Recreational Mechanics: A Source Book for Walkers and Track Coaches

By James Lockett

There are two great attractions in my life: running and the study of engineering mechanics. Interestingly, the latter relates to mental discipline and the former to physical discipline. The competitive-running part spanned the greater part of my youth as a member of high school, college, and university intramural, and ending with a service team (army). After completing this competitive phase, my interest centered on noncompetitive recreational running (as a concession to aging legs) and a regimen of fairly vigorous walking. Conversely, my attraction with topics of a mechanical nature grew with my increasing maturity. Consequently, this book is devoted to combining these dual fascinations into a book with a rational title of Recreational Mechanics.

• Language: English
• Publisher: Xlibris US
• Release date: Jun 12, 2018
• ISBN: 9781984532084

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Copyright © 2018 by James Lockett.

ISBN:                  Softcover                      978-1-9845-3209-1

                            eBook                           978-1-9845-3208-4

All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner.

Any people depicted in stock imagery provided by Getty Images are models, and such images are being used for illustrative purposes only.

Certain stock imagery © Getty Images.

Rev. date: 06/11/2018

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CONTENTS

Introduction

Part I

On the Track and in the Field

Chapter 1     Details of a Running Track Geometry

In which the author addresses the differences between the non-Olympic versus the Olympic track physical dimensions. An interesting comparison of the differences is tabulated.

Chapter 2     Distance, Rate and Time Aspects around a Constant Circuit

In which the author examines the physical elements and the effect that changes on these elements have on running this circuit.

Chapter 3     Competitive Fairness in Track Competition

In which the author analyzes whether or not the positioning of competitors in specific lanes of the track is a equitable deal.

Chapter 4     Finding an Invariant Property in the Track Geometry

In which the author posits that certain point(s) along a running track that may affect a runner’s performance during a competition.

Chapter 5     A Proposed Training Tool for Track Coaches

In which the author demonstrates a computer-tool for sprint runners that uses actual performance data to indicate where future improvements are possible.

Chapter 6     Field Events

In which the author uses trajectory analysis to demonstrate how all field events may be examined with two specific events (long jump and high jump) trajectories are calculated and plotted as examples.

Part II

On the Road

Chapter 7     Analysis of Forces/Energy Expenditures on Level/Elevated Surfaces

In which the author examines the various forces, road surface differences and energy expenditures which occur on both level and hilly planes.

Chapter 8     Energy and Power Requirements for Walking and Running

In which the author considers the conditions for individual expenditure of power/energy during the action of walking and running.

Chapter 9     Stride Analysis

In which the author addresses the particular variables associated with an human being’s stride length on a level and elevated surface. In particular, the effect on a person’s stability when going down hill will be examined in detail.

Chapter 10   A Look at Walking Up Steep Hills

In which the author seeks to find an optimum solution.

Chapter 11   A Strategy for Running Uphill

In which the author seeks to find an optimal solution for running up a given hill by controlling the stride length for the particular gradient.

Chapter 12   A Pedestrian Probability Problem

In which the author solves the probability whereby a walker or jogger exercising on a narrow road may be struck by the simultaneous passage of two opposing vehicles.

SUPPORTING

APPENDICES

Appendix A   Overview of the Basic Mathematics Used in Parts I and II

Appendix B   Overview of the Basic Physics Used in Sections I and II

Appendix C   Analysis for Finding an Invariant Property in the Track Geometry

Appendix D   A Proposed Training Tool for Track Coaches (the analysis)

Appendix E   Additional Notes for A Look at Walking Up Steep Hills [Chapter 10]

Appendix F   FORTRAN Source Programs used in Support of Sections I and II

Introduction

There are two great attractions in my life – running and the study of engineering mechanics. Interestingly, the later relates to a mental and the former to a physical discipline. The competitive running part spanned the greater part of my youth as a member of high school, college and university (intramural) and ending with a service team (Army). After completing this competitive phase, my interest centered on non-competitive recreational running (as a concession to aging legs) and a regimen of fairly vigorous walking. Conversely, my attraction with topics of a mechanical¹ nature grew with my increasing maturity. Consequently, this book is devoted to combining these dual fascinations into a book with a rational title of Recreational Mechanics.

The reader should be aware that this will not be the usual book on recreational activities (such as running or jogging). It contains no chapters with topics on the why, how or the zen about these activities. In retrospect, there are a number of sport-related books that do cover these topics in sufficient detail to satisfy even the most devoted recreational runners. In fact, my library contains several of these handbooks, including the best-seller at the time on the subject. The author of this volumn had established his reputation by positing that even if an individual had experienced a lifetime of bad physical habits (he had), one could reverse any negative consequences through therapeutic running (i.e., jogging). Evidently a bad premise, as I have his obituary pasted within my copy of his book. He apparently died of a heart attack attempting a routine early morning jog.

The motivation for writing this book was two-fold:

1) It has been my experience that competitive running needed more structured instruction instead of repetitive sprints and/or laps as training aids. There were few (if any) training tools available to novice track athletes.

2) After the competitive running phase, jogging and walking were primarily necessary for maintaining good health. Also a new physical element was introduced; namely, hills. The question now is it possible to examine the physics involved in these activities to lessen the attendant mental boredom and/or the physical discomforts of this activity?

Consequently, this book is divided into two parts: Part 1 deals with running activities within an environment that contains a level, structured path called a track which contains an inclosed area called a field. The track portion contains information concerning competitive running topics. It will also describe what the author has discovered to be an unknown invariant relationship present in the track structure as well as providing a training tool for specific running events. Finally, the field segment examines aspects of the non-running events.

Part 2 examines running and walking activities in an environment that may not be level and is decidedly unstructured. The later part of the book is heavily-energy related with one chapter devoted to a solution to a walker-vehicle probability problem and its attendant solution.

Since the whole book relies on basic engineering principles, the reader is urged to review appendix A and B. Regardless of your previous mathematical and/or physics background, a review of these two topics will assist you to better understand the scope and intent of this book. Also, you will gain much insight of the symbolic conventions used in the text and the structure sought by the author.

The mathematics embodied in Part 1 and 2 use basic algebraic and trigonometric operations. A few chapters depend on elemental calculus applications; primarily, simple calculus differentiation to determine the maximum value of a point on a line curve and the use of a integration technique to find the area under a particular curve line. The chapter employing the probability analysis is explained in some detail and is designed not to require any prior knowledge on the topic. In fact, all the analyzes of Part 1 and 2 are conducted in an easy step by step format within the particular chapter and any excluded operations are fully explained in an accompanying appendix. The final appendix will contain the source computer program which generated the data tables and the graphical results displayed in specific chapters.

CHAPTER ONE

Details of a Running Track Geometry

Track events are measured by time t while field events are measured by distance d using the relationship (where v is the velocity of the athlete) resulting in relationship:

d = vt

The principal variable in the above equation is the velocity the athlete is able to produce in the running event.

Within any stadium, track events are conducted on the inner and outer peripheries (lanes) which define the area within where the field events are conducted. This structure allows both types of events to be conducted simultaneously.

Track events are conducted in distances which measure from 100 to 10000 units in length with some adding obstruction (hurdles of different heights) for the runners to navigate.

Most individuals are familiar with the typical sport ‘track’ which typically belong to local public schools, junior colleges, colleges and universities which are primarily employed in spring-time sporting competition. These also provide excellent facilities for individuals to get back in shape during