Table Of ContentThe Physics of scuba Diving
THE PHYSICS OF SCUBA DIVING
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The Physics of scuba Diving
Nottingham University Press
Manor Farm, Main Street, Thrumpton
Nottingham, NG11 0AX, United Kingdom
www.nup.com
NOTTINGHAM
First published 2011
© Nottingham University Press
All rights reserved. No part of this publication
may be reproduced in any material form
(including photocopying or storing in any
medium by electronic means and whether or not
transiently or incidentally to some other use of
this publication) without the written permission
of the copyright holder except in accordance with
the provisions of the Copyright, Designs and
Patents Act 1988. Applications for the copyright
holder’s written permission to reproduce any part
of this publication should be addressed to the publishers.
British Library Cataloguing in Publication Data
The Physics of Scuba Diving
M Anderson
ISBN 978-1-907284-78-6
Cover photo adapted from www.morguefile.com
Typeset by Nottingham University Press, Nottingham
Printed and bound by Berforts Group, Hertfordshire, England
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The Physics of scuba Diving
The Physics of Scuba
Diving
Marlow Anderson
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The Physics of scuba Diving
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The Physics of scuba Diving
T C
able of onTenTs
Introduction vii
Chapter 1 Pressure 1
Air & Water Pressure 1
How is air pressure measured? 5
The Scuba Cylinder 6
Metric Units 7
Breathing underwater 9
Chapter 2 Buoyancy 17
Specific Gravity 17
Buoyancy of the human body 22
Chapter 3 Boyle’s Law 27
Gas in a rigid container 27
Gas in a flexible container and Boyle’s Law 29
Consequences of Boyle’s Law for divers 32
Chapter 4 Ideal Gas Laws 43
Temperature 43
The general gas law 45
Air 46
Oxygen toxicity 48
Carbon monoxide 49
Chapter 5 Water 55
Cold 55
The molecular structure of water 58
Surface waves 59
Sound 61
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The Physics of scuba Diving
Sight 63
The world ocean 67
Currents 67
Tides 69
Chapter 6 The Exponential Function 77
Exponential growth 77
Exponential decay 83
For the mathematically inclined only! 87
Newton’s law of cooling 88
Chapter 7 Modeling Nitrogen Absorption 97
The rate of on-gassing and off-gassing 98
Haldane’s model 99
The absorption of oxygen 101
Chapter 8 The Bends 109
What is decompression sickness? 109
Other barotraumas 111
Historical background 112
Haldane’s protocols 113
Chapter 9 The Navy Dive Tables 125
Historical background 125
Using the Navy Tables for a single dive 126
Using the Navy Dive Tables for repetitive dives 128
Special Cases 131
Chapter 10 The Mathematics of the Navy Tables 137
M-values and no-decompression limits 137
Repetitive dives 141
Chapter 11 Variations on Table Use 149
Fresh water 149
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The Physics of scuba Diving
Effects of altitude 150
A note about depth gauges 154
Nitrox 154
Nitrogen narcosis 156
Chapter 12 Recreational Diving 163
Problems with the Navy Tables 163
The development of the PADI Tables 164
Dive computers 167
Safety stops 169
Safe dive profiles 170
Appendix A Units of Measurement 175
Appendix B Specific Gravity 177
Appendix C Air 179
Appendix D Rules of Exponents 181
Appendix E The US Navy Dive Tables 185
Suggestions for Further Reading 191
Index 193
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The Physics of scuba Diving
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The Physics of scuba Diving
P
refaCe
When taking my Open Water training course in scuba diving,
I was immediately captivated by the columns and rows of
numbers that make up the dive tables we were learning how
to use. As a mathematician and educator, I naturally wondered: where
do these numbers come from? They were obviously based on physics and
mathematics somehow. My personal quest to understand those dive tables
has resulted in this book.
After training, my wife and I immediately became enthusiastic divers,
and now have 15 years of great scuba diving adventures to look back on.
Along the way, we continued our diving education, eventually becoming
PADI Assistant Instructors. Getting involved in diving education was
natural for me, since I love to share my passions with other people. In this
book I am able to share two passions at once: science and scuba diving! I have
had the great opportunity to teach this material a number times in a course
at The Colorado College, the liberal arts college where I am a mathematics
professor. The course I teach does not assume much mathematical or scientific
background, and is intended to entice students into appreciating the power
of scientific thinking in understanding the real world, in this particular case
the wonderful underwater world of scuba diving.
The students in my course, and the readers of this book, need only have
a willingness to represent physical phenomena by using equations, and to
manipulate these equations with a little algebra. With these tools, the reader
will be able to better appreciate the rules and protocols she might have
learned in her dive training. On the other hand, I have also had students
of science or mathematics who had no dive training, who have enjoyed
seeing how scientific thinking illuminates the practical endeavour of diving
underwater. I always arrange a chance for such students to try out scuba
diving in a swimming pool.
The fundamental science behind scuba diving encompasses a wide
range of topics from physics including: pressure, Boyle’s Law, buoyancy, the
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