Aerodynamic Theory

Division A Mathematical Aids.- Preface.- I. The Complex Variable (x + iy).- 1. Introductory.- 2. Properties of the Functions ? and ?.- 3. The Inverse Relation z = F (w).- 4. The Complex x + iy as the Location of a Point in a Plane.- 5. Results Growing Out of the Expression of the Complex Variable in the Exponential and Circular Function Forms.- 6. The Integration of Functions of a Complex Variable.- 7. Influence of Singularities.- 8. Cauchy’s Theorem.- 9. Cauchy’s Integral Formula.- 10. Hyperbolic Functions.- 11. Hyperbolic Functions of Imaginaries and Complexes.- 12. Inverse Relations.- 13. Derivatives of Hyperbolic Functions.- 14. Illustrations of Complex Functions.- II. Integration of Partial Derivative Expressions.- III. Fourier Series.- 1. Fourier Series.- 2. Fourier Series Continued.- IV. Theory of Dimensions.- 1. Introductory.- 2. Kinematic Similitude.- 3. The II Theorem.- 4. Non-Dimensional Coefficients.- V. Vector Algebra: Two-Dimensional Vectors.- 1. Definition of Vector and Scalar.- 2. Algebraic Representation of a Vector.- 3. Representation by Rectangular Components.- 4. Exponential Representation of a Vector.- 5. Addition of Vectors.- 6. Subtraction of Vectors.- 7. Multiplication of a Vector by a Scalar.- 8. Multiplication of a Vector by a Vector.- 9. Division of a Vector by a Vector.- 10. Powers and Roots of a Vector.- 11. Vector Equations of Common Curves.- 12. Differentiation of a Vector.- VI. Vector Fields.- 1. Introductory.- 2. Vector Components.- 3. Line Integral.- 4. Line Integral in Two Dimensions.- 5. Vector Flux.- 6. Vector Flux through a Volume.- 7. Vector Flux in Two Dimensions.- 8. Rotational and Irrotational Motion.- 9. Rotational and Irrotational Motion in Three Dimensions.- VII. Potential.- 1. Potential.- 2. Addition Theorem for Velocity Potentials.- 3. Conditions in Order that a Potential ? may Exist.- 4. Conditions for the Existence of a Velocity Potential in a Two-Dimensional Vector Field.- 5. The Functions ? and ? of Chapter I as Potential Functions for a Two-Dimensional Field.- 6. Given the Function w, Required to Find the Remaining Functions and the Field.- 7. Given the Function ? or ?, Required to Find the Remaining Functions and the Field.- 8. Given a Field of Velocity Distribution as Determined by u and v, to Find ?, ? and w.- 9. Illustrations of 6, 7, 8.- VIII. Potential—Continued.- 1. Interpretation of ?.- 2. Interpretation of ?.- 3. Reciprocal Relations of ? and ? to a Vector Field.- 4. Geometrical Relation Between Derivatives of the Functions ? and ?p.- 5. Velocity Relations in an Orthogonal Field of ? and ?.- IX. Special Theorems.- 1. Gauss’ Theorem.- 2. Green’s Theorem.- 3. Stokes’ Theorem.- X. Conformal Transformation.- 1. Introductory.- 2. Application of Vectors to the Problem of Conformal Transformation.- 3. Typical Forms which the Transforming Function May Take.- 4. Illustrative Transformations.- 5. Transformation of a Field of Lines.- 6. Illustrative Field Transformations.- 7. Special Conditions.- 8. Singular Points.- Division B Fluid Mechanics, Part I.- Preface.- I. Fundamental Equations.- 1. Introductory, Characteristics of a Fluid.- 2. Physical Conditions, Notation.- 3. A Field of Fluid Flow as a Vector Field.- 4. The Equation of Continuity.- 5. The Equation of Force and Acceleration.- 6. Bernoulli’s Equation.- 7. A Field of Flow; A Tube of Flow; Conditions of Equilibrium of a Field Within a Portion of a Tube of Flow; Momentum Theorem.- 8. Impulse and Impulsive Forces.- 9. Energy of the Field in Terms of Velocity Potential.- 10. Virtual Mass.- 11. Pressure at any Point in a Field Undergoing a Time Change.