| |

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Preface to the Second Edition | |

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Preface to the First Edition | |

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Acknowledgments | |

| |

| |

List of Main Symbols | |

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Introduction: A History of Helicopter Flight | |

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Rising Vertically | |

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Producing Thrust | |

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Key Technical Problems in Attaining Vertical Flight | |

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Early Thinking | |

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The Hoppers | |

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The First Hoverers | |

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Not Quite a Helicopter | |

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Engines: A Key Enabling Technology | |

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On the Verge of Success | |

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The First Successes | |

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Toward Mass Production | |

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Maturing Technology | |

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Compounds, Tilt-Wings, and Tilt-Rotors | |

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| |

Chapter Review | |

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| |

| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Fundamentals of Rotor Aerodynamics | |

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| |

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Introduction | |

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| |

| |

Momentum Theory Analysis in Hovering Flight | |

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| |

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Flow Near a Hovering Rotor | |

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Conservation Laws of Aerodynamics | |

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Application to a Hovering Rotor | |

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| |

Disk Loading and Power Loading | |

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| |

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Induced Inflow Ratio | |

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| |

Thrust and Power Coefficients | |

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| |

| |

Comparison of Theory with Measured Rotor Performance | |

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| |

| |

Nonideal Effects on Rotor Performance | |

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| |

| |

Figure of Merit | |

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| |

| |

Estimating Nonideal Effects from Rotor Measurements | |

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| |

| |

Induced Tip Loss | |

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| |

| |

Rotor Solidity and Blade Loading Coefficient | |

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| |

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Power Loading | |

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| |

| |

Momentum Analysis in Axial Climb and Descent | |

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Axial Climb | |

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Axial Descent | |

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| |

Region between Hover and Windmill State | |

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Power Required in Axial Climbing and Descending Flight | |

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Four Working States of the Rotor in Axial Flight | |

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Vortex Ring State | |

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Autorotation | |

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| |

Momentum Analysis in Forward Flight | |

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Induced Velocity in Forward Flight | |

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Special Case, [alpha] = 0 | |

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| |

| |

Numerical Solution to Inflow Equation | |

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| |

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General Form of the Inflow Equation | |

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| |

| |

Validity of the Inflow Equation | |

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| |

| |

Rotor Power Requirements in Forward Flight | |

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| |

Other Applications of the Momentum Theory | |

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| |

| |

Coaxial Rotor Systems | |

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| |

| |

Tandem Rotor Systems | |

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| |

| |

Chapter Review | |

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| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Blade Element Analysis | |

