# Versine measurement

## General information on the horizontal route taken:

The elements of the horizontal route are:

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

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

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

## Formulae (pure circular curve):

Circular curve formulae

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”