Mathematical Methods for Accident Reconstruction: A Forensic Engineering Perspective

324 Pages·2009·5.72 MB·English

by  Harold Franck

MATHEMATICAL
METHODS FOR
ACCIDENT
RECONSTRUCTION
A FORENSIC ENGINEERING PERSPECTIVE
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MATHEMATICAL
METHODS FOR
ACCIDENT
RECONSTRUCTION
A FORENSIC ENGINEERING PERSPECTIVE
HAROLD FRANCK DARREN FRANCK
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
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Library of Congress Cataloging-in-Publication Data
Franck, Harold.
Mathematical methods for accident reconstruction : a forensic engineering
perspective / Harold Franck and Darren Franck.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-4200-8897-7 (alk. paper)
1. Forensic engineering--Mathematics. 2. Traffic accidents. I. Franck, Darren. II.
Title.
TA219.F73 2009
363.12’5650151--dc22 2009013022
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
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Acknowledgments
The authors wish to acknowledge the diligent conscientious efforts of Janice
Franck, their wife and mother, in the long process of the preparation of this
book. Her patience, insight, constructive criticism, and extensive computer
and grammatical skills proved invaluable. The authors also wish to acknowl-
edge the invaluable help from Taylor & Francis.
v
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Table of Contents
Symbols and Units xiii
Preface xv
1 Introduction 1
2 Basic Principles 7
2.1 Introduction 7
2.2 Coordinate Systems 7
2.3 Basic Principles of Physics 1 1
2.4 Uniformly Accelerated Linear Motion 1 2
2.5 Motion in a Plane 1 3
2.6 Projectile Motion 1 4
2.7 Uniformly Accelerated Curvilinear Motion 1 6
2.8 Relation between Angular and Linear Velocity and
Acceleration 1 8
2.9 Newton’s First Law 1 9
2.10 Newton’s Second Law 2 1
2.11 Newton’s Third Law 2 2
2.12 Center of Gravity or Mass 2 3
2.13 Impulse and Momentum 2 4
2.14 Conservation of Momentum 2 8
2.15 Conservation of Energy and Work 29
2.16 Kinetic Energy 32
2.17 Potential Energy due to Gravity 3 3
2.18 Elastic Potential Energy 34
2.19 Dissipation and Conservation of Forces 3 6
2.20 Internal Work, Energy, Power, and Velocity 3 7
2.21 Change in Velocity 39
3 Evidence Gathering 4 1
3.1 Introduction 4 1
3.2 Measurements 4 2
3.2.1 Site Inspection 4 3
vii
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viii Table of Contents
3.2.2 Vehicle Inspection 4 5
3.2.3 Component Inspection 4 8
3.3 Photography 5 1
3.4 Computer Techniques 5 2
3.5 Photogrammetry 52
4 Energy Methods 5 9
4.1 Introduction 59
4.2 Friction 6 1
4.3 Critical Speed—Straight Trajectory 63
4.4 Stopping Distances 67
4.5 Friction and the Speed of a Vehicle 6 8
4.6 Newton’s Second Law Argument 7 1
4.7 Work–Energy Argument 7 3
4.8 Critical Speed—Curved Trajectory 7 5
4.9 Critical Speed to Negotiate a Turn Including
Superelevation 8 0
4.10 Conservation of Energy Analysis 8 3
4.11 Generalized Critical Speed Analysis 8 7
4.12 Critical Speed from Yaw and Rollover 9 1
4.13 Extension on Minimum Speed Calculations when
Radius Cannot Be Determined Uniquely 9 4
4.14 Crush Analysis 9 7
4.15 Tree Impacts 100
5 Momentum Methods 103
5.1 Introduction 103
5.2 Elastic and Inelastic Collisions 103
5.3 Elastic Collisions 104
5.4 Conservation of Linear Momentum 106
5.5 Conservation of Linear Momentum with Restitution 108
5.6 Conservation of Rotational Momentum 111
5.7 Combined Linear and Rotational Momentum 114
5.8 Rotational Momentum—Alternate Solution 115
5.9 Parametric Analysis for Left of Center Collisions 118
5.10 Plastic–Elastic Analysis 120
6 Vehicle Specifications 125
6.1 Introduction 125
6.2 Calculation of Center of Mass Techniques 125
6.3 Rollover/Tipover 129
6.4 Gouge Spacing 131
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Table of Contents ix
7 Vehicle Performance Characteristics 135
7.1 Introduction 135
7.2 Systems and Performance Characteristics 135
7.2.1 Braking 135
7.2.1.1 Vacuum Assisted Brake Booster 136
7.2.1.2 Brake Line Pressure Control
Devices 137
7.2.1.3 Step Bore Master Cylinder 137
7.2.1.4 Brake Designs 138
7.2.1.5 Large Vehicles 139
7.2.2 Steering 139
7.2.3 Acceleration 144
7.2.4 Electrical Systems 146
7.3 Failure Analysis 147
7.3.1 Brake Performance Characteristics 147
7.3.2 Seat Failure 150
7.3.2.1 Analysis of the Circular
Cross-Section 153
7.3.2.2 Analysis of the Elliptical
Cross-Section 155
7.3.3 Seatbelts and Air Bags 159
7.3.4 Light Bulbs and Filaments 160
7.4 Testing of Components 162
8 Bicycles, Motorcycles, and Pedestrians 165
8.1 Introduction 165
8.2 Gyroscopic Action in Two-Wheeled Vehicles 167
8.3 Vaulting of Pedestrians 169
8.4 Determination of Pedestrian Speed from Vehicle
Damage 172
8.5 Vehicular Collisions with Pedestrians or Cyclists 173
9 Geometrical Characteristics of Highways 177
9.1 Introduction 177
9.2 Classification and Design Speed 178
9.3 Cross Sectional Elements 180
9.4 Traffic Control Devices (TCDs) 181
9.5 Sight Distance 182
9.6 Horizontal Curves 185
9.7 Vertical Curves—Sag and Crest 187
9.8 Conclusions 189
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