Collected Works of H. S. Tsien (1938-1956)

Table of contents

1. Cover image
2. Title page
3. Table of Contents
4. Copyright
5. About This Book
6. Hsue-Shen Tsiens Biography
7. Boundary Layer in Compressible Fluids
   1. I
   2. II
   3. References
8. Supersonic Flow over an Inclined Body of Revolution
   1. References
9. Problems in Motion of Compressible Fluids and Reaction Propulsion
   1. PART (I). Boundary Layer in Compressible Fluids
   2. PART (II). Supersonic Flow over an Inclined Body of Revolution
   3. PART (III). Application of Tschapligin’s Transformation to Two Dimensional Subsonic Flow
   4. PART (IV). Flight Analysis of a Sounding Rocket with Special Reference to Propulsion by Successive Impulses
10. Flight Analysis of a Sounding Rocket with Special Reference to Propulsion by Successive Impulses
    1. Introduction
    2. Notation
    3. I
    4. II
    5. III
    6. IV
    7. Conclusion
    8. References
11. Two-Dimensional Subsonic Flow of Compressible Fluids
    1. Introduction
    2. Approximation to the Adiabatic Relation
    3. Section I
    4. Section II
    5. Concluding Remarks
    6. References
12. The Buckling of Spherical Shells by External Pressure*
    1. General Considerations
    2. The Energy Expression and the Equation of Equilibrium for a Spherical Segment Under Uniform External Pressure
    3. Approximate Solution by the Rayleigh-Ritz Method
    4. Application to the Buckling Problem. Comparison with the Experiment
    5. References
13. The Influence of Curvature on the Buckling Characteristics of Structures
    1. Section I
    2. Section II
    3. Section III
    4. Concluding Remarks
    5. References
14. A Method for Predicting the Compressibility Burble
    1. Introduction
    2. Part I
    3. Part II
    4. Part III
    5. Appendix 1
    6. References
15. The Buckling of Thin Cylindrical Shells under Axial Compression
    1. Stresses in the Median Surface and the expression for the Total Energy of the System
    2. Calculation of the Total Energy
    3. Relation Between the compression Stress and the Amplitude of Waves
    4. The Relation Between the Compression Stress and the Shortening of the Shell in the Axial Direction
    5. The Effect of the Elastic Characteristic of the testing Machine on the Buckling Phenomenon
    6. Conclusions
    7. References
16. Buckling of a Column with Non-Linear Lateral Supports
    1. Introduction
    2. General Theory for Straight Columns
    3. Case of Two Equally Spaced Supports
    4. Case of a Single Lateral Support, Effect of Initial Deflection
    5. Case of a Single Lateral Support, Effect of Elasticity of the Testing Machine
    6. Stability of the Equilibrium Positions Under Infinitesimal Disturbances
    7. Conclusions
    8. References
17. A Theory for the Buckling of Thin Shells
    1. Introduction
    2. The Criterions for Buckling
    3. Column with a Nonlinear Elastic Lateral Support
    4. Thin Uniform Cylindric Shell Under Axial Compression
    5. Spherical Shells under External Pressure
    6. Concluding Remarks
    7. References
18. Heat Conduction across a Partially Insulated Wall
19. On the Design of the Contraction Cone for a Wind Tunnel
    1. Formulation of the Problem
    2. Solution of the Problem
    3. The Results
    4. References
20. Symmetrical Joukowsky Airfoils in Shear Flow
    1. 1. Problem
    2. 2. Method of solution
    3. 3. Shear flow over a circular cylinder
    4. 4. Force and moment
    5. 5. Symmetrical Joukowsky airfoils
    6. 6. Strength of circulation
    7. 7. Strengths of doublets and quadruplets
    8. 8. Lift and moment coefficients
    9. 9. Aerodynamic center
    10. References
21. The “Limiting Line” in Mixed Subsonic and Supersonic Flow of Compressible Fluids
    1. Criterion for the Breakdown of Isentropic Irrotational Flow
    2. Axially Symmetric Flow
    3. The Limiting Line
    4. Limiting Hodograph and the Streamlines
    5. Envelope of Characteristics in Hodograph Plane and Lines of Constant Velocity in Physical Plane
    6. The Lost Solution
    7. Continuation of Solution Beyond The Limiting Line
    8. General Three-Dimensional Flow
