The Flight of Uncontrolled Rockets

The Flight of Uncontrolled Rockets

International Series of Monographs on Aeronautics and Astronautics

1st Edition - January 1, 1964

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  • Authors: F. R. Gantmakher, L. M. Levin
  • eBook ISBN: 9781483164946

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International Series of Monographs on Aeronautics and Astronautics, Division VII, Volume 5: The Flight of Uncontrolled Rockets focuses on external ballistics of uncontrolled rockets. The book first discusses the equations of motion of rockets. The rocket as a system of changing composition; application of solidification principle to rockets; rotational motion of rockets; and equations of motion of the center of mass of rockets are described. The text looks at the calculation of trajectory of rockets and the fundamentals of rocket dispersion. The selection further focuses on the dispersion of finned rockets. Topics include the critical section of the trajectory; standard formula for calculating angular deviation; dispersion of actual rockets; and effective launcher length. The text also describes the dispersion of finned rotated rockets and of finned anti-tank rockets. The book also examines the effect of wind on the flight of rockets. Topics include correction to the coordinates of the point of impact for finned rockets; general effect of wind on dispersion; and general treatment of powered flight in the presence of wind. The text is important for readers interested in the ballistics of uncontrolled rockets.

Table of Contents

  • Contents


    Editor's Note

    Definitions and Symbols

    Chapter 1. Equations of Motion of A Rocket

    1. The Rocket As A System of Changing Composition

    2. Equations of Motion of A Particle and of A System of Constant Composition

    3. Systems of Changing Composition. Rockets

    4. Application of the Solidification Principle to Rockets

    5. Equations of Motion of the Center of Mass of A Rocket

    6. Rotational Motion of the Rocket

    Chapter 2. Calculation of the Trajectory of A Rocket

    7. Statement of the Problem

    8. The Thrust

    9. Equations for the Motion of the Mass-Center of A Rocket During Powered Flight

    10. The Tsiolkovskii Formula

    11. Variation in the Rocket Velocity During Powered Flight. Determination of the Arc-Length of the Trajectory

    12. Direction of the Rocket Velocity During Powered Flight

    13. The Influence of the Drag and Gravitational Forces On The Magnitude of the Velocity of A Rocket

    14. Calculation of the Complete Trajectory. Problems

    Chapter 3. Fundamentals of Rocket Dispersion

    15. Introduction

    16. Factors Causing Lateral Dispersion

    17. Continuous Random Variables

    18. The Role of the Powered and Unpowered Sections of the Trajectory in the Lateral Dispersion of A Rocket

    19. Angular Deviation At the End of Powered Flight and Its Horizontal and Vertical Projections

    20. Random Vectors

    21. Angular Deviation and Its Connection With Lateral Dispersion

    Chapter 4. The Dispersion of Finned Rockets

    23. Introduction

    24. Statement of the Problem

    25. Equations of Motion

    26. Integration of the Equations of Motion

    27. Integration of the Equations of Motion With An Incomplete Set of Forces and Moments

    28. Thrust Asymmetry As The Principal Factor Causing Angular Deviation of Finned Rockets

    29. The Dispersion of Actual Rockets

    30. Simplification of the Fundamental Formulae

    31. The Critical Section of the Trajectory

    32. Formulae For The Angle of Attack δ and The Angular Deviation ψ

    33. A Graphical Method. The Cornu Spiral

    34. The Standard Formula For Calculating Angular Deviation

    35. Angular Deviation As A Function of the Structural Parameters of the Rocket and the Length of the Launcher

    36. Effective Launcher Length

    37. The Stepped Acceleration Diagram. Mortar Rockets and Multi-Stage Rockets

    38. Rockets Launched From Aircraft

    39. The Angular Deviation Due To Initial Perturbations

    40. Methods of Improving The Dispersion of Finned Rockets

    41. Integration of the Fundamental Differential Equation With A Complete Set Of Forces and Moments

    42. Formulae For The Angles D and \P Using A Complete Set of Forces and Moments

    43. Analysis of the Formulae. Major and Minor Forces and Moments

