1、Accident Analysis Reconstruction Methods Second Edition Raymond M. Brach and R. Matthew BrachERRATA Vehicle Accident Analysis and Reconstruction Methods, Second Edition (R-397) Corrections to equations: Chapter 3 () C y b h R (3.44) 1 1 1 1 22 1 2 3 4 ( ) 1 1 1 1 y c e c e c e c e (3.50) Chapter 4 (
2、 ) ( ) , , , x a y b R i i i 2 2 2 1 2 3(4.1) Chapter 9 2 1 2 3 4 5 6 2( ) /10 K L C C C C C C (9.4) 1 2 3 4 5 6 2 /10 avg C C C C C C C (9.15) Vehicle Accident Analysis and Reconstruction MethodsOther related resources from SAE International: Tire Forensic Investigation By Thomas Giapponi (Product
3、Code: R-387) Automotive Safety Handbook, Second Edition By Ulrich W . Seiffert and Lothar Wech (Product Code: R-377) An Engineer in the Courtroom By William J. Lux (Product Code: R-155) Crash Reconstruction Research Edited by Michael S. Varat (Product Code: PT-138) For more information or to order a
4、 book, contact SAE International at 400 Commonwealth Drive, Warrendale, PA 15096-0001 USA; phone 877-606-7323 (U.S. and Canada only) or 724-776-4970 (outside U.S. and Canada); fax (724) 776-0790; e-mail CustomerServicesae.org; website http:/books.sae.org.Vehicle Accident Analysis and Reconstruction
5、Methods Raymond M. Brach and R. Matthew Brach Warrendale, Pennsylvania, USA Copyright 2011 SAE International eISBN: 978-0-7680-5740-9400 Commonwealth Drive Warrendale, PA 15096-0001 USA E-mail: CustomerServicesae.org Phone: 877-606-7323 (inside USA and Canada) 724-776-4970 (outside USA) Fax: 724-776
6、-1615 Copyright 2011 SAE International. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, distributed, or transmitted, in any form or by any means without the prior written permission of SAE. For permission and licensing requests, contact SAE Permissio
7、ns, 400 Commonwealth Drive, Warrendale, PA 15096-0001 USA; e-mail: copyrightsae.org; phone: 724-772-4028; fax: 724-772-9765. ISBN 978-0-7680-3437-0 SAE Order No. R-397 DOI 10.4271/R-397 Library of Congress Cataloging-in-Publication Data Brach, Raymond M.Vehicle accident analysis and reconstruction m
8、ethods / Raymond M. Brach and R. Matthew Brach.p. cm.Includes bibliographical references and index.ISBN 978-0-7680-3437-01. Traffic accident investigation. 2. Traffic accidentsSimulation methods. 3. Traffic accidents Mathematical models. 4. AutomobilesDynamics. I. Brach, R. Matthew. II. Title. HV807
9、9.55.B723 2011363.12565-dc222010053248 Information contained in this work has been obtained by SAE International from sources believed to be reliable. However, neither SAE International nor its authors guarantee the accuracy or completeness of any information published herein and neither SAE Interna
10、tional nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that SAE International and its authors are supplying information, but are not attempting to render engineering or other professional
11、 services. If such services are required, the assistance of an appropriate professional should be sought. To purchase bulk quantities, please contact: SAE Customer Service E-mail: CustomerServicesae.org Phone: 877-606-7323 (inside USA and Canada) 724-776-4970 (outside USA) Fax: 724-776-1615 Visit th
12、e SAE Bookstore at http:/store.sae.orgv Dedication A great deal of support was provided by our families during the preparation of this work. Our wives, Carol Brach and Paula Brach, encouraged this endeavor and shared in the effort required to complete the task. Matts children, Elizabeth, Olivia, and
13、 Daniel, sacrificed family time to permit writing to be done. This book is dedicated to them.vii Foreword_ xv Preface to Second Edition_ xvii Preface to First Edition_ xix Acknowledgments_ xxiii Chapter 1 Uncertainty in Measurements and Calculations_ 11.1 Introduction 11.2 Upper and Lower Bounds 41.