    9. References
22. Loss in Compressor or Turbine due to Twisted Blades
    1. Problem
    2. The Vortex System and the Induced Velocity
    3. The General Blade Equation
    4. Application I
    5. Application II
    6. Appendix
    7. REFERENCE
23. Lifting-Line Theory for a Wing in Non-uniform Flow*
    1. 1. Introduction
    2. 2. General theory of a lifting line
    3. 3. Conditions far downstream
    4. 4. Minimum induced drag
    5. 5. Flow with velocity varying in the direction of span only
    6. References
24. Atomic Energy
    1. Introduction
    2. The Equivalence of Energy and Mass
    3. Atomic Structure
    4. Nuclear Reactions
    5. Nuclear Structure — Binding Energy
    6. Energy Production in the Stars
    7. Nuclear Fission — Chain Reaction
    8. Engineering Approach to the Nuclear Reaction
    9. References
25. Two-Dimensional Irrotational Mixed Subsonic and Supersonic Flow of a Compressible Fluid and the Upper Critical Mach Number
    1. Introduction
    2. Notations
    3. Part I. Differential Equations of Compressible Flow and Properties of Their Particular Solutions
    4. 2. Transformation of the Differential Equations
    5. 3. The Particular Solutions of the Differential Equations
    6. 4. The Properties of the Hypergeometric Functions of Large Order
    7. Part II. Construction of the Solutions for Compressible Flow Around a Body
    8. 6. The Functions for Incompressible Flow
    9. 7. Conformal Mapping of Incompressible Flow on the Hodograph Plan
    10. 8. Construction of a Solution about the Origin
    11. 9. Analytic Continuation of the Solution Branch Point or Order 1
    12. 10. Continuation Logarithmic Singularity
    13. 11. Transition to Physical Plane
    14. Part III. Improvement of the Convergence of Solution by the Asymptotic Properties of Hypergeometric Functions
    15. 13. Asymptotic Solutions of the Hypergeometric Equations
    16. 14. The Asymptotic Representation of F(av, bv; cv; τ) and F(av + β, bv + β; cv; τ)
    17. 15. Transformation of the Function W(w; τ) Branch Point of Order 1
    18. 16. Continuation: Lo garithmic Singularity
    19. 17. The Coordinate Functions x (q, θ) and y (q, θ)
    20. Part IV. Criteria for the Upper Critical Mach Number
    21. 19. The Condition for the Limiting Line
    22. 20. The Approximate Determination of the Upper Critical Mach Number
    23. Part V. Application — Elliptic Cylinders
    24. 22. The Functions z0(w), W0 (w) and Λ0 (w)
    25. 23. Expansions of W0 (w) and Λ0 (w)
    26. 24. The Stream Function ψ(q, θ)
    27. 25. The Coordinate Functions x(q, θ) and y(q, θ)
    28. Conclusions
    29. References
    30. Appendix A Proof of Theorem (52)
    31. Appendix B Proof of Theorem (88)
    32. Appendix C Proof of Theorem (98)
    33. Tables of the Hypergeometric Functions
26. Superaerodynamics, Mechanics of Rarefied Gases
    1. Introduction
    2. Mean Free Path and Realms of Fluid Mechanics
    3. Stresses and Boundary Conditions in Slip Flow
    4. Boundary Conditions for Slip Flows of Small Mach Number
    5. Slip Flows at Small Mach Numbers
    6. Free Molecule Flows at Small Mach Numbers
    7. Free Molecule Flow at Large Mach Numbers
    8. Free Molecule Flow Over an Inclined Plate
    9. References
27. Propagation of Plane Sound Waves in Rarefied Gases
    1. 1. Introduction
    2. 2. Symbols
    3. 3. Basic Equations
    4. 4. Solution of the Differential Equations
    5. 5. Numerical Calculation
    6. 6. Results
    7. References
28. Similarity Laws of Hypersonic Flows
    1. Introduction
    2. Differential Equation for Hypersonic Flows
    3. Similarity Laws in Two-Dimensional Flow
    4. Axially Symmetrical Flows
    5. References
29. One-Dimensional Flows of a Gas Characterized by van der Waals Equation of State*
    1. Introduction
    2. Isentropic Expansion of a van der Waal Gas
    3. Expansion in a Nozzle
    4. Shock Wave in Supersonic Flow
    5. Parameters for Constants a and b
    6. Properties of Air
    7. Tabulation of Functions for Air
    8. Application of Results to a Hypersonic Wind Tunnel
    9. References
