The history of the helicopter may be traced back to the Chinese flying top (c. 400 B.C.) and to the work of Leonardo da Vinci, who sketched designs for a vertical flight machine utilizing a screw-type propeller. In the late nineteenth century, Thomas Edison experimented with helicopter models, realizing that no such machine would be able to fly until the development of a sufficiently lightweight engine. When the internal combustion gasoline engine came on the scene around 1900, the stage was set for the real development of helicopter technology.While this text provides a concise history of helicopter development, its true purpose is to provide the engineering analysis required to design a highly successful rotorcraft. Toward that end the book offers thorough, comprehensive coverage of the theory of helicopter flight: the elements of vertical flight, forward flight, performance, design, mathematics of rotating systems, rotary wing dynamics and aerodynamics, aeroelasticity, stability and control, stall, noise and more.Wayne Johnson has worked for the U.S. Army and NASA at the Ames Research Center in California. Through his company Johnson Aeronautics, he is engaged in the development of software that is used throughout the world for the analysis of rotorcraft. In this book, Dr. Johnson has compiled a monumental resource that is essential reading for any student or aeronautical engineer interested in the design and development of vertical-flight aircraft.

Acknowledgements Notation1. Introduction 1-1 The Helicopter 1-1.1 The Helicopter Rotor 1-1.2 Helicopter Configuration 1-1.3 Helicopter Operation 1-2 History 1-2.1 Helicopter Development 1-2.2 Literature 1-3 Notation 1-3.1 Dimensions 1-3.2 Physical Description of the Blade 1-3.3 Blade Aerodynamics 1-3.4 Blade Motion 1-3.5 Rotor Angle of Attack and Velocity 1-3.6 Rotor Forces and Power 1-3.7 Rotor Disk Planes 1-3.8 NACA Notation2. Vertical Flight I 2-1 Momentum Theory 2-1.1 Actuator Disk 2-1.2 Momentum Theory in Hover 2-1.3 Momentum Theory in Climb 2-1.4 Hover Power Losses 2-2 Figure of Merit 2-3 Extended Momentum Theory 2-3.1 Rotor in Hover or Climb 2-3.2 Swirl in the Wake 2-3.3 Swirl Due to Profile Torque 2-4 Blade Element Theory 2-4.1 History of the Development of Blade Element Theory 2-4.2 Blade Element Theory for Vertical Flight 2-4.2.1 Rotor Thrust 2-4.2.2 Induced Velocity 2-4.2.3 Power or Torque 2-5 Combined Blade Element and Momentum Theory 2-6 Hover Performance 2-6.1 Tip Losses 2-6.2 Induced Power Due to Nonuniform Inflow and Tip Losses 2-6.3 Root Cutout 2-6.4 Blade Mean Lift Coefficient 2-6.5 Equivalent Solidity 2-6.6 The Ideal Rotor 2-6.7 The Optimum Hovering Rotor 2-6.8 Effect of Twist and Taper 2-6.9 Examples of Hover Polars 2-6.10 "Disk Loading, Span Loading, and Circulation" 2-7 Vortex Theory 2-7.1 Vortex Representation of the Rotor and Its Wake 2-7.2 Actuator Disk Vortex Theory 2-7.3 Finite Number of Blades 2-7.3.1 Wake Structure for Optimum Rotor 2-7.3.2 Prandtl's Tip Loading Solution 2-7.3.3 Goldstein's Propeller Analysis 2-7.3.4 Applications to Low Inflow Rotors 2-7.4 Nonuniform Inflow (Numerical Vortex Theory) 2-7.5 Literature 2-8 Literature3. Vertical Flight II 3-1 Induced Power in Vertical Flight 3-1.1 Momentum Theory for Vertical Flight 3-1.2 Flow States of the Rotor in Axial Flight 3-1.2.1 Normal Working State 3-1.2.2 Vortex Ring