1st Edition

Mathematical Methods for Accident Reconstruction A Forensic Engineering Perspective

    322 Pages 125 B/W Illustrations
    by CRC Press

    Over the past 25 years, Harold and Darren Franck have investigated hundreds of accidents involving vehicles of almost every shape, size, and type imaginable. In Mathematical Methods for Accident Reconstruction: A Forensic Engineering Perspective, these seasoned experts demonstrate the application of mathematics to modeling accident reconstructions involving a range of moving vehicles, including automobiles, small and large trucks, bicycles, motorcycles, all-terrain vehicles, and construction equipment such as hoists and cranes.

    The book is anchored on basic principles of physics that may be applied to any of the above-named vehicles or equipment. Topics covered include the foundations of measurement, the various energy methods used in reconstruction, momentum methods, vehicle specifications, failure analysis, geometrical characteristics of highways, and softer scientific issues such as visibility, perception, and reaction.

    The authors examine the fundamental characteristics of different vehicles, discuss the retrieval of data from crash data recorders, and review low speed impacts with an analysis of staged collisions. Finally, the book details standards and protocols for accident reconstruction.

    Exploring a broad range of accident scenarios and also acknowledging the limits of applicability of the various physical methods employed, the breadth and depth of the book’s coverage makes it a critical reference for engineers and scientists who perform vehicular accident reconstructions.

    Introduction

    Basic Principles

    Introduction

    Coordinate Systems

    Basic Principles of Physics

    Uniformly Accelerated Linear Motion

    Motion in a Plane

    Projectile Motion

    Uniformly Accelerated Curvilinear Motion

    Relation Between Angular and Linear Velocity and Acceleration

    Newton’s First Law

    Newton’s Second Law

    Newton’s Third Law

    Center of Gravity or Mass

    Impulse and Momentum

    Conservation of Momentum

    Conservation of Energy and Work

    Kinetic Energy

    Potential Energy due to Gravity

    Elastic Potential Energy

    Dissipation and Conservation of Forces

    Internal Work, Energy, Power, and Velocity

    Change in Velocity

    Evidence Gathering

    Introduction

    Measurements

    Photography

    Computer Techniques

    Photogrammetry

    Energy Methods

    Introduction

    Friction

    Critical Speed - Straight Trajectory

    Stopping Distance

    Friction and the Speed of a Vehicle

    Critical Speed - Curved Trajectory

    Critical Speed - Curved Trajectory with Superelevation

    Conservation of Energy Analysis

    Generalized Critical Speed Analysis

    Critical Speed from Yaw and Rollover

    Extension on Minimum Speed Calculations When Radius Cannot be Determined Uniquely

    Crush Analysis

    Tree Impacts

    Momentum Methods

    Introduction

    Elastic and Inelastic Collisions

    Elastic Collisions

    Conservation of Linear Momentum

    Conservation of Linear Momentum with Restitution

    Conservation of Rotational Momentum

    Combined Linear and Rotational Momentum

    Rotational Momentum - Alternate Solution

    Parametric Analysis for Left-of-Center Collisions

    Plastic - Elastic Analysis

    Vehicle Specifications

    Introduction

    Calculation of Center of Mass Techniques

    Rollover/Tipover

    Gouge Spacing

    Vehicle Performance Characteristics

    Introduction

    Systems and Performance Characteristics

    Failure Analysis

    Testing of Components

    Bicycles, Motorcycles, and Pedestrians

    Introduction

    Vaulting of Pedestrians

    Gyroscopic Action in Two-Wheeled Vehicles

    Determination of Pedestrian Speed from Vehicle Damage

    Vehicular Collisions with Pedestrians or Bicyclists

    Geometrical Characteristics of Highways

    Introduction - Interstates, Limited Access Highways, and Rural Roads

    Classification and Design Speed

    Traffic Control Devices

    Site Distance

    Horizontal Curves

    Vertical Curves - Sag and Crest

    Conclusions

    Train Accidents

    Introduction

    Train Resistance and Effect of Curvature and Grade

    Computation of Train Speed

    Train Crossings

    Train Manifest and Recorders

    Site Distance Triangle

    Commercial and Off-Road Vehicles

    Introduction

    Federal Motor Vehicle Regulations - FMV 49

    Tractor-Trailers

    Off-Tracking for Coupled Vehicles

    Construction Equipment

    Visibility, Perception, and Reaction

    Introduction

    Limitations of Human Factors Analysis

    Design Standards

    Capability of Drivers

    Computer Methods

    Introduction

    Numerical Methods

    Commercially Available Programs

    Reconstruction Tools

    Low Speed Impacts and Injury

    Introduction

    Methods of Analysis

    Biomechanics of Injury

    Standards and Protocols

    Introduction

    Protocol for Inspections

    ASTM Standards

    FMV Requirements

    SAE Standards

    Sensitivity and Uncertainty

    Introduction

    Sensitivity and Uncertainty

    References

    Biography

    Harold Franck and Darren Franck are experts in accident reconstruction and have worked on hundreds of investigations.