    10. Corrections on the Paper “One-Dimensional Flows of a Gas Characterized by van der Waals Equation of State”
30. Flow Conditions near the Intersection of a Shock Wave with Solid Boundary
    1. 1. Introduction
    2. 2. Basic Equations
    3. 3. Relations of Quantities on the Two Sides of Shock
    4. References
31. Lower Buckling Load in the Non-Linear Buckling Theory for Thin Shells
32. Rockets and Other Thermal Jets Using Nuclear Energy: With a General Discussion on the Use of Porous Pile Materials
    1. 1. Simple Theory of Space Rockets
    2. 2. Relativistic Theory of Space Rockets
    3. 3. Idealized Optimum Design using Nuclear Energy
    4. 4. Nuclear Energy Rocket
    5. 5. Specific Examples of Nuclear Energy Rocket
    6. 6. Possibilities of Reducing the Critical Size
    7. 7. Application of Nuclear Fuel to other Thermal Jets
    8. 8. Advantages of Using Porous Pile Material
    9. References
33. Engineering and Engineering Sciences*
    1. Introduction
    2. Contributions of an Engineering Scientist to Engineering Development
    3. The Feasibility of a Proposal—Long Range Rockets
    4. Rocket Propellants
    5. Best Method of Attack— Manufacture of Fissionable Material
    6. Reason and Remedy for a Failure — the Tacoma Narrows Bridge
    7. Unification—Basic Research in Engineering Science
    8. Training of an Engineering Scientist
    9. Concluding Remarks
    10. References
34. On Two-Dimensional Non-steady Motion of a Slender Body in a Compressible Fluid
    1. 1. Introduction
    2. 2. General formulation of the problem
    3. 3. Introduction of parameters
    4. 4. Theory of small perturbations
    5. 5. Further simplification in special cases
    6. 6. Influence of wind tunnel walls
    7. 7. The Case of Large Pressure Disturbance
    8. 8. The Transonic case with M1= 1
    9. References
35. Wind-Tunnel Testing Problems in Superaerodynamics
    1. Introduction
    2. (1) Tunnel Design
    3. (2) Flow Measurement
    4. (3) Hot-Wire Anemometer
    5. (4) Parameters of Flow
    6. Appendix
    7. References
36. Airfoils in Slightly Supersonic Flow
    1. Introduction
    2. Oblique Shock
    3. Prandtl-Meyer Expansion
    4. Flat Plate Airfoil
    5. Asymmetric Wedge Airfoil
    6. References
37. Interaction between Parallel Streams of Subsonic and Supersonic Velocities*
    1. Introduction
    2. Incident Wave
    3. Inclined Wall
    4. Numerical Results and Discussion
    5. References
    6. Appendix
38. Research in Rocket and Jet Propulsion*
    1. Variable Stress
    2. Heat Transfer
    3. Wall-Temperature Effects
    4. Long-Range Trajectory
    5. References
39. A Generalization of Alfrey’s Theorem for Visco-elastic Media
    1. 1. Introduction
    2. 2. First boundary value problem
    3. REFERENCE
40. Instruction and Research at the Daniel and Florence Guggenheim Jet Propulsion Center
    1. Jet-Propulsion Centers
    2. Instruction and Research of Jet Propulsion
    3. Characteristics of Rocket and Jet-Propulsion Engineering
    4. Material Problems
    5. Heat Transfer
    6. Combustion
    7. Performance of Rocket and Jet-Propelled Vehicles
    8. References
41. Influence of Flame Front on the Flow Field
    1. Flame Front
    2. Production of Vorticity by Flame
    3. Flame Width in a Uniform Channel
    4. Effect of Compressibility on Flame Width
    5. Appendix
    6. References
42. Optimum Thrust Programming for a Sounding Rocket
    1. Formulation of the Problem
    2. Quadratic Drag Law
    3. Linear Drag Law
    4. Discussion of Results
    5. Acknowledgment
    6. References
43. The Emission of Radiation from Diatomic Gases. III. Numerical Emissivity Calculations for Carbon Monoxide for Low Optical Densities at 300K and Atmospheric Pressure ①
    1. I. Introduction
    2. II. Summary of Theoretical Relations
    3. III. Representative Emissivity Calculations for CO at 300K
    4. IV. Limits of Validity of the Treatment for Nonoverlapping Rotational Lines for CO17
    5. V. Approximate Emissivity Calculations for Diatomic Molecules with Nonoverlapping Rotational Lines
    6. VA Emissivity Calculations for CO at 300K for Nonoverlapping Rotational Lines, Assuming Equal Spacing and Intensity of Lines