| |

| |

| |

Introduction | |

| |

| |

| |

Blade Element Analysis in Hover and Axial Flight | |

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| |

| |

Integrated Rotor Thrust and Power | |

| |

| |

| |

Thrust Approximations | |

| |

| |

| |

Torque-Power Approximations | |

| |

| |

| |

Tip-Loss Factor | |

| |

| |

| |

Blade Element Momentum Theory (BEMT) | |

| |

| |

| |

Assumed Radial Distributions of Inflow on the Blades | |

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| |

| |

Radial Inflow Equation | |

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| |

| |

Ideal Twist | |

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| |

| |

BEMT: Numerical Solution | |

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| |

| |

Distributions of Inflow and Airloads | |

| |

| |

| |

Effects of Swirl Velocity | |

| |

| |

| |

The Optimum Hovering Rotor | |

| |

| |

| |

Circulation Theory of Lift | |

| |

| |

| |

Power Estimates for the Rotor | |

| |

| |

| |

Prandtl's Tip-Loss Function | |

| |

| |

| |

Blade Design and Figure of Merit | |

| |

| |

| |

BEMT in Climbing Flight | |

| |

| |

| |

Further Comparisons of BEMT with Experiment | |

| |

| |

| |

Compressibility Corrections to Rotor Performance | |

| |

| |

| |

Equivalent Blade Chords and Weighted Solidity | |

| |

| |

| |

Mean Wing Chords | |

| |

| |

| |

Thrust Weighted Solidity | |

| |

| |

| |

Power-Torque Weighted Solidity | |

| |

| |

| |

Weighted Solidity of the Optimum Rotor | |

| |

| |

| |

Weighted Solidities of Tapered Blades | |

| |

| |

| |

Mean Lift Coefficient | |

| |

| |

| |

Blade Element Analysis in Forward Flight | |

| |

| |

| |

Determining Blade Forces | |

| |

| |

| |

Definition of the Approximate Induced Velocity Field | |

| |

| |

| |

Chapter Review | |

| |

| |

| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Rotating Blade Motion | |

| |

| |

| |

Introduction | |

| |

| |

| |

Types of Rotors | |

| |

| |

| |

Equilibrium about the Flapping Hinge | |

| |

| |

| |

Equilibrium about the Lead-Lag Hinge | |

| |

| |

| |

Equation of Motion for a Flapping Blade | |

| |

| |

| |

Physical Description of Blade Flapping | |

| |

| |

| |

Coning Angle | |

| |

| |

| |

Longitudinal Flapping Angle | |

| |

| |

| |

Lateral Flapping Angle | |

| |

| |

| |

Higher Harmonics of Blade Flapping | |

| |

| |

| |

Dynamics of Blade Flapping with a Hinge Offset | |

| |

| |

| |

Blade Feathering and the Swashplate | |

| |

| |

| |

Review of Rotor Reference Axes | |

| |

| |

| |

Dynamics of a Lagging Blade with a Hinge Offset | |

| |

| |

| |

Coupled Flap-Lag Motion | |

| |

| |

| |

Coupled Pitch-Flap Motion | |

| |

| |

| |

Other Types of Rotors | |

| |

| |

| |

Teetering Rotor | |

| |

| |

| |

Semi-Rigid or Hingeless Rotors | |

| |

| |

| |

Introduction to Rotor Trim | |

| |

| |

| |

Equations for Free-Flight Trim | |

| |

| |

| |

Typical Trim Solution Procedure for Level Flight | |

| |

| |

| |

Chapter Review | |

| |

| |

| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Helicopter Performance | |

| |

| |

| |

Introduction | |

| |

| |

| |

The International Standard Atmosphere | |

| |

| |

| |

Hovering and Axial Climb Performance | |

| |

| |

| |

Forward Flight Performance | |

| |

| |

| |

Induced Power | |

| |

| |

| |

Blade Profile Power | |

| |

| |

| |

Compressibility Losses and Tip Relief | |

| |

| |

| |

Reverse Flow | |

| |

| |

| |

Parasitic Power | |

| |

| |

| |

Climb Power | |

| |

| |

| |

Tail Rotor Power | |

| |

| |

| |

Total Power | |

| |

| |

| |

Performance Analysis | |

| |

| |

| |

Effect of Gross Weight | |

| |

| |

| |

Effect of Density Altitude | |

| |

| |

| |

Life-to-Drag Ratios | |

| |

| |

| |

Climb Performance | |

| |

| |

| |

Engine Fuel Consumption | |

| |

| |

| |

Speed for Minimum Power | |

| |

| |

| |

Speed for Maximum Range | |

| |

| |

| |

Range-Payload and Endurance-Payload Relations | |

| |

| |

| |

Maximum Altitude or Ceiling | |

| |

| |

| |

Factors Affecting Maximum Attainable Forward Speed | |

| |

| |

| |

Performance of Coaxial and Tandem Dual Rotor Systems | |

| |

| |

| |

Autorotational Performance | |

| |

| |

| |

Autorotation in Forward Flight | |

| |

| |

| |

Height-Velocity (H-V) Curve | |

| |

| |

| |

Autorotation Index | |

| |

| |

| |

Vortex Ring State (VRS) | |

| |

| |

| |

Quantification of VRS Effects | |

| |

| |

| |

Implications of VRS on Flight Boundary | |

| |

| |

| |

Ground Effect | |

| |

| |

| |

Hovering Flight Near the Ground | |

| |

| |

| |

Forward Flight Near the Ground | |

| |

| |

| |

Performance in Maneuvering Flight | |

| |

| |

| |

Steady Maneuvers | |

| |

| |

| |

Transient Maneuvers | |

| |

| |

| |

Factors Influencing Performance Degradation | |

| |

| |

| |

Chapter Review | |

| |

| |

| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Aerodynamic Design of Helicopters | |

