Modelling the Flying Bird

C.J. Pennycuick

• Publisher: Academic Press
• Year: 2008
• eBook ISBN: 9780080557816
• Topic: Biological Sciences
• Subtopic: Ecology
• Index: Biological Sciences

This book outlines the principles of flight, of birds in particular. It describes a way of simplifying the mechanics of flight into a practical computer program, which will predict in some detail what any bird, real or hypothetical, can and cannot do. The Flight program, presented on the companion website, generates performance curves for flapping and gliding flight, and simulations of long-distance migration and accounts successfully for the consumption of muscles and other tissues during migratory flights. The program is effectively a working model of a flying bird (or bat or pterosaur) and is the skeleton around which the book is built. The book provides a wider background and then explains how Flight works and shows how to set up and test hypotheses generated by the program.The book and the program are based on adapting the conventional (and well-tested) thinking of aeronautical engineers to the biological problems of bird flight. Their primary aim is to convince biologists that this is the appropriate way to handle problems that involve flight, to make the engineering background accessible to biologists, and to provide a tool kit in the shape of the Flight program, which they can use to solve practical problems involving bird flight and migration. In addition, the book will be readily accessible to engineers who want to know how birds work, and should be of interest to the ever-growing community working on flapping "micro air vehicles" (MAVs). The program can be used to predict the flight performance and capabilities of reconstructed fossil birds and pterosaurs, flying in ancient atmospheres that differ from present conditions, and also, of course, to predict and account for the results of experiments and observations on living birds and bats.* An up to date work by the world's leading expert on bird flight* Examines the biology and biomechanics of bird flight with added reference to the flight of bats and pterosaurs.* Uses proven aeronautical principles to help solve biological issues in understanding and predicting the flight capabilities of birds and other vertebrates.* Provides insights into the evolution of flight and the likely capabilities of extinct birds and reptiles.* Gives a detailed explanation of the science behind, and use of, the author's predictive bird flight simulation program - Flight - which is available on a companion website.* Presents often difficult concepts in easily understood language.

Chapter 1 Background to the Model

C.J. Pennycuick

Abstract

The Flight computer model, which calculates the rate at which a flying animal requires energy for whatever it is doing, is based on classical aerodynamics. This is itself a branch of Newtonian mechanics, which is basically the same for aircraft and birds. Calculating the mechanical power requires information about wing measurements, which are defined in this chapter. The physiological requirements for fuel and oxygen are calculated as a second step, from the mechanical requirements. This approach requires care with the physical dimensions of variables, introduced in this chapter.

My objective in writing this book is to understand what a bird does when it flies, to explain in physical terms how it does it and to provide tools that can be used to predict quantitatively what any bird (not just those that have been studied) can and cannot do. The quest is ambitious but not new. Would‐be aeronauts have studied the wings of birds with great care down the centuries, hoping to understand them well enough to copy them, and fly themselves. With hindsight we can see now why Otto Lilienthal's meticulous studies and drawings of the wings of storks (Lilienthal, 1889) produced disappointingly little at the time, by way of insight into how wings work. His difficulty was that he had no theory in the 1880s with which to describe and explain what he saw. Now we have theory aplenty, thanks to the efforts of the world's aeronautical research institutions, and it is time for us birdwatchers to turn the process around, and look at birds through the new eyes that aeronautical engineers have given us.

The book is descriptive in parts, especially in the chapters that introduce the wings of flying vertebrates, but these descriptions will look strange to many biologists, because the conventions of morphology are hopelessly inadequate for describing how wings work. It is not possible to explain what wings do, without introducing concepts that are not a traditional part of a biologist's education. This chapter introduces the aeronautical conventions for describing and measuring wings, adapted for birds, and Chapter 2 is about the characteristics of the environment in which birds fly. Chapters 3 and 4, about the principles of flight, introduce a number of concepts that are familiar to engineers, but not to most biologists, and attempt to give the biological reader an intuitive feel for what these ideas mean. Chapters 5 and 6 describe the wings of birds, bats and pterosaurs, and Chapter 7 is on muscles seen as engines. After that the scope broadens to cover such topics as the simulation of long‐distance migration, gliding and soaring, the sensory requirements of flight, the use of wind tunnels and the design of experiments on flight. The evolution of flight comes last, because it is not possible to understand how it happened, without invoking the mechanical principles covered in earlier chapters.

