The Engineering Approach to Winter Sports (eBook)

Preface 6
Contents 8
1 Ice and Snow for Winter Sports 10
1.1 Structure and Friction Properties of Ice 11
1.1.1 Structure of Ice 11
1.1.2 Compressive Strength of Ice 13
1.1.3 Friction Coefficient of Ice 14
1.1.4 Friction Mechanisms of Ice 16
1.2 Structure and Friction Properties of Snow 18
1.2.1 Structure of Snow 18
1.2.2 Compressive Strength of Snow 20
1.2.3 Friction Coefficient of Snow 20
References 22
2 Friction Between Ski and Snow 25
2.1 Introduction 25
2.2 Theory of Snow Friction 26
2.2.1 Dry Friction 26
2.2.2 Wet Friction 27
2.2.3 Mixed Friction 27
2.2.4 Quasi-Liquid Layer 28
2.3 Heat Considerations 28
2.3.1 Basic Considerations 28
2.3.2 Modeling of Heat Flow Between Ski and Snow 30
2.4 Experiments 31
2.4.1 Field Tests 32
2.4.2 Laboratory Tests 34
2.4.3 Friction Measurements with the Linear Tribometer 35
2.4.3.1 Effect of Snow Temperature 37
2.4.3.2 Effect of Speed 38
2.4.3.3 Effect of Normal Load 38
References 39
3 Friction Between Runner and Ice 41
3.1 Measurement of Runner–Ice Interaction 42
3.2 Modeling of Runner–Ice Friction 51
References 58
4 Alpine Ski 60
4.1 Introduction 60
4.2 Equipment and Materials 62
4.2.1 Helmet 62
4.2.2 Ski Suit 63
4.2.3 Boots 65
4.2.4 Skies 67
4.3 Experimental Tests 68
4.3.1 Measurement Systems for Capturing 3D Kinetics and Kinematics of Alpine Skiers 70
4.3.1.1 Video-Based 3D Kinematics Systems 70
4.3.1.2 GPS/IMU-Based Systems 74
4.3.2 Measurement of Ground Forces 78
4.3.2.1 Force Transducers 80
4.3.2.2 Pressure Measurement Systems 80
4.3.2.3 3D Kinematics 81
4.3.2.4 Comparison of Ground Reaction Force Measuring Methods 81
4.3.3 Aerodynamic Forces 82
4.3.4 Evaluation and Analysis of Skiing Technique and Performance 85
4.3.4.1 Comparison of Traditional Parallel Skiing and Carving Techniques 85
4.3.4.2 Evaluation of Alpine Skiing Performance 86
4.4 Mathematical Models for Alpine Skiing 89
4.4.1 Aims of Models for Alpine Skiing 89
4.4.2 Ski Modelling 91
4.4.2.1 Prediction of the Effect of Bindings Position on Ski Turn 91
4.4.2.2 Prediction of Carved Turns Radius Through a Finite Element Model 94
4.4.3 Skier Modelling 97
4.4.3.1 Point Mass Model: Trajectory Optimization in Slalom 97
4.4.3.2 2D Multibody Model: Analysing Skier Motion Vertical Plane 100
4.4.3.3 3D Multi-Body Models 105
References 109
5 Cross-Country Ski 114
5.1 Cross-Country Skiing and Roller Skiing 114
5.1.1 Mechanical Experiments on Gliding Friction and Rolling Resistance 116
5.1.2 Physiological Effects of Different Rolling Resistance Coefficients 118
5.1.2.1 Summary 120
5.1.3 Classical Style Cross-Country Skis and Roller Skis 120
5.1.4 Mechanical Experiments on Static Friction Coefficients 121
5.1.5 Physiological Effects of Different Static Friction Coefficients 122
5.1.5.1 Summary 123
5.1.6 The Multifunctional Roller Ski 123
5.2 Describing the Locomotion of Cross-Country Skiing 124
5.2.1 Numerical Simulation and Optimization of the Pacing Strategy in Cross-Country Skiing 126
5.3 Optimization of an Early Skating Ski 128
5.3.1 Introduction 129
5.3.2 Problem Definition 130
5.3.2.1 Traditional Ski 130
5.3.2.2 The Early Skating Ski 130
5.3.2.3 The New Design of the Skating Ski 130
5.3.2.4 Material Configuration 131
5.3.2.5 Load Case 132
5.3.2.6 Optimization Problem, Objective Function, and Variables 133
5.3.2.7 Optimization 133
5.3.3 Results 134
5.3.3.1 Material Configuration I 134
5.3.3.2 Material Configuration II 134
5.3.3.3 Material Configuration III 135
5.3.4 Discussion 136
5.4 Ski and Snowboard Friction 136
5.4.1 Static and Dynamic Friction 137
5.4.2 Gliding Speed Effects 138
5.4.3 Friction Dependence on the Loading Pressure 143
5.4.4 Gliding, Friction and Vibration 145
5.4.5 Loading Pressure 150
References 154
6 Aerodynamics of Ski Jumping 159
6.1 Introduction 159
6.1.1 Historical Background 159
6.1.2 V-Style Replaced the Classic Flight Style 163
6.2 Aerodynamics in Different Phases of Ski Jumping Performance 165
6.2.1 Inrun 169