| |

| |

| |

Introduction | |

| |

| |

| |

Overall Design Requirements | |

| |

| |

| |

Conceptual and Preliminary Design Processes | |

| |

| |

| |

Design of the Main Rotor | |

| |

| |

| |

Rotor Diameter | |

| |

| |

| |

Tip Speed | |

| |

| |

| |

Rotor Solidity | |

| |

| |

| |

Number of Blades | |

| |

| |

| |

Blade Twist | |

| |

| |

| |

Blade Planform and Tip Shape | |

| |

| |

| |

Airfoil Sections | |

| |

| |

| |

Case Study: The BERP Rotor | |

| |

| |

| |

Fuselage Aerodynamic Design Issues | |

| |

| |

| |

Fuselage Drag | |

| |

| |

| |

Vertical Drag and Download Penalty | |

| |

| |

| |

Vertical Drag Recovery | |

| |

| |

| |

Fuselage Side-Force | |

| |

| |

| |

Empennage Design | |

| |

| |

| |

Horizontal Stabilizer | |

| |

| |

| |

Vertical Stabilizer | |

| |

| |

| |

Role of Wind Tunnels in Aerodynamic Design | |

| |

| |

| |

Design of Tail Rotors | |

| |

| |

| |

Physical Size | |

| |

| |

| |

Thrust Requirements | |

| |

| |

| |

Precessional Stall Issues | |

| |

| |

| |

"Pushers" versus "Tractors" | |

| |

| |

| |

Design Requirements | |

| |

| |

| |

Representative Tail Rotor Designs | |

| |

| |

| |

Other Anti-Torque Devices | |

| |

| |

| |

Fan-in-Fin | |

| |

| |

| |

NOTAR Design | |

| |

| |

| |

High-Speed Rotorcraft | |

| |

| |

| |

Compound Helicopters | |

| |

| |

| |

Tilt-Rotors | |

| |

| |

| |

Other High-Speed Concepts | |

| |

| |

| |

Smart Rotor Systems | |

| |

| |

| |

Human-Powered Helicopter | |

| |

| |

| |

Hovering Micro Air Vehicles | |

| |

| |

| |

Chapter Review | |

| |

| |

| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Aerodynamics of Rotor Airfoils | |

