Versine measurement

General information on the horizontal route taken:

The elements of the horizontal route are:

  • Tangent track.
  • Transition curve.
  • Full curve.

Tangent track
Tangent track
© Thorsten Schaeffer

Transition curves are a set of route elements, which are formed by variable curvature (radius). The reason for the use of transition curves lies in the dynamics of vehicle movement. When running round a curve there is a radial acceleration of the vehicle which depends on the speed and the radius of the curve. By inserting a transition curve, e.g. between two successive routing elements, tangent track and full curve, an abrupt change of radial acceleration is avoided. By far the most common form of transition curve is Cornu’s spiral, there are also other forms such as the Bloss curve or the cubic parabola.

The radius (curvature) of the track can be determined with the help of versine measurements. It is measured in the middle of a chord where the length ls = 16 m or = 20 m the perpendicular distance hf of the track is measured.

The following formula applies to the measurement of the versine hf at any point of the chord is with the distances a and b of the chord endpoints.
Versine at any given point.

Versine at any point
Versine at any point
© Matthias Müller

For the assessment of the track curvature the curve should be divided into 5 m long sections. A piece of string is stretched over each four of these sections of a chord and the versine hf is progressively measured in the middle between marked point to marked Point.

Versine measurement in a 20 m long chord:

Versine measurement in a 20 m chord
Versine measurement in a 20 m chord
© Matthias Müller

Formulae (pure circular curve):

Circular curve formulae
Circular curve formulae
© Matthias Müller

h = a⋅b ÷ 2⋅R

h = a² ÷ 2⋅R

h = a⋅b² ÷ 2⋅R⋅(a+b)

h = a² ÷ 4⋅R

In this way, the ACTUAL radius of a curve is calculated and shown graphically. If it is compared with the TARGET curve, it Is easy to determine the horizontal shift necessary to put the track back to the TARGET location.

The TARGET position of the track in height and direction is usually produced with tamping - aligning machines mechanically. The use of manual tamping only makes sense with the smallest works.

Portable long chord procedure:

  • String device - this reading of the versine values is done from the rail head running edge.
  • The Wuppertal Latte - this reading of the versine is done from the track axis by means of a yardstick.

Standing chord procedure:

“Fixed fitted string chord”
“Fixed fitted string chord”
© Robel Bahnbaumaschinen GmbH
  • A chord which is bolted onto the base of the rail can also be read out from the running edge of the rail head.


You can find suitable specialist literature to the topic here:

The Basic Principles of Mechanised Track Maintenance

The Basic Principles of Mechanised Track Maintenance

This book is dedicated to the many people involved in the day to day planning and performance of track maintenance activities. Providing a practical approach to everyday challenges in mechanised track maintenance, it is not just intended as a theoretical approach to the track system. 
Railways aim at transporting people and freight safely, rapidly, regularly, comfortably and on time from one place to another. This book is directed to track infrastructure departments contributing to the above objective by ensuring the track infrastructure’s reliability, availability, maintainability and safety – denoted by the acronym RAMS. Regular, effective and affordable track maintenance enable RAMS to be achieved.