- II. Plane Irrotational Flow.- 1. Two-Dimensional Flow.- 2. Rotational and Irrotational Motion.- 3. Fields of Flow.- 4. Rectilinear Flow Parallel to Axis of X.- 5. Rectilinear Flow Parallel to Axis of Y.- 6. Rectilinear Flow Oblique to Axes.- 7. Sources and Sinks.- 8. Functions ? and ? for Source.- 9. Functions ? and ? for Sink.- III. Vortex Flow.- 1. Vortex Flow.- 2. Induced Velocity.- 3. Functions ? and ? for Plane Vortex Flow.- IV. Combination Fields of Flow.- 1. Combinations of Fields of Flow.- 2. Two Rectilinear Fields, One Parallel to X and One Parallel to Y.- 3. Rectilinear Flow Combined with Source.- 4. Rectilinear Flow Combined with Sink.- 5. Two Sources of Equal Strength.- 6. Two Sinks of Equal Strength.- 7. Two Sources of Unequal Strength.- 8. Source and Sink of Equal Strength.- 9. Source and Sink of Unequal Strength.- 10. Doublet.- 11. Combination of Sources and Sinks Distributed Along a Line.- 12. Field of Flow for a Continuous Source and Sink Distribution Along a Line.- 13. Combination of Sources and Sinks Distributed in any Manner in a Plane.- V. Combination Fields of Flow Continued—Kutta-Jou-Kowski Theorem.- 1. Rectilinear Flow with Source and Sink of Equal Strength.- 2. Rectilinear Flow with Doublet—Infinite Flow About a Circle.- 3. Rectilinear Flow with Any of the Source and Sink Distributions of IV, 11, 12, 13.- 4. Indefinite Stream with Circular Obstacle Combined with Vortex Flow—Indefinite Flow with Circulation.- 5. Pressure on a Circular Boundary in the Field of 4.- 6. Change of Momentum within any Circular Boundary in the Field of 4.- 7. Total Resultant Force on any Body in Field of 4.- VI. Application of Conformal Transformation to Fields of Flow.- 1. The Application of Conformal Transformation to the Study of Fields of Fluid Motion.- 2. Velocity Relations between Fields of Flow on the z and Z Planes.- 3. Conformal Transformation of the Circle.- 4. Transformation of the Flow Along the Axis of X into the Flow about a Circle.- 5. Transformation of the Flow about a Circle into the Flow about a Straight Line at Right Angles to the Flow.- 6. Flow of Indefinite Field about any Inclined Line.- VII. Particle Paths, Fields of Flow Relative to Axes Fixed in Fluid.- 1. Relative Motions in a Field of Flow—Stream-Lines and Particle Paths.- 2. Path of a Particle Relative to Axes Fixed in the Fluid.- 3. Derivation of Velocity Potential and Stream Function for Fields of Motion Relative to Axes Fixed in the Fluid.- 4. Field of Flow for a Thin Circular Disk Moving in Its Own Plane in an Indefinite Fluid Field.- 5. Field of Flow Produced by a Circle Combined with Vortex Flow Moving in an Indefinite Fluid Field.- 6. Field of Flow for a Straight Line Moving at Right Angles to Itself in an Indefinite Fluid Field.- VIII. Derivation of Potentials by Indirect Methods.- 1. The Derivation of Velocity Potential and Stream Functions by Indirect Methods.- 2. Field of Flow through an Opening in an Infinite Rectilinear Barrier.- 3. Field Produced in an Indefinite Fluid Sheet by the Movement of a Thin Lamina in its Own Plane.- 4. Field of Flow Produced by an Elliptic Contour Moving in the Direction of its Axes.- IX. Three-Dimensional Fields of Flow.- 1. Stream and Velocity Potential Functions for Three-Dimensional Flow.- 2. Sources and Sinks—Three Dimensional Field.- 3. Stream and Velocity Potential Functions for a Source or Sink— Three-Dimensional Space.- 4. Combination of a Source and Sink of Equal Strength—Three-Dimensional Field.- 5. Combination of Two Sources of Equal Strength—Three-Dimensional Field.