This document provides an introduction to helicopter flight dynamics, including: - Definitions of helicopter flight dynamics, characteristics of helicopter flight, and scopes and methodologies used. - Coordinate systems used including gravity, body, wind, and hub axes. - Transformations between different coordinate systems. - Angles used to describe helicopter orientation and motion, including Euler angles. - Prerequisites, syllabus, and references for further study are also included.

1. Helicopter Flight Dynamics Chapter 1: Introduction

11. Definition of Helicopter Flight Dynamics The subject of studying external forces applied on helicopter as well as motions and controls External Forces: Only those changing flight path such as aerodynamic, inertial and gravity forces. Motions: Accelerations(angular acceleration), velocities and position Controls: Pilot controls from cockpit, augment stability and control Flight qualities: Specification and flight quality assessment

12. Characteristics of Helicopter Flight Example: from hover to forward flight Pilot Push forward Apply Long. cyclic pitch Rotor disc tilt forward Adjustment Apply Collective pitch control Paddle control Tail rotor Apply lateral Cyclic control Rotor disc tilt side

14. Scope of Helicopter Flight Dynamics Pilot Cockpit controls Aerodynamic surfaces (rotor, tail rotor) Change aerodynamic Forces and moments Gust disturbance External force disturbance SCAS Helicopter motions Flight quality specification Flight quality assessment

18. Teetering or See-Saw Rotor

19. Underslung Teetering Rotor

20. Articulated Rotor

21. Hingeless Rotor

27. Definition of Angles The Euler angles: The orientation of any axes relative to another can be given by three angles, which are the consecutive rotations about three axes in that order to carry one frame along with the other. This is a particular case of Euler angles . In helicopter flight dynamics, only one sets is commonly used, that for the body axes. 1. A rotation ψ about OY D , carrying the axes to OX 1 YZ 1 , is the azimuth angle. 2. A rotation υ about OZ 1 , carrying the axes to OXY 2 Z 1 , is the pitch angle. 3. A rotation γ about OX, carrying the axes to OXYZ, is the bank angle. Quatemions Z 1 X 1 Y 2

28. Definition of Angles The Aerodynamic angles : The linear motion V of the vehicle relative to the atmosphere can be given either by its three orthogonal components (v x ,v y ,v z ) in the body axes system, or alternatively by the magnitude V and two suitable angles. These angles, which are of fundamental importance in determining the aerodynamic forces that act on the vehicle, are defined as: Angle of attack : Sideslip angle : It will be observed that, in the sense of Euler angles, the aerodynamic angles related the bode axes and wind axes by the rotation sequence (  ,  ,0) which carrying the former into the latter X 1

29. Transformation from Gravity Axes to Body Axes A rotation of ψ: A rotation of : A rotation of γ: The complete coordinate transformation from gravity axes to body axes is: Z 1 X 1 Y 2

30. Transformation from Body Axes to Wind Axes A rotation of  : A rotation of  : The complete coordinate transformation from body axes to wind axes is: X 1

31. Transformation from Body Axes to Hub Axes In order to improve the flight performance and pilot Vision in cruse flight, the rotor shaft always tilts Forward as an angle  . Thus: In the sense of Euler angles, the rotor shaft tilt angle related the bode axes and hub axes by the rotation sequence (0,  ,0) which carrying the former into the latter

32. Comparison of Coordinate System in Different Country China and Russia West Country X Z O Y X Z O Y

33. Comparison of Definition of Parameters in Different Country O O

34. Comparison of Definition of Parameters in Different Country Meanings Hide force coeff. Side force coeff. Anti torque coeff. Lock Number China and Russia West country Thrust coeff.