14、3 Differential Variations 51.4 Statistics of Related Variables 81.4.1 Linear Functions 81.4.2 Arbitrary Functions (Approximate Method) 91.5 Application Issues 111.5.1 Other Methods of Evaluating Uncertainty 12 Chapter 2 Tire Forces_ 152.1 Introduction 152.2 Rolling Resistance 172.3 Slip, Longitudina
15、l Force, and Lateral Force 172.3.1 Longitudinal Slip 192.3.2 Comments, the Coefficient of Friction, and the Frictional Drag Coefficient 22 Contentsviii Contents2.3.3 Longitudinal Tire Force 232.3.4 Lateral Tire Force 252.4 Friction Circle and Friction Ellipse 272.4.1 Idealized Friction Circle and Id
16、ealized Friction Ellipse 282.4.2 Actual Friction Circle and Actual Friction Ellipse 302.5 Modeling Combined Steering and Braking Tire Forces 312.5.1 The Bakker-Nyborg-Pacejka Model for Lateral and Longitudinal Tire Forces 312.5.2 Modified Nicholas-Comstock Combined Tire Force Model 332.6 Application
17、 Issues 372.6.1 Antilock Braking Systems (ABS) 392.6.2 Light Vehicle Frictional Drag Coefficients 402.6.3 Frictional Drag Coefficients for Heavy Trucks 412.6.4 Hydroplaning 46 Chapter 3 Straight-Line Motion_ 513.1 Uniform Acceleration and Braking Motion 513.1.1 Equations of Constant Acceleration 513
18、.1.2 Grade and Equivalent Drag Coefficients 543.2 Vehicle Forward-Motion Performance Equations 543.3 Stopping Distance 593.3.1 Distance from Speed 603.3.2 Speed from Distance 603.4 Application Issues 623.4.1 Stopping Distance 623.4.2 Motion Around Curves 633.5 Vehicle Fall Equations 643.5.1 Equation
19、s of Motion of a Vehicle Leading to a Fall 64 Chapter 4 Critical Speed from Tire Y aw Marks_ 694.1 Estimation of Speed from Y aw Marks 694.2 Y aw Marks 714.2.1 Radius from Y aw Marks 734.3 Critical Speed 734.3.1 Critical Speed Formula 734.3.2 Roadway with Superelevation 74ix Contents4.4 Application
20、Issues 764.4.1 Tire Marks in Practice 764.4.2 Other Curved Tire Marks 764.4.3 Coefficient of Friction, f 764.4.4 Driver Control Modes 774.4.5 Tire Forces in a Severe Y aw 774.4.6 The Critical Speed Formula and Edge Drop Off (Road Edge Reentry) 794.5 Uncertainty of Critical Speed Calculations 794.5.1
21、 Estimation of Uncertainty by Differential Variations 794.5.2 Accuracy of the Critical Speed Method 804.5.3 Statistical Variations 81 Chapter 5 Reconstruction of Vehicular Rollover Accidents_ 855.1 Introduction 855.2 Rollover Test Methods 865.3 Documentation of the Accident Site 885.4 Pretrip Phase
22、895.5 Trip Phase 955.5.1 Analysis of Vehicle Trip 965.5.2 Complex Vehicle Trip Models 1015.5.3 Reconstruction of the Trip Phase 1025.5.4 Rim Contact 1055.6 Roll Phase 1065.6.1 Speed Analysis 1075.6.2 Analysis of the Rolling Vehicle 1095.6.3 Information about the Accident Scene and Site 1105.6.4 Info
23、rmation about the Accident Vehicle 1115.6.5 Rollover Reconstruction Tools 1155.7 Example Rollover Reconstruction 1175.7.1 Speed Analysis 1175.7.2 Detailed Roll Analysis 1205.8 Vehicle Roll Rate During Rollover 1265.9 Further Considerations 128 Chapter 6 Analysis of Collisions, Impulse-Momentum Theor
24、y_ 1296.1 Introduction 1296.2 Quantitative Concepts 1316.3 Point-Mass Impulse-Momentum Collision Theory 132x Contents6.3.1 Coefficient of Restitution, Frictionless Point-Mass Collisions 1366.3.2 Collisions Where Sliding Ends; the Critical Impulse Ratio, 01366.3.3 Sideswipe Collisions and Common-Velo