- 6. Combinations of Sources and Sinks of Unequal Strengths—Three-Dimensional Field.- 7. Doublet in Three-Dimensional Space.- 8. Combinations of Sources and Sinks Along a Straight Line—Three-Dimensional Space.- 9. Field for a Continuous Distribution of Sources and Sinks Along a Straight Line—Three-Dimensional Space.- 10. Combination of Source with Uniform Flow: Three-Dimensional Space.- 11. Combination of Space Doublet with Indefinite Flow Parallel to the Axis of X—Indefinite Flow About a Sphere.- 12. Field of Flow for a Sphere Moving in a Straight Line in an Indefinite Fluid Field.- 13. Rectilinear Flow with the Source and Sink Distributions of 8 and 9.- 14. Any Field of Flow as the Result of a Distributed System of Sources and Sinks or of Doublets.- X. Aerostatics: Structure of the Atmosphere.- 1. Buoyancy.- 2. Center of the System of Surface Pressures.- 3. Structure of the Atmosphere: Standard Atmosphere.- 4. Derivation of Formulae.- Division C Fluid Mechanics, Part II.- Preface.- I. Kinematics of Fluids.- 1. Velocity Field.- 2. Surface Integrals.- 3. Line Integral.- 4. Scalar Triple Vector Products.- 5. Vectorial Triple Vector Products.- 6. Helmholtz’ First Theorem.- 7. Stream-lines.- 8. Dyadic Multiplication.- 9. The Derivation of a Vector Field.- 10. Acceleration of Fluid Particles.- 11. Boundary Conditions. Superposition.- II. Dynamics of Fluids.- 1. Pressure.- 2. Materiality of the Vortices.- 3. Irro-tational Flow.- 4. Bernoulli’s Pressure Equation.- 5. Fictitious Flows.- 6. Physical Interpretation of the Velocity Potential.- III. Motion of Solids in a Fluid.- 1. The Velocity Distribution.- 2. Apparent Mass.- 3. Apparent Momentum.- 4. Momentum of a Surface of Revolution.- 5. Remarks on Lift.- IV. Sources and Vortices.- 1. Sources and Sinks.- 2. Superposition of Two Sources.- 3. Doublet.- 4. Polar Coordinates.- 5. Motion of a Sphere.- 6. Apparent Mass of the Sphere.- 7. Apparent Mass of Other Source Distributions.- 8. Vortices.- 9. Forces Between Sources and Vortices.- V. Fluid Motion with Axial Symmetry.- 1. Stream Function.- 2. Equation of Continuity.- 3. Zonal Spherical Harmonics.- 4. Differential Equation for Zonal Surface Harmonics.- 5. Superposition of Sources.- 6. Elongated Surfaces of Revolution.- VI. Lateral Motion of Surfaces of Revolution.- 1. Doublets.- 2. Equation of Continuity in Semi-Polar Coordinates.- 3. General Relations.- 4. Elongated Surfaces of Revolution.- 5. Equation of Continuity in Polar Coordinates.- 6. Tesseral Spherical Harmonics.- VII. Ellipsoids of Revolution.- 1. General.- 2. Ovary Semi-Elliptic Coordinates.- 3. Equation of Continuity in Ovary Semi-Elliptic Coordinates.- 4. Method of Obtaining Solutions.- 5. The Axial Motion of an Ovary Ellipsoid.- 6. Discussion of the Solution.- 7. Apparent Mass.- 8. The Stream Function.- 9. Lateral Motion of the Ovary Ellipsoid.- 10. Rotation of the Ovary Ellipsoid.- 11. Modification of the Method for Planetary Ellipsoids.- 12. Most General Motion of Ellipsoids of Revolution.- VIII. Ellipsoid with Three Unequal Axes.- 1. Remarks on Elliptical Coordinates.- 2. Equation of Continuity in Elliptical Coordinates.- 3. Solution for the Motion Parallel to a Principal Axis.- 4. Discussion of the Solution.- 5. Evaluation of the Constants.- 6. The Elliptic Disc.- 7. Rotation of an Ellipsoid.- 8. Concluding Remarks.- Division D Historical Sketch.- Preface.- I. Period of Early Thought: From Antiquity to the End of the XVII Century.- II. Period of Classic Hydrodynamics: From the End of the XVII Century to the End of the XIX Century.- III. Period of Modern Aerodynamics: From the End of the XIX Century Onward.