Modelling the Flying Bird

C.J. Pennycuick Senior Research Fellow, University of Bristol

У " * 1 Я 1 1 AMSTERDAM • BOSTON • HEIDELBERG • LONDON # Ч&Ль». N E W Y O R K * OXFORD • PARIS • SAN DIEGO

ügSfläBHte S A N FRANCISCO • SINGAPORE • SYDNEY • TOKYO E L S E V I E R Academic Press is an imprint of Elsevier

CONTENTS

PREFACE ix FOREWORD xi ACKNOWLEDGEMENTS xiii

1 • BACKGROUND TO THE MODEL 1

1.1. The Flight Model 2 1.2. The Engineering Approach to Numbers 15 1.3. Dimensions and Units 18 1.4. Literature Citations 20

2-THE FLIGHT ENVIRONMENT 21

2.1. The Earth's Gravity Field 22 2.2. The Earth's Atmosphere 24 2.3. Air Density in Flight 31 2.4. Gravity and the Atmosphere in Former Times 32

3 • MECHANICS OF LEVEL FLIGHT 37

3.1. Power Required for Horizontal Flight 38 3.2. The Power Curve Calculation in Flight 46 3.3. Significance of the Characteristic Speeds 63 3.4. Effect of Air Density on Speed and Power 66 3.5. Adaptive Significance of Morphology 68 3.6. Two-Dimensional Aerofoil Properties 69 3.7. Scale and Reynolds Number 78

4 • VORTICES AND VORTEX WAKES 79

4.1. The Concept of the Line Vortex 80 4.2. Vortex Concepts Applied to Fixed Wings 81 4.3. Lifting-Line Theory Applied to Flapping Wings 91 4.4. Wind Tunnel Studies of Bird Wakes 93 4.5. Feathered Wings 102

5 • THE FEATHERED WINGS OF BIRDS 105

5.1. General Structural Requirements 106 5.2. Mechanics of the Bird Wing 119

v

Vi CONTENTS

5.3. Flapping the Wings 128 5.4. The Rest of the Skeleton 130 5.5. Adaptations for Gliding 133

6«THE MEMBRANE WINGS OF BATS AND PTEROSAURS 135

6.1. Bats 136 6.2. Pterosaurs 149

7«MUSCLES AS ENGINES 161

7.1. General Requirements 163 7.2. The Sliding Filament Engine 164 7.3. Muscle Performance in Locomotion 169 7.4. Adaptations for Aerobic Flight 194

8 • SIMULATING LONG-DISTANCE MIGRATION 209

8.1. Estimating Range 210 8.2. Ultra Long-Distance Migrants 213 8.3. The Concept of Energy Height 227 8.4. Effect of Flying Height on Range 239 8.5. Aerobic Capacity and Climb 240 8.6. Basal Metabolism 241 8.7. Water Economy 243 8.8. Sleep 244

9 - ACCELERATED FLIGHT AND MANOEUVRING 245

9.1. Intermittent Flight Styles in Flapping Flight 246 9.2. Manoeuvring Frame of Reference: Flight Controls 253 9.3. Transient Manoeuvres 268

10-GLIDING FLIGHT AND SOARING 271

10.1. Gliding Performance 272 10.2. Soaring 280

11 • INFORMATION SYSTEMS FOR FLYING ANIMALS 305

11.1. Senses 309 11.2. Orientation and Navigation 320

Contents vii

12-WATER BIRDS 333

12.1. Waterproofing and Thermal Insulation 334 12.2. Mechanics of Swimming 335 12.3. Morphological Trends in Waterbirds 343 12.4. Other Aquatic Adaptations 347

13-ALLOMETRY 351

13.1. Allometry of Morphological Variables 352 13.2. Allometry of Calculated Variables 364 13.3. Variations on Allometry 374

14-WIND TUNNEL EXPERIMENTS WITH BIRDS AND BATS 377

14.1. Wind Tunnel Basics 378 14.2. Wind Tunnel Layouts 379 14.3. Wind Tunnel Components and Their Functions 382 14.4. Birds in Wind Tunnels 394

15 - THEORY AS THE BASIS FOR OBSERVATION 409

15.1. Flight Speed Measurements 410 15.2. Wind Tunnel Results Related to Field Studies 428 15.3. Wingbeat Frequency 435 15.4. The Theoretical Backbone 439

16 • EVOLUTION OF FLIGHT 443

16.1. Evolution in Engineering and in Nature 444 16.2. Past the Squirrel Barrier 451 16.3. Evolution of the Bird Wing 454 16.4. Adding an Engine 459 16.5. Size Restrictions 460 16.6. Time Scale of Evolution 461

REFERENCES 463

INDEX 471