Railway Track Geometry by the Numbers

About this book

Track geometry is the shape of the railway: the curves and straights it follows across the country, the cant that tilts it on curves, the grades and vertical curves that carry it over hills and through dips, the turnouts that let trains change tracks, and the precise gauge, alignment and level that let wheels roll smoothly at speed. Good geometry lets trains run fast, safely and comfortably with little wear; poor geometry limits speed, wears out rails and wheels, and in the extreme derails trains. Geometry is also decided early and lasts long: a curve laid out too sharp, a grade too steep or a loop too short will constrain every train for decades.

This book is for civil designers, rail project engineers, track supervisors and the developers of sidings and loading facilities. It assumes basic mathematics and some engineering background. It explains, with numbers, how curves are described and set out with chords and versines, how cant is chosen for the speeds of the trains that use a curve, how cant deficiency and excess limit speed, how transitions and vertical curves are sized, how grades and curves resist trains, how turnouts work, how balloon loops and loading facilities are laid out, and how new track is built to tolerance, handed over and recorded.

The sources and their limits

The book draws on two Australian Rail Track Corporation engineering standards for New South Wales, carried over from the former Rail Infrastructure Corporation standards and issued in 2005: one for the construction of track, and one for unit train loading and unloading facilities. Where a value from them is quoted, it is cited, and it is quoted for teaching: those issues may since have been revised or replaced. The design limits that govern a real line, its speeds, cant, transitions, grades and turnouts, come from the rail infrastructure manager’s current standards, which this book does not reproduce. Everything else is worked from first principles.

The running case

This is an illustration. A regional grain cooperative is building a balloon loop and loading bin beside a single standard gauge main line, so that whole trains can be loaded without uncoupling. The main line curves near the junction, carrying both fast passenger trains and slower freight. The cooperative’s engineers must lay out the loop and its junction turnout, choose the grades through the loading bin, check the effect on the main line’s curve, build the track to tolerance, and hand it over to the infrastructure manager.

The cooperative, its engineers, the trains and all the numbers are invented for teaching. They are not KEVOS® work.

How to use the book

Chapter 1 describes the track as a structure. Chapter 2 covers curves, chords and versines, Chapter 3 cant and equilibrium speed, and Chapter 4 cant deficiency, excess and speed. Chapter 5 deals with transitions, and Chapter 6 with grades, vertical curves and train resistance. Chapter 7 covers turnouts, Chapter 8 sidings, loops and loading facilities, Chapter 9 construction tolerances, and Chapter 10 handover and the geometry record. Every chapter ends with an exercise and its worked answer.

Professional responsibility

This book is educational. Track design and construction on a railway network are safety-critical and are governed by the rail infrastructure manager’s current standards and approvals and by rail safety law; they need qualified design, review and certification. Nothing here replaces those.

An original treatment

The Library covers the clearances affected by track geometry in Railway Clearances by the Numbers; this book links to it rather than repeating it. The explanations, the cooperative case, the derivations, figures and exercises are original KEVOS® writing, built from geometry and mechanics. The ARTC documents are copyright; a small number of their values are quoted with citation for teaching, and none of their text, tables or drawings is reproduced.