    44. The Coriolis Force and Moment

    45. The Effect of the Coriolis Force and Moment On The Angular Deviation of A Finned Rocket

    Chapter 5. The Dispersion of Finned Rotated Rockets

    46. Introduction

    47. Statement of the Problem

    48. Rotational Thrust Moments

    49. The Equation of Rotational Motion

    50. Integration of the Rotational Equation of Rotation

    51. Analysis of the Rotational Motion

    52. The Angular Deviation of Finned Rotated Rockets

    53. The Angular Deviation Expressed In Terms of the Kernel R(s,σ)

    54. Analysis of Angular Deviation Calculations For Finned Rotated Rockets

    55. The Role of Thrust Eccentricity As A Cause of Lateral Dispersion of Finned Rockets

    56. Arbitrary Acceleration On The Launcher. Firing From Aircraft

    Chapter 6. The Dispersion of Finned Anti-Tank Rockets

    57. Introduction

    58. Aspects of the Ballistics of Anti-Tank Rockets

    59. The Effects of Aerodynamic Forces and Moments On The Angular Deviation of Antitank Rockets

    60. Integration of the Equations of Motion

    61. Calculation of the Angular Deviation

    62. The Maximum Effective Range

    63. Analysis of the Angular Deviation and Lateral Dispersion of Anti-Tank Rockets

    64. The Vertical Dispersion of Anti-Tank Rockets

    65. The Calculation of Angular Deviation For Arbitrary Time-Dependence of the Acceleration

    66. The Effect of the Coriolis Force and Moment On The Dispersion of Anti-Tank Rockets

    Chapter 7. Rocket Motion In Three Dimensions

    67. Introduction

    68. The Equations of Motion of the Mass-Centre of A Rocket

    69. The Equations of Rotational Motion of A Rocket

    70. The Forces and Moments Acting On the Rocket

    71. Linearization of the Equations of Motion

    72. Integration of the Equations of Motion

    73. Spin-Stabilized Rockets

    74. Non-Rotated Finned Rockets

    75. Finned Rotated Rockets

    Chapter 8. Spin-Stabilized Rockets

    76. Criteria For The Stability of the Unpowered Flight of Spin-Stabilized Rockets

    77. The Condition For Stable Powered Flight

    78. Calculation of the Angular Deviation During Powered Flight For Spin-Stabilized Rockets

    Chapter 9. The Effect of Wind On The Flight of Rockets

    79. Introduction

    80. The Physics of the Phenomenon

    81. The Angular Deviation of Finned Rockets During Powered Flight

    82. Corrections to the Coordinates of the Point of Impact For Finned Rockets

    83. The General Effect of Wind On Dispersion

    84. The General Treatment of Powered Flight in the Presence of Wind

    85. Non-Rotated Finned Rockets

    86. Rotated Finned Rockets

    87. Spin-Stabilized Rockets

    Appendix 1. Formulae For the Additional Forces in the Equations of Motion of A Rocket

    1. An Alternative Form of the Linear and Angular Momentum Equations For the Body S.

    2. Formulae For Linear Momentum, Coriolis Force and Coriolis Moment

    3. Movement of the Centre of Mass Relative to the Body of the Rocket

    Appendix 2. Brief Notes On the Aerodynamics of Rockets

    1. Introduction

    2. Elements of Similarity Theory

    3. Methods of Describing Aerodynamic Forces and Moments

    4. The Drag

    5. The Lift Force

    6. The Lateral Aerodynamic Moment

    7. The Lateral Damping Moment

    8. Longitudinal Aerodynamic Moments

    9. The Effect of Aerodynamic Characteristics On The Flight of A Rocket

    Appendix 3. British and American Works On The Motion of Unguided Rockets During The Burning Period

    1. Introduction

    2. Unrotated Rockets

    3. Finned Rotated Rockets

    4. Spin-Stabilized Rockets

    5. Rocker Accuracy

    References To Appendix 3

    Tables of A(X) and B(X) For Appendix 3

    Tables :

    Table 1

    Table 2

    Table 3 a

    Table 3 b

    Table 4

    Table 5

    Table 6

    Table 7

    Table 8 a

    Table 8 b

    Table 8 c

    Table 8 d



    Other Titles in the Series In Aeronautics and Astronautics

Product details

  • No. of pages: 396
  • Language: English
  • Copyright: © Pergamon 1964
  • Published: January 1, 1964
  • Imprint: Pergamon
  • eBook ISBN: 9781483164946

About the Authors

F. R. Gantmakher

L. M. Levin

About the Editor

H. L. Dryden

Affiliations and Expertise

Case Institute of Technology, Cleveland, Ohio

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