6.2.2 Take-Off Aerodynamics 171
6.2.3 Flight Phase 173
6.2.4 Landing 183
References 185
7 Bobsleigh and Skeleton 188
7.1 Introduction 188
7.2 Rules 190
7.2.1 Bobsleigh Weights (Rule 14.1.3.1) 191
7.2.2 Bobsleigh Functional Dimensions (Rule 14.1.3.2) 192
7.2.2.1 Gauge (Rule 14.1.3.2.1) 192
7.2.2.2 Axle Base (Rule 14.1.3.2.2) 193
7.2.3 Bobsleigh Construction and Functioning (Rule 14.2) 193
7.2.3.1 Articulation (Rule 14.2.2.1) 194
7.2.4 Frame and Running Gear (Rule 14.2.3) 194
7.2.4.1 Front Portion of the Frame (Rule 14.2.3.3) 195
7.2.4.2 Rear Portion of the Frame (Rule 14.2.3.4) 196
7.2.4.3 Front Runner Carriers (Rule 14.2.3.3.4) and Rear Runner Carriers (Rule 14.2.3.4.4) 196
7.2.5 Cowling (Rule 14.2.4) 197
7.2.5.1 General Cowling Stipulations (Rule 14.2.4.2) 197
7.2.5.2 Cowling Shapes (Rule 14.2.4.4) 198
7.2.6 Connection Between Frame and Cowling (Rule 14.2.5) 198
7.2.7 Bumpers (Rule 14.2.6) 199
7.2.8 Runners (Rule 14.2.7) 199
7.2.8.1 Reference Runner and Runners Temperature 200
7.2.9 Skeleton 201
7.2.10 Track 203
7.3 Experimental Tests 204
7.3.1 Statistical Analysis of Luge, Bobsleigh, and Skeleton Competitions 205
7.3.2 Performance Analysis 206
7.3.3 Full Scale Tests on Skeleton 210
7.3.3.1 Analysis of Skeleton Start Phase 210
7.3.3.2 Analysis of Skeleton Sled Dynamics and Deformation 213
7.3.4 Full Scale Tests on Bobsleigh 215
7.3.4.1 Full Scale Tests to Assess Ice-Runners Friction Coefficient 216
7.3.4.2 Full Scale Measurements with Instrumented Bobsled 219
7.3.5 Full Scale Tests on Luge 228
7.4 The Sled 230
7.4.1 Dynamic Modelling and Optimization 230
7.4.1.1 Single Degree of Freedom Particle Model 230
7.4.1.2 Two Degrees of Freedom Particle Model 235
7.4.1.3 Multi-Body Model 239
7.4.2 Bobsleigh Aerodynamics 245
7.4.3 Skeleton Aerodynamics 252
7.5 The Track 253
7.5.1 Design and Verification 254
7.5.2 Notes on Optimization and Safety 257
7.6 The Athletes 259
7.6.1 Optimum Steering Control Approach 259
7.6.2 Trajectory Planning and Steering Control Approach 263
7.6.2.1 Trajectory Planning 263
7.6.2.2 Controller Design 265
7.6.2.3 Results 268
7.7 Simulator 270
7.7.1 Introduction 270
7.7.2 Characteristics of a Bobsled Simulator 271
7.7.3 US Bobsled Team Simulator 273
7.7.4 Virtual Reality Simulator 275
7.7.5 Bobsled Start Simulator 277
References 279
8 Ice Skating 282
8.1 Introduction 282
8.1.1 Historical Notes 282
8.1.2 Rules 283
8.1.3 Track 285
8.2 Dynamic Model 285
8.2.1 Primary Observations 285
8.2.1.1 The Influence of Clap Skates 288
8.2.2 A Two Dimensional Model 289
8.2.3 Power Balance Model 292
8.3 Aerodynamics of an Ice Speed Skater 293
8.3.1 Wind Tunnel Tests 294
8.3.2 Suits and Fabrics 297
8.4 Sliding on Ice 299
8.4.1 Fundamental Aspects 299
8.4.2 Ice Friction 301
8.4.2.1 Dry Friction 302
8.4.2.2 Boundary Friction 303
8.4.2.3 Mixed Friction 303
8.4.2.4 Hydrodynamic Friction 303
8.4.3 Ice Friction for a Speed Skate Blade: FAST 2.0i Model 303
8.4.3.1 Contact Geometry 304
8.4.3.2 Normal Force 305
8.4.3.3 Ploughing Force 307
8.4.3.4 Shear Stress Force 307
8.4.3.5 Squeeze Flow 308
8.4.3.6 Heat Conduction and Frictional Melting 309
8.4.3.7 Frictional Melting 309
8.4.3.8 Total Equation of Lubrication 309
8.4.3.9 Results 310
8.4.3.10 Conclusions 311
References 312
9 Ice Hockey Skate, Stick Design and Performance Measures 316
9.1 Skate Design and Performance Measures 316
9.2 Stick Design and Performance Measures 324
9.3 Stick Skills 326
References 329
10 Curling 332
10.1 Origin and History of Curling 332
10.2 Ice Sheet 333
10.3 Stone and Broom 335
10.4 Dynamics of a Curling Stone 336
10.5 Curl Ratio 340
10.6 Sweeping 342
10.7 Pebble Density 343
10.8 Level of Ice Sheet 345
10.9 Mechanisms of Curl 346
10.10 Measurements of Curl Distance 349
References 351
11 Why Did We Lose? Towards an Integrated Approach to Winter Sports Science 353
11.1 Physics and Models 357
11.2 Environment and Variability 361
11.3 Biology 363
11.4 What Winter Sports Engineer Can Do? 368
11.5 Conclusions 371
References 374
Index 383