The Physics of Hockey ALAIN HACHE The Johns Hopkins University Press Baltimore and London © 2002 The Johns Hopkins University Press All rights reserved. Published 2002 Printed in the United States of America on acid-free paper 246897531 The Johns Hopkins University Press 2715 North Charles Street Baltimore, Maryland 21218-4363 www.press.jhu.edu Library of Congress Cataloging-in-Publication Data Hache, Alain, 1970- The physics of hockey / Alain Hache. p. cm. Includes bibliographical references and index. ISBN 0-8018-7071-2 1. Physics. 2. Hockey. 3. Force and energy. I. Title. QC28 .H23 2002 530-dc21 2001008643 A catalog record for this book is available from the British Library. To all my teammates through the years and to the championship J996-97 U of T Physics hockey team Contents Introduction IX Chapter 1 I ON ICE 1 Chapter 2 I SKATING 33 Chapter 3 I SHOOTING 64 Chapter 4 I COLLISIONS AND PROTECTIVE GEAR 101 Chapter 51 KEEPING THE NET 126 Chapter 6 I THE GAME 144 Appendixes: On Heating Ice, Winning Streaks, and Other Details 159 Glossary 173 Further Reading 177 Index 179 vii Introduction his book combines two very different elements-a science and a sport-each ofwhich has its own attraction. The beauty T of physics is its ability to reduce very complex phenomena to a few simple rules and equations. With these we can make predictions and understand how nature generally works, even though in reality there is great complexity. Because high school physics typically covers a small range of subjects, many people have a limited idea of what physics is used for. Some will tell you that physics is about finding out how long it takes for a falling stone to reach the ground or calculating the current through a light bulb. Although it can certainly be used to do that, physics is applicable to a much wider array of complex problems. To give an example, a team of scientists recently used physical models to predict the behavior of large crowds in a state of panic, like that which occurs when a fire breaks out in a building. 1 It is well known that the tremendous pressures caused by fans pushing against one another in an overcrowded stadium can have tragic results, such as in 1989 when 95 soccer fans were crushed in Hillsborough Stadium in Sheffield, England. Scientists made an important discovery with their physical model of crowd behavior: they found that strategically located columns near the exits could reduce the pressure and increase the flow of people through the doors. In other words, adding apparent obstructions could actually save lives. This counterintuitive finding was not derived from experience or trial and error (no one would dare set fires just to study crowd behavior), but rather it was the result of harmless simulations on a computer using models that obey simple physical laws. This is just 1. Popular Science, January 2001, p. 29. ix x Introduction one remarkable example of how physics is used to deal with seemingly unsolvable problems. After all, what is more complex and chaotic than a panic-stricken crowd? Likewise, much insight can be gained on the game of hockey using physical modeling. The beauty of hockey seems quite different from what physics offers. Using a few simple game rules, talented athletes can turn the sport of hockey into an awesome spectacle full of unpredictable twists and turns. It is this unpredictability that makes the game so much fun to watch. From that viewpoint, physics and hockey appear to be at opposite ends of the spectrum, but, put together, they render each other service. Exploring that relationship is the main objective of this book. Applying physics to hockey helps us understand how aspects of the sport work and lets us make use of that knowledge to improve our game. On the flip side, talking about hockey in a physics con­ text may promote interest in science for the public at large and, by the same token, help create a better scientific culture (which many will agree is somewhat lacking in our society). I know this from experience, as students in my freshman mechanics class usually be­ come interested when real-life examples are used, especially exam­ ples from hockey. Applications such as these make abstract theories come alive. Physics has a long history of being successfully applied to sports. Over the last 30 years there has been an explosion of research in biomechanics and related fields. The knowledge has served, among other things, to develop better designs for equipment and help reduce sports injuries. The science and medicine of sports is now a well­ established discipline with a strong academic presence in universities around the world. Already, physics books have been published on baseball, golf, skiing, running, sprinting, skating, and a whole slew of other activities. I hope that this book will help fill a void by discussing the physics of hockey. Hockey may be fun to watch and study, but it's even more fun to play. During my humble amateur career, I've had a chance to play in many places and enjoy the company of people from all walks of life. One great thing about the game is that it makes us leave our cozy homes in the middle of the winter to meet and play with other people. I must also say I've had a lot of fun writing this book. As Introduction xi a physicist and a hockey player, I sometimes can't help but think about the game in a scientific way. Fortunately, hockey involves many facets of physics, perhaps more than any other sport. Because it is played on ice, we need to take into account elements of thermo­ dynamics and molecular physics. Skating makes use of a great deal of mechanics, as does shooting. Puck trajectories are influenced by air drag and ice friction, which involve fluid dynamics. And because hockey is a contact sport, the physics of collisions is also part of the game. In a way, my position as a goalie has given me a privileged view of the game. Half the time, when the action is away from my zone, I have the leisure to observe the game up close. This book greatly benefited from countless hours of observation done over the years. But of course, you don't need to be a goaltender or a scientist to enjoy a good game of hockey! This book could easily have been turned into a boring scientific monograph. Instead, it is peppered with stories, real-life examples, and anecdotes, and should be accessible to a wide range of readers, including those with limited or no scientific background. I assumed the average reader would have nothing more than a bit of high school physics. However I did not want to leave out the scientifically inclined readers, so there is also enough mathematics to satisfy their appetite. Appendixes discuss the details of some important results covered in this book. To many people, including myself, equations sometimes can be a turnoff. Though they are not the central part of this book, they are included to help the reader apply the knowledge gleaned to other situations. For example, someone may want to use the equation de­ scribing puck motion to estimate how much it has slowed down by the time it reaches the net after being shot from the red line. The shape of the equation is often as instructive as the equation itself: it tells us what parameters are important. In most cases, however, a reader can skim the formulas and go through the discussion without missing the main point. An important point about physical units: because we are accus­ tomed to speaking in terms of feet, miles per hour, and pounds, I often use this language for discussions in the book. Unfortunately, these units can create confusion if used in physics. So, unless stated xii Introduction otherwise, standard physics units such as meters, kilograms, and sec­ onds are used in formulas. Refer to Appendix 1 for a conversion table of units. The reader should keep in mind the limitations intrinsic to all physical models. Models are meant to be accurate to a certain extent, but, because simplifications are made, no model can reproduce a real-world situation with complete accuracy. For example, when the force of impact between two colliding players is calculated, the result is only an approximation of what happens in reality. Because hockey players are complicated three-dimensional bodies, there are many parameters that influence their impact. Each collision is different, and some cause injuries while others don't. In principle, there is nothing preventing us from creating more detailed models, but in doing so we would risk falling into tedious and boring details, which, in the end, would not give us much more insight. We can instead appreciate the essence of what goes on with simpler models. The book is organized in a logical order of complexity. The physics of ice-the one main element of hockey-is the object of the first chapter. The unique combination of properties ice exhibits, especially its remarkable slipperiness, is an interesting topic in itself. Scientists have been mind-boggled by it for more than a century. In Chapter 2 we take a close look at the science of skating and the properties of the skate. There are different techniques commonly used by hockey players to move around on the ice. Also, the expenditure of energy needed to accelerate and to overcome air drag and ice friction is an important problem.