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Rotorcraft Aeromechanics

Book Description

A rotorcraft is a class of aircraft that uses large-diameter rotating wings to accomplish efficient vertical take-off and landing. The class encompasses helicopters of numerous configurations (single main rotor and tail rotor, tandem rotors, coaxial rotors), tilting proprotor aircraft, compound helicopters, and many other innovative configuration concepts. Aeromechanics covers much of what the rotorcraft engineer needs: performance, loads, vibration, stability, flight dynamics, and noise. These topics include many of the key performance attributes and the often-encountered problems in rotorcraft designs. This comprehensive book presents, in depth, what engineers need to know about modelling rotorcraft aeromechanics. The focus is on analysis, and calculated results are presented to illustrate analysis characteristics and rotor behaviour. The first third of the book is an introduction to rotorcraft aerodynamics, blade motion, and performance. The remainder of the book covers advanced topics in rotary wing aerodynamics and dynamics.

Table of Contents

  1. Cover
  2. Half Title
  3. Series
  4. Title Page
  5. Copyright
  6. Table of Contents
  7. Preface
  8. 1 Introduction
    1. 1.1 The Helicopter
      1. 1.1.1 The Helicopter Rotor
      2. 1.1.2 Helicopter Configuration
      3. 1.1.3 Helicopter Operation
    2. 1.2 Design Trends
    3. 1.3 History
    4. 1.4 Books
  9. 2 Notation
    1. 2.1 Dimensions
    2. 2.2 Nomenclature
      1. 2.2.1 Physical Description of the Blade
      2. 2.2.2 Blade Aerodynamics
      3. 2.2.3 Blade Motion
      4. 2.2.4 Rotor Angle-of-Attack and Velocity
      5. 2.2.5 Rotor Forces and Power
      6. 2.2.6 Rotor Disk Planes
    3. 2.3 Other Notation Conventions
    4. 2.4 Geometry and Rotations
    5. 2.5 Symbols, Subscripts, and Superscripts
    6. 2.6 References
  10. 3 Hover
    1. 3.1 Momentum Theory
      1. 3.1.1 Actuator Disk
      2. 3.1.2 Momentum Theory in Hover
      3. 3.1.3 Momentum Theory in Climb
    2. 3.2 Hover Power
    3. 3.3 Figure of Merit
    4. 3.4 Extended Momentum Theory
      1. 3.4.1 Rotor in Hover or Climb
      2. 3.4.2 Swirl in the Wake
    5. 3.5 Blade Element Theory
      1. 3.5.1 History of Blade Element Theory
      2. 3.5.2 Blade Element Theory for Vertical Flight
      3. 3.5.3 Combined Blade Element and Momentum Theory
    6. 3.6 Hover Performance
      1. 3.6.1 Scaling with Solidity
      2. 3.6.2 Tip Losses
      3. 3.6.3 Induced Power due to Nonuniform Inflow
      4. 3.6.4 Root Cutout
      5. 3.6.5 Blade Mean Lift Coefficient
      6. 3.6.6 Equivalent Solidity
      7. 3.6.7 The Ideal Rotor
      8. 3.6.8 The Optimum Hovering Rotor
      9. 3.6.9 Elementary Hover Performance Results
    7. 3.7 Vortex Theory
      1. 3.7.1 Vortex Representation of the Rotor and Wake
      2. 3.7.2 Actuator Disk Vortex Theory
      3. 3.7.3 Finite Number of Blades
    8. 3.8 Nonuniform Inflow
      1. 3.8.1 Hover Wake Geometry
      2. 3.8.2 Hover Performance Results from Free Wake Analysis
    9. 3.9 Influence of Blade Geometry