25、city Conditions 1376.4 Controlled Collisions 1396.4.1 Coefficients of Restitution 1416.4.1.1 Stiffness Equivalent Collision Coefficient of Restitution 1426.4.1.2 Mass Equivalent Collision Coefficient of Restitution 1436.5 Planar Impact Mechanics 1446.5.1 Overview of Planar Impact Mechanics Model 150
26、6.5.2 Application Issues: Coefficients, Dimensions, and Angles 1536.5.2.1 Coefficient of Restitution and Impulse Ratio 1536.5.2.2 Distances, Angles, and Point C 1556.5.3 Work of Impulses and Energy Loss (Crush Energy) 1556.6 RICSAC Collisions 158 Chapter 7 Reconstruction Applications, Impulse-Moment
27、um Theory_ 1637.1 Introduction 1637.2 Point-Mass Collision Applications 1647.3 Rigid Body, Planar Impact Mechanics Applications; Vehicle Collisions with Rotation 1687.4 Collision Reconstruction Using a Solution of the Planar Impact Equations 1717.5 Reconstructions Using a Spreadsheet Solution of the
28、 Planar Impact Equations 1727.6 Low-Speed In-Line (Central) Collisions 1867.7 Airbags, Event Data Recorders (EDR), and V 1897.7.1 Crash Data 1917.7.2 Precrash Data 192 Chapter 8 Collisions of Articulated Vehicles, Impulse-Momentum Theory_ 1938.1 Introduction 1938.2 Assumptions for Application of Pla
29、nar Impact Mechanics to Articulated Vehicles 195xi Contents8.3 Articulated Vehicle Impact Equations 1988.4 Validation of the Articulated Vehicle Impact Equations Using Experimental Data 2068.5 Appendix: Data Sheets for Example 8.4 222 Chapter 9 Crush Energy and V_ 2259.1 Introduction 2259.2 Crush St
30、iffness Coefficients Based on Average Crush from Rigid Barrier Tests 2369.3 Application Issues 2419.3.1 Crush Stiffness Coefficients from Vehicle-to-Vehicle Collisions 2419.3.2 Damage to One Vehicle Unknown 2439.3.3 Side Crush Stiffness Coefficients, Two-Vehicle, Front-to-Side Crash Tests 2439.3.4 N
31、onlinear Models of Crush 2439.3.5 Arbitrary Number of Crush Measurements 243 Chapter 10 Frontal Vehicle-Pedestrian Collisions_ 24510.1 Introduction 24510.2 General and Supplementary Information 24810.3 Hybrid Wrap Model 24810.4 Forward Projection Model 24810.5 Analysis Model 24910.5.1 Pedestrian Mot
32、ion 24910.5.2 Vehicle Motion 25210.6 Values of Physical Variables 25210.6.1 Pedestrian-Ground Drag Coefficient 25310.7 Reconstruction Model 254 Chapter 11 Photogrammetry for Accident Reconstruction_ 25911.1 Introduction 25911.2 Reverse Projection Photogrammetry 26011.2.1 Overview and Requirements of
33、 the Reverse Projection Process 26111.2.2 Reverse Projection Procedure 26311.2.3 Summary of the Main Steps in the Reverse Projection Photogrammetry Process 268xii Contents11.3 Planar Photogrammetry 27411.4 Three-Dimensional Photogrammetry 28111.4.1 The Fundamental Information Related to Three-Dimens
34、ional Photogrammetry 28311.4.2 Mathematical Basis of Three-Dimensional Photogrammetry 28411.4.3 Projection Equations 28511.4.4 Collinearity Equations 28711.4.5 Coplanarity Equations 28711.4.6 Multiple Image Considerations 28711.4.7 Considerations of the Use of Three-Dimensional Photogrammetry in Pra
35、ctice 28811.5 Appendix: Projective Relation for Planar Photogrammetry 297 Chapter 12 Railroad Grade Crossing and Road Intersection Conflicts_ 29912.1 Introduction 29912.2 Clearing a Crossing or Intersection Using a Sight Triangle 30012.3 Sight Distance for Stopping Before a Crossing or Intersection
36、30412.4 FHW A Grade Crossing Equations 30912.4.1 Stopping Distance 30912.4.2 Stopping Sight Distance 31112.4.3 Clearing Sight Distance 31112.5 Locomotive Horn Sound Levels at Railroad Grade Crossings 31312.5.1 Computation of Horn Sound Levels at a Distance from a Point Source 31312.5.2 Insertion Los
