Wing Theory in Supersonic Flow

Preface

Acknowledgments

I. Recapitulative Survey of the Equations of Motion of Perfect Fluids in Supersonic Flow

I.1. General Equations

I.2. Propagation of Small Disturbances

I.3. Velocity Potential Equation

I.4. Pressure Coefficient under the Assumption of Small Disturbances

I.5. Theory of Wings of Infinite Aspect Ratio in Supersonic Flow under the Assumption of Small Disturbances

I.6. Theory of Axially-Symmetric Bodies under the Assumption of Small Disturbances (Application to the Circular Cone)

I.7. Conical Motions in Supersonic Flow

I.8. High-Order Conical Flows

II. Unified Theory of Angular Wings Based on High-Order Conical Flow Determination of the Axial Disturbance Velocity (u) and of the Downwash (w) in the Direct, Indirect and Mixed Problems

II.1. General Considerations

II.2. Behavior of the Axial Disturbance Velocity u in the Neighborhood of the Subsonic Leading Edges or the Subsonic Ridges on the Thin Wing (Direct Problem)

II.3. Contribution of the Subsonic Leading Edges of Thin Wings and of the Separation Ridges to the Construction of the Velocity u (Direct Problem)

II.4. Examples of Application to Ordinary Wings in the Direct Problem

II.5. Determination of Constants

II.6. Examples of the Determination of Constants

II.7. Contribution of the Ridges and the Leading Edge to the Calculation of the Downwash w, when the Pressures are Given on the Wing (Indirect Problem)

II.8. Some Considerations on the Indirect Problem

II.9. Wing whose Incidence Variation and Pressure Distribution are Given Alternatively on Separate Portions (Mixed Problem)

III. The Calculation of the Overall Forces and Moments on Wings with Trailing Edges of Arbitrary Planform Shape

III.1. Preliminary Considerations

III.2. Calculation of Forces

III.3. Calculation of Moments

III.4. Some Special Applications of the Formula for Calculating the Forces and Moments

III.5. Calculation of the Suction Force Induced by the Subsonic Leading Edges of a Thin Wing

IV. Study of Ordinary Delta Wings

IV.1. Introductory Considerations on the Delta Wing

IV.2. Thin Delta Wing with Subsonic Leading Edges having Symmetrical Incidences

IV.3. Thin Delta Wing with Subsonic Edges having Antisymmetrical Incidences

IV.4. Thin Delta Wing with Supersonic Edges and Symmetry of Incidence

IV.5. Wing of Symmetrical Thickness

IV.6. Thin Delta Wing with Supersonic Edges and Antisymmetry of Incidence

IV.7. Delta Wing with Sonic Leading Edges

IV.8. Thin Delta Wing with given Pressure on the Surface (Indirect Problem)

IV.9. Examples of Delta Wing of Symmetrical Thickness with a Given Pressure Distribution on the Surface (Indirect Problem)

IV.10. Mixed Problem Applied to a Thin Delta Wing in a True Conical Motion (n = 1)

V. Yawed Delta Wings. Delta Wings with General Variation of Incidence

V.1. Study of Yawed Delta Wings

V.2. Thin Yawed Delta Wing with Subsonic Edges

V.3. Case of Yawed Thin Delta Wing having One Subsonic and One Supersonic Edge

V.4. Yawed Thin Delta Wing having both Edges Supersonic

V.5. Yawed Delta Wing of Symmetrical Thickness

V.6. Delta Wing with Incidence or Slope Varying According to a Homogeneous Function

VI. Trapezoidal and Rectangular Wings

VI.1. Generalities on Trapezoidal Wings

VI.2. Thin Trapezoidal Wing with Subsonic Lateral Edges

VI.3. Application to a Thin Rectangular Wing

VI.4. Thin Trapezoidal Wing having Supersonic Lateral Leading Edges

VI.5. Wing of Symmetrical Thickness

VI.6. Thin Trapezoidal Wing having a Given Pressure Distribution (Indirect Problem)

VI.7. Trapezoidal and Rectangular Wings of Symmetrical Thickness having a Given Pressure Distribution (Indirect Problem)

VII. Study of Polygonal Wings

VII.1. Polygonal Wings of Symmetrical Thickness

VII.2. Application to a Double Trapezoidal Swept-Back Wing

VII.3. Examples of Polygonal Wings of Symmetrical Thickness, the Interference between the Two Vertices O1 and O2 being taken into Consideration. Application to the Rectangular Wing

VII.4. Polygonal Wings of Symmetrical Thickness with Diamond-Shaped Profile

VII.5. Thin Polygonal Wings

VII.6. Some Examples of Thin Polygonal Wings

VII.7. Arrow-Head or Diamond-Shaped Wings

VII.8. Thin Angular Wing with Swept-Back or Arrow-Head-Shaped Enclosing Line

VIII. Cruciform Wings

VIII.1. Theory of Cruciform Wing

VIII.2. Determination of the Axial Velocities u on the Cruciform Wing

VIII.3. Application to the Cruciform Wing having Subsonic Leading Edges and Antisymmetrical Incidences, in the True Conical Motion (n = 1)

VIII.4. Cruciform Wing with Antisymmetrical Incidences in the Conical Motion of Order n = 2

VIII.5. Thin Cruciform Wing with Antisymmetrical Incidences having Subsonic Plate Edges and Supersonic Wing Edges

VIII.6. Wing System with Three Arms

VIII.7. Determination of the Wing and Plate Surfaces upon which a Given Pressure is Exerted. Indirect Problem for the Cruciform Wing

VIII.8. Mixed Problems of Cruciform Wings

IX. Simple or Cruciform Wing Fitted with a Conical Body

IX.1. Fundamental Preliminary Relations

IX.2. Conical Flow (n = 1) Around a Wing-Body System having Subsonic Leading Edges

IX.3. Wing-Body System having a Thin Wing with Supersonic Edges or a Wedge-Shaped Wing of Symmetrical Thickness (Conical Flow)

IX.4. Considerations on High-Order Conical Flows about the Wing-Body System

IX.5. Considerations on the Flow about a Cruciform Wing-Conical Body System

X. Miscellaneous

X.1. Theory of Ailerons

X.2. Low Frequency Harmonic Oscillations of Wings in Supersonic Flow

X.3. Delta Wings with Subsonic Edges and Two Symmetrical Lateral Ridges

X.4. Theory of a Thin Delta Wing with Flow Separation at the Leading Edges

XI. Determination of Pressures and Aerodynamic Characteristics of Wings beyond the Assumption of Small Disturbances, in Supersonic and Moderate Hypersonic Flows. Experimental Verifications

XI.1. Determination of Pressure in Supersonic and Hypersonic Flows

XI.2. Aerodynamic Characteristics of Profiles

XI.3. Extension of the Unitary Formula for Compression-Expansion to Wings of Finite Span

XI.4. Aerodynamic Characteristics of Delta and Rectangular Wings in Supersonic-Moderate Hypersonic Flow

XII. Some Theoretical Considerations on Wings with Curved Leading Edges and Wing-Fusiform Body Systems

XII.1. Definition of Quasi-Conical Motions

XII.2. Wing with Central Fusiform Body

Appendixes

References

Index

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