Transit Systems Theory

by J. Edward Anderson, Ph.D.

Principal, PRT International, LLC

This book was published in 1978 but several of its chapters have been updated since then. A photocopy of the updated book can be obtained from Dr. Anderson as indicated below. The Table of Contents of the original book is shown below. It deals with the major systems engineering and cost-effectiveness issues that are involved in the design of a Personal Rapid Transit (PRT) system. Dr. Anderson makes extensive use of mathematics but the content should be accessible to most persons with an undergraduate degree in engineering or the sciences. It is highly recommended for those who wish to understand fully the engineering aspects of designing a PRT system. The updated text was used by Dr. Anderson in a quarter-long course that he taught on this subject offered by the University of Minnesota Extension Program in the Fall of 1996. He also conducted a 2-day short course on this topic in November of 1996 in Minneapolis, following an International Conference on PRT and Other Emerging Technologies.

Chapter 1 - Introduction (6 pp)

Chapter 2 - Basic Performance Relationships (15 pp)

----2.1 The Acceleration Profile

----2.2 The Velocity Profile and Stopping Distance

----2.3 Acceleration Power

----2.4 Trip Time and Average Velocity

----2.5 Time and Distance Loss due to Speed Reduction

----2.6 Average Power Consumption

----2.7 Summary, Problems

Chapter 3 - Transitions from Straight to Curved Guideways (23 pp)

----3.1 The Differential Equations for the Transition Curve

----3.2 The Constant Speed Sprial

----3.4 A Right-Angle Curve at Constant Speed

----3.5 The Constant Deceleration Sprial

----3.6 The Lateral Response of a Vehicle due to a Sudden Change in the Curvature of the Path

----3.7 Superelevation

----3.8 Summary, Problems

Chapter 4 - Performance Relationships for Specific Systems (49 pp)

----4.1 Shuttle Systems

----4.2 Station Throughput

----4.3 Loop Systems

----4.4 Line-Haul Systems

----4.5 Network Systems

----4.6 Summary, Problems

Chapter 5 - Cost Effectiveness (35 pp)

----5.1 Cost Equations

----5.2 Equations for Cost Effectiveness

----5.3 Cost Effectiveness of Bus Systems

----5.4 Cost Effectiveness of Shuttles

----5.5 Cost Effectiveness of Loop Systems

----5.6 Cost Effectiveness of Line-Haul Systems

----5.7 Cost Effectiveness of Guideway Network Systems

----5.8 Summary, Problems

Chapter 6 - Patronage Analysis (23 pp)

----6.1 Relationship between Yearly, Daily and Peak-Hour Patronage

----6.2 Mobility

----6.3 Required Precision of Patronage Estimates

----6.4 Trip Generation

----6.5 Trip Distribution

----6.6 Mode Split Analysis - A Probability Argument

----6.7 Mode Split Analysis - the Logit Model

----6.8 Factors that Influence Patronage

----6.9 Summary

Chapter 7 - Requirements for Safe Operation (45 pp)

----7.1 Introduction

----7.2 Requirements for Collision Avoidance

----7.3 Constant Force, Constant Displacement Shock Absorber

----7.4 Criteria for Avoidance of Passenger Injury in Collisions

----7.5 Collision with a Constraint Device in a Develerating Vehicle

----7.6 Safe Velocities of Collision between Vehicles

----7.7 Oblique Collisions

Chapter 8 - Life Cycle Cost and the Theory of Reliability Allocation (17 pp)

----8.1 Introduction

----8.2 Availability and Unavailability

----8.3 Subsystems of an Automated Transit System

----8.4 Classes of Failure

----8.5 Passenger-Hours of delay per Year and Unavailability

----8.6 The Constrained MinimumLife Cycle Cost

----8.7 Approximate Solution to the Problem of Reliability Allocation

----8.8 Approximate Solution to the Problem of Minimization of Life Cycle Cost and Reliability Allocation

----8.9 Reliability Allocation in Sub-systems

----8.10 Simultaneous Failures

----8.11 Summary

Chapter 9 - Redundancy, Failure Modes and Effects, and Reliability Allocation (35 pp)

----9.1 Introduction

----9.2 Redundancy

----9.3 Subsystems and Classes of Failure

----9.4 Vehicle Failures

----9.5 Station Entry Monitoring Equipment

----9.6 Failures of Passenger-Processing Equipment in Stations

----9.7 Merge-Equipment Failures

----9.8 Diverge Equipment Failures

----9.9 Failures in Wayside Communications Equipment

----9.10 Failures in Central Control Equipment

----9.11 Escape Mechanisms

----9.12 Reliability Allocation

----9.13 Summary

Chapter 10 - Guideway Structures (57 pp)

----10.1 Introduction

----10.2 Optimum Cross-Section Based on Bending Stress

----10.3 Dynamic Loading - Single Vehicle Crossing a Span

----10.4 Dynamic Loading - Cascade of Vehicles Crossing a Span

----10.5 Limit Value of Speed Based on Ride Comfort

----10.6 Torsion

----10.7 Plate Buckling

----10.8 Plate Vibration

----10.9 Optimum Span Length

----10.10 Summary

Chapter 11 - Design for Maximum Cost Effectiveness (17 pp)

----11.1 Introduction

----11.2 Guideways

----11.3 Vehicle Fleet Costs

----11.4 Propulsion and Braking

----11.5 Standing versus Seated Passengers

----11.6 Reliability

----11.7 Dual Mode versus Captive Vehicles

----11.8 Guideway Configurations

----11.9 Control

----11.10 Energy Conservation

----11.11 Capacity Requirements

Appendix A - Derivation of the Amortization Factor (4 pp)
About the Author

Dr. Anderson can be reached via e-mail at or via surface mail at 5164 Rainier Pass N.E., Fridley, Minnesota 55421-1338, Ph: (612) 586-0877, fax: (612) 586-0878. An updated photocopy of this book is available for $30, which includes postage charges within the USA. The original text (published by Lexington Books: D.C. Heath and Company, Lexington, MA.) can probably be obtained at many University libraries or through an Interlibrary Loan service in most US locations.

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Last modified: January 01, 2008