Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods

Many textbooks are unable to step outside the classroom and connect with industrial practice, and most describe difficult-to-rationalize ad hoc derivations of the modal parameters. In contrast, Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods uses an optimal mix of physical insight and mathematical presentation to lead students to the heart of professional aircraft flight dynamics in a pleasant and informative manner.

Presenting an updated version of the aerodynamic model with the corrected definition of the rate (dynamic) derivatives, the book is peppered with examples of real-life airplanes, real airplane data, and solved examples. It plunges directly into the core concepts of aircraft flight dynamics with minimal mathematical fuss. When the 6-degree-of-freedom equations are presented in the final chapter, the students are already familiar with most of the physical concepts and the math is easier to absorb.

Aimed at junior and senior undergraduate students, this book covers recent developments in airplane flight dynamics and introduces bifurcation and continuation methods as a tool for flight dynamic analysis. Designed to help students make the transition from classroom calculations to the real-world of computational flight dynamics, it offers a practical perspective, enhanced by the inclusion of an open source computational tool.

Introduction
What, Why and How?
Aircraft as a Rigid Body
Six Degrees of Freedom
Position, Velocity and Angles
Aircraft Motion in Wind
Longitudinal Flight Dynamics
Longitudinal Dynamics Equations
A Question of Timescales
Longitudinal Trim
Aerodynamic Coefficients CD, CL, Cm
Wing–Body Trim

Stability Concept
Linear First-Order System
Linear Second-Order System
Nonlinear Second-Order System
Pitch Dynamics about Level Flight Trim
Modelling Small-Perturbation Aerodynamics
Pitch Dynamics about Level Flight Trim (Contd.)
Short-Period Frequency and Damping
Forced Response
Response to Pitch Control

Longitudinal Trim and Stability
Wing–Body Trim and Stability
Wing–Body Plus Tail: Physical Arguments
Wing–Body Plus Tail: Math Model
Role of Downwash
Neutral Point
Replacing VH with VH /
Effect of CG Movement
Rear CG Limit due to Airplane Loading and Configuration at Take-Off
Cm, CL Curves—Non-Linearities

Longitudinal Control
All-Moving Tail
Elevator
Tail Lift with Elevator
Airplane Lift Coefficient with Elevator
Airplane Pitching Moment Coefficient with Elevator
Elevator Influence on Trim and Stability
Longitudinal Manoeuvres with the Elevator
Most Forward CG Limit
NP Determination from Flight Tests
Effect of NP Shift with Mach Number

Long-Period (Phugoid) Dynamics
Phugoid Mode Equations
Energy
Phugoid Mode Physics
Phugoid Small-Perturbation Equations
Aerodynamic Modelling with Mach Number
Phugoid Dynamics
Phugoid Mode Frequency and Damping
Accurate Short-Period and Phugoid Approximations
Derivative CmMa
Derivative Cmq1 in Pitching Motion
Derivative Cmq1 in Phugoid Motion
Flow Curvature Effects

Lateral-Directional Motion
Review
Directional Disturbance Angles
Directional versus Longitudinal Flight
Lateral Disturbance Angles
Lateral-Directional Rate Variables
Small-Perturbation Lateral-Directional Equations
Lateral-Directional Timescales
Lateral-Directional Aerodynamic Derivatives
Lateral-Directional Small-Perturbation Equations (Contd.)........ 202
Lateral-Directional Dynamics Modes

Lateral-Directional Dynamic Modes
Roll (Rate) Mode
Roll Damping Derivative Clp2
Roll Control
Aileron Control Derivative, Clδa
Yaw due to Roll Control
Aileron Input for a Bank Angle
Dutch Roll Mode
Directional Derivatives CYβ and Cnβ
Lateral Derivative: Clβ
Damping Derivatives: Cnr1 and Clr1
Rudder Control
Spiral Mode
Real-Life Airplane Data

Computational Flight Dynamics
Aircraft Equations of Motion
Derivation of Aircraft Equations of Motion
3–2–1 Rule
Derivation of Aircraft Equations of Motion (Contd.)
Numerical Analysis of Aircraft Motions
Standard Bifurcation Analysis
Extended Bifurcation Analysis