Of considerable interest to applied mathematicians as well as sporting enthusiasts is the mathematical theory underlying the many sporting activities documented here, ranging from the high jump to frisbees and soccer to table tennis.

How can we predict the trajectory of a baseball from bat to outfield? How do the dimples in a golf ball influence its flight from tee to pin? What forces determine the path of a soccer ball steered over a defensive wall by an elite player? An understanding of the physical processes involved in throwing, hitting, firing and releasing sporting projectiles is essential for a full understanding of the science that underpins sport. This is the first book to comprehensively examine those processes and to explain the factors governing the trajectories of sporting projectiles once they are set in motion. From a serve in tennis to the flight of a ’human projectile’ over a high jump bar, this book explains the universal physical and mathematical principles governing movement in sport, and then shows how those principles are applied in specific sporting contexts. Divided into two sections, addressing theory and application respectively, the book explores key concepts such as: friction, spin, drag, impact and bounce computer and mathematical modelling variable sensitivity the design of sports equipment materials science. Richly illustrated throughout, and containing a wealth of research data as well as worked equations and examples, this book is essential reading for all serious students of sports biomechanics, sports engineering, sports technology, sports equipment design and sports performance analysis.

This fascinating book explores the mathematics involved in all your favourite sports. The Hidden Mathematics of Sport takes a unique and fascinating look at sport by exploring the mathematics behind the action. You'll discover the best tactics for taking a penalty, the pros and cons of being a consistent golfer, the surprising connection between American football and cricket, the quirky history of league tables, the unusual location of England's earliest 'football' matches and how to avoid marathon tennis matches. Whatever your sporting interests, from boxing to figure skating, from rugby to horse racing, you will find plenty to absorb and amuse you in this insightful book. Word count: 35,000 words

Modern Exterior Ballistics is a comprehensive text covering the basic free flight dynamics of symmetric projectiles. The book provides a historical perspective of early developments in the 19th century, the technology leading to World War I and that through World War II into the modern post-war era. Historical topics include the first ballistic firing tables, early wind tunnel experiments, the development of free flight spark ranges and the first supercomputer, ENIAC, which was designed to compute artillery trajectories for the U.S. Army Ballistic Research Laboratory. The level of the text requires an undergraduate education in mathematics, physics, and mechanical or aerospace engineering. The basic principles of ballistic science are developed from a comprehensive definition of the aerodynamic forces that control the flight dynamics of symmetric projectiles. The author carefully starts with the basic vacuum point mass trajectory, adds the effects of drag, discusses the action of winds, simple flat fire approximations, Coriolis effects and concludes with the classic modified point mass trajectories. Included in the discussion are analytical methods, change of variables from time to distance, numerical solutions and a chapter on the Siacci Method. The Siacci Method provides a historical perspective for computing flat fire trajectories by simple quadrature and is used in the sporting arms industy. The final six chapters of the book present an extensive physical and mathematical analysis of the motion of symmetric projectiles. The linearized equations of angular and swerving motion are derived in detail. The effects of mass asymmetry, in-bore yaw, cross wind and launch in a slipstream are discussed. Special consideration is given to the derivation and explanation of aerodynamic jump. These subjects are then expanded to include a complete chapter on nonlinear aerodynamic forces and moments. The final chapter in the book presents an overview of experimental methods for measuring the flight dynamics of projectiles. The great forte of Modern Exterior Ballistics is the author's effort to provide many fine specific examples of projectile motion illustrating key flight behaviors. The extensive collection of data on projectiles from small arms to artillery used to substantiate calculations and examples is alone a valuable reference. The ultimate joy of the book is the incomparable comprehensive set of flow field shadow graphs illustrating the entire spectrum of projectile flight from subsonic, through transonic and supersonic. The volume is a necessary addition to any undergraduate or graduate course in flight dynamics.