State 3-1.2.3 Turbulent Wake State 3-1.2.4 Windmill Brake State 3-1.3 Induced Velocity Curve 3-1.3.1 Hover Performance 3-1.3.2 Autorotation 3-1.3.3 Vortex Ring State 3-1.4 Literature 3-2 Autorotation in Vertical Descent 3-3 Climb in Vertical Flight 3-4 Vertical Drag 3-5 Twin Rotor Interference in Hover 3-6 Ground Effect4. Forward Flight I 4-1 Momentum Theory in Forward Flight 4-1.1 Rotor Induced Power 4-1.2 "Climb, Descent, and Autorotation in Forward Flight" 4-1.3 Tip Loss Factor 4-2 Vortex Theory in Forward Flight 4-2.1 Classical Vortex Theory Results 4-2.2 Induced Velocity Variation in Forward Flight 4-2.3 Literature 4-3 Twin Rotor Interference in Forward Flight 4-4 Ground Effect in Forward Flight5. Forward Flight II 5-1 The Helicopter Rotor in Forward Flight 5-2 Aerodynamics of Forward Flight 5-3 Rotor Aerodynamic Forces 5-4 Power in Forward Flight 5-5 Rotor Flapping Motion 5-6 Examples of Performance and Flapping in Forward Flight 5-7 Review of Assumptions 5-8 Tip Loss and Root Cutout 5-9 Blade Weight Moment 5-10 Linear Inflow Variation 5-11 Higher Harmonic Flapping Motion 5-12 Profile Power and Radial Flow 5-13 Flap Motion with a Hinge Spring 5-14 Flap Hinge Offset 5-15 Hingeless Rotor 5-16 Gimballed or Teetering Rotor 5-17 Pitch-Flap Coupling 5-18 "Helicopter Force, Moment, and Power Equilibrium" 5-19 Lag Motion 5-20 Reverse Flow 5-21 Compressibility 5-22 Tail Rotor 5-23 Numerical Solutions 5-24 Literature6. Performance 6-1 Hover Performance 6-1.1 Power Required in Hover and Vertical Flight 6-1.2 Climb and Descent 6-1.3 Power Available 6-2 Forward Flight Performance 6-2.1 Power Required in Forward Flight 6-2.2 Climb and Descent in Forward Flight 6-2.3 D/L Formulation 6-2.4 Rotor Lift and Drag 6-2.5 P/T Formulation 6-3 Helicopter Performance Factors 6-3.1 Hover Performance 6-3.2 Minimum Power Loading in Hover 6-3.3 Power Required in Level Flight 6-3.4 Climb and Descent 6-3.5 Maximum Speed 6-3.6 Maximum Altitude 6-3.7 Range and Endurance 6-4 Other Performance Problems 6-4.1 Power Specified (Autogyro) 6-4.2 Shaft Angle Specified (Tail Rotor) 6-5 Improved Performance Calculations 6-6 Literature7. Design 7-1 Rotor Types 7-2 Helicopter Types 7-3 Preliminary Design 7-4 Helicopter Speed Limitations 7-5 Autorotational Landings after Power Failure 7-6 Helicopter Drag 7-7 Rotor Blade Airfoil Selection 7-8 Rotor Blade Profile Drag 7-9 Literature8. Mathematics of Rotating Systems 8-1 Fourier Series 8-2 Sum of Harmonics 8-3 Harmonic Analysis 8-4 Fourier Coordinate Transformation 8-4.1 Transformation of the Degrees of Freedom 8-4.2 Conversion of the Equations of Motion 8-5 Eigenvalues and Eigenvectors of the Rotor motion 8-6 "Analysis of Linear, Periodic Systems" 8-6.1 "Linear, Constant Coefficient Equations" 8-6.2 "Linear, Periodic Coefficient Equations"9. Rotary Wing Dynamics I 9-1 Sturm-Liouville Theory 9-2 Out-of-Plane Motion 9-2.1 Rigid Flapping 9-2.2 Out-of-Plane Bending 9-2.3 Nonrotating Frame 9-2.4 Bending Moments 9-3 In-plane Motion 9-3.1 Rigid Flap and Lag 9-3.2 In-Plane Bending 9-3.3 In-Plane and Out-of-Plane Bending 9-4 Torsional Motion 9-4.1 Rigid Pitch and Flap 9-4.2 Structural Pitch-Flap and Pitch-Lag Coupling 9-4.3 Torsion and Out-of-Plane Bending 9-4.4 Nonrotating Frame 9-5 Hub Reactions 9-5.1 Rotating Loads 9-5.2 Nonrotating Loads 9-6 Shaft Motion 9-7 Coupled Flap-Lag Torsion Motion 9-8 