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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] | |