Mathematical Methods for Accident Reconstruction ─ A Forensic Engineering Perspective

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.

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

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