      1. 3.9.1 Twist and Taper
      2. 3.9.2 Blade Tip Shape
    10. 3.10 References
  11. 4 Vertical Flight
    1. 4.1 Induced Power in Vertical Flight
      1. 4.1.1 Momentum Theory for Vertical Flight
      2. 4.1.2 Flow States of the Rotor in Axial Flight
      3. 4.1.3 Induced Velocity Curve
    2. 4.2 Vortex Ring State
    3. 4.3 Autorotation in Vertical Descent
    4. 4.4 Climb in Vertical Flight
    5. 4.5 Optimum Windmill
    6. 4.6 Twin Rotor Interference in Hover
      1. 4.6.1 Coaxial Rotors
      2. 4.6.2 Tandem Rotors
    7. 4.7 Vertical Drag and Download
    8. 4.8 Ground Effect
    9. 4.9 References
  12. 5 Forward Flight Wake
    1. 5.1 Momentum Theory in Forward Flight
      1. 5.1.1 Rotor Induced Power
      2. 5.1.2 Climb, Descent, and Autorotation in Forward Flight
      3. 5.1.3 Rotor Loading Distribution
    2. 5.2 Vortex Theory in Forward Flight
      1. 5.2.1 Actuator Disk Results
      2. 5.2.2 Induced Velocity Variation in Forward Flight
    3. 5.3 Twin Rotor Interference in Forward Flight
      1. 5.3.1 Tandem and Coaxial Configurations
      2. 5.3.2 Side-by-Side Configuration
    4. 5.4 Ducted Fan
    5. 5.5 Influence of Ground in Forward Flight
      1. 5.5.1 Ground Effect
      2. 5.5.2 Ground Vortex
    6. 5.6 Interference
      1. 5.6.1 Rotor-Airframe Interference
      2. 5.6.2 Tail Design
      3. 5.6.3 Rotor Interference on Horizontal Tail
      4. 5.6.4 Pylon and Hub Interference on Tail
      5. 5.6.5 Tail Rotor
    7. 5.7 References
  13. 6 Forward Flight
    1. 6.1 The Helicopter Rotor in Forward Flight
      1. 6.1.1 Velocity
      2. 6.1.2 Blade Motion
      3. 6.1.3 Reference Planes
    2. 6.2 Aerodynamics of Forward Flight
    3. 6.3 Rotor Aerodynamic Forces
    4. 6.4 Power in Forward Flight
    5. 6.5 Rotor Flapping Motion
    6. 6.6 Linear Inflow Variation
    7. 6.7 Higher Harmonic Flapping Motion
    8. 6.8 Reverse Flow
    9. 6.9 Blade Weight Moment
    10. 6.10 Compressibility
    11. 6.11 Reynolds Number
    12. 6.12 Tip Loss and Root Cutout
    13. 6.13 Assumptions and Examples
    14. 6.14 Flap Motion with a Hinge Spring
    15. 6.15 Flap-Hinge Offset
    16. 6.16 Hingeless Rotor
    17. 6.17 Gimballed or Teetering Rotor
    18. 6.18 Pitch-Flap Coupling
    19. 6.19 Tail Rotor
    20. 6.20 Lag Motion
    21. 6.21 Helicopter Force and Moment Equilibrium
    22. 6.22 Yawed Flow and Radial Drag
    23. 6.23 Profile Power
    24. 6.24 History
      1. 6.24.1 The Beginning of Aeromechanics
      2. 6.24.2 After Glauert
    25. 6.25 References
  14. 7 Performance
    1. 7.1 Rotor Performance Estimation
      1. 7.1.1 Hover and Vertical Flight Performance
      2. 7.1.2 Forward Flight Performance
      3. 7.1.3 D/L Formulation
      4. 7.1.4 Rotor Lift and Drag
      5. 7.1.5 P/T Formulation
      6. 7.1.6 Rotorcraft Performance
      7. 7.1.7 Performance Charts
    2. 7.2 Rotorcraft Performance Characteristics
      1. 7.2.1 Hover Performance
      2. 7.2.2 Power Required in Level Flight
      3. 7.2.3 Climb and Descent
      4. 7.2.4 Maximum Speed
      5. 7.2.5 Ceiling
      6. 7.2.6 Range and Endurance
      7. 7.2.7 Referred Performance