1.1 The Flight Model

The skeleton of the book is the Flight computer model, a programme that incorporates the concepts introduced in the book, and allows the user to apply them to a chosen bird to answer questions about speed, distance, energy consumption and suchlike performance matters. Flight is not a model of a particular bird, nor is it based on regressions describing direct measurements of the quantities that it calculates. It is essentially a set of physical rules which are assumed to be general, in the sense that they can be applied to any bird, real or hypothetical, for which the user can provide the measurements required to define the bird and its environment. Flight accepts the user's input describing the bird, and provides a variety of options that determine the assumptions to be made in the calculation. Then it predicts how the bird's performance in flapping or gliding flight, or in long‐distance migration, would follow from that particular set of assumptions. It is designed in a way that makes it easy to vary the starting assumptions, which can be seen as hypotheses about how the bird works, and immediately observe the effect of a changed assumption on the predicted performance.

Flight is, in effect, a working model of a bird, according to the theory given in the book. It comes with its own online manual and databases of bird measurements, which can be loaded directly into the programme. The book contains many examples that have been calculated with Flight, showing how the output follows from the assumptions that underlie the programme, and how it can be used to test hypotheses about how the bird works. Flight is available as a free download from http://books.elsevier.com/companions/9780123742995, and also from http://www.bio.bristol.ac.uk/people/pennycuick.htm. These websites are updated from time to time with the latest version of the programme.

1.1.1 The Mathematical Idiom

It is easiest to explain what Flight does, and the concepts underlying it, in the idiom of aeronautical theory on which it is based, that is, in the language of applied mathematics, but this takes a little getting used to, and it is a known fact that many biologists are somewhat resistant to it. I have tried to make the book accessible to readers who are averse to equations, by structuring each chapter with an equation‐free main text that explains what the topic of the chapter is about, and isolating the more technical aspects in boxes. I hope that the main text will convey the gist of the argument to mathematical and non‐mathematical readers alike, while those who want to know what Flight actually does will find the equations in the boxes. Each box that presents a mathematical argument contains its own local variable list, which applies within that box, but not necessarily elsewhere in the book. The conventions for notation and so on are outlined in Box 1.1 in this chapter. Not all the boxes are mathematical. Some deal with the implications of a particular published experiment, an anatomical digression or some other limited topic.

Box 1.1 Mathematical conventions

Variable names in this book follow the usual conventions of physics, to the extent that a variable name is a single letter, with subscripts to distinguish between different variables of the same physical type. Variable names are italicised, but subscripts are not. For example, the letter P (for Power) is used to stand for a number of different variables that have the physical dimensions of work/time. Subscripts distinguish different kinds of power from each other. P_mech, the mechanical power produced by a bird's flight muscles, and P_chem, the rate at which the bird consumes chemical energy from fuel, are different variables with the same dimensions. Lower case p is used for “specific power”, a related group of variables with different dimensions, power/volume for volume‐specific power (p_v), and power/mass for mass‐specific power (p_m).

Acronyms are not used as variable names, because they look like several variables multiplied together. “BMR” is a familiar acronym that is mentioned in the text, but it is not used as a variable name, because it looks like “B times M times R”. Basal metabolic rate is a variable with the dimensions of power, and it is denoted by P_bmr. A notable exception to the one‐letter rule is that two‐letter variable names are traditionally used in engineering for dimensionless numbers named after famous scientists, notably Re for Reynolds number. Like other variables, Re can be subscripted to distinguish Re_wing from Re_body.

Capital “B” for wing span

The use of particular symbols to represent particular variables is a tradition that builds up over time, but it is not a law. The law, which applies internally in boxes in this book, but not always globally throughout the book, is that the definition of every symbol must be stated in the local contex...

Table of contents

• Cover image
• Title page
• Table of Contents
• Preface
• Foreword
• Acknowledgements
• Chapter 1 Background to the Model
• Chapter 2 The Flight Environment
• Chapter 3 Mechanics of Level Flight
• Chapter 4 Vortices and Vortex Wakes
• Chapter 5 The Feathered Wings Of Birds
• Chapter 6 The Membrane Wings of Bats and Pterosaurs
• Chapter 7 Muscles as Engines
• Chapter 8 Simulating Long‐Distance Migration
• Chapter 9 Accelerated Flight and Manoeuvring
• Chapter 10 Gliding Flight and Soaring
• Information Systems for Flying Animals
• Chapter 12 Water Birds
• Chapter 13 Allometry
• Chapter 14 Wind Tunnel Experiments With Birds And Bats
• Chapter 15 Theory as the Basis For Observation
• Chapter 16 Evolution of Flight
• References
• Index