Modeling of Complex Systems

Application to Aeronautical Dynamics

Emanuel Grunn, Tuan Anh Pham

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781848214484
• eBook ISBN: 9781118579862
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Aeronautic & Astronautic Engineering
• Index: Technology & Engineering

In the field of aeronautical dynamics, this book offers readers a design tool which enables them to solve the different problems that can occur during the planning stage of a private project. The authors present a system for the modeling, design and calculation of the flying qualities of airplanes and drones, with a complete mathematical model by Matlab/Simulink. As such, this book may be useful for design engineers as well as for keen airplane amateurs.
The authors expound the various phases involved in the design process of an airplane, starting with the formulation of a design tool, under the form of a 0D mathematical model (dimensionless, time dependent), before moving on to explore the behavior of the airplane under certain circumstances and offering insights into the optimization of airplane flying qualities. As validation of this model, they present a numerical result, drawn from data collected on an existing plane – the Concorde.
The dimensional process is then explored and applied to a realistic drone project. Recommendations on the development of the principal characteristics of the plane (i.e. mass distribution, air load, wing span) are given.

Contents

1. 0D Analytical Modeling of theAirplane Motions.
2. Design and Optimizationof an Unmanned Aerial Vehicle (UAV).
3. Organization of the Auto-Pilot.

This book provides a description of the modeling, design, and calculation of the aeronautical qualities of airplanes and drones. Divided into several parts, this book first summarizes all the necessary theoretical developments about the equations of motions and trajectory calculations of the machine. It then goes on to describe practical building processes and considers piloting methods. The last part makes a comparison between theoretical calculations and measured recorded data of the real flying machine.
Accompanied by a complete mathematical model in MATLAB/SIMULINK

Chapter 1

0D Analytical Modeling of Airplane Motions

The 0D modeling process tries to obtain variations as functions of time for all parameters of the motions of the plane.

The plane is considered here as a solid body moving freely through open space and therefore includes six degrees of freedom (DOF):

– three translational motions by three rectangular directions;

– three rotational motions classically described by Euler angles.

The plane is also under the influence of three external force systems which are:

– aerodynamic forces;

– propulsion forces;

– gravitational forces.

1.1. References: axis systems on use

In order to define the spatial motion of the airplane, we make use of two geometrical references.

1.1.1. Galilean reference: R₀

This geometrical reference has its origin center matched with the center of mass G of the airplane. The three principal rectangular axes are:

– Gx₀: horizontal, generally oriented to the West;

– Gy₀: horizontal, oriented to the North;

– Gz₀: vertically downward.

Gx₀, Gy₀ and Gz₀ form a direct rectangular reference.

NOTE.– Gz₀ is directed downward, due to the natural tendency of the airplane to descend when left to the effects of gravity.

This Galilean reference is in accordance with Newton’s first principle which makes use of the absolute components of the accelerations to be equal to the components of external forces.

1.1.2. Airplane reference: R_B (body) also called “linked reference”

This geometrical reference also has its center matched with G, the center of mass of the plane, but is physically linked to the airframe. Its three principal axes are: GX, GY and GZ.

GX, GY, GZ are preferably the principal axes of inertia of the plane and (GXYZ) is direct.

GXZ is the plane of symmetry of the airplane, with the exception of a few particular airplanes with asymmetric engine setups (Blohm and Voss, for instance; see Figure 1.1).

Figure 1.1. Blohm and Voss BV 141

(GXYZ), also called R_B, is the preferred reference for use with torque equations due to the fact that the inertias remain constant.

We can move from the Galilean reference to the body reference by making three Eulerian rotations, which are:

– Ψ (Psi): Yaw angl...

Table of contents

• Cover
• Table of Contents
• Title page
• Copyright
• Introduction
• Chapter 1: 0D Analytical Modeling of the Airplane Motions
• Chapter 2: Design and Optimization of an Unmanned Aerial Vehicle (UAV)
• Chapter 3: Organization of the Auto-Pilot
• Bibliography
• Index