P H Y S I C S О F /SN N к&

S K I I N G A T T H E T R I P L E P O I N T

DAVID LIND Department of Physics University of Colorado

Boulder, Colorado

SCOTT P. SANDERS Department of English Language and Literature

University of New Mexico Albuquerque, New Mexico

AIP

American Institute of Physics Woodbury, New York

CONTENTS

Preface

Chapter 1

Introduction: At the Triple Point

Skiing Through the Ages, 2

Three Classes of Skiing, 4

Snow: The Playing Field, 6

Equipment, 6

Skiing Technique, 7

From Tracks to Treks, 7

Friction: Glide and Grab, 8

Epilogue: Physics, Skiing, and the Future, 9

Conclusion, 9

References, 9

Chapter 2

Snow: The Playing Field

The Formation of Snow in the Atmosphere, 13

Making Artificial Snow, 17

The Snow Cover on the Ground, 21

The Water Molecule, 30

References, 43

Chapter 3

Equipment: Properties and Performance Ski Geometry, 45

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Ski Materials and Construction, 48

Mechanical and Dynamical Properties, 52

The Load-Distribution Problem, 62

Bindings and Boots, 68

Snowboard Equipment, 71

Conclusion, 74

References, 75

Chapter 4

Alpine Skiing Techniques: Gliding, Wedging, and Carving . . . 76 Fundamentals of Newtonian Mechanics, 77

Dynamics of Straight Gliding, 85

Mechanics of the Traverse, 90

Edging and Angulation, 91

Mechanics of Wedging and the Wedge Turn, 94

Mechanics of the Carved Turn, 97

Snowboarding and the Carved Turn, 104

Free-Heel or Telemark Skiing, 106

Conclusion, 107

References, 108

Chapter 5

Interactive Dynamics of Alpine Maneuvers 109 Skiing Nonplanar Surfaces, 109

Rotation and Counterrotation, 113

Lateral Projection, 115

Leg Thrust, 116

Body Angulation, 120

Independent Leg Action, 122

Canting, 123

Fore and Aft Shuffle, 124

Arm and Pole Action, 125

References, 126

CONTENTS

Chapter 6

High-Performance Skiing

Aerodynamic Drag, 127

Quickest Descent Trajectories, 129

Turning with Maximum Speed, 130

Pumping to Increase Velocity, 133

Balancing and Edging on One Ski, 135

Edging, Skidding, and Carving, 137

Field Study of Carving Turns, 141

References, 145

Chapter 7

Nordic Track, Cross-Country, and Adventure Skiing

Track and Cross-Country Equipment, 146

Nordic Track Techniques, 149

Adventure Skiing in the Backcountry, 156

Equipment, 157

Snow Compaction, 158

Dynamics of Carved Turns in Soft Snow, 161

The Physics of Survival, 166

References, 168

Chapter 8

Friction: Glide and Grab

Snow Compaction and Plowing, 170

Dry Friction, 171

Meltwater Lubrication and Viscous Friction, 172

Capillary and Triboelectric Drag Effects, 174

Empirical Models of Ski Friction, 176

Waxing for Glide and Grab, 177

Friction as Art, 183

References, 184

Chapter 9

Epilogue: Physics, Skiing, and the Future References, 191

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Tech note 1

Thermodynamics of Phase Changes 192 Clausius-Clapeyron Relation for Curved Surfaces, 196

Reference, 198

Technote 2

Ski Loading and Flexure on a Groomed Snow Surface 199 Reference, 202

Technote 3

The Loads on a Running Ski 203

Technote 4

Geometry of the Edged and Flexed Ski 205

Technote 5

The Dynamics of Carving a Turn 208 Reference, 215

Technote 6

Up-and-Down Unweighting 216

Technote 7

Analysis of Prejumping 219

Technote 8

Aerodynamic Drag 222 References, 227

Technote 9

The Brachistocrone Problem: The Path of Quickest

Descent 229 References, 232

Technote 10

Pumping to Increase Velocity 233 Reference, 235

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Technote 1 1

The Skier as an Inverted Pendulum 236 Reference, 243

Technote 12

Ski Flexure in Uncompacted Snow 244

Reference, 248

Technote 13

Meltwater Lubrication 249 Reference, 252

Glossary of Commonly Used Notations and Symbols 253 Units and Conversions, 255

Bibliography 257

Physics, 257

Snow, 258

Ski Mechanics, 258

Friction and Waxing, 259

Backcountry Skiing, 259

Biomechanics and Mountain Medicine, 259

Handbooks, Guides, and Symposia, 260

Bibliography of Authored and Edited Sources, 261

Subject Index 265