37、s of Light Vehicles 316 Chapter 13 Vehicle Dynamic Simulation_ 32113.1 Introduction 32113.2 Planar Vehicle Dynamics Simulation 32213.3 Tire Side-Force Stiffness Coefficients 32513.3.1 Light-Vehicle Side-Force Coefficients 32513.3.2 Heavy-Vehicle Side-Force Coefficients 32613.4 Examples 32613.5 Appen
38、dix: Differential Equations of Planar Vehicular Motion 338Variables 339Notation 339xiii Contents Appendix A Units and Numbers_ 341A.1 Use of SI (Metric Units of Measure in SAE Technical Papers) 341A.2 Numbers, Significant Figures, and Rounding 342A.2.1 Significant Figures 342A.2.2 Rounding of Number
39、s 343A.2.3 Consistency of Significant Figures When Adding and Subtracting 344A.2.4 Consistency of Significant Figures When Multiplying and Dividing 344A.2.5 Other Forms of Number Manipulation 345A.3 Unit Conversions for Common Units 346 Appendix B Glossary of Common Terms and Acronyms in Accident Re
40、construction_ 355 References_ 383 Bibliography of Vehicle Dynamics Books_ 407 Index_ 409 About the Authors_ 417xv Vehicle accident reconstruction is a discipline which has developed and grown enormously over the (nearly) forty years that it has been my good fortune to be involved in it. In the early
41、 1970s the methods were crude, being largely confined to simple calculations on skidding and stopping distances and on how far this vehicle or that person would move in a given time. It was as well that the calculations were simple, since slide rules were the only practicable portable calculator, an
42、d personal computers were an improbable dream. In those days the ordinary practitioner knew very little about such things as tire dynamics, road surface properties, vehicle crush behavior, or what happens when a pedestrian is hit by a car. But gradually accident reconstructionists picked up knowledg
43、e on these matters from various fields of learningvehicle and highway engineering, safety research, driver psychology, trauma medicineand at the same time the means of handling it, in the shape of calculators, computers, and eventually the internet came into being. A good example is the CRASH progra
44、m, developed for NHTSA as a road safety research tool. Although by around 1980 it was being recognised as something that reconstructionists could use, it required a mainframe computer, and even then there were no graphics, so the scope for misusing it was considerable. Yet by 1990 a number of versio
45、ns of it, complete with graphics and much greater flexibility than the original, were available for use in portable personal computers. But a problem throughout this period was how to get a deep but practical knowledge of what was an ever-widening field of study. The admirable manuals published by N
46、orthwestern University both then and now covered a great deal of the field at a practical but relatively shallow level, being primarily directed at police officers rather than engineers. Anyone wishing to delve deeper was confronted by daunting volumes on the rigorous analysis of tire and vehicle dy
47、namics, or the construction of highways, or Forewordxvi Foreword the medical details of occupant and pedestrian trauma. One response was the advent of accident reconstruction societies and conferences for the dissemination of information and pieces of research: as far as I can ascertain, the first society with a wide reach was IAARS, founded in 1980, while notable among conferences has been
