Simply and Multiply Connected Regions | |
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| Uniqueness of the Solution | |
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| Vortex Quantities | |
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| Two-Dimensional Vortex | |
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| The Biot-Savart Law | |
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| The Velocity Induced by a Straight Vortex Segment | |
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| The Stream Function | |
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| General Solution of the Incompressible, Potential Flow Equations | |
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| Statement of the Potential Flow Problem | |
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| The General Solution, Based on Green's Identity | |
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| Summary: Methodology of Solution | |
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| Basic Solution: Point Source | |
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| Basic Solution: Point Doublet | |
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| Basic Solution: Polynomials | |
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| Two-Dimensional Version of the Basic Solutions | |
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| Basic Solution: Vortex | |
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| Principle of Superposition | |
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| Superposition of Sources and Free Stream: Rankine's Oval | |
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| Superposition of Doublet and Free Stream: Flow around a Cylinder | |
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| Superposition of a Three-Dimensional Doublet and Free Stream: Flow around a Sphere | |
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| Some Remarks about the Flow over the Cylinder and the Sphere | |
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| Surface Distribution of the Basic Solutions | |
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| Small-Disturbance Flow over Three-Dimensional Wings: Formulation of the Problem | |
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| Definition of the Problem | |
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| The Boundary Condition on the Wing | |
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| Separation of the Thickness and the Lifting Problems | |
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| Symmetric Wing with Nonzero Thickness at Zero Angle of Attack | |
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| Zero-Thickness Cambered Wing at Angle of Attack-Lifting Surfaces | |
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| The Aerodynamic Loads | |
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| The Vortex Wake | |
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| Linearized Theory of Small-Disturbance Compressible Flow | |
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| Small-Disturbance Flow over Two-Dimensional Airfoils | |
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| Symmetric Airfoil with Nonzero Thickness at Zero Angle of Attack | |
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| Zero-Thickness Airfoil at Angle of Attack | |
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| Classical Solution of the Lifting Problem | |
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| Aerodynamic Forces and Moments on a Thin Airfoil | |
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| The Lumped-Vortex Element | |
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| Summary and Conclusions from Thin Airfoil Theory | |
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| Exact Solutions with Complex Variables | |
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| Summary of Complex Variable Theory | |
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| The Complex Potential | |
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| Simple Examples | |
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| Uniform Stream and Singular Solutions | |
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| Flow in a Corner | |
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| Blasius Formula, Kutta-Joukowski Theorem | |
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| Conformal Mapping and the Joukowski Transformation | |
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| Flat Plate Airfoil | |
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| Leading-Edge Suction | |
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| Flow Normal to a Flat Plate | |
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| Circular Arc Airfoil | |
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| Symmetric Joukowski Airfoil | |
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| Airfoil with Finite Trailing-Edge Angle | |
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| Summary of Pressure Distributions for Exact Airfoil Solutions | |
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| Method of Images | |
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| Generalized Kutta-Joukowski Theorem | |
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| Perturbation Methods | |
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| Thin-Airfoil Problem | |
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| Second-Order Solution | |
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| Leading-Edge Solution | |
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| Matched Asymptotic Expansions | |
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| Thin Airfoil between Wind Tunnel Walls | |
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| Three-Dimensional Small-Disturbance Solutions | |
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| Finite Wing: The Lifting Line Model | |
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| Definition of the Problem | |
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| The Lifting-Line Model | |
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| The Aerodynamic Loads | |
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| The Elliptic Lift Distribution | |
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| General Spanwise Circulation Distribution | |
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| Twisted Elliptic Wing | |
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| Conclusions from Lifting-Line Theory | |
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| Slender Wing Theory | |
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| Definition of the Problem | |
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| Solution of the Flow over Slender Pointed Wings | |
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| The Method of R. T. Jones | |
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| Conclusions from Slender Wing Theory | |
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| Slender Body Theory | |
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| Axisymmetric Longitudinal Flow Past a Slender Body of Revolution | |
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| Transverse Flow Past a Slender Body of Revolution | |
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| Pressure and Force Information | |
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| Conclusions from Slender Body Theory | |
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| Far Field Calculation of Induced Drag | |
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| Numerical (Panel) Methods | |
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| Basic Formulation | |
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| The Boundary Conditions | |
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| Physical Considerations | |
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| Reduction of the Problem to a Set of Linear Algebraic Equations | |
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| Aerodynamic Loads | |
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| Preliminary Considerations, Prior to Establishing Numerical Solutions | |
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| Steps toward Constructing a Numerical Solution | |
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| Example: Solution of Thin Airfoil with the Lumped-Vortex Element | |
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| Accounting for Effects of Compressibility and Viscosity | |
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| Singularity Elements and Influence Coefficients | |
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| Two-Dimensional Point Singularity Elements | |
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| Two-Dimensional Point Source | |
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| Two-Dimensional Point Doublet | |
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| Two-Dimensional Point Vortex | |
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| Two-Dimensional Constant-Strength Singularity Elements | |
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| Constant-Strength Source Distribution | |