How can we predict the trajectory of a baseball from bat to outfield? How do the dimples in a golf ball influence its flight from tee to pin? What forces determine the path of a soccer ball steered over a defensive wall by an elite player? An understanding of the physical processes involved in throwing, hitting, firing and releasing sporting projectiles is essential for a full understanding of the science that underpins sport. This is the first book to comprehensively examine those processes and to explain the factors governing the trajectories of sporting projectiles once they are set in motion. From a serve in tennis to the flight of a ’human projectile’ over a high jump bar, this book explains the universal physical and mathematical principles governing movement in sport, and then shows how those principles are applied in specific sporting contexts. Divided into two sections, addressing theory and application respectively, the book explores key concepts such as: friction, spin, drag, impact and bounce computer and mathematical modelling variable sensitivity the design of sports equipment materials science. Richly illustrated throughout, and containing a wealth of research data as well as worked equations and examples, this book is essential reading for all serious students of sports biomechanics, sports engineering, sports technology, sports equipment design and sports performance analysis.

Please note: This text was replaced with a fourth edition. This version is available only for courses using the third edition and will be discontinued at the end of the semester. Taking a unique approach to the presentation of mechanical concepts, Biomechanics of Sport and Exercise eBook, Third Edition With Web Resource, introduces exercise and sport biomechanics in simple terms. By providing mechanics before functional anatomy, the book helps students understand forces and their effects before studying how body structures deal with forces. Students will learn to appreciate the consequences of external forces, how the body generates internal forces to maintain position, and how forces create movement in physical activities. Rather than presenting the principles as isolated and abstract, the text enables students to discover the principles of biomechanics for themselves through observation. By examining ordinary activities firsthand, students will develop meaningful explanations resulting in a deeper understanding of the underlying mechanical concepts. This practical approach combines striking visual elements with clear and concise language to encourage active learning and improved comprehension. This updated edition maintains the organization and features that made previous editions user friendly, such as a quick reference guide of frequently used equations printed on the inside cover and review questions at the end of each chapter to test students’ understanding of important concepts. The third edition also incorporates new features to facilitate learning: • Two online resources incorporate sample problems and use of video to allow practical application of the material. • New art and diagrams enhance problem sets and help students visualize the mechanics of real-world scenarios. • Increased number of review questions (200) and problem sets (120) provide an opportunity for practical application of concepts. • Greater emphasis on the basics, including improved descriptions of conversions and an expanded explanation of the assumption of point mass when modeling objects, provides a stronger foundation for understanding. • New content on deriving kinematic data from video or film and the use of accelerometers in monitoring physical activity keeps students informed of technological advances in the field. Biomechanics of Sport and Exercise eBook, Third Edition With Web Resource, is supplemented with two companion resources that will help students better comprehend the material. Packaged with this e-book, the web resource includes all of the problems from the book, separated by chapter, plus 18 sample problems that guide students step by step through the process of solving. This e-book may also be enhanced with access to MaxTRAQ Educational 2D software for Windows. MaxTRAQ Educational 2D software enables students to analyze and quantify real-world sport movements in video clips and upload their own video content for analysis. The software supplements the final section of the text that bridges the concepts of internal and external forces with the application of biomechanics; it also provides an overview of the technology used in conducting quantitative biomechanical analyses. The MaxTRAQ Educational 2D software must be purchased separately to supplement this e-book at the MaxTRAQ website. Instructors will benefit from an updated ancillary package. An instructor guide outlines each chapter and offers step-by-step solutions to the quantitative problems presented, as well as sample lecture topics, student activities, and teaching tips. A test package makes it easy to prepare quizzes and tests, and an image bank contains most of the figures and tables from the text for use in developing course presentations. Biomechanics of Sport and Exercise, Third Edition, is ideal for those needing a deeper understanding of biomechanics from a qualitative perspective. Thoroughly updated and expanded, this text makes the biomechanics of physical activity easy to understand and apply.

First published in 1996. Routledge is an imprint of Taylor & Francis, an informa company.