Theory of Lift

Introductory Computational Aerodynamics in MATLAB/Octave

G. D. McBain, Peter Belobaba, Jonathan Cooper, Roy Langton, Allan Seabridge, Peter Belobaba, Jonathan Cooper, Roy Langton, Allan Seabridge

• Publisher: Wiley
• Year: 2012
• Print ISBN: 9781119952282
• eBook ISBN: 9781118346280
• Edition: 1
• Topic: Tecnología e ingeniería
• Subtopic: Ingeniería aeronáutica y astronáutica

Starting from a basic knowledge of mathematics and mechanics gained in standard foundation classes, Theory of Lift: Introductory Computational Aerodynamics in MATLAB/Octave takes the reader conceptually through from the fundamental mechanics of lift  to the stage of actually being able to make practical calculations and predictions of the coefficient of lift for realistic wing profile and planform geometries.

The classical framework and methods of aerodynamics are covered in detail and the reader is shown how they may be used to develop simple yet powerful MATLAB or Octave programs that accurately predict and visualise the dynamics of real wing shapes, using lumped vortex, panel, and vortex lattice methods.

This book contains all the mathematical development and formulae required in standard incompressible aerodynamics as well as dozens of small but complete working programs which can be put to use immediately using either the popular MATLAB or free Octave computional modelling packages.

Key features:

• Synthesizes the classical foundations of aerodynamics with hands-on computation, emphasizing interactivity and visualization.
• Includes complete source code for all programs, all listings having been tested for compatibility with both MATLAB and Octave.
• Companion website (www.wiley.com/go/mcbain) hosting codes and solutions.

Theory of Lift: Introductory Computational Aerodynamics in MATLAB/Octave is an introductory text for graduate and senior undergraduate students on aeronautical and aerospace engineering courses and also forms a valuable reference for engineers and designers.

Part One

Plane Ideal Aerodynamics

Chapter 1

Preliminary Notions

1.1 Aerodynamic Force and Moment

An aircraft in flight is subject to several forces: gravity causes the weight force; the propulsion provides a thrust, and the air the aerodynamic force A.¹

The central problem of aerodynamics is the prediction of the aerodynamic force; as important is its line of action, or equivalently its moment.

The motion of the aircraft through the air forces the air to move, setting up aerodynamic stresses. In turn, by Newton's Third Law of Motion, the stress in the air is transmitted back across the surface of the aircraft. The stresses include pressure stresses and viscous stresses. The aggregates of the stresses on the surface are the aerodynamic force and moment.

1.1.1 Motion of the Frame of Reference

Newton's equations of motion are unchanged if the frame of reference is replaced with one moving at a constant relative velocity; that is, the aerodynamic force can be computed or measured equally well by an observer in the aircraft in steady flight as by an observer on the ground. In the aeroplane's frame of reference, it's stationary and the air moves at a velocity −V.

The equivalence is very useful in aerodynamics; e.g. instead of mounting models of wings on force-measuring apparatus atop an express train as John Stringfellow did in the first half of the nineteenth century, the aerodynamic force can be

• measured in a wind tunnel where a model of the aircraft is held fixed in an air-stream; or
• computed by a numerical solution of the governing equations on a grid fixed to the aircraft surface.

Of course, other factors are involved in the interpretation of wind tunnel data (e.g. the effect of the walls), or computational fluid dynamics (e.g. grid dependence).

1.1.2 Orientation of the System of Coordinates

Various choices of coordinate system in the frame of reference are possible; e.g.

• a geocentric system with coordinates latitude, longitude, and altitude;
• a Cartesian system defined by the instantaneous velocity, curvature, and torsion of the flight; or
• a Cartesian system fixed to the aircraft, moving and rotating with it.

Although all physical results obtained must be independent of the choice of orientation, in aerodynamics we almost always use the last of these, after carefully and explicitly defining it in each case.

Most aircraft have an approximate plane of symmetry naturally dividing the craft into left and right halves. (This symmetry is deliberately broken during independent deployment of the left and right control surfaces.) The reference line is always chosen within this plane, and generally approximately coincides with the long direction of the craft and the usual direction of travel.

Our system of coordinates then consists of:

• the air...

Table of contents

• Cover
• Series Page
• Title Page
• Copyright
• Dedication
• Preface
• Series Preface
• Part One: Plane Ideal Aerodynamics
• Part Two: Three-Dimensional Ideal Aerodynamics
• Part Three: Nonideal Flow in Aerodynamics
• Appendix A: Notes on Octave Programming
• Glossary
• Nomenclature
• Index