    3. 7.3 Performance Metrics
    4. 7.4 References
  15. 8 Design
    1. 8.1 Rotor Configuration
    2. 8.2 Rotorcraft Configuration
    3. 8.3 Anti-Torque and Tail Rotor
    4. 8.4 Helicopter Speed Limitations
    5. 8.5 Autorotation, Landing, and Takeoff
    6. 8.6 Helicopter Drag
    7. 8.7 Rotor Blade Airfoils
    8. 8.8 Rotor Blade Profile Drag
    9. 8.9 References
  16. 9 Wings and Wakes
    1. 9.1 Rotor Vortex Wake
    2. 9.2 Lifting-Line Theory
    3. 9.3 Perturbation Solution for Lifting-Line Theory
    4. 9.4 Nonuniform Inflow
    5. 9.5 Wake Geometry
    6. 9.6 Examples
    7. 9.7 Vortex Core
    8. 9.8 Blade-Vortex Interaction
    9. 9.9 Vortex Elements
      1. 9.9.1 Vortex Line Segment
      2. 9.9.2 Vortex Sheet Element
      3. 9.9.3 Circular-Arc Vortex Element
    10. 9.10 History
    11. 9.11 References
  17. 10 Unsteady Aerodynamics
    1. 10.1 Two-Dimensional Unsteady Airfoil Theory
    2. 10.2 Lifting-Line Theory and Near Shed Wake
    3. 10.3 Reverse Flow
    4. 10.4 Trailing-Edge Flap
    5. 10.5 Unsteady Airfoil Theory with a Time-Varying Free Stream
    6. 10.6 Unsteady Airfoil Theory for the Rotary Wing
    7. 10.7 Two-Dimensional Model for Hovering Rotor
    8. 10.8 Blade-Vortex Interaction
    9. 10.9 References
  18. 11 Actuator Disk
    1. 11.1 Vortex Theory
    2. 11.2 Potential Theory
    3. 11.3 Dynamic Inflow
    4. 11.4 History
    5. 11.5 References
  19. 12 Stall
    1. 12.1 Dynamic Stall
    2. 12.2 Rotary-Wing Stall Characteristics
    3. 12.3 Elementary Stall Criteria
    4. 12.4 Empirical Dynamic Stall Models
    5. 12.5 References
  20. 13 Computational Aerodynamics
    1. 13.1 Potential Theory
    2. 13.2 Rotating Coordinate System
    3. 13.3 Lifting-Surface Theory
      1. 13.3.1 Moving Singularity
      2. 13.3.2 Fixed Wing
      3. 13.3.3 Rotary Wing
    4. 13.4 Boundary Element Methods
      1. 13.4.1 Surface Singularity Representations
      2. 13.4.2 Integral Equation
      3. 13.4.3 Compressible Flow
    5. 13.5 Transonic Theory
      1. 13.5.1 Small-Disturbance Potential
      2. 13.5.2 History
    6. 13.6 Navier-Stokes Equations
      1. 13.6.1 Hover Boundary Conditions
      2. 13.6.2 CFD/CSD Coupling
    7. 13.7 Boundary Layer Equations
    8. 13.8 Static Stall Delay
    9. 13.9 References
  21. 14 Noise
    1. 14.1 Helicopter Rotor Noise
    2. 14.2 Rotor Sound Spectrum
    3. 14.3 Broadband Noise
    4. 14.4 Rotational Noise
      1. 14.4.1 Rotor Pressure Distribution
      2. 14.4.2 Hovering Rotor with Steady Loading
      3. 14.4.3 Vertical Flight and Steady Loading
      4. 14.4.4 Stationary Rotor with Unsteady Loading
      5. 14.4.5 Forward Flight and Steady Loading
      6. 14.4.6 Forward Flight and Unsteady Loading
      7. 14.4.7 Doppler Shift
      8. 14.4.8 Thickness Noise
    5. 14.5 Sound Generated Aerodynamically
      1. 14.5.1 Lighthill’s Acoustic Analogy
      2. 14.5.2 Ffowcs Williams-Hawkings Equation
      3. 14.5.3 Kirchhoff Equation
      4. 14.5.4 Integral Formulations
      5. 14.5.5 Far Field Thickness and Loading Noise
      6. 14.5.6 Broadband Noise
    6. 14.6 Impulsive Noise
    7. 14.7 Noise Certification