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| Constant-Strength Doublet Distribution | |
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| Constant-Strength Vortex Distribution | |
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| Two-Dimensional Linear-Strength Singularity Elements | |
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| Linear Source Distribution | |
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| Linear Doublet Distribution | |
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| Linear Vortex Distribution | |
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| Quadratic Doublet Distribution | |
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| Three-Dimensional Constant-Strength Singularity Elements | |
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| Quadrilateral Source | |
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| Quadrilateral Doublet | |
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| Constant Doublet Panel Equivalence to Vortex Ring | |
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| Comparison of Near and Far Field Formulas | |
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| Constant-Strength Vortex Line Segment | |
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| Vortex Ring | |
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| Horseshoe Vortex | |
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| Three-Dimensional Higher Order Elements | |
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| Two-Dimensional Numerical Solutions | |
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| Point Singularity Solutions | |
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| Discrete Vortex Method | |
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| Discrete Source Method | |
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| Constant-Strength Singularity Solutions (Using the Neumann B.C.) | |
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| Constant Strength Source Method | |
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| Constant-Strength Doublet Method | |
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| Constant-Strength Vortex Method | |
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| Constant-Potential (Dirichlet Boundary Condition) Methods | |
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| Combined Source and Doublet Method | |
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| Constant-Strength Doublet Method | |
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| Linearly Varying Singularity Strength Methods (Using the Neumann B.C.) | |
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| Linear-Strength Source Method | |
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| Linear-Strength Vortex Method | |
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| Linearly Varying Singularity Strength Methods (Using the Dirichlet B.C.) | |
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| Linear Source/Doublet Method | |
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| Linear Doublet Method | |
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| Methods Based on Quadratic Doublet Distribution (Using the Dirichlet B.C.) | |
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| Linear Source/Quadratic Doublet Method | |
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| Quadratic Doublet Method | |
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| Some Conclusions about Panel Methods | |
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| Three-Dimensional Numerical Solutions | |
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| Lifting-Line Solution by Horseshoe Elements | |
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| Modeling of Symmetry and Reflections from Solid Boundaries | |
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| Lifting-Surface Solution by Vortex Ring Elements | |
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| Introduction to Panel Codes: A Brief History | |
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| First-Order Potential-Based Panel Methods | |
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| Higher Order Panel Methods | |
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| Sample Solutions with Panel Codes | |
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| Unsteady Incompressible Potential Flow | |
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| Formulation of the Problem and Choice of Coordinates | |
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| Method of Solution | |
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| Additional Physical Considerations | |
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| Computation of Pressures | |
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| Examples for the Unsteady Boundary Condition | |
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| Summary of Solution Methodology | |
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| Sudden Acceleration of a Flat Plate | |
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| The Added Mass | |
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| Unsteady Motion of a Two-Dimensional Thin Airfoil | |
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| Kinematics | |
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| Wake Model | |
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| Solution by the Time-Stepping Method | |
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| Fluid Dynamic Loads | |
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| Unsteady Motion of a Slender Wing | |
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| Kinematics | |
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| Solution of the Flow over the Unsteady Slender Wing | |
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| Algorithm for Unsteady Airfoil Using the Lumped-Vortex Element | |
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| Some Remarks about the Unsteady Kutta Condition | |
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| Unsteady Lifting-Surface Solution by Vortex Ring Elements | |
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| Unsteady Panel Methods | |
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| The Laminar Boundary Layer | |
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| The Concept of the Boundary Layer | |
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| Boundary Layer on a Curved Surface | |
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| Similar Solutions to the Boundary Layer Equations | |
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| The von Karman Integral Momentum Equation | |
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| Solutions Using the von Karman Integral Equation | |
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| Approximate Polynomial Solution | |
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| The Correlation Method of Thwaites | |
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| Weak Interactions, the Goldstein Singularity, and Wakes | |
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| Two-Equation Integral Boundary Layer Method | |
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| Viscous-Inviscid Interaction Method | |
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| Concluding Example: The Flow over a Symmetric Airfoil | |
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| Enhancement of the Potential Flow Model | |
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| Wake Rollup | |
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| Coupling between Potential Flow and Boundary Layer Solvers | |
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| The Laminar/Turbulent Boundary Layer and Transition | |
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| Viscous-Inviscid Coupling, Including Turbulent Boundary Layer | |
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| Influence of Viscous Flow Effects on Airfoil Design | |
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| Low Drag Considerations | |
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| High Lift Considerations | |
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| Flow over Wings at High Angles of Attack | |
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| Flow Separation on Wings with Unswept Leading Edge - Experimental Observations | |
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| Flow Separation on Wings with Unswept Leading Edge - Modeling | |
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| Flow Separation on Wings with Highly Swept Leading Edge - Experimental Observations | |
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| Modeling of Highly Swept Leading-Edge Separation | |
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| Possible Additional Features of Panel Codes | |
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| Airfoil Integrals | |
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| Singularity Distribution Integrals | |
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| Principal Value of the Lifting Surface Integral I[subscript L] | |