Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods: 1st Edition (Paperback) book cover

Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation Methods

1st Edition

By Nandan K. Sinha, N. Ananthkrishnan

CRC Press

372 pages | 185 B/W Illus.

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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.


"Flight dynamics is a topic that can cause difficulties to aerospace engineering students. This text leads the reader gently through the material with plenty of practical examples and student exercises. As such, it is easy to follow the material and to gradually develop a deep understanding of a demanding topic. The book is ideal for undergraduate students and is a good text for graduate students."

––James F Whidborne, Cranfield University, United Kingdom

"This textbook is written by two experienced university lecturers who, after ascertaining the views of their students on the most difficult aspects of this challenging subject, optimised the order in which these are taught and presented here. The book covers all the aspects of flight dynamics traditionally found in such texts interspersed with examples of the treatment of features of current air vehicles. … In my opinion, this book covers the subject comprehensively and is a desirable reference source for undergraduates and graduates alike."

––R. J. Poole, MRAeS, The Aeronautical Journal

"The authors … are well-known and respected professionals in teaching and research, especially in the areas of flight dynamics, stability and control, nonlinear dynamics and bifurcation methods. … The book design and the methodology of interpretation are directed to a wide range of target audience/population interested in studying the dynamics of flight. Bachelor students can use it as recommended reading. For master and doctoral students, it is not only basic study material for particular problems of flight dynamics, but it also gives an idea of current professional approaches and computational methods for analysing dynamic properties. Given the scale and organization of information, the book will also be a useful tool in the analysis of flight dynamics for professionals in this field. The book is sure to appeal to anyone interested in the dynamics of flight."

––Jaroslav Salga, Advances in Military Technology, Vol. 9, No. 1, June 2014

Table of Contents


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


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


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


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

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mechanics / General