Rotor Blade Bending Modes 9-8.1 Engineering Beam Theory for a Twisted Blade&nbs 10-8.2 Finite-Length Vortex Line Element 10-8.3 Rectangular Vortex Sheet11. Rotary Wing Aerodynamics II 11-1 Section Aerodynamics 11-2 Flap Motion 11-3 Flap and Lag Motion 11-4 Nonrotating Frame 11-5 Hub Reactions 11-5.1 Rotating Frame 11-5.2 Nonrotating Frame 11-6 Shaft Motion 11-7 Summary 11-8 Pitch and Flap Motion12. Rotary Wing Dynamics II 12-1 Flapping Dynamics 12-1.1 Rotating Frame 12-1.1.1 Hover Roots 12-1.1.2 Forward Flight Roots 12-1.1.3 Hover Transfer Function 12-1.2 Nonrotating Frame 12-1.2.1 HoverRoots and Modes 12-1.2.2 Hover Transfer Functions 12-1.3 Low Frequency Response 12-1.4 Hub Reactions 12-1.5 Two-Bladed Rotor 12-1.6 Literature 12-2 Flutter 12-2.1 Pitch-Flap Equations 12-2.2 Divergence Instability 12-2.3 Flutter Instability 12-2.4 Other Factors Influencing Pitch-Flap Stability 12-2.4.1 Shed Wake Influence 12-2.4.2 Wake-Excited Flutter 12-2.4.3 Influence of Forward Flight 12-2.4.4 Coupled Blades 12-2.4.5 Additional Degrees of Freedom 12-2.5 Literature 12-3 Flap-Lag Dynamics 12-3.1 Flap-Lag Equations 12-3.2 Articulated Rotors 12-3.3 Hingeless Rotors 12-3.4 Improved Analytical Models 12-3.5 Literature 12-4 Ground Resonance 12-4.1 Ground Resonance Equations 12-4.2 No-Damping Case 12-4.3 Damping Required for Ground Resonance Stability 12-4.4 Two-Bladed Rotor 12-4.5 Literature 12-5 Vibration and Loads 12-5.1 Vibration 12-5.2 Loads 12-5.3 Calculation of Vibration and Loads 12-5.4 Blade Frequencies 12-5.5 Literature13. Rotary Wing Aerodynamics III 13-1 Rotor Vortex Wake 13-2 Nonuniform Inflow 13-3 Wake Geometry 13-4 Vortex-Induced Loads 13-5 Vortices and Wakes 13-6 Lifting-Surface Theory 13-7 Boundary Layers14 Helicopter Aeroelasticity 14-1 Aeroelastic Analyses 14-2 Integration of the Equations of Motion 14-3 Literature15 Stablity and Control 15-1 Control 15-2 Stability 15-3 Flying Qualities in Hover 15-3.1 Equations of Motion 15-3.2 Vertical Dynamics 15-3.3 Yaw Dynamics 15-3.4 Longitudinal Dynamics 15-3.4.1 Equations of Motion 15-3.4.2 Poles and Zeros 15-3.4.3 Loop Closures 15-3.4.4 Hingeless Rotors 15-3.4.5 Response to Control 15-3.4.6 Examples 15-3.4.7 Flying Qualities Characteristics 15-3.5 Lateral Dynamics 15-3.6 Coupled Longitudinal and Lateral Dynamics 15-3.7 Tandem Helicopters 15-4 Flying Qualities in Forward Flight 15-4.1 Equations of Motion 15-4.2 Longitudinal Dynamics 15-4-2.1 Equations of Motion 15-4-2.2 Poles 15-4-2.3 Short Period Approximation 15-4-2.4 Static Stability 15-4-2.5 Example 15-4-2.6 Flying Qualities Characteristics 15-4.3 Lateral Dynamics 15-4.4 Tandem Helicopters 15-4.5 Hingeless Rotor Helicopters 15-5 Low Frequency Rotor Response 15-6 Stability Augmentation 15-7 Flying Qualities Specifications 15-8 Literature16 Stall 16-1 Rotary Wing Stall Characteristics 16-2 NACA Stall Research 16-3 Dynamic Stall 16-4 Literature17 Noise 17-1 Helicopter Rotor Noise 17-2 Vortex Noise 17-3 Rotational Noise 17-3.1 Rotor Pressure Distribution 17-3.2 Hovering Rotor with Steady Loading 17-3.3 Vertical Flight and Steady Loading 17-3.4 Stationary Rotor with Unsteady Loading 17-3.5 Forward Flight and Steady Loading 17-3.6 Forward Flight and Unsteady Loading 17-3.7 Thickness Noise 17-3.8 Rotating Frame Analysis 17-3.9 Doppler Shift 17-4 Blade Slap 17-5 Rotor Noise Reduction 17-6 LiteratureCited LiteratureIndex