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I N A S A T E C H N I C A L T R A N S L A T I O N *o h I Y, c c 4 c/I 4 z f HELICOPTER AERODYNAMICS by D. I, B ~ Z O V i\ 1i Transport Press, Moscow, 1969 'i' NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. MAY 1972 TECH LIBRARY KAFB,NM 1I1111l1l1l1ll111l1l1lll11l11l11l1l1 l1 1111111 00b9L82 NASA TT F-676 HELICOPTER AERODYNAMICS By D. I. Bazov Translation of "Aerodinamika vertoletov.lr Transport Press, Moscow, 1969 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION . . -.. . For sale by the National Technical Information Service, Springfield, Virginia 22151 $3.00 ANNOTATION Principles of helicopter flight under various conditions are reviewed, giving special attention to the operation of the main rotor. A brief history of helicopter development is presented, together with a summary of the main components of a helicopter and a classification of the various types of helicopters. The characteristics of the main rotor and its operation during autorotation and during axial and oblique flow are considered. Also considered are vertical and horizontal flight, altitude gain and descent, takeoff and landing, equilibrium, stability, and controllability, taking into account the aerodynamic forces acting on the helicopter during the various maneuvers. iii TABLE OF CONTENTS /194 PAGE CHAPTER I. PRINCIPLES OF HELICOPTER JTLIGHT 1 § 1. Brief History of Helicopter Development 1 § 2. The Helicopter and Its Basic Components 4 § 3. Classification of Helicopters 6 CHAPTER 11. BASIC CHARACTERISTICS OF THE MAIN ROTOR 10 § 4. General Characteristics 10 5 5. Geometric Characteristics 11 5 6. Basic Regimes of Operation 16 5 7. The Operating Regime Coefficient of the Main Rotor 18 CHAPTER 111. OPERATION OF THE MAIN ROTOR IN THE AXIAL FLOW REGIME 20 5 8. Impulsive Theory of an Ideal Rotor 20 5 9. Blade Element Theory 24 5 10. Forces Resisting Rotation of the Main Rotor 26 5 11. Power and Torque Required to Rotate Main Rotor 28 § 12. Main Rotor RPM Control 31 § 13. Techniques for Counteracting Main Rotor Reactive Torque 33 5 14. Techniques for Transmitting Torque From Engine to Main Rotor 35 § 15. Main Rotor Power Available 39 5 16. Main Rotor Thrust in Vertical Climb and Vertical Desc ent 41 5 17. Losses of the Real Rotor 43 § 18. Characteristics of Operation of Coaxial System of Two Main Rotors 46 Programmed Testing Questions and Answers 50 CHAPTER IV. MAIN ROTOR OPERATION IN FORWARD FLIGHT 56 § 19. Characteristics of Main Rotor Operation in Forward Flight 56 § 20. Main Rotor Thrust as a Function of Flight Speed 59 V - PAGE § 21. Blade Thrust and Its Azimuthal Variation 62 § 22. Resultant Flow Velocity Over Blade Element i n the Hub Rotation Plane 64 § 23. Variation of Circumferential and Resultant Velocities Along Main Rotor Radius 66 5 24. Drawbacks of Main Rotor With Rigid Blade Retention 68 § 25. Purpose of Main Rotor Hub Horizontal Hinges 71 § 26. Conditions for Blade Equilibrium Relative to the Horizontal Hinge 71 § 27. Main Rotor Cone of Revolution 74 § 28. Blade Flapping Motions 75 § 29. Main Rotor Coning Axis Tilt 78 § 30. Blade Flapping Motion Restriction and Flapping Compensator 80 § 31. Blade Element Angle of Attack Change Owing to Flapping Motions 83 § 32. Effect of Number of Blades on Main Rotor Aerodynamic Characteristics 85 - § 33. Azimuthal Variation of Rotational Resistance Forces 1195 and Reactive Torque 85 § 34. Inertial Forces Acting on Main Rotor Blades 87 § 35. Oscillatory Blade Motions 91 § 36. Damping of Oscillatory Blade Motions 94 § 37. Possibility of Loss of Blade Flapping Motion Stability 97 Programmed Testing Questions and Answers 100 CHAPTER V. HELICOPTER VERTICAL FLIGHT OPERATING REGIMES 107 § 38. Hovering Regime. General Characteristics. 