| |

| |

| |

Introduction | |

| |

| |

| |

Helicopter Rotor Airfoil Requirements | |

| |

| |

| |

Reynolds Number and Mach Number Effects | |

| |

| |

| |

Reynolds Number | |

| |

| |

| |

Concept of the Boundary Layer | |

| |

| |

| |

Mach Number | |

| |

| |

| |

Model Rotor Similarity Parameters | |

| |

| |

| |

Airfoil Shape Definition | |

| |

| |

| |

Airfoil Pressure Distributions | |

| |

| |

| |

Pressure Coefficient | |

| |

| |

| |

Critical Pressure Coefficient | |

| |

| |

| |

Synthesis of Chordwise Pressure | |

| |

| |

| |

Measurements of Chordwise Pressure | |

| |

| |

| |

Aerodynamics of a Representative Airfoil Section | |

| |

| |

| |

Integration of Distributed Forces | |

| |

| |

| |

Pressure Integration | |

| |

| |

| |

Representative Force and Moment Results | |

| |

| |

| |

Pitching Moment and Related Issues | |

| |

| |

| |

Aerodynamic Center | |

| |

| |

| |

Center of Pressure | |

| |

| |

| |

Effect of Airfoil Shape on Pitching Moment | |

| |

| |

| |

Use of Trailing Edge Tabs | |

| |

| |

| |

Reflexed Airfoils | |

| |

| |

| |

Drag | |

| |

| |

| |

Maximum Lift and Stall Characteristics | |

| |

| |

| |

Effects of Reynolds Number | |

| |

| |

| |

Effects of Mach Number | |

| |

| |

| |

Advanced Rotor Airfoil Design | |

| |

| |

| |

Representing Static Airfoil Characteristics | |

| |

| |

| |

Linear Aerodynamic Models | |

| |

| |

| |

Nonlinear Aerodynamic Models | |

| |

| |

| |

Table Look-Up | |

| |

| |

| |

Direct Curve Fitting | |

| |

| |

| |

Beddoes Method | |

| |

| |

| |

High Angle of Attack Range | |

| |

| |

| |

Circulation Controlled Airfoils | |

| |

| |

| |

Very Low Reynolds Number Airfoil Characteristics | |

| |

| |

| |

Effects of Damage on Airfoil Performance | |

| |

| |

| |

Chapter Review | |

| |

| |

| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Unsteady Airfoil Behavior | |

| |

| |

| |

Introduction | |

| |

| |

| |

Sources of Unsteady Aerodynamic Loading | |

| |

| |

| |

Concepts of the Blade Wake | |

| |

| |

| |

Reduced Frequency and Reduced Time | |

| |

| |

| |

Unsteady Attached Flow | |

| |

| |

| |

Principles of Quasi-Steady Thin-Airfoil Theory | |

| |

| |

| |

Theodorsen's Theory | |

| |

| |

| |

Pure Angle of Attack Oscillations | |

| |

| |

| |

Pure Plunging Oscillations | |

| |

| |

| |

Pitching Oscillations | |

| |

| |

| |

The Returning Wake: Loewy's Problem | |

| |

| |

| |

Sinusoidal Gust: Sears's Problem | |

| |

| |

| |

Indicial Response: Wagner's Problem | |

| |

| |

| |

Sharp-Edged Gust: Kussner's Problem | |

| |

| |

| |

Traveling Sharp-Edged Gust: Miles's Problem | |

| |

| |

| |

Time-Varying Incident Velocity | |

| |

| |

| |

General Application of the Indicial Response Method | |

| |

| |

| |

Recurrence Solution to the Duhamel Integral | |

| |

| |

| |

State-Space Solution for Arbitrary Motion | |

| |

| |

| |

Indicial Method for Subsonic Compressible Flow | |

| |

| |

| |

Approximations to the Indicial Response | |

| |

| |

| |

Indicial Lift from Angle of Attack | |

| |

| |

| |

Indicial Lift from Pitch Rate | |

| |

| |

| |

Determination of Indicial Function Coefficients | |

| |

| |

| |

Indicial Pitching Moment from Angle of Attack | |

| |

| |

| |

Indicial Pitching Moment from Pitch Rate | |

| |

| |

| |

Unsteady Axial Force and Airfoil Drag | |

| |

| |

| |

State-Space Aerodynamic Model for Compressible Flow | |

| |

| |

| |

Comparison with Experiment | |

| |

| |

| |

Nonuniform Vertical Velocity Fields | |

| |

| |

| |

Exact Subsonic Linear Theory | |

| |

| |

| |

Approximations to the Sharp-Edged Gust Functions | |

| |

| |

| |

Response to an Arbitrary Vertical Gust | |

| |

| |

| |

Blade-Vortex Interaction (BVI) Problem | |

| |

| |

| |

Convecting Vertical Gusts in Subsonic Flow | |

| |

| |

| |

Time-Varying Incident Mach Number | |

| |

| |

| |

Unsteady Aerodynamics of Flaps | |

| |

| |

| |

Incompressible Flow Theory | |

| |

| |

| |

Subsonic Flow Theory | |

| |

| |

| |

Comparison with Measurements | |

| |

| |

| |

Principles of Noise Produced by Unsteady Forces | |

| |

| |

| |

Retarded Time and Source Time | |

| |

| |

| |

Wave Tracing | |

| |

| |

| |

Compactness | |

| |

| |

| |

Trace or Phase Mach Number | |

| |

| |

| |

Ffowcs-Williams-Hawkins Equation | |

| |

| |

| |

BVI Acoustic Model Problem | |

| |

| |

| |

Comparison of Aeroacoustic Methods | |

| |

| |

| |

Methods of Rotor Noise Reduction | |

| |

| |

| |

Chapter Review | |

| |

| |

| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Dynamic Stall | |

| |

| |

| |

Introduction | |

| |

| |

| |

Flow Morphology of Dynamic Stall | |

| |

| |

| |

Dynamic Stall in the Rotor Environment | |

| |

| |

| |

Effects of Forcing Conditions on Dynamic Stall | |

| |

| |

| |

Modeling of Dynamic Stall | |

| |

| |

| |

Semi-Empirical Models of Dynamic Stall | |

| |

| |

| |

Capabilities of Dynamic Stall Modeling | |

| |

| |

| |

Future Modeling Goals with Semi-Empirical Models | |

| |

| |

| |

Torsional Damping | |

| |

| |

| |

Effects of Sweep Angle on Dynamic Stall | |

| |

| |

| |

Effect of Airfoil Shape on Dynamic Stall | |

| |

| |

| |

Three-Dimensional Effects on Dynamic Stall | |

| |

| |

| |

Time-Varying Velocity Effects on Dynamic Stall | |

| |

| |

| |

Prediction of In-Flight Airloads | |

| |

| |

| |

Stall Control | |

| |

| |

| |

Chapter Review | |

| |

| |

| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Rotor Wakes and Blade Tip Vortices | |

| |

| |

| |

Introduction | |

| |

| |

| |

Flow Visualization Techniques | |

| |

| |

| |

Natural Condensation Effects | |

| |

| |

| |

Smoke Flow Visualization | |

| |

| |

| |

Density Gradient Methods | |

| |

| |

| |

Characteristics of the Rotor Wake in Hover | |

| |

| |

| |

General Features | |

| |

| |

| |

Wake Geometry in Hover | |

| |

| |

| |

Characteristics of the Rotor Wake in Forward Flight | |

| |

| |

| |

Wake Boundaries | |

| |

| |

| |

Blade-Vortex Interactions (BVIs) | |

| |

| |

| |

Other Characteristics of Rotor Wakes | |

| |

| |

| |

Periodicity versus Aperiodicity | |

| |

| |

| |

Vortex Perturbations and Instabilities | |

| |

| |

| |

Detailed Structure of the Tip Vortices | |

| |

| |

| |

Velocity Field | |

| |

| |

| |

Models for the Tip Vortex | |

| |

| |

| |

Vorticity Diffusion Effects and Vortex Core Growth | |

| |

| |

| |

Correlation of Rotor Tip Vortex Data | |

| |

| |

| |

Flow Rotation Effects on Turbulence Inside Vortices | |

| |

| |

| |

Vortex Models of the Rotor Wake | |

| |

| |

| |

Biot-Savart Law | |

| |

| |

| |

Vortex Segmentation | |

| |

| |

| |

Governing Equations for the Convecting Vortex Wake | |

| |

| |

| |

Prescribed Wake Models for Hovering Flight | |

| |

| |

| |

Prescribed Vortex Wake Models for Forward Flight | |

| |

| |

| |

Free-Vortex Wake Analyses | |

| |

| |

| |

Aperiodic Wake Developments | |

| |

| |

| |

Wake Stability Analysis | |

| |

| |

| |

Flow Visualization of Transient Wake Problems | |

| |

| |

| |

Dynamic Inflow | |

| |

| |

| |

Time-Marching Free-Vortex Wakes | |

| |

| |

| |

Simulation of Carpenter & Friedovich Problem | |

| |

| |

| |

General Dynamic Inflow Models | |

| |

| |

| |

Descending Flight and the Vortex Ring State | |

| |

| |

| |

Wake Developments in Maneuvering Flight | |

| |

| |

| |

Chapter Review | |

| |

| |

| |

Questions | |

| |

| |

Bibliography | |

| |

| |

| |

Rotor-Airframe Interactional Aerodynamics | |

| |

| |

| |

Introduction | |

| |

| |

| |

Rotor-Fuselage Interactions | |

| |

| |

| |

Effects of the Fuselage on Rotor Performance | |

| |

| |

| |

Time-Averaged Effects on the Airframe | |

| |

| |

| |

Unsteady Rotor-Fuselage Interactions | |

| |

| |

| |

Fuselage Side-Forces | |

| |

| |

| |

Modeling of Rotor-Fuselage Interactions | |

| |

| |

| |

Rotor-Empennage Interactions | |

| |

| |

| |

Airloads on the Horizontal Tail | |

| |

| |

| |

Modeling of Rotor-Empennage Interactions | |

| |

| |

| |

Rotor-Tail Rotor Interactions | |

| |

| |

| |

Chapter Review | |

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Questions | |

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Bibliography | |

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Autogiros and Gyroplanes | |

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Introduction | |

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The Curious Phenomenon of Autorotation | |

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Review of Autorotational Physics | |

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Rolling Rotors: The Dilemma of Asymmetric Lift | |

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Innovation of the Flapping and Lagging Hinges | |

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Prerotating the Rotor | |

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Autogiro Theory Meets Practice | |

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Vertical Flight Performance of the Autogiro | |

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Forward Flight Performance of the Autogiro | |

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Comparison of Autogiro Performance with the Helicopter | |

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Airfoils for Autogiros | |

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NACA Research on Autogiros | |

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Giving Better Control: Orientable Rotors | |

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Improving Performance: Jump and Towering Takeoffs | |

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Ground and Air Resonance | |

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Helicopters Eclipse Autogiros | |

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Renaissance of the Autogiro? | |

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Chapter Review | |

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Questions | |

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Bibliography | |

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Aerodynamics of Wind Turbines | |

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Introduction | |

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History of Wind Turbine Development | |

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Power in the Wind | |

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Momentum Theory Analysis for a Wind Turbine | |

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Power and Thrust Coefficients for a Wind Turbine | |

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Theoretical Maximum Efficiency | |

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Representative Power Curve for a Wind Turbine | |

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Elementary Wind Models | |

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Blade Element Model for the Wind Turbine | |

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Blade Element Momentum Theory for a Wind Turbine | |

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Effect of Number of Blades | |

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Effect of Viscous Drag | |

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Tip-Loss Effects | |

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Tip Losses and Other Viscous Losses | |

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Effects of Stall | |

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Airfoils for Wind Turbines | |

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Yawed Flow Operation | |

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Vortex Wake Considerations | |

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Unsteady Aerodynamic Effects on Wind Turbines | |

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Tower Shadow | |

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Dynamic Stall and Stall Delay | |

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Advanced Aerodynamic Modeling Requirements | |

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Chapter Review | |

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Questions | |

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Bibliography | |

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Computational Methods for Helicopter Aerodynamics | |

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Introduction | |

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Fundamental Governing Equations of Aerodynamics | |

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Navier-Stokes Equations | |

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Euler Equations | |

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Vorticity Transport Equations | |

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Vortex Methods | |

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Boundary Layer Equations | |

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Potential Equations | |

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Surface Singularity Methods | |

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Thin Airfoil Theory | |

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Lifting-Line Blade Model | |

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Applications of Advanced Computational Methods | |

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Unsteady Airfoil Performance | |

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Tip Vortex Formation | |

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CFD Modeling of the Rotor Wake | |

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Airframe Flows | |

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Vibrations and Acoustics | |

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Ground Effect | |

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Vortex Ring State | |

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Comprehensive Rotor Analyses | |

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Chapter Review | |

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Questions | |

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Bibliography | |

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Appendix | |

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Index | |