Mathematical Methods for Accident Reconstruction: A Forensic Engineering Perspective (Hardback) book cover

Mathematical Methods for Accident Reconstruction

A Forensic Engineering Perspective

By Harold Franck, Darren Franck

© 2009 – CRC Press

328 pages | 125 B/W Illus.

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Hardback: 9781420088977
pub: 2009-09-15
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pub: 2009-09-15
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About the Book

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.

Table of Contents


Basic Principles


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




Computer Techniques


Energy Methods



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


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


Calculation of Center of Mass Techniques


Gouge Spacing

Vehicle Performance Characteristics


Systems and Performance Characteristics

Failure Analysis

Testing of Components

Bicycles, Motorcycles, and Pedestrians


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


Train Accidents


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


Federal Motor Vehicle Regulations - FMV 49


Off-Tracking for Coupled Vehicles

Construction Equipment

Visibility, Perception, and Reaction


Limitations of Human Factors Analysis

Design Standards

Capability of Drivers

Computer Methods


Numerical Methods

Commercially Available Programs

Reconstruction Tools

Low Speed Impacts and Injury


Methods of Analysis

Biomechanics of Injury

Standards and Protocols


Protocol for Inspections

ASTM Standards

FMV Requirements

SAE Standards

Sensitivity and Uncertainty


Sensitivity and Uncertainty


About the Authors

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

Subject Categories

BISAC Subject Codes/Headings:
LAW / Forensic Science
SCIENCE / Mechanics / General