    7. VB Emissivity Calculations for CO at 300K for Nonoverlapping Rotational Lines Using Asymptotic Expressions for the Modified Bessel Functions
    8. Appendix
    9. References
44. The Transfer Functions of Rocket Nozzles
    1. Flow Conditions
    2. Formulation of the Problem in Nozzle
    3. Solution for Small Frequency
    4. Solution for Large Frequencies
    5. Concluding Remarks
    6. References
45. A Similarity Law for Stressing Rapidly Heated Thin-Walled Cylinders①
    1. Stresses and Strains of a Thin-Walled Cylinder
    2. Nondimensional Quantities and Equations of Equilibrium
    3. Infinite Cylinder Under Uniform Internal Pressure
    4. Linearized Theory for General Secondary Loading
    5. Similarity Law for General Loading
    6. Example of Dimensioning the Equivalent Cold Cylinder
    7. Junction Stress Between Cylinder and Head
    8. Ring Stiffener Around Cylinder
    9. References
46. On the Determination of Rotational Line Half-Widths of Diatomic Molecules*
    1. I. Introduction
    2. II. Calculation of Rotational Half-Widths from Experimental Data
    3. References
47. Automatic Navigation of a Long Range Rocket Vehicle
    1. Equations of Motion
    2. Normal Flight Path
    3. Disturbance Equations
    4. Adjoint Functions for Range Correction
    5. Cut-Off Condition
    6. Condition for Automatic Navigation
    7. Discussion
    8. Appendix
    9. References
48. A Method for Comparing the Performance of Power Plants for Vertical Flight
    1. General Relation
    2. Applications
    3. Detail Improvement of Rocket Engine
    4. References
49. Servo-Stabilization of Combustion in Rocket Motors
    1. Time Lag in Combustion
    2. Intrinsic Instability
    3. System Dynamics with Servo Control
    4. Instability Without Servo Control
    5. Complete Stability with Servo Control
    6. Stability Criteria
    7. Concluding Remarks
    8. Appendix
    9. References
50. Physical Mechanics, A New Field in Engineering Science
    1. Basic Concepts
    2. Physical Mechanics as an Engineering Science
    3. Use of Approximate Models
    4. A Question of Methodology
    5. Concluding Remarks
    6. References
51. The Properties of Pure Liquids
    1. Lennard-Jones and Devonshire Theory of Liquids
    2. Specific Heat at Constant Volume
    3. Thermal Expansion and Compressibility
    4. Specific Heat at Constant Pressure
    5. Liquid Metals
    6. Velocity of Sound
    7. Transport Properties
    8. Thermal Conductivity
    9. Concluding Remarks
    10. Appendix
    11. References
52. Similarity Laws for Stressing Heated Wings
    1. Introduction
    2. Basic Equations for Heated Plate
    3. Plateat Constant Temperature
    4. Similarity Laws for Solid Thin Wings
    5. Alternate Test Procedure for Thin Solid Wings
    6. Box Wing
    7. Discussion
    8. Appendix—Young’s Modulus Profile
    9. References
53. Take-Off from Satellite Orbit
    1. Basic Equations
    2. Radial Thrust
    3. Circumferential Thrust
    4. Discussion
    5. References
54. Analysis of Peak-Holding Optimalizing Control
    1. Introduction
    2. Principle of Operation
    3. Formulation of the Mathematical Problem
    4. First-Order Input and Output Groups
    5. Design Charts
    6. Concluding Remarks
    7. Appendix
    8. References
55. The Poincaré-Lighthill-Kuo Method
    1. I. Introduction
    2. II. Ordinary Differential Equations
    3. III. Hyperbolic Partial Differential Equations
    4. IV. Elliptic Partial Differential Equations
    5. V. Applications to Fluid Boundary Layer Problems
    6. VI. Concluding Remarks
    7. References
56. Thermodynamic Properties of Gas at High Temperatures and Pressures
    1. 1. Equation of States of Dense Gas
    2. 2. Lennard-Jones and Devonshire Theory
    3. 3. Other Thermodynamic Functions
    4. References
57. Thermonuclear Power Plants
    1. 1. Introduction
    2. 2. Thermonuclear Reaction Rate
    3. 3. Example: Deuterium Reaction
    4. 4. Thermonuclear Reaction Chamber
    5. 5. Thermonuclear Power Station
    6. 6. Ignition
    7. 7. Thermonuclear Power Industry
    8. References
58. Index