    8. 14.8 References
  22. 15 Mathematics of Rotating Systems
    1. 15.1 Fourier Series
    2. 15.2 Sum of Harmonics
    3. 15.3 Harmonic Analysis
    4. 15.4 Multiblade Coordinates
      1. 15.4.1 Transformation of the Degrees of Freedom
      2. 15.4.2 Matrix Form
      3. 15.4.3 Conversion of the Equations of Motion
      4. 15.4.4 Reactionless Mode and Two-Bladed Rotors
      5. 15.4.5 History
    5. 15.5 Eigenvalues and Eigenvectors of the Rotor Motion
    6. 15.6 Analysis of Linear, Periodic Systems
      1. 15.6.1 Linear, Constant Coefficient Equations
      2. 15.6.2 Linear, Periodic Coefficient Equations
    7. 15.7 Solution of the Equations of Motion
      1. 15.7.1 Early Methods
      2. 15.7.2 Harmonic Analysis
      3. 15.7.3 Time Finite Element
      4. 15.7.4 Periodic Shooting
      5. 15.7.5 Algebraic Equations
      6. 15.7.6 Successive Substitution
      7. 15.7.7 Newton-Raphson
    8. 15.8 References
  23. 16 Blade Motion
    1. 16.1 Sturm-Liouville Theory
    2. 16.2 Derivation of Equations of Motion
      1. 16.2.1 Integral Newtonian Method
      2. 16.2.2 Differential Newtonian Method
      3. 16.2.3 Lagrangian Method
      4. 16.2.4 Normal Mode Method
      5. 16.2.5 Galerkin Method
      6. 16.2.6 Rayleigh-Ritz Method
      7. 16.2.7 Lumped Parameter and Finite Element Methods
    3. 16.3 Out-of-Plane Motion
      1. 16.3.1 Rigid Flapping
      2. 16.3.2 Out-of-Plane Bending
      3. 16.3.3 Non-Rotating Frame
      4. 16.3.4 Bending Moments
    4. 16.4 In-Plane Motion
      1. 16.4.1 Rigid Flap and Lag
      2. 16.4.2 Structural Coupling
      3. 16.4.3 In-Plane Bending
      4. 16.4.4 In-Plane and Out-of-Plane Bending
    5. 16.5 Torsional Motion
      1. 16.5.1 Rigid Pitch and Flap
      2. 16.5.2 Structural Pitch-Flap and Pitch-Lag Coupling
      3. 16.5.3 Torsion and Out-of-Plane Bending
      4. 16.5.4 Non-Rotating Frame
    6. 16.6 Hub Reactions
      1. 16.6.1 Rotating Loads
      2. 16.6.2 Non-Rotating Loads
    7. 16.7 Shaft Motion
    8. 16.8 Aerodynamic Loads
      1. 16.8.1 Section Aerodynamics
      2. 16.8.2 Flap Motion
      3. 16.8.3 Flap and Lag Motion
      4. 16.8.4 Non-Rotating Frame
      5. 16.8.5 Hub Reactions in Rotating Frame
      6. 16.8.6 Hub Reactions in Non-Rotating Frame
      7. 16.8.7 Shaft Motion
      8. 16.8.8 Summary
      9. 16.8.9 Large Angles and High Inflow
      10. 16.8.10 Pitch and Flap Motion
    9. 16.9 References
  24. 17 Beam Theory
    1. 17.1 Beams and Rotor Blades
    2. 17.2 Engineering Beam Theory for a Twisted Rotor Blade
    3. 17.3 Nonlinear Beam Theory
      1. 17.3.1 Beam Cross-Section Motion
      2. 17.3.2 Extension and Torsion Produced by Bending
      3. 17.3.3 Elastic Variables and Shape Functions
      4. 17.3.4 Hamilton’s Principle
      5. 17.3.5 Strain Energy
      6. 17.3.6 Extension-Torsion Coupling
      7. 17.3.7 Kinetic Energy
      8. 17.3.8 Equations of Motion
      9. 17.3.9 Structural Loads
    4. 17.4 Equations of Motion for Elastic Rotor Blade
    5. 17.5 History
    6. 17.6 References
  25. 18 Dynamics
    1. 18.1 Blade Modal Frequencies
    2. 18.2 Rotor Structural Loads
    3. 18.3 Vibration