108 § 39. Diagram of Forces Acting on Helicopter and Hovering Conditions 109 § 40. Thrust and Power Required for Hovering 112 § 41. Vertical Climb 119 § 42. Helicopter Vertical Descent With Operating Engine 123 § 43. Vortex Ring Regime 125 Programmed Testing Questions and Answers 126 CHAPTER VI. HELICOPTER HORIZONTAL FTJGHT 129 § 44. General Characteristics of Horizontal Flight 129 § 45. Thrust and Power Required for Horizontal Flight 131 § 46. Characteristic Helicopter Horizontal Flight Speeds 136 § 47. Effect of Helicopter Weight and Flight Altitude on Performance 138 § 48. Factors Limiting Maximal Horizontal Flight Speed and Ways to Increase This Speed 141 § 49. Horizontal Flight Endurance and Range 144 Programmed Testing Questions and Answers 148 vi I - PAGE CHAPTER VII. QLIMB ALONG INCLINED TRAJECTORY 152 5 50. General Characteristics of the Climb Regime Along an Inclined Trajectory 152 I51. Thrust and Power Required for Climb 153 5 52. Vertical Rate of Climb 155 5 53. Variation of Vertical Rate of Climb With Altitude 156 CHAF'TER VIII. HELICOPTER DESCENT ALONG INCLINED TRAJECTORY 160 5 54. General Characteristics of the Descent Regime 160 5 55. Thrust and Power Required for Helicopter Descent 162 5 56. Helicopter Rate of Descent With Operating Engine 164 Progranrmed Testing Questions and Answers 166 CHAPTER IX. HELICOPTER FLIGHT IN MAIN ROTOR AUTOROTATIVE REGIME 171 5 57. Vertical Descent 171 5 58. Blade Aerodynamic Forces 176 § 59. Main Rotor Autorotation Conditions and Regimes 177 § 60. Conditions for Autorotation of Different Blade Elements 182 § 61. Gliding 187 § 62. Vertical Rate of Descent in a Glide 191 § 63. Safety Height 195 5 64. Transition From Flight With Engine Operating to Flight in the Main Rotor Autorotation Regime 197 § 65. G l id ing Ch aracteristics of Dual-Rotor Helicopters 200 Programmed Testing Questions and Answers 202 CHAPTER X. HELICOPTER TAKEOFF AND LANDING 208 /196 § 66. Takeoff 208 § 67. Landing 2 13 CHAPTER XI. HELICOPTER BALANCE STABILITY AND CONTROL 222 5 68. Helicopter Center of Gravity and Balance 222 5 69. General Analysis of Helicopter Equilibrium 225 5 70. Helicopter Equilibrium in the Hovering Regime 227 § 71. Helicopter Static Stability 236 5 72. Helicopter Dynamic Stability 242 5 73. Concept of Helicopter Control 245 5 74. Change of Main Rotor Collective and Cyclic Pitch 246 5 75. Purpose and Principle of the Main Rotor Tilt Control System 247 vii PAGE § 76. Single-Rotor Helicopter Control Principles 252 5 77. Dual-Rotor Helicopter Control Principles 254 § 78. Concept of Helicopter Controllability 257 CHAPTER XII. HELICOPTER VIBRATIONS 262 § 79. General Analysis of Vibrations 262 § 80. Helicopter Forced Vibrations 264 § 81. Self-Excited Vibrations 267 § 82. Bending and Bending-Torsion Vibrations of Rigidly Restrained Blade 271 APPENDIX I. SYMBOL LIST 28 1 APPENDIX 11. PROGRAMMED TESTING ANSWERS 284 REFERENCES 285 viii CHAPTER I PRINCIPLES OF HELICOPTER FLIGHT 5 1. Brief History ef H-elicopter Development * The idea of creating a flying apparatus with an aerial screw, which 12. created a lifting force, was suggested for the first time in 1475 by Leonard0 de Vinci. This idea was too premature owing to the impossibility of technical realization of the project and opposition by religiousopPnions. The idea was buried in the archives. A sketch and description of this flying apparatus was displayed in the Milan library and published at the end of the lgth century. In 1754, M. V. Lomonosov substantiated the possibility of creating a heavier than air flying apparatus and built a model of a dual rotor helicopter with the rotors arranged coaxially. In the lgth century many Russian scientists and engineers developed projects for flying machines with main rotors. In 1869, electrical engineer A. N. Lodygin proposed a projected helicopter powered by an electric motor. In 1870 the well known scientist M. A. Rykachev was engaged in the develop ment of propellers. Metallurgist-scientist D. K. Chernov devised a helicopter scheme with longitudinal, transverse, and coaxially arranged rotors. __ * ~ Numbers i n the margin indicate pagination in the original foreign text. 1