    4. 18.4 Vibration Requirements and Vibration Reduction
    5. 18.5 Higher Harmonic Control
      1. 18.5.1 Control Algorithm
      2. 18.5.2 Helicopter Model
      3. 18.5.3 Identification
      4. 18.5.4 Control
      5. 18.5.5 Time-Domain Controllers
      6. 18.5.6 Effectiveness of HHC and IBC
    6. 18.6 Lag Damper
    7. 18.7 References
  26. 19 Flap Motion
    1. 19.1 Rotating Frame
      1. 19.1.1 Hover Roots
      2. 19.1.2 Forward Flight Roots
      3. 19.1.3 Hover Transfer Function
    2. 19.2 Non-Rotating Frame
      1. 19.2.1 Hover Roots and Modes
      2. 19.2.2 Hover Transfer Functions
    3. 19.3 Low-Frequency Response
    4. 19.4 Hub Reactions
    5. 19.5 Wake Influence
    6. 19.6 Pitch-Flap Coupling and Feedback
    7. 19.7 Complex Variable Representation of Motion
    8. 19.8 Two-Bladed Rotor
    9. 19.9 References
  27. 20 Stability
    1. 20.1 Pitch-Flap Flutter
      1. 20.1.1 Pitch-Flap Equations
      2. 20.1.2 Divergence Instability
      3. 20.1.3 Flutter Instability
      4. 20.1.4 Shed Wake Influence
      5. 20.1.5 Forward Flight
      6. 20.1.6 Coupled Blades
    2. 20.2 Flap-Lag Dynamics
      1. 20.2.1 Flap-Lag Equations
      2. 20.2.2 Articulated Rotors
      3. 20.2.3 Stability Boundary
      4. 20.2.4 Hingeless Rotors
      5. 20.2.5 Pitch-Flap and Pitch-Lag Coupling
      6. 20.2.6 Blade Stall
      7. 20.2.7 Elastic Blade and Flap-Lag-Torsion Stability
    3. 20.3 Ground Resonance
      1. 20.3.1 Ground Resonance Equations
      2. 20.3.2 No-Damping Case
      3. 20.3.3 Damping Required for Ground Resonance Stability
      4. 20.3.4 Complex Variable Representation of Motion
      5. 20.3.5 Two-Bladed Rotor
      6. 20.3.6 Air Resonance
      7. 20.3.7 Dynamic Inflow
      8. 20.3.8 History
    4. 20.4 Whirl Flutter
      1. 20.4.1 Whirl Flutter Equations
      2. 20.4.2 Propeller Whirl Flutter
      3. 20.4.3 Tiltrotor Whirl Flutter
    5. 20.5 References
  28. 21 Flight Dynamics
    1. 21.1 Control
    2. 21.2 Aircraft Motion
    3. 21.3 Motion and Loads
    4. 21.4 Hover Flight Dynamics
      1. 21.4.1 Rotor Forces and Moments
      2. 21.4.2 Hover Stability Derivatives
      3. 21.4.3 Vertical Dynamics
      4. 21.4.4 Directional Dynamics
      5. 21.4.5 Longitudinal Dynamics
      6. 21.4.6 Response to Control and Loop Closures
      7. 21.4.7 Lateral Dynamics
      8. 21.4.8 Coupled Longitudinal and Lateral Dynamics
    5. 21.5 Forward Flight
      1. 21.5.1 Forward Flight Stability Derivatives
      2. 21.5.2 Longitudinal Dynamics
      3. 21.5.3 Short Period Approximation
      4. 21.5.4 Lateral-Directional Dynamics
    6. 21.6 Static Stability
    7. 21.7 Twin Main Rotor Configurations
      1. 21.7.1 Tandem Helicopter
      2. 21.7.2 Side-by-Side Helicopter or Tiltrotor
    8. 21.8 Hingeless Rotor Helicopters
    9. 21.9 Control Gyros and Stability Augmentation
    10. 21.10 Flying Qualities Specifications
      1. 21.10.1 MIL-H-8501A
      2. 21.10.2 Handling Qualities Rating
      3. 21.10.3 Bandwidth Requirements
      4. 21.10.4 ADS-33
    11. 21.11 References
  29. 22 Comprehensive Analysis
    1